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https://zbmath.org/?q=an:0614.22005
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# zbMATH — the first resource for mathematics
Classification of unitary representations in irreducible representations of general linear group (non-Archimedean case). (English) Zbl 0614.22005
The author classifies the irreducible unitary representations of the general linear group GL(n) over a local, non-Archimedean field. He constructs a set B so that every unitary representation is either in B or is unitarily induced from a representation in B. The representations in B are either irreducible quotients of representations induced from square integrable representations or complementary series representations. The classifications of the unitary dual is given in Langlands as well as in Zelevinski parameters.
A similar classification of the unitary dual for Archimedean fields was obtained by D. Vogan.
Reviewer: B.Speh
##### MSC:
2.2e+51 Representations of Lie and linear algebraic groups over local fields
Full Text:
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2021-04-11 04:52:36
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https://www.fastrawviewer.com/comment/208
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# Underexposure limit and DR
I’m using a RAW 14bit (ISO 64) file from a D810.
In preferences the default underexposure limit is set to 8EV. I have customised the value to 2EV lower (10.EV).
After performing a shadow boost (S) set to the 2.0EV I still get visually clean shadows.
Does this mean I can assume the camera’s DR is 10EV (or 7 below EV0) when I go to meter a future scene at ISO64.
### Yes, but it also depends on
Dear Saul,
Yes, but it also depends on the lens you are using. Lens flare can have some effect on this, too. My test with good primes on D810 resulted in 10 1/2 stops of linear photographic dynamic range.
Thanks Iliah
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2021-05-07 17:01:58
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https://cs.stackexchange.com/questions/143519/number-partition-subjected-to-the-cardinality-of-subset
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Number partition subjected to the cardinality of subset
I hope someone can take some time to consider the following problem and welcome to discuss together.
Number partition problem is one of well-known NP-hard problems.
Now I am considering the hardness of constrained partition problem. In particular, the cardinality of multiset $$S$$ is n, denoted by $$|S|=n$$. Now is it NP-completeness to determine whether a given multiset $$S$$ of positive integers can be partitioned into two subsets $$S_1$$ and $$S_2$$ such that the sum of the numbers in $$S_1$$ equals the sum of the numbers in S2, and subjected to the cardinality of sub multiset $$S_1$$ is equals $$k$$, that is $$|S_1|=k$$ where $$k <= n$$
• Did you try the reduction from Number partition problem? Aug 29 '21 at 4:25
• Intuitively, i think the constrained number partition is harder than that original one Aug 29 '21 at 7:27
• You are right! For a formal proof, try to show a polynomial-time reduction from the Number partition problem to the constrained number partition problem. It is not that difficult. Aug 29 '21 at 7:46
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2022-01-24 13:18:41
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https://www.zbmath.org/?q=an%3A0851.11019
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# zbMATH — the first resource for mathematics
The number of solutions of decomposable form equations. (English) Zbl 0851.11019
Decomposable form equations, being the common generalization of several types of classical diophantine equations (among others Thue equations, norm form equations, discriminant form and index form equations) have an extensive literature. Using his famous subspace theorem, in 1972 W. M. Schmidt [Ann. Math., II. Ser. 96, 526-551 (1972; Zbl 0245.10008)] proved the finiteness of the number of solutions of nondegenerate norm form equations. In 1977 H. P. Schlickewei [J. Number Theory 9, 370-380 (1977; Zbl 0365.10016)], extended Schmidt’s result to $$p$$-adic norm form equations, and in 1984 M. Laurent [Invent. Math. 78, 299-327 (1984; Zbl 0554.10009)] to norm form equations over number fields. The first finiteness results on decomposable form equations were obtained by the author and K. Györy in 1988 [Acta Arith. 50, 357-379 (1988; Zbl 0595.10013)]. In 1989 the author, the reviewer and K. Györy [Arch. Math. 52, 337-353 (1989; Zbl 0671.10013)] showed the existence of a uniform bound $$C$$ (depending only on the number of variables, the $$S$$-unit group involved, and the splitting field) such that any nondegenerate decomposable form equation (with the above parameters) can have at most $$C$$ cosets of solutions. These results applied to Schmidt’s subspace theorem and its $$p$$-adic generalization given by Schlickewei.
In 1989 W. M. Schmidt [Compos. Math. 69, 121-173 (1989; Zbl 0683.10027)] gave a quantitative version of his subspace theorem which enabled him to derive an explicit upper bound for the number of solutions of norm form equations with a non-degenerate module. H. P. Schlickewei [Compos. Math. 82, 245-273 (1992; Zbl 0751.11033)] extended the quantitative subspace theorem to the number field case and obtained also an explicit upper bound for the number of solutions of $$S$$-unit equations over number fields. In 1993 K. Györy [Publ. Math. 42, 65-101 (1993; Zbl 0792.11004)] applied this result to give an explicit bound for the number of cosets of solutions of arbitrary decomposable form equations, and, extending the results of Schmidt and Schlickewei on norm form equations, derived also a bound for the number of families of solutions of possibly degenerate decomposable form equations.
In the present paper the author considers the number of non-degenerate solutions of possibly degenerate decomposable form equations. The only restrictive condition on the linear factors of the decomposable form equation is the following: for every proper nonempty subset of its linear factors there exist algebraic coefficients which can be used to make an identically zero linear combination of these linear factors without vanishing subsums. The bounds derived for the number of solutions improve the above mentioned quantitative results on the number of solutions of norm form and decomposable form equations. The author also derives an improvement of Schlickewei’s upper bound on the number of solutions of $$S$$-unit equations. The main tool of the proofs is an improvement of the quantitative subspace theorem given by the author [An improvement of the quantitative subspace theorem, Compos. Math. 101, No. 3, 225-311 (1996)].
Reviewer: I.Gaál (Debrecen)
##### MSC:
11D57 Multiplicative and norm form equations 11D75 Diophantine inequalities
Full Text:
##### References:
[1] E. Bombieri: On the Thue-Mahler equation II. Acta Arith.67, 69-96 (1994) · Zbl 0820.11017 [2] E. Bombieri, W.M. Schmidt: On Thue’s equation. Invent. Math.88, 69-81 (1987) · Zbl 0614.10018 · doi:10.1007/BF01405092 [3] J.H. Evertse: On equations inS-units and the Thue-Mahler equation. Invent. Math.75, 561-584 (1984) · Zbl 0521.10015 · doi:10.1007/BF01388644 [4] J.H. Evertse: On sums ofS-units and linear recurrences. Compos. Math.53, 225-244 (1984) [5] J.H. Evertse: Decomposable form equations with a small linear scattering. J. reine angew. Math.432, 177-217 (1992) · Zbl 0754.11009 · doi:10.1515/crll.1992.432.177 [6] J.H. Evertse: An improvement of the quantitative Subspace theorem. Compos. Math. (to appear) [7] J.H. Evertse, I. Gaál, K. Györy: On the numbers of solutions of decomposable polynomial equations. Arch. Math.52, 337-353 (1989) · Zbl 0671.10013 · doi:10.1007/BF01194408 [8] J.H. Evertse, K. Györy: Finiteness criteria for decomposable form equations. Acta Arith.50, 357-379 (1988) · Zbl 0595.10013 [9] K. Györy: On the numbers of families of solutions of systems of decomposable form equations. Publ. Math. Debrecen42, 65-101 (1993) · Zbl 0792.11004 [10] M. Laurent: Equations diophantiennes exponentielles. Invent. Math.78, 299-327 (1984) · Zbl 0554.10009 · doi:10.1007/BF01388597 [11] K. Mahler: Zur Approximation algebraischer Zahlen, II. Über die Anzahl der Darstellungen ganzer Zahlen durch Binärformen. Math. Ann.108, 37-55 (1933) · Zbl 0006.15604 · doi:10.1007/BF01452821 [12] A.J. v.d. Poorten, H.P. Schlickewei: Additive relations in fields. J. Austral. Math. Soc (A)51, 154-170 (1991) · Zbl 0747.11017 · doi:10.1017/S144678870003336X [13] H.P. Schlickewei: Thep-adic Thue-Siegel-Roth-Schmidt theorem. Arch. Math.29, 267-274 (1977) · Zbl 0365.10026 · doi:10.1007/BF01220404 [14] H.P. Schlickewei: On norm form equations. J. Number Th.9, 370-380 (1977) · Zbl 0365.10016 · doi:10.1016/0022-314X(77)90072-5 [15] H.P. Schlickewei: The quantitative Subspace Theorem for number fields. Comp. Math.82, 245-274 (1992) [16] H.P. Schlickewei:S-unit equations over number fields. Invent. Math.102, 95-107 (1990) · Zbl 0711.11017 · doi:10.1007/BF01233421 [17] H.P. Schlickewei: On linear equations in elements of finitely generated groups. Lecture at MSRI, Berkeley, February 1993 [18] W.M. Schmidt: On heights of algebraic subspaces and diophantine approximations. Ann. Math.85, 430-472 (1967) · Zbl 0152.03602 · doi:10.2307/1970352 [19] W.M. Schmidt: Linearformen mit algebraischen Koeffizienten II. Math. Ann.191, 1-20 (1971) · Zbl 0207.35402 · doi:10.1007/BF01433465 [20] W.M. Schmidt: Norm form equations. Ann. Math.96, 526-551 (1972) · Zbl 0226.10024 · doi:10.2307/1970824 [21] W.M. Schmidt: The subspace theorem in Diophantine approximations. Compos. Math.69, 121-173 (1989) · Zbl 0683.10027 [22] W.M. Schmidt: The number of solutions of norm form equations. Trans. Am. Math. Soc.317, 197-227 (1990) · Zbl 0693.10014 · doi:10.2307/2001459 [23] A. Thue: Über Annäherungswerte algebraischer Zahlen. J. reine angew. Math.135, 284-305 (1909) · JFM 40.0265.01 · doi:10.1515/crll.1909.135.284
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.
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2021-06-17 17:37:26
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https://amp.en.depression.pp.ua/14143537/1/chloridazon-catechol-dioxygenase.html
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# ⓘ Chloridazon-catechol dioxygenase is an enzyme that catalyzes the chemical reaction 5-amino-4-chloro-2-2.3-dihydroxyphenyl-32H-pyridazinone + O 2 ⇌ {\displaystyl ..
## ⓘ Chloridazon-catechol dioxygenase
Chloridazon-catechol dioxygenase is an enzyme that catalyzes the chemical reaction
5-amino-4-chloro-2-2.3-dihydroxyphenyl-32H-pyridazinone + O 2 ⇌ {\displaystyle \rightleftharpoons } 5-amino-4-chloro-2-2-hydroxymuconoyl-32H-pyridazinone
Thus, the two substrates of this enzyme are 5-amino-4-chloro-2-2.3-dihydroxyphenyl-32H-pyridazinone and oxygen, whereas its product is 5-amino-4-chloro-2-2-hydroxymuconoyl-32H-pyridazinone.
This enzyme belongs to the family of oxidoreductases, specifically those acting on single donors with O 2 as oxidant and incorporation of two atoms of oxygen into the substrate oxygenases. The oxygen incorporated need not be derived from O 2. The systematic name of this enzyme class is 5-amino-4-chloro-2-2.3-dihydroxyphenyl-32H-pyridazinone 1.2-oxidoreductase decyclizing. It employs one cofactor, iron.
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2021-07-30 17:03:31
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https://www.math.uni-bielefeld.de/documenta/vol-20/29.html
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#### DOCUMENTA MATHEMATICA, Vol. 20 (2015), 1039-1053
Ivan Arzhantsev, Polina Kotenkova
Equivariant Embeddings of Commutative Linear Algebraic Groups of Corank One
Let $\KK$ be an algebraically closed field of characteristic zero, $\GG_m=(\KK\setminus{0},\times)$ be its multiplicative group, and $\GG_a=(\KK,+)$ be its additive group. Consider a commutative linear algebraic group $\GG=(\GG_m)^r\times\GG_a$. We study equivariant $\GG$-embeddings, i.e. normal $\GG$-varieties $X$ containing $\GG$ as an open orbit. We prove that $X$ is a toric variety and all such actions of $\GG$ on $X$ correspond to Demazure roots of the fan of $X$. In these terms, the orbit structure of a $\GG$-variety $X$ is described.
2010 Mathematics Subject Classification: Primary 14M17, 14M25, 14M27; Secondary 13N15, 14J50
Keywords and Phrases: Toric variety, Cox ring, locally nilpotent derivation, Demazure root
Full text: dvi.gz 34 k, dvi 101 k, ps.gz 293 k, pdf 203 k.
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2017-10-21 06:35:06
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https://www.vedantu.com/question-answer/length-of-y-intercept-made-by-the-circle-5x2-+-class-10-maths-cbse-5ee862757190f464f77a1c62
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# Length of y - intercept made by the circle $5{{\text{x}}^2} + 5{{\text{y}}^2} - 2{\text{x + 6y - 8 = 0 is:}}$ ${\text{A}}{\text{.}}\dfrac{{19}}{5}. \\ {\text{B}}{\text{.}}\dfrac{{14}}{5}. \\ {\text{C}}{\text{.}}\dfrac{{11}}{5}. \\ {\text{D}}{\text{.}}\dfrac{9}{5}. \\$
Last updated date: 14th Mar 2023
Total views: 303.3k
Views today: 6.84k
Answer
Verified
303.3k+ views
Hint: In this question, the equation of circle is given. To find the y-intercept made by a circle we will first convert the given circle equation into the standard circle equation and then use the formula for y-intercept to the value of y-intercept.
Complete step-by-step answer:
In the question, it is given that:
Equation of circle is $5{{\text{x}}^2} + 5{{\text{y}}^2} - 2{\text{x + 6y - 8 = 0}}$ .
We have to find the y-intercept made by the given circle.
We know that the standard equation of circle is given by:
${{\text{x}}^2} + {{\text{y}}^2} + 2{\text{gx + 2fy + c = 0}}$. (1)
Y-intercept of this circle is given by $2\sqrt {{{\text{f}}^2} - c}$ .
But the equation of the circle given is not in the standard form. So we will first convert this equation in standard form.
$\Rightarrow 5{{\text{x}}^2} + 5{{\text{y}}^2} - 2{\text{x + 6y - 8 = 0}} \\$
On dividing the above equation by 5, we get,
$\Rightarrow {{\text{x}}^2} + {{\text{y}}^2} - \dfrac{2}{5}{\text{x + }}\dfrac{6}{5}{\text{y - }}\dfrac{8}{5}{\text{ = 0}} \\$
So the above equation is the standard equation of a circle.
On comparing the above equation with equation 1, we get:
$2{\text{g = - }}\dfrac{2}{5} \\ \Rightarrow {\text{g = - }}\dfrac{1}{5}. \\ {\text{And}} \\ {\text{2f = }}\dfrac{6}{5}. \\ \Rightarrow {\text{f = }}\dfrac{3}{5},{\text{ and c = - }}\dfrac{8}{5}. \\$
Y-intercept made by circle =$2\sqrt {{{\text{f}}^2} - c}$.
Putting the value of ‘f’ and ‘c’ in the above formula, we get:
Y-intercept made by circle = $2\sqrt {{{\text{f}}^2} - c} = 2\sqrt {{{\left( {\dfrac{3}{5}} \right)}^2} - \left( { - \dfrac{8}{5}} \right)} = 2\sqrt {\dfrac{9}{{25}} + \dfrac{8}{5}} = 2\sqrt {\dfrac{{49}}{{25}}} = 2 \times \dfrac{7}{5} = \dfrac{{14}}{5}.$
Note: In this type of question, the first important thing is to clearly see the question whether it is asking y-intercept or x-intercept. Then convert the given equation into a standard form of equation. You should remember the formula for finding y-intercept. Compare the transformed given equation with the standard equation to get the value of parameters required for computing the y-intercept.
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2023-03-20 10:54:24
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https://solvedlib.com/what-is-the-frequency-of-the-photons-emitted-by-a,150763
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# What is the frequency of the photons emitted by a He-Ne laser with a wavelength of 632.8 nm?
###### Question:
What is the frequency of the photons emitted by a He-Ne laser with a wavelength of 632.8 nm?
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##### Circle all that represent a valid setof quantum numbers:a) n=7 , l = 1 , ml = +1 ,ms = +1/2b) n=5 , l = 1 , ml = 0 ,ms = +1/2c) n=3 , l = 2 , ml = +2 ,ms = +1/2d) n=2 , l = 2 , ml = +1 , ms = +1/2e) n=1 , l = 2 , ml = +1 ,ms = +1/2
Circle all that represent a valid set of quantum numbers: a) n=7 , l = 1 , ml = +1 , ms = +1/2 b) n=5 , l = 1 , ml = 0 , ms = +1/2 c) n=3 , l = 2 , ml = +2 , ms = +1/2 d) n=2 , l = 2 , ml = +1 , ms = +1/2 e) n=1 , l = 2 , ml = +1 , ms = +1/2...
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##### Consider the following mixed-integer linear program: Max 2xl 4x2Axl+ 10x2 = 36 7x1 6x2 =< 35 X1,x2 >= 0 and xl IntegerGraph the constraints for this problem: Indicate on your graph all feasible mixed integer solutions
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##### Use Laplace transforms to solve the following value problem y''-y'=e^(t)cost y(0)=1 y'(0)=-1
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2022-12-10 03:16:45
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|
https://community.plotly.com/t/how-can-i-left-align-yaxis-in-horizontal-bar/36616
|
# How can I left align yaxis in horizontal bar
I use this sample to make horizontal bar chart but don’t know how to left align text in yaxis. Please help.
import plotly.graph_objects as go
fig = go.Figure(go.Bar(
x=[20, 14, 23],
y=[‘giraffes’, ‘orangutans’, ‘monkeys’],
orientation=‘h’))
fig.show()
Hi @hao.dn, you cannot configure ticks directly to do this (see Left align category labels on y-axis or Ticks: left-align first, right align last on x-axis). However, here is a workaround (courtesy of @alexcjohnson and @nicolaskruchten) which add a second axis, considered to be on the right (hence tick labels are left aligned), but positioned on the left. Hacky, but I hope it solves your problem :-).
``````import plotly.graph_objects as go
y = ['boa', 'giraffe', 'monkey', 'orangeoutans']
fig = go.Figure(go.Bar(
x=[20, 14, 23, 4],
y=y,
yaxis='y2',
orientation='h',
))
fig.update_layout(xaxis=dict(domain=[0.15, 0.9]),
yaxis2=dict(anchor='free', position=0.02,
side='right'))
fig.show()
``````
thanks. It’s ok to me.
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2020-04-07 05:51:05
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|
https://wiki.veriqloud.fr/index.php?title=Classical_Fully_Homomorphic_Encryption_for_Quantum_Circuits
|
# Classical Fully Homomorphic Encryption for Quantum Circuits
The example protocol achieves the functionality of Delegated Quantum Computation by a method which involves fully classical offline and no quantum communication. It uses only classical Homomorphic Encryption (HE) scheme to evaluate quantum circuits for classical input/output. It allows a fully classical Client to hide her data such that Server can carry out any arbitrary quantum computation on the encrypted data without having any knowledge about Client’s inputs. It hides the output and input of the computation while Server is allowed to choose the unitary operation (any quantum gate) for required computation. Quantum offline communication would be required if Client’s input and output is quantum.
Tags: Two Party, Quantum Functionality, Universal Task, Secure Client- Server Delegated Quantum Computation, Prepare and Send Quantum FHE, Classical Offline Communication, Superposition, Trapdoor Claw-Free Functions, Learning With Errors, Encrypted CNOT Operation.
## Assumptions
• This protocol is secure against honest but curious adversary setting.
• HE is a classical leveled fully homomorphic encryption scheme which is quantum capable for given depth of one layer of circuit, ${\displaystyle L_{c}}$ (See Notations below).
• A BQP Server (a quantum computer) can generate a superposition of inputs for the encryption function over some distribution given the public key used for encryption. The protocol takes learning with errors assumption.
## Outline
FHE presents a classical protocol with the help of which a completely classical Client could assign Server a quantum computation for her encrypted (hidden) input/output. Similar to any classical HE this scheme is divided into four steps: Key Generation generates keys for encryption, decryption and evaluation of the circuit; Encryption encodes the input into a secret text using the encryption key generated during Key Generation; Evaluation performs operations (implements the circuit) on the encrypted input using evaluation key generated and Decryption transforms result of the evaluation step hidden in the secret text, to outcome of the circuit for Client's input using decryption key. Following the stages of Secure Delegated Quantum Computation, in preparation stage, Client encrypts her input by performing one time pad to hide it from the Server, who, in the computation stage, performs quantum computation by a completely classical evaluation step. There are two kinds of gates in Quantum Computation (See Glossary) Clifford Gates, which consists of Hadamard gate, CNOT and Pauli gates (X, Y, Z) and Toffoli gates (any single qubit phase/rotation gate). A universal scheme can perform both these types of gates implying that it can perform any quantum operation. Now, applying Clifford gates remains a simple step as it leaves the state with only Pauli corrections (X, Z) which are easy to handle as these gates commute with every quantum gate and hence can be shifted and cancelled out by applying corresponding inverse gate later by the Client, but when applying Toffoli Gates, it leaves the state with some Pauli corrections and Clifford gate corrections depending on the one pad key used for encryption key used by Client. Decryption key cannot deal with Clifford gate errors as they do not commute with all quantum operations and hence it needs to be corrected by applying corresponding inverse gate before the operation of next gate for computation by the Server. These Clifford gate corrections are a combination of CNOT corrections dependent on encryption key and a Hadamard correction independent of encryption key. Thus, applying Hadamard requires no extra information but CNOT gate errors require revelation of the encryption key. FHE deals with this problem via Encrypted CNOT operation using Trapdoor Claw-Free Function (TCF) without revelation of encryption key to the Server. Finally, in the Output Correction stage, Client gets her inputs and updated encryption keys to get the correct final outcome from the secret text using her decryption key. Following is an outline of the steps to illustrate the above mentioned scheme, assuming depth of circuit (see notations used) equal to L.
The preparation stage incorporates,
• Key Generation: Client generates ${\displaystyle L+1}$ classical homomorphic key sets consisting of public key, evaluation key, secret key, trapdoor information (a piece of information required to invert the function used for encrypted CNOT operation, as explained in Circuit Evaluation) using HE.KeyGen() (classical HE step). Evaluation key consists of first L pairs of secret key-trapdoor information encrypted with last L public keys such that secret key-trapdoor key pair and public key do not belong to the same key set. Evaluation key also contains this public key used to encrypt the pair.
• Encryption: Client uses classical one time pad to hide her input and encrypts the pad key with the first public key (not used to encrypt any trapdoor-secret key pair) using HE.Enc() (classical HE step). She then sends the hidden classical input with encrypted pad key and classical evaluation key to the Server over classical channel. This step marks the end of preparation stage.
Further, the computation stage incorporates,
• Circuit Evaluation: Server starts with the classical one time padded states from the Client and generates the required quantum states. For each gate of the circuit that Server applies, he updates the encrypted Pauli encryption according to rules given in Pseudo code below. In case of Toffoli gate operation, an additional step is incorporated where he corrects the extra Clifford gate error performing encrypted CNOT operation and then Hadamard operation on the target qubit. This step uses evaluation key and can be explained as follows.
Encrypted CNOT operation All errors imposed by Toffoli gates can be represented using encrypted CNOT operation, a Hadamard operation and a set of Pauli gates (X, Z). All errors imposed by Clifford gates can be represented by a combination of Pauli gates. A mathematical representation of this step can be found in the Pseudo Code below.
1. TCF: This operation uses Trapdoor Claw Free function pairs which have the same image (output) for different pre-images(inputs) called 'random claw pair'. Given the image, it is rendered a hard problem to find this corresponding random claw without its trapdoor information (example, a piece of information required to invert the function). For this protocol, the HE Encryption function (HE.Enc()) is taken as one of the functions. A second function whose distribution is shifted from the previous function by a natural (homomorphic) XOR operation (a requirement for the classical HE scheme used) of encrypted key bit used for that encryption function. This means, the functions have a common range such that for every image (output), the pre-images (input) for each of the functions stated above would also differ by a XOR operation of actual (not encrypted) key bit. Thus, any element in the said range set would have one pre-image in the domain set of each function, together called random claw pair. If one performs a XOR operation on the pair, the result is pad key bit. This is implied from the properties of homomorphic XOR. In simple words, the above paragraph implies that if two functions are separated by encrypted pad key via a homomorphic XOR operation, their inputs for a common output (random claw pair) would be separated by the (not encrypted) pad key bit. Thus, any pre-image pair (random claw) thus, obtained, hides the pad key (to be used later for Encrypted CNOT operation).
2. Server's preparation Thus, Server creates a superposition of inputs for the functions over some distribution. Next, he creates a superposition of quantum states generated from Client's input. After applying the gates on qubits, for correction of CNOT errors, Server creates three registers. First has the superposition of quantum states generated from Client's input, second has the superposition on a distribution chosen for inputs of the function while third register has the output of one of the two functions illustrated above, where the function (one of the two) is chosen according to the first qubit of the first register and its quantum input is taken from the second register. Hence, these registers are entangled. Server, now measures the third register which reduces second register to a random claw pair as discussed before, hiding the pad key. It is still hidden from the Server as he does not know trapdoor information to be able to know the random claw pair and he cannot compute it from the measured output as it is a hard problem.
3. Server's Toffoli gate operation After some calculations it can be shown that if Server performs Hadamard operation on the second register and then measures it, the first register is reduced to corrected quantum state with some extra Pauli corrections. These final Pauli corrections require trapdoor information and measurement outcome of the second register. To perform the above operation one needs the secret text to be same throughtout the protocol and existence of a natural XOR operation. This is not known to have been achieved by a single HE together. Hence, this protocol uses AltHE (an alternate HE) which can operate XOR for encrypted CNOT operation while he uses HE for updation of Pauli keys. In order to do this, HE provides a conversion of secret text under HE to secret text under AltHE and vice versa. Thus, after encrypted CNOT operation, encrypted pad key bit and other measurement outcomes are recrypted using public key provided in the evaluation key for that step, under HE. Thus, the trapdoor information and pad key bit are encrypted under same public key. Now, using the measurement outcome and the encrypted trapdoor information with recrypted pad key, Server obtains Pauli corrections. The Server encrypts Pauli corrections under public key for corresponding layer and hence updates the recrypted pad key
4. Server's Clifford gate operation Server obtains with Pauli corrections according to rules described in the Pseudo code and updates the recrypted pad key as before.
• Decryption Server repeats the same procedure for each layer and at the end of last layer, sends the updated recryption of pad key and classical measurement output of the first register (containing the corrected quantum state encrypted by pad key) to Client. Client converts the pad key to another secret text using AltHE. The sent pad key is recrypted with public key of the last (${\displaystyle L_{th}}$) evaluation key used. This is the ${\displaystyle (L+1)_{th}}$ public key. Hence, Client uses ${\displaystyle (L+1)_{th}}$ secret key (which was not included in the evaluation keys) to decrypt the updated encryption of pad key sent by the Server. She (Client) uses the resulting pad key to undo the one time pad on the sent output.
## Properties
• Quantum Capable A classical HE is quantum capable i.e. can perform quantum computation efficiently if there exists AltHE which can execute natural XOR operations.
• Indistinguishability under Chosen Plaintext Attacks by adversary(IND-CPA) The presented classical FHE scheme is CPA secure i.e. it is not possible for any polynomial time adversary to distinguish between the encrypted classical message bits 0 and 1, by learning with errors.
• Compactness This protocol is compact i.e. decryption does not depend on the complexity of the quantum circuit.
• Correctness Correctness is implied from the correctness of encrypted CNOT operation.
• Circuit Privacy This protocol is not circuit private as both Client and Server know the quantum circuit used for performing the computation.
• Full Homomorphism This protocol is fully homomorphic i.e. Server can operate any quantum circuit using this protocol.
• Circular Security This protocol has a stronger notion of circular security where not only the secret key but also the trapdoor functions are encrypted when provided to the Server.
## Notation
• ${\displaystyle m}$: classical data of client's required quantum input states
• ${\displaystyle \lambda }$: security parameter
• ${\displaystyle k}$: security parameter
• ${\displaystyle {\tilde {x}}}$: encrypted pad key
• ${\displaystyle s}$: concatenated pad key elements
• ${\displaystyle c=HE.Enc_{pk}(s)}$ Encryption of s using public key ${\displaystyle pk}$ via classical HE encryption step.
• ${\displaystyle {\hat {c}}}$: converted c using classical HE in order to use it with ${\displaystyle AltHE}$
• ${\displaystyle {\tilde {x}}^{[l]}}$: ${\displaystyle l^{th}}$ bit of encrypted pad key
• ${\displaystyle L_{c}}$: depth of a layer of circuit where each layer contains Clifford gates and Toffoli gates
• ${\displaystyle L}$: depth of the circuit (no. of layers in the circuit)
• ${\displaystyle \{pk_{i},sk_{i},evk_{i},t_{sk_{i}}\}}$: ${\displaystyle i_{th}}$ homomorphic key set generated from HE.KeyGen(). Public key for encryption, secret key for decryption, evaluation function key, trapdoor information required for randomness recovery from secret texts.
• ${\displaystyle y}$: measurement outcome of third register
• ${\displaystyle (\mu _{0},r_{0})(\mu _{1},r_{1})}$: random claw for pair, for given y
• ${\displaystyle d}$: measurement outcome of the second register
## Requirements
• Network Stage: Quantum Memory
• Required Network Parameters:
• ${\displaystyle \epsilon _{j}}$, which measures the error due to noisy operations.
• Number of communication rounds
• Circuit depth
• Number of physical qubits used
• The concerned protocol requires classical HE scheme.
• Communication can be performed over a classical network with only one quantum node (in case of classical input and output).
• The functions ${\displaystyle f_{0},f_{1}}$ used must be trapdoor claw-free(TCF) such that one it is not possible to find a triple ${\displaystyle (\mu _{0},\mu _{1},y)}$ such that ${\displaystyle f_{0}(\mu _{0})=f_{1}(\mu _{1})=y}$
## Protocol Description
• Boxed texts are not part of the code but contain proofs used in various steps, illustrated for a better understanding of the protocol.
### Stage 1 Client’s Preparation
• Input: ${\displaystyle k,L,L_{c}}$, classical message ${\displaystyle m}$
• Output: Homomorphic key sets ${\displaystyle (pk_{i},evk_{i},sk_{i},t_{sk_{i}})}$, encrypted pad key ${\displaystyle {\tilde {z}},{\tilde {x}}}$, One time Padded message (${\displaystyle l}$)
• Key Generation (FHE.KeyGen(${\displaystyle 1^{\lambda },1^{L}}$))
1. For ${\displaystyle 1\leq i\leq L+1}$,
2. Client generates homomorphic key set, ${\displaystyle (pk_{i},evk_{i},sk_{i},t_{sk_{i}})=}$HE.Keygen(${\displaystyle 1^{\lambda },1^{L_{c}}}$).
The public key ${\displaystyle pk}$ is ${\displaystyle pk_{1}}$ and the secret key ${\displaystyle sk}$ is ${\displaystyle sk_{L+1}}$.
The evaluation key ${\displaystyle evk_{i}}$ consists of ${\displaystyle (pk_{i+1},}$HE.Enc${\displaystyle _{pk_{i+1}}(sk_{i})}$, HE.Enc${\displaystyle _{pk_{i+1}}(t_{sk_{i}})}$) for ${\displaystyle 1\leq i\leq L}$.
• Encryption (FHE.Enc${\displaystyle _{pk}(m)}$))
1. Client chooses pad key for each message bit ${\displaystyle z,x\in \{0,1\}^{\lambda }}$.
2. She one time pads the message m, ${\displaystyle l=x\oplus m}$
//z is used for quantum input ${\displaystyle Z^{z}X^{x}|\psi \rangle }$ where ${\displaystyle |\psi \rangle }$ is quantum input.
3. She then encrypts the pad key. HE.Enc${\displaystyle _{pk_{1}}(z,x)}$
4. She sends the encrypted message and pad key to the Server with the evaluation keys.
### Stage 2 Server’s Computation
• Input: ${\displaystyle \mathrm {evk} _{i}}$, pad key elements concatenation (${\displaystyle s}$), encryption of s under HE (${\displaystyle c=\mathrm {HE.Enc} _{pk}(s)}$), one time padded message (${\displaystyle l}$)
• Output: Updated encryption of pad key ${\displaystyle {\tilde {z}},{\tilde {x}}}$ and final classical outcome after performing the circuit.
• Circuit Evaluation (FHE.Eval())
1. Server creates a quantum superposition state for encrypted input ${\displaystyle l}$: ${\displaystyle Z^{z}X^{x}|\psi \rangle }$, where
${\displaystyle |\psi \rangle =\sum _{a,b\epsilon \{0,1\}}\alpha _{ab}|a,b\rangle }$ represents the two qubits superposition state for classical message m,
${\displaystyle Z^{z}X^{x}}$ represents quantum one time pad.
2. For all i, Server applies gate ${\displaystyle c_{i}}$ on qubit l and the ${\displaystyle l_{th}}$ bits of pad key ${\displaystyle ({\tilde {x}}^{[l]},{\tilde {z}}^{[l]})}$ are updated to ${\displaystyle ({\tilde {x}}'^{[l]},{\tilde {z}}'^{[l]})}$ as follows.
1. If ${\displaystyle c_{i}=\{P,H,CNOT\}}$, a Clifford gate then
//(${\displaystyle c_{i}Z^{z^{[l]}}X^{x^{[l]}}|\psi \rangle =Z^{z'^{[l]}}X^{x'^{[l]}}c_{i}|\psi \rangle }$)
1. if ${\displaystyle c_{i}=}$H then
${\displaystyle ({\tilde {x}}^{[l]},{\tilde {z}}^{[l]})\rightarrow ({\tilde {z}}^{[l]},{\tilde {x}}^{[l]})}$
//Hadamard tranforms X gate into Z and Z into X
2. if ${\displaystyle c_{i}=}$P then
//Pauli Gate
${\displaystyle ({\tilde {x}}^{[l]},{\tilde {z}}^{[l]})\rightarrow ({\tilde {x}}^{[l]},{\tilde {x}}^{[l]}\oplus {\tilde {z}}^{[l]})}$
3. if ${\displaystyle c_{i}=CNOT_{l,n}}$ with m as target bit and n as control bit then
//CNOT
(${\displaystyle {\tilde {x}}^{[l]},{\tilde {z}}^{[l]};{\tilde {x}}^{[n]},{\tilde {z}}^{[n]})\rightarrow ({\tilde {x}}^{[l]},{\tilde {z}}^{[l]}\oplus {\tilde {z}}^{[n]};{\tilde {x}}^{[l]}\oplus {\tilde {x}}^{[n]},{\tilde {z}}^{[n]})}$
2. If ${\displaystyle c_{i}=T}$ gate then
//Toffoli Gate on ${\displaystyle l_{th},n_{th},o_{th}}$ key bits
The Toffoli gate application can be deduced as follows:
${\displaystyle TZ^{z^{[l]}}X^{x^{[l]}}Z^{z^{[n]}}X^{x^{[n]}}Z^{z^{[o]}}X^{x^{[o]}}|\psi \rangle }$
${\displaystyle =TZ^{z^{[l]}}X^{x^{[l]}}Z^{z^{[n]}}X^{x^{[n]}}Z^{z^{[o]}}X^{x^{[o]}}T\dagger T|\psi \rangle }$
${\displaystyle =CNOT_{l,o}^{x^{[n]}}CNOT_{n,o}^{x^{[l]}}CZ_{l,n}^{z^{[o]}}Z^{z^{[l]}}X^{x^{[l]}}T|\psi \rangle }$
${\displaystyle =CNOT_{l,o}^{x^{[n]}}CNOT_{n,o}^{x^{[l]}}H_{n}CNOT_{l,n}^{z^{[o]}}H_{n}Z^{z^{[l]}}X^{x^{[l]}}T|\psi \rangle }$
${\displaystyle =C_{zx}P_{zx}T|\psi \rangle }$, where ${\displaystyle C\epsilon \{{\text{CNOT,H}}\}}$ and ${\displaystyle P\epsilon \{X,Z\}}$
1. The Pauli key encryptions are homomorphically updated according to ${\displaystyle P_{zx}}$.
(${\displaystyle {\tilde {x}}^{[l]},{\tilde {z}}^{[l]};{\tilde {x}}^{[n]},{\tilde {z}}^{[n]};{\tilde {x}}^{[o]},{\tilde {z}}^{[o]})\rightarrow ({\tilde {x}}^{[l]},{\tilde {z}}^{[l]};0,0;0,0)}$
2. Three encrypted CNOTs are used to correct ${\displaystyle C^{zx}}$ as follows under ${\displaystyle \mathrm {AltHE} }$.
• Server's Preparation:
1. Server converts ${\displaystyle {\hat {c}}=\mathrm {HE.Convert(c)} }$.
2. Server generates superposition on distribution D: ${\displaystyle \sum _{\mu \in \{0,1\},r}{\sqrt {D(\mu ,r)}}|\mu ,r\rangle }$
3. Server entangles above superposition and ${\displaystyle |\psi \rangle }$ with a third register:${\displaystyle \sum _{a,b,\mu \in \{0,1\},r}\alpha _{ab}{\sqrt {D(\mu ,r)}}|a,b\rangle |\mu ,r\rangle |f_{a}(r)\rangle }$, such that
${\displaystyle f_{0}=\mathrm {AltHE.Enc} _{pk}()}$;
${\displaystyle f_{1}(\mu _{1},r_{1})=f_{0}(\mu _{0},r_{0})\oplus _{H}{\hat {c}}=\mathrm {AltHE.Enc} _{pk}(\mu _{0},r_{0})\oplus _{H}\mathrm {AltHE.Enc} _{pk}(s)}$
${\displaystyle \therefore \mu _{0}\oplus \mu _{1}=s}$
4. Server measures the last register to get ${\displaystyle y=\mathrm {AltHE.Enc} (\mu _{0},r_{0})=\mathrm {AltHE.Enc} _{pk}(\mu _{1},r_{1})\oplus _{H}AltHE.Enc_{pk}(s)}$.
The resulting superposition state is:${\displaystyle \sum _{a,b\in \{0,1\}}\alpha _{ab}{\sqrt {D(\mu _{0},r_{0})}}|a,b\rangle |\mu _{a},r_{a}\rangle |\mathrm {AltHE.Enc} (\mu _{0},r_{0})\rangle =\sum _{a,b\in \{0,1\}}\alpha _{ab}{\sqrt {D(\mu _{0},r_{0})}}|a,b\rangle |\mu _{a},r_{a}\rangle |y\rangle }$
• Encrypted CNOT operation:
${\displaystyle \sum _{a,b\in \{0,1\}}\alpha _{ab}CNOT_{a,b}^{s}|a,b\rangle }$
${\displaystyle =\sum _{a,b\in \{0,1\}}\alpha _{ab}|a,b\oplus a\cdot s\rangle }$
${\displaystyle =\sum _{a,b\in \{0,1\}}\alpha _{ab}|a,b\oplus a\cdot (\mu _{0}\oplus \mu _{1})\rangle }$
${\displaystyle =\sum _{b\in \{0,1\}}\alpha _{0b}|0,b\oplus \mu _{0}\oplus \mu _{0}\rangle +\alpha _{1b}|1,b\oplus \mu _{0}\oplus \mu _{1}\rangle }$, ${\displaystyle \because q\oplus q=0}$
${\displaystyle =\sum _{b\in \{0,1\}}\alpha _{0b}|0\rangle \otimes X^{\mu _{0}}|b\oplus \mu _{0}\rangle +\alpha _{1b}|1\rangle \otimes X^{\mu _{0}}|b\oplus \mu _{1}\rangle }$, ${\displaystyle \because |q\oplus y\rangle =X^{y}|q\rangle }$
${\displaystyle =\sum _{a,b\in \{0,1\}}\alpha _{ab}|a\rangle \otimes X^{\mu _{0}}|b\oplus \mu _{a}\rangle }$
${\displaystyle =\sum _{a,b\in \{0,1\}}\alpha _{ab}(I\otimes X^{\mu _{0}})|a,b\oplus \mu _{a}\rangle }$
1. Server XORs the second qubit of first register with ${\displaystyle \mu _{a}}$ to get:
${\displaystyle \sum _{a,b\in \{0,1\}}\alpha _{ab}{\sqrt {D(\mu _{0},r_{0})}}(I\otimes X^{\mu _{0}})CNOT_{a,b}^{s}|a,b\rangle \otimes |\mu _{a},r_{a}\rangle |y\rangle }$
2. Server performs Hadamard on second register. The resulting superposition state is:
${\displaystyle \sum _{a,b\in \{0,1\}}\alpha _{ab}{\sqrt {D(\mu _{0},r_{0})}}(I\otimes X^{\mu _{0}})CNOT_{ab}^{s}|a,b\rangle \otimes H^{k}|\mu _{a},r_{a}\rangle |y\rangle }$
${\displaystyle =\sum _{a,b\in \{0,1\}}\alpha _{ab}{\sqrt {D(\mu _{0},r_{0})}}(I\otimes X^{\mu _{0}})CNOT_{ab}^{s}|a,b\rangle \otimes {\bigg (}\sum _{e\in \{0,1\}^{k}}(-1)^{e\cdot (\mu _{a},r_{a})}|e\rangle {\bigg )}|y\rangle }$, ${\displaystyle \because H^{k}|q\rangle =\sum _{e\in \{0,1\}^{k}}(-1)^{e\cdot q}|e\rangle }$, where q has k qubits
3. Server measures the second register to get d. The resulting superposition is:
${\displaystyle =\sum _{a,b\in \{0,1\}}\alpha _{ab}{\sqrt {D(\mu _{0},r_{0})}}(I\otimes X^{\mu _{0}})CNOT_{ab}^{s}|a,b\rangle \otimes (-1)^{d\cdot (\mu _{a},r_{a})}|d\rangle |y\rangle }$
The first register could be equivalently written as:
${\displaystyle (-1)^{d\cdot (\mu _{0},r_{0})}|0,b\rangle +(-1)^{d\cdot (\mu _{1},r_{1})}|1,b\rangle }$
${\displaystyle =(-1)^{d\cdot (\mu _{0},r_{0})}((-1)^{d\cdot ((\mu _{0},r_{0})\oplus (\mu _{0},r_{0}))}|0,b\rangle +(-1)^{d\cdot ((\mu _{0},r_{0})\oplus (\mu _{1},r_{1}))}|1,b\rangle )}$
${\displaystyle =(-1)^{d\cdot (\mu _{0},r_{0})}((-1)^{0\cdot (d\cdot ((\mu _{0},r_{0})\oplus (\mu _{1},r_{1}))})|0,b\rangle +(-1)^{1\cdot (d\cdot ((\mu _{0},r_{0})\oplus (\mu _{1},r_{1})))}|1,b\rangle )}$
${\displaystyle =(-1)^{d\cdot (\mu _{0},r_{0})}((-1)^{a\cdot (d\cdot ((\mu _{0},r_{0})\oplus (\mu _{1},r_{1}))})|a,b\rangle }$
${\displaystyle =(-1)^{d\cdot (\mu _{0},r_{0})}(Z^{d\cdot ((\mu _{0},r_{0})\oplus (\mu _{1},r_{1}))}|a,b\rangle )}$, ${\displaystyle \because Z|q\rangle =(-1)^{q}|q\rangle }$
Thus, the resulting state (upto a global phase) is:
${\displaystyle \approx (Z^{d\cdot ((\mu _{0},r_{0})\oplus (\mu _{1},r_{1}))}\otimes X^{\mu _{0}})CNOT_{12}^{s}\sum _{a,b\in \{0,1\}}\alpha _{ab}|a,b\rangle }$
Final superposition at the end of encrypted CNOT operation is:
${\displaystyle (Z^{d\cdot ((\mu _{0},r_{0})\oplus (\mu _{1},r_{1}))}\otimes X^{\mu _{0}})\mathrm {CNOT} _{1,2}^{s}|\psi _{12}\rangle }$
where ${\displaystyle (\mu _{0},r_{0})=(\mu _{1},r_{1})\oplus _{H}s}$, as ${\displaystyle \oplus _{H}}$ is the homomorphic XOR operation.
1. The server uses ${\displaystyle pk_{i+1}}$ to recrypt 'c' (previously encrypted using ${\displaystyle pk_{i}}$) and encrypt other variables under HE: ${\displaystyle \mathrm {HE.Enc} _{pk_{i+1}}(c)}$, ${\displaystyle \mathrm {HE.Enc} _{pk_{i+1}}({\hat {c}},y,d)}$.
2. The server computes the encryption of ${\displaystyle z,x}$ (stored in ${\displaystyle {\tilde {z}},{\tilde {x}}}$) under ${\displaystyle pk_{i+1}}$ by performing decryption circuit on ${\displaystyle \mathrm {HE.Enc} _{pk_{i+1}}(c)}$ using ${\displaystyle \mathrm {HE.Enc} _{pk_{i+1}}(sk_{i})}$ (provided by the evaluation key). Here, c, as stated before is the concatenation of encryption of x, z under ${\displaystyle pk_{i}}$, provided by the Client.
3. The server (homomorphically) computes ${\displaystyle (\mu _{0},r_{0})}$ and ${\displaystyle (\mu _{1},r_{1})}$, using ${\displaystyle \mathrm {HE.Enc} _{pk_{i+1}}(t_{sk_{i}},sk_{i})}$, provided by the evaluation key ${\displaystyle \mathrm {evk} _{i}}$ encrypted under ${\displaystyle pk_{i+1}}$, and ${\displaystyle \mathrm {HE.Enc} _{pk_{i+1}}({\hat {c}},y,d)}$, from the previous step.
4. The server then uses this results of the last three steps, to (homomorphically) update Pauli encryptions for encrypted ${\displaystyle CNOT_{l,n}^{s}}$:
(${\displaystyle {\tilde {x}}^{[l]},{\tilde {z}}^{[l]};{\tilde {x}}^{[n]},{\tilde {z}}^{[n]})\rightarrow ({\tilde {x}}^{[l]},{\tilde {z}}^{[l]}+d\cdot ((\mu _{0},r_{0})\oplus (\mu _{1},r_{1});{\tilde {x}}^{[n]}+\mu _{0},{\tilde {z}}^{[n]})}$
3. Server sends updated encryptions of Pauli corrections ${\displaystyle {\tilde {x}},{\tilde {z}}}$ and the classical outcome after measurement of the output state to Client.
### Stage 3 Client’s Output Correction
• Input: Classical output state (${\displaystyle l\in \{0,1\}^{\lambda }}$), encrypted Pauli corrections (${\displaystyle {\tilde {z}},{\tilde {x}}}$)
• Output: Decrypted classical message (${\displaystyle l\oplus x}$)
• Decryption (FHE.Dec${\displaystyle _{sk}}$)
1. Client decrypts ${\displaystyle {\tilde {z}},{\tilde {x}}}$ using ${\displaystyle sk_{L+1}}$ to obtain ${\displaystyle z,x}$.
2. She then uses the decrypted Pauli corrections to get the correct output ${\displaystyle l\oplus x}$.
## Further Information
In case of Quantum Input, the client additionally sends quantum one tie padded input state. In case of quantum output the Server instead of classical outcome sends the final quantum one time padded output state (operated by the required circuit). Client gets the output by using the updated encryption sent by the server to perform Pauli corrections on the output state. This protocol is first and only protocol currently, to use a classical functionality to solve a quantum task. It provides computationally security. Verification of this protocol is still an open question.
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2020-02-21 08:50:31
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https://www.physicsforums.com/threads/square-roots-of-positive-numbers.385106/
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# Homework Help: Square roots of positive numbers
1. Mar 9, 2010
### bluskies
1. The problem statement, all variables and given/known data
If a and b are positive real numbers, and $$\lambda^{2} = ab$$, then $$\lambda = \pm \sqrt{ab}$$.
2. Relevant equations
None.
3. The attempt at a solution
This is more of a conceptual question that has always escaped me. I do not understand how the square root of two positive numbers could possibly be negative. Since a and b are positive, how can there be any negatives in the square root of their product? Any guidance on this subject would be very much appreciated.
2. Mar 9, 2010
### rock.freak667
(-1)2 =1
so squaring -√(ab) will give (ab) regardless of a + or - before the square root.
3. Mar 9, 2010
### dacruick
I think you might be looking too hard into this. There are no negatives in the square root. the negative is outside it. say both a and b are 5. then lambda² = 25. lambda therefore is equal to positive root(25) or negative root(25). Or in other terms, lambda² = 5² or (-5)²
4. Mar 9, 2010
### Fightfish
A numerical example can illustrate this. Let a = 1 and b = 4 for instance. Then we have $$\lambda^{2} = 4$$. We realise however, that because negatives cancel upon multiplication, in fact $$(-2)^2 = 2^(2) = 4$$, and so both -2 and 2 are possible solutions.
5. Mar 9, 2010
### bluskies
Thank y'all for your help, that makes sense now. :)
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2018-09-26 03:32:47
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http://mathhelpforum.com/pre-calculus/194457-evaluating-log-print.html
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# Evaluating log
• December 18th 2011, 02:34 PM
Bashyboy
Evaluating log
If log_b 6 = .4040 then b^-.4040 is equal to...I am not to sure about how to solve this.
• December 18th 2011, 02:37 PM
Plato
Re: Evaluating log
Quote:
Originally Posted by Bashyboy
If log_b 6 = .4040 then b^-.4040 is equal to...I am not to sure about how to solve this.
If $\log_b(X)=a$ then $b^a=X~.$
• December 18th 2011, 03:10 PM
Bashyboy
Re: Evaluating log
Well, the exponent on b is negative, does that change the definition you gave me at all?
• December 18th 2011, 03:14 PM
Plato
Re: Evaluating log
Quote:
Originally Posted by Bashyboy
Well, the exponent on b is negative, does that change the definition you gave me at all?
No indeed. It just requires one more step.
If $b^a=X$ then $b^{-a}=\frac{1}{X}~.$
• December 18th 2011, 03:28 PM
Bashyboy
Re: Evaluating log
Oh, yes--I undserstand now. I do have another one, though: If log 2 = .3010 then log sqroot(20) is equal to.
• December 18th 2011, 03:44 PM
Plato
Re: Evaluating log
Quote:
Originally Posted by Bashyboy
Oh, yes--I undserstand now. I do have another one, though: If log 2 = .3010 then log sqroot(20) is equal to.
First, you should start a new thread for a new question.
Note that $\log(\sqrt{a})=\tfrac{1}{2}\log(a)$.
$\log(20)=\log(10)+\log(2)$
Now contrary to modern trends it seems that here $\log$ means $\log_{10}$ so $\log(10)=1$.
• December 18th 2011, 03:57 PM
Bashyboy
Re: Evaluating log
Do I sense condescension in your writing, or am I thoroughly mistaken?
• December 18th 2011, 04:33 PM
Plato
Re: Evaluating log
Quote:
Originally Posted by Bashyboy
Do I sense condescension in your writing, or am I thoroughly mistaken?
You either have the largest chip on your shoulder or you can't read.
Are you angry at me for not giving a complete and polished solution?
Do you not want to learn how to do these?
• December 18th 2011, 04:49 PM
Bashyboy
Re: Evaluating log
No, I am absolutely not angry. I inferred that impression on my first reading of your post; but, after re-reading it, I have found that impression to be wrong. I am terrible sorry. I sensitive when it comes to scorning my mathematical knowledge; and I know it is scarce, due to myself having studied it a little later in life than normal, and that is why I was a bit jumpy. Again, sorry.
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2014-03-16 03:52:17
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https://earthscience.stackexchange.com/questions/19266/why-are-atmospheric-bro-and-clo-important-to-measure-by-satellite/19267
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# Why are atmospheric BrO and ClO important to measure by satellite?
The announcement Arianespace orbits two satellites – JCSAT-17 and GEO-KOMPSAT-2B – to support connectivity and environmental monitoring in Asia mentions GEO-KOMPSAT-2B which hosts the Geostationary Environmental Monitoring Spectrometer or GEMS UV/Vis (300-500 nm) imaging spectrometer for hyperspectral imaging of Earth's atmosphere.
The instrument's purpose is given as
Ozone profile and total-column or gross profile of other species. Tracked species: BrO, NO2, O3, OClO, SO2 and aerosol
and its primary mission objectives are listed as
• BrO Mole Fraction
• ClO Mole Fraction
• H2O Mole Fraction
• HC3Br Mole Fraction
• HCHO Mole Fraction
with the following as other mission objectives
• HCHO Total Column
• NO Mole Fraction
• NO2 Total Column
• NO2 Mole Fraction
• O3 Mole Fraction
• O3 Total Column
• SO2 Mole Fraction
• SO2 Total Column
I think that "Mole fraction" is a relative concentration and "Total column" is absolute?
I see that some of the species listed in the instrument's purpose are not in its primary objectives, but oh well.
Question: Why exactly are atmospheric BrO and ClO so important to measure, and measure by satellite, and what is the difference between ClO in the "objectives" and OClO in the "purpose"?
• A guess (I don't have to research at the moment): BrO and ClO play a role in ozone destruction (→ ozone hole). – njuffa Feb 22 '20 at 6:00
• As noted in my answer, the OSCAR entry on the GEMS instrument is severely flawed: GEMS will not measure BrO or ClO. Those flaws do not detract from the primary question regarding the importance of measure atmospheric BrO and ClO, or from the auxiliary question regarding molar fraction vs total column. – David Hammen Feb 24 '20 at 1:02
BrO and ClO significantly deplete ozone from the atmosphere.
Researchers at Harvard University state:
It is a remarkable fact that perhaps the most important observation coupling climate forcing to UV dosage levels at the surface at mid-latitudes is the observation of high (e.g. > 10 ppmv) water vapor and low temperatures (< 210 K) with the simultaneous determination of BrO and ClO in the lower stratosphere at mid-latitudes.
Similarly, Science magazine states:
Halogen-radical chemistry was responsible for approximately one-third of the photochemical removal of O3; reactions involving BrO account for one-half of this loss.
... where the chlorine and bromine thus released participate in the catalytic destruction of ozone.
pretext: Seeing this question on the list of network questions caught my interest to the site.
I agree with the arguments put forward in the answer by Fred, gravitating on the radical character of halogene oxides listed (e.g., BrO, ClO), where unpaired electrons contribute to reactivity to the specis. Some of them are created in situ under light radiation and hence may interfere in the constant generation and decomposition of ozone in the Chapman cycle.
To expand the picture, there is a large «family» of chlorine oxydes, for some of them the structural formulae are given below (each containing a dot already is a radical in a chemical sense) and individual details (chlorine oxides), and bromine dioxide in addition:
However, I would point out that the original listing on OSCAR about GEMS' mission as-such accidentally may contain errors as it lists HC3Br Mole Fraction. For one, there isn't such a compound as a stable one you could store in a bottle like copper sulfate. Indeed I speculate, in analogy to CFCs like methylene chloride and chloroform, their target is bromoform, $$\ce{CHBr3}$$ which has natural sources, and is relevant to atmospheric ozone, too.
side note: Similar to the putative chemical error here, some elder data entries in crystallographic databases erroneously state a symmetry in $$P1$$. While initially submitted by the authors as $$P\bar{1}$$, the bar sometimes was lost during the processing (mentioned, for example, by Hofman here), like the first SHG signal described by Franken et al.
• That's great news, welcome to the site and thank you for your answer! – uhoh Feb 23 '20 at 0:50
• – uhoh Feb 23 '20 at 0:57
Regarding the Geostationary Environmental Monitoring Spectrometer (GEMS) itself:
The instrument's purpose is given as
Ozone profile and total-column or gross profile of other species. Tracked species: BrO, NO2, O3, OClO, SO2 and aerosol
That is rather inaccurate and misleading. GEMS does not track BrO or OClO (or ClO). It does track ozone, but the target is tropospheric rather than stratospheric ozone. GEMS is a satellite instrument whose primary goal is tropospheric air quality monitoring rather than stratospheric chemistry.
I think that "Mole fraction" is a relative concentration and "Total column" is absolute?
Mole fraction is the relative concentration of some atmospheric component as a function of altitude. Converting this relative concentration to an absolute quantity (e.g., number of moles, or mass) and integrating from the bottom of the atmosphere to the top yields the "total column" quantity for that component.
Why are atmospheric BrO and ClO important to measure by satellite?
This is the question raised in the title of the question.
A large number of halogenated hydrocarbons indirectly contribute to ozone depletion. Those halogenated hydrocarbons by themselves are not ozone-depleting substances. But if those compounds reach the upper stratosphere, sunlight can split a halogen atom off of those components. Split-off fluorine atoms tend to bind rather quickly with hydrogen and form an extremely stable hydrogen fluoride molecule. Fluorine barely registers as an ozone-depleting substance because hydrogen fluoride is so stable. Stratospheric hydrogen fluoride eventually diffuses into the troposphere, where it gets dissolved by water and falls as rain.
Split-off chlorine and bromine atoms have a different fate. Hydrogen chloride and hydrogen bromide aren't nearly as stable as is hydrogen fluoride. Chlorine and bromine instead alternate between reservoirs such as HCl and hBr and atomic/oxide forms that catalytically deplete ozone. The key reason it is important to monitor these halogens is that most (about 80%) of the chlorine and almost half (40-50%) of the bromine in the stratosphere is anthropogenic.
References:
Molina, Mario J., et al. "Antarctic stratospheric chemistry of chlorine nitrate, hydrogen chloride, and ice: Release of active chlorine." Science 238.4831 (1987): 1253-1257.
Poulet, Gilles, et al. "Role of the BrO+ HO2 reaction in the stratospheric chemistry of bromine." Geophysical research letters 19.23 (1992): 2305-2308.
Choi, Won Jun, et al. "Introducing the geostationary environment monitoring spectrometer." Journal of Applied Remote Sensing 12.4 (2018): 044005.
Kim, Jhoon, et al. "New era of air quality monitoring from space: Geostationary Environment Monitoring Spectrometer (GEMS)." Bulletin of the American Meteorological Society 2019 (2019): 00.
In addition to the above scientific articles, there are many web pages on stratospheric chemistry. For example, https://personal.ems.psu.edu/~brune/m532/meteo532_ch7_stratospheric_chemistry.htm
• yikes! it's going to take me a few days just to download and/or skim these, but I'm looking forward to it, thanks! – uhoh Feb 24 '20 at 2:41
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2021-03-05 10:29:44
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https://www.physicsforums.com/threads/kobe-treaty.7620/
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# Kobe Treaty
1. Oct 22, 2003
Staff Emeritus
We have some good discussions going on the pros and cons of global warming, so here's a thread for discussion the Kobe treaty on cutting greenhouse gasses. As we recall, the Europeans and third world countries were enthusiastic about it, but opponents raised serious questions of cost/benefit and the US refused to ratify it. Russia is currently discussing ratification.
What do our panel of experts thinlk?
2. Oct 23, 2003
### milton friedman
Hmm. Ill have to do more research on it. Coming from a economic stand point, if the cost are greater then the benefits, I’m against it. Again I somewhat question where we are putting our recourses. While many argue that this is a natural process or that it is a natural process but we are accelerating it with our CO2 emissions, I question the relevancy of spending billions (note: cost to the consumer, taxpayer) on trying to cut emissions when we could spend that money elsewhere trying to prepare our infrastructure and food sources for the inevitable. (note: I’m not a oil man and support complete removal of certain environmental regulations. To tell you the truth, I’m not very fond of the activities of certain oil companies )
I recently heard a interview done by art bell on coast to coast about this very topic. I tuned in a bit late so I really didn’t get to hear what he thought of it. Is Dr. kaku for cutting our co2 emmisions? Also what is his political affiliation
3. Oct 23, 2003
### FZ+
IMHO, the trouble with such approaches is that the nations expected to be worst hit by any further climate change would tend to be the poorer ones, and hence be less able to adopt a "weather it out" technique. Damage to third world crops, for example, by increased frequency of severe weather conditions, could cause huge humanitarian issues.
4. Oct 23, 2003
### TENYEARS
You could cut the total emssions of the whole planet right now by 75% and that would still be to much. In order to save the planet it would require the reformatting of the all humanity into a new way of life. The life would be basic and consumption would have to go to it's lowest level of food clothing and shelter with few extras. Humanity likes it's candy at any cost and it will cost will be great. The inevitable is on it's way debate all you like, sign treaties with fools, and listen to scientist who know nothing.
5. Oct 24, 2003
### milton friedman
I’m curious, I must do more research but if we cut the CO2 emissions by 75%, how much time would it buy us and how much would it cost??? Do the marginal benefits supercede the marginal cost?
6. Oct 24, 2003
### theroyprocess
Cost vs Benefit
Dear Milton,
I only WISH science and government policy WAS based on cost vs benefit
analysis! My efforts promoting the Roy Process invention for cost effective
transmutation of high level nuclear waste has shown the real life ethic IS
NOT for efficiency....but for the steady siphoning of tax payer money BY NOT
employing good science! The below article illuminates this:
---------------------------------------------------------------------------------
DOE Squandered Billions on Useless
Nuke Waste Technologies
By Brian Hansen
WASHINGTON, DC, November 13, 2000 (ENS) - The U.S.
Department of Energy has "squandered hundreds of
millions of dollars" since the end of the Cold War
trying to develop innovative technologies for
cleaning up the nation's contaminated nuclear weapons
sites, concludes a Congressional report unveiled last
week.
The report, "Incinerating Cash," was authored by
staff members of the House Commerce Committee's
Republican majority. The committee's Democratic
members
did not participate in drafting the report.
The report charges that the Department of Energy
(DOE) has wasted much of the $3.4 billion that it has spent over the last decade on efforts to develop new technologies for cleaning up nuclear weapons wastes. Congress ordered the DOE in 1989 to initiate the program to address the environmental issues resulting from decades of nuclear weapons production. The committee's report concludes that the DOE has spent hundreds of millions of dollars on technologies that "have not proved useful" in the clean up mission. Moreover, the "useful" clean up technologies that the DOE has produced have not been used effectively by the agency or its private contractors, the report found. Of the 918 technologies that the DOE has funded, just 31 - less than 4 percent - have been deployed more than three times at contaminated nuclear weapons sites, the report notes. Of the technologies that have been deployed, more than half have been used only once, the report adds. The report attributes the failure of the program to an "ongoing pattern of mismanagement and lack of focus" within the DOE's Office of Science and Technology, which is implementing the initiative. Carolyn Huntoon, the DOE's assistant secretary for environmental management, was quick to dispute the findings of the Commerce Committee's report. In a written statement, Huntoon rejected claims that the technology program has not produced results. "One out of every five research and development projects have resulted in a viable technology being used by the department," Huntoon said. The DOE's nuclear waste complex consists of 113 geographic waste sites located throughout the country. The DOE recently estimated that it will cost between$151 and $195 billion over the next 70 years to clean up the complex, not including the$51 billion already
spent between 1990 and 1999.
The Commerce Committee's report cited a number of
case studies in concluding that those costs will not
be appreciably reduced by the application of
technologies developed by the DOE's Office of Science
and Technology (OST).
Those case studies were based in large part on a
survey conducted earlier this year, in which several
large DOE site contractors were asked to describe
their use of commercially available OST funded
technologies.
One DOE site analyzed in the committee's survey was
the Rocky Flats facility near Denver, Colorado, where
large quantities of wastes containing plutonium and
other radioactive constituents must be characterized,
stabilized, packaged and moved off site. The DOE's
environmental management program has to date spent
some $4.9 billion at Rocky Flats, and the agency plans to spend another$4.5 billion over the next five years
to complete environmental cleanup activities by the
year 2006.
However, the Kaiser-Hill Company, the DOE's
contractor at the site, has so far found use for just
seven commercially available clean up technologies,
the Commerce Committee's report found. The company
will likely deploy no more than three of the DOE's
technologies in the year 2000, the committee's
survey found.
"Thus, after 10 years and $3.4 billion spent to develop technologies to reduce costs and speed cleanup, few [DOE] funded technologies have been used for cleanup at Rocky Flats, and few will likely be used in the future," the report declares. The report also notes how DOE funded technologies have been ineffective in advancing remediation activities at the Hanford nuclear reservation in Washington state, where the cleanup of 177 underground tanks containing radioactive wastes is one of the most expensive and significant long term waste management projects within the DOE complex. The report notes that Hanford's radioactive tank wastes represent a huge potential impact to human health and the environment. Hanford's Office of River Protection (ORP) spends more than$300 million
each year for characterization, interim stabilization,
and resolution of tank safety issues to control the
approximately 200 million curies of cesium, strontium
and other radioactive constituents stored in rapidly
Some 30 tanks are known to have leaked in the past.
Since 1990, the DOE has spent $4 billion on this project, and the agency plans to spend$13 billion
over the next 70 years on tank farm operations. To
date, the DOE has funded 80 technologies and has
spent hundreds of millions of dollars at Hanford.
But the committee's report finds that the
commercially available technologies funded by the DOE
have provided "no significant use" for characterizing
or stabilizing the Hanford tank wastes, nor will they
do so in the future. According to the CH2M Hill
Hanford
Group, the DOE's contractor at the site, none of the
commercially available technologies have been deployed
at the Hanford tank farms.
The report is also critical of the DOE's use of
taxpayer funded technologies to improve operations at
the Waste Isolation Pilot Plant in New Mexico, where
feet below the surface of the desert.
7. Oct 24, 2003
### TENYEARS
Everybody wants a piece of pie and they want it for free. Nothing is for free. It is the law of conservation of matter and energy. We are ants and nothing more, like ants or locust we will consume until there is nothing left and move on. The only difference is that ants and locust do not pullute when they leave and they have been around for millions of years in a balance with nature. We are not. For after we consume, we posion the land, the air the water and the very conciousness of humankind. I have seen the future and it has come to pass. This post is simple inevitable logic.
So you want to promote clean up of nukes? What about chemicals on a daily basis, sulfur which when combined with the elements creates acid rain which decomposes the rock and posins the waters. The co2, the tens of thousands of man make composites which are all toxic in their decomposition. If not to us directly then to other forms of the natural environment. Mankind will get what it deserves, it is comming and it will be fast and it will be slow. Keep consuming people. Maybe I will take my piece of pie and become an unconcious dam fool.
Who do you blame? How do you change it? You can't. You are in a car traveling at 1000 miles an hour heading towards a brick wall with no brakes to steering you are in space. If you jump from the car you will go splat to the wall. If you push from the side of the car you will still go splat because you were unconcious for so long enjoying the ride that the wall is to close. The wall is thousands of miles wide. You cannot get clear. So what do you do?
8. Oct 24, 2003
### theroyprocess
What do you do?
First thing they teach you on your new job in DC.
WHAT EVER YOU DO.....JUST DON'T BREAK THE 11th COMMANDMENT!
{THOU SHALT NOT GET CAUGHT...BREAKING THE FIRST TEN}
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2017-11-19 22:33:08
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https://calculator-online.net/standard-form-calculator/
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Uh Oh! It seems you’re using an Ad blocker!
We always struggled to serve you with the best online calculations, thus, there's a humble request to either disable the AD blocker or go with premium plans to use the AD-Free version for calculators.
Or
# Standard Form Calculator
Calculate Standard Form
Turn a number into a Standard Form, Scientific E-Notation, Engineering Notation, and Real Number format.
Enter a Number
Table of Content
1 What Is A Board Foot In Lumber (BF)? 2 Board Foot Formula: 3 Board Foot Units: 4 Important Thickness: 5 How To Calculate Board Feet? 6 What do you mean by the term “Surface Measure”? 7 What is meant by nominal measurement? 8 How do you define lineal measurement?
Get the Widget!
Add this calculator to your site and lets users to perform easy calculations.
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How easy was it to use our calculator? Did you face any problem, tell us!
Standard form calculator is the tool that allows you to convert the number in the standard form.
All you need to enter any number and convert it into standard form. It helps you to write standard form equation into its ordinary form.
## What Is Standard Form In Math?
Well, any number that you can write as a decimal number, between 1.0 and 10.0, and multiplied by a power of 10 is known as the standard form. In other words, it is a way of writing down very large/very small numbers easily. No doubt, it is difficult to read numbers like 675678888000 or 0.000012345675, for the ease you can write it in the form of power of 10.
### Example of Standard Form:
A number is (600000)
So, the number is in the standard form written as (6 ×10^5)
For better understanding, look at the given table:
12345 1.2345 x 10^ 4 5.0043e+06 5.0043 x 10^ 6 45 4.5 x 10^ 1 1e-05 0.1 x 10^ -4 0.0003012 0.3012 x 10^ -3 0.00049 0.49 x 10^ -3 3.2e+06 3.2 x 10^ 6 0.00147 0.147 x 10^ -2 23500 2.35 x 10^ 4 80000 8 x 10^ 4 0.4184 0.4184 x 10^ 0 1.496e+08 1.496 x 10^ 8 2.2794e+08 2.2794 x 10^ 8 1.416e+08 1.416 x 10^ 8 9.29e+07 9.29 x 10^ 7 8.603e+07 8.603 x 10^ 7
## How to Convert a Number into Standard Form:
Our Standard form calculator helps to write equation in standard form, this tool is 100% free and makes calculations within a fraction of seconds. Just stick to these steps and turn your number into standard form.
Inputs:
• All you need to enter the number that you want to convert into standard form
• Very next, just hit the calculate button
Outputs:
The standard notation calculator will show:
• Standard Form for a given number (that is a number and a power of (10))
• Scientific E-Notation
• Engineering Notation
• Real Number
## How To Write In Standard Form?
This is the standard form equation helps you in writing a number in a standard form, even our standard form calculator also uses the same equation.
$$a = b times 10^n$$
Let’s take a look!
A number is 71900000000000 – convert to standard notation:
• Then, you ought to add a decimal point after it 7.
• Very, you have to count the number of digits after 7 – you can see there are 13 digits
• So, 71 900 000 000 000 is 7.19 ×10^{13}
A number is 0.000 0014:
• First of all, you have to write the very first non-zero digit – here you can see it is 1
• Very next, you have to add a decimal point after it: 1.
• Remember that the decimal point shifts 6 places to the right
• So, it represent as 1.4 ×10^{-6}
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2023-03-24 16:24:40
|
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https://bastian.rieck.me/blog/posts/2019/iclr_analysis/
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A short analysis of ICLR 2020 reviews
Tags: research
« Previous post: On writing reviews — Next post: Ideas and creativity »
With ICLR 2020, the International Conference on Learning Representations, being already well into its rebuttal period, I wanted to take a look at all the reviews and try to spot interesting patterns. This is a write-up of some of the (preliminary) results.
Getting and preparing the data
Thanks to the great folks of OpenReview, who provide an easy-to-use Python API, getting all reviews is a walk in the park (skip to the end of the article to see the code). Storing all reviews in JSON format took Michael and me only a few minutes. We did not change anything in the raw data except for a simple mapping of experience levels:
Experience Meaning
1 I have read many papers in this area.
2 I have published one or two papers in this area.
3 I have published in this field for several years.
For all other fields, we used the respective numerical scale. This year, there are only the following options:
Rating Meaning
1 Reject
3 Weak Reject
6 Weak Accept
8 Accept
In the interest of readability, the following plots only contain these numerical labels.
How long are the reviews?
Let us look at some distributions now. First, the obligatory histogram of word counts of a review. The median number of words per review is 338, while the mean is 395.5. As expected, there is a tail of very long reviews, but in general, ICLR 2020 reviews appear to be rather terse.
A closer inspection of the very short reviews shows that some of them deal with desk rejections, so their length is not too surprising. Are there maybe differences in word count that depend on the rating of a paper? To visualise this, here is a set of boxplots, partitioned by the final rating of a paper.
This is mildly surprising to me—I would have expected that strongly-opinionated reviews (1 and 8) would use longer reviews to justify their decision. Yet, the plot shows that this is only true for reviews that reject a paper: more outlier reviews (in terms of their length) are shown here. Curiously, reviews that fully endorse a paper have the lowest mean:
Rating Mean number of words
1 424.70
3 420.65
6 352.41
8 340.28
What about the experience assessment, though? Do experienced reviewers write longer reviews? As it turns out, this is not exactly true, as the following plot shows:
There is a clear difference in the mean review length in that inexperienced reviewers tend to write shorter reviews, most likely because they (feel) unable to judge the content of the paper accurately. The jump between the means is quite sizeable:
Experience Mean number of words
0 313.94
1 378.28
2 429.63
3 425.14
Reviewers with experience level 21 write reviews that are on average 37% longer than those of reviewers with experience level 02. To dig more into this, we need to partition by experience level and by rating. Here are the resulting boxplots:
This yields some interesting patterns:
• Inexperienced reviewers write longer reviews when they rejecting a paper. This strikes me as a good; if someone with no knowledge about my research area recommends to reject my paper, a good and long justification is appreciated.
• Weak rejects, with a rating of 3, are on average the longest reviews. I cannot check this assumption easily3, but I assume that these reviews also discuss steps that authors could do in order to ‘sway’ the rating into a more favourable one.
• Again, accepts, with a rating of 8, are among the shortest reviews. Maybe reviewers feel that they do not have to justify the acceptance of a paper as much as its rejection? Alternatively, maybe the papers that receive such ratings are of such stellar quality that there is nothing left to improve? I doubt that this is the case, but analysing this further would be interesting—I will keep that idea for a future blog post, though.
How tough are the reviewers?
As a last analysis, let us compare the ‘toughness’ of reviewers. Does the experience level shift the final rating of a reviewer? This is just a matter of counting across categories:
As we can see, inexperienced reviewers tend not to be strongly-opinionated about a paper; most of their reviews (about 80%) are either weak rejects or weak accepts. For the remaining experience levels, the story is different: here, most reviews are weak rejects (for experience levels 1–3), followed by weak accepts (for experience levels 1 and 2). Interestingly, the second-most common rating for highly experienced reviewers is reject. It appears that veteran reviewers are relatively tough for their final verdict. Moreover, with only 6.8% of their reviews being rated as accept, in contrast to 7.5% (level 2), 9.9% (level 1), and 10.0% (level 0), getting a veteran reviewer appears to slightly decrease your chances of getting your paper accepted.
I have to admit that some of these results are surprising to me—I always though that after a certain level of experience, the rating algorithm applied by reviewers is essentially the same. This is definitely not the case. Of course, such an analysis suffers from inevitable caveats, the most glaring one being the fact that reviewers themselves decide on their level of competence…
Code, data, and coda
Everything (code and data for 2020 as well as 2019) is available on GitHub. It is clear that this analysis only scratched the surface here. An interesting direction would be the integration of NLP techniques to go down on the level of individual reviews. In addition, the extraction code and the analysis scripts are still somewhat unpolished. I would love to make this into a repository that contains all reviews from the past ICLR conferences because I am convinced that we, i.e. the machine learning community, should closely watch and analyse our review process. Everyone complains about peer review for their own reasons, but collections such as this one make it possible to investigate certain issues.
Ideally, I would like to close this article with some recommendations for improving the review process. However, I feel I am not in the position to ‘enact’ these changes in our community. If you, my dear reader, happen to be among the ‘movers and shakers’ of the machine learning world, I hope this article gave you some food for thought.
Until next time; may your reviews always be fair!
Acknowledgements: This article was inspired by the scripts and plots of Shao-Hua Sun, whose analysis covers some aspects of this article but focuses more on review scores per paper. Check out the repository for a great overview and ranking of all papers!
1. ‘I have published one or two papers in this area.’ ↩︎
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2021-05-14 16:21:00
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http://muratbuffalo.blogspot.com/2018/01/
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## Posts
Showing posts from January, 2018
### Paxos derived
Lamport's fault-intolerant state machine replication algorithmIn 1978, Lamport published his classic "Time, Clocks, and the Ordering of Events in a Distributed System". As an application of logical clocks, he presented a distributed replicated state machine algorithm (and then he instantiated that algorithm to solve mutual exclusion as an example). Lamport complains that no one seemed to be aware of the distributed replicated state machine algorithm introduced in the paper:
"This is my most often cited paper. Many computer scientists claim to have read it. But I have rarely encountered anyone who was aware that the paper said anything about state machines. People seem to think that it is about either the causality relation on events in a distributed system, or the distributed mutual exclusion problem. People have insisted that there is nothing about state machines in the paper. I’ve even had to go back and reread it to convince myself that I really did remember wha…
### Modeling the DAO attack in PlusCal
Maurice Herlihy's paper: "Blockchains from a distributed computing perspective" explains the DAO attack as follows:
"Figure 1 shows a fragment of a DAO-like contract, illustrating a function that allows an investor to withdraw funds. First, the function extracts the client's address (Line 2), then checks whether the client has enough funds to cover the withdrawal (Line 3). If so, the funds are sent to the client through an external function call (Line 4), and if the transfer is successful, the client’s balance is decremented (Line 5). This code is fatally flawed. In June 2016, someone exploited this function to steal about $50 million funds from the DAO. As noted, the expression in Line 3 is a call to a function in the client's contract. Figure 2 shows the client's code. The client's contract immediately calls withdraw() again (Line 4). This re-entrant call again tests whether the client has enough funds to cover the withdrawal (Line 3), and becaus… ### Spring 18 Distributed Systems Seminar ### Erasable pens for editing papers I recently discovered the Pilot Frixion pens and I like them a lot. (I am not getting any advertisement money from them I swear :-) The pens have erasable ink, so they are great for marking your comments/edits on a paper while reading. They erase via heat. Each pen comes with a plastic nub, and if you apply friction to the page with the plastic nub at the top, and it erases the writing --mostly clean. A word of caution though, this means if you leave your writing in a hot car, you will find it erased, which you can remedy by putting it in a freezer. I am not kidding. So, don't use it for writing you want to keep permanently, but it is great for writing comments and marking on a paper when you are reading. I print the research paper I am reading and I do a lot of marking on paper. If I use a regular pen, I cross over some of my guesswork, nonsensical questions, or misinformed comments, and it messes up the paper. But using Frixion pens, I erase and modify my comments without creatin… ### Remember peer-to-peer systems? Traditionally computer systems use client server model. This is more of a centralized approach; server sits there and responds to clients requests. If one server is not enough for computation/analysis, a "hierarchical" organization of servers model is adopted in datacenter and cloud computing. One node becomes the master, other nodes act as workers. This is called the master-worker model. This simple model make sense if you have an infrastructure. Centralized control architecture is simple, so you can keep the coordination simple and efficient. Peer-to-peer model is on the other end of the spectrum: it calls for a fully decentralized system model. There is no distinguished master. Each node acts as both server and client, each node is a peer. This model does not require stable infrastructure and it can self-organize with what is presently available. As such, they are great for circumventing laws, bans, and censorship. In 2000s, peer-to-peer systems were all the craze. Peer-… ### Paper summary. A Berkeley view of systems challenges for AI This position paper from Berkeley identifies an agenda for systems research in AI for the next 10 years. The paper also serves to publicize/showcase their research, and steer interest towards these directions, which is why you really write position papers. The paper motivates the systems agenda by discussing how systems research/development played a crucial role in fueling AI’s recent success. It says that the remarkable progress in AI has been made possible by a "perfect storm" emerging over the past two decades, bringing together: (1) massive amounts of data, (2) scalable computer and software systems, and (3) the broad accessibility of these technologies. The rest of the paper talks about the trends in AI and how those map to their systems research agenda for AI. Trends and challenges The paper identifies 4 basic trends in the AI area: Mission-critical AI: Design AI systems that learn continually by interacting with a dynamic environment in a timely, robust, and secure man… ### The Lambda and the Kappa Architectures This article, by Jimmy Lin, looks at the Lambda and Kappa architectures, and through them considers a larger question: Can one size fit all? The answer, it concludes, is it depends on what year you ask! The pendulum swings between the apex of one tool to rule them all, and the other apex of multiple tools for maximum efficiency. Each apex has its drawbacks: One tool leaves efficiency on the table, multiple tools spawns integration problems. In the RDBMS world, we already saw this play out. One size RDBMS fitted all, until it couldn't anymore. Stonebraker declared "one size does not fit all", and we have seen a split to dedicated OLTP and OLAP databases connected by extract-transform-load (ETL) pipelines. But these last couple years we are seeing a lot of one size fits all "Hybrid Transactional/Analytical Processing (HTAP)" solutions being introduced again. Lambda and Kappa OK, back to telling the story from the Lambda and Kappa architectures perspective. What a… ### Paper summary. TFX: A TensorFlow-Based Production-Scale Machine Learning Platform This paper from Google appeared at KDD 2017 Applied Data Science track. The paper discusses Google's quality assurance extensions to their machine learning (ML) platforms, called TensorFlow Extended (TFX). (Google is not very creative with names, they should take cue from Facebook.) TFX supports continuous training and serving pipelines and integrates best practices to achieve production-level reliability and scalability. You can argue that the paper does not have a deep research component and a novel insight/idea. But you can argue the same thing for the checklist manifesto by Atul Gowande, which nevertheless does not decrease from its effectiveness, usefulness, and impact. On the other hand, the paper could definitely have been written much succinctly. In fact, I found this blog post by Martin Zinkevich, the last author of the paper, much easier to follow than the paper. (Are we pushed to make papers artificially obfuscated to be publication-worthy?) This blog post on serving s… ### Why you should use modeling [with TLA+/PlusCal] I recently gave a two day seminar on "debugging your designs with TLA+/PlusCal" at Dell. So I wanted to write some of the motivation for modeling and debugging your models while this is still fresh in my mind. You need modeling No, not that kind of modeling! Actually the naming clash is not accidental after all: fashion designers need models to test/showcase their designs. You need modeling because: Failing to plan is planning to fail Everything is a distributed systemThe corner cases ... they are so manyDo it for the development processBeing smart does not scale Failing to plan is planning to fail This is from the paper, "Use of formal methods at Amazon Web Services, 2014". "Before launching any complex service, we need to reach extremely high confidence that the core of the system is correct. We have found that the standard verification techniques in industry (deep design reviews, code reviews, static code analysis, stress testing, fault-injection testing, et… ### Salute to Prof. Mohamed Gouda: Elegance in computing A couple months ago, I attended a special half-day workshop organized honoring Prof. Mohamed Gouda's contributions to computer science, and particularly the self-stabilizing systems community. Mohamed is the Mike A. Myers Centennial Professor at University of Texas at Austin. He has been at Austin Texas since 1980, for almost 40 years. His research contributions to the distributed systems has been phenomenal (borrowing a word Mohamed likes to use for things that excite him.) I am proud that Mohamed is my academic grandfather; he was the PhD advisor of my PhD advisor, Prof. Anish Arora. I wrote about "how to find your advisor" in my previous post, I hope elegance/rigor from Mohamed and Anish rubbed off on me a bit. At the workshop, there were about 10 talks technical in nature, but at the end of the talks, each speaker mentioned how their research and career has been enriched by Mohamed's contributions/help. I talked about my technical report on "Does the cloud n… ### How to find your advisor I had tweeted this earlier about "Rocking your PhD": Find a hardworking advisorGet a senior PhD student mentorRead a lot of papers criticallyWrite a lot, get feedbackPublish your first paper early to build confidencePublish your 2nd, 3rd, 4th papersTo sustain, exercise regularly It is that simple. This is actually a concise version of a longer advice I provided earlier. Since I haven't talked about it before, I like to now write some suggestions on finding an advisor. How to find your advisorAsk around and get advice from senior PhD students in the department about faculty as potential advisors. In the first semester of your graduate studies, take 3-4 classes you are interested in. This provides a good opportunity to meet and impress your prospective advisor. If there is a class project, go overboard and exceed expectations. Try to improve on an algorithm mentioned in the class, and discuss this with the prospective advisor. Before you commit with an advisor, make sure it… ### Logical clocks and Vector clocks modeling in TLA+/PlusCal In a distributed system, there is no shared state, counter, or any other kind of global clock. So we can not implicitly associate an event with its time, because one node may have a different clock than another. Time synchronization is not easy to achieve, and failures complicate things. It turns out we care about time because of its utility in ordering of the events. Using this observation, in 1978, Leslie Lamport offered a time-free definition for "happens before": Event A happens before event B (denoted as A hb B) if and only if A can causally affect B. In the context of distributed systems, A hb B iff 1. A and B are on the same node and A is earlier in computation than B 2. A is the send of a message and B is the receive event for that message 3. There is some third event C, which A hb C, and C hb B. This also suggest the definition for "concurrent" relation. Events A and B are concurrent iff$\neg( A ~hb~ B) \land \neg( B ~hb~ A)\$
To capture the hb relation, …
I am a very curious natured person. Every child starts asking lots of questions around 3-4, but according to my mom, I took that to another level constantly asking "but why?" and drove her crazy. On the other hand, I believe I owe my being curious to my mom. She was an elementary school teacher (a damn good one), and was instrumental in my development. She was (and still is) a very curious person, and she taught me how to ask more and better questions. For example, while traveling, she would notice different plants and would ask me why the landscape is different here? And we would make guesses.
The Turkish education system was not big on asking questions (these days it is waaaay waaaaay worse). Since the lazy path is to memorize and regurgitate answers, that is what it demanded from the students. But I think my questioning skills mostly survived. Among my friends, I was famous for replying questions with questions of my own, and if not, my answer was often "I don't …
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2020-07-10 20:24:12
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https://www.gradesaver.com/textbooks/math/precalculus/precalculus-6th-edition-blitzer/chapter-7-section-7-3-partial-fractions-exercise-set-page-841/2
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Precalculus (6th Edition) Blitzer
The simplified partial fraction expansion is $\frac{5x+7}{\left( x-1 \right)\left( x+3 \right)}=\frac{A}{\left( x-1 \right)}+\frac{B}{\left( x+3 \right)}$
The provided rational expression is as follows: $\frac{5x+7}{\left( x-1 \right)\left( x+3 \right)}$ Now, solving the expression as given below: We set up the partial fraction expansion with unknown constants coefficients and then write a constant coefficients over each of the two distinct algebraic linear factors in the denominator of the expression. Then, decompose the fractional part as follows: $\frac{5x+7}{\left( x-1 \right)\left( x+3 \right)}=\frac{A}{\left( x-1 \right)}+\frac{B}{\left( x+3 \right)}$ Thus, $\frac{A}{\left( x-1 \right)}+\frac{B}{\left( x+3 \right)}$ is a partial fraction expansion of the rational expression $\frac{5x+7}{\left( x-1 \right)\left( x+3 \right)}$ with constants $A$ and $B$.
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2023-03-22 12:08:37
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https://pub.uni-bielefeld.de/publication/1644972
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TRILINEAR COUPLINGS AMONG THE ELECTROWEAK VECTOR BOSONS AND THEIR DETERMINATION AT LEP2
BILENKY M, KNEUR JL, RENARD FM, Schildknecht D (1993)
NUCLEAR PHYSICS B 409(1): 22-68.
Es wurde kein Volltext hochgeladen. Nur Publikationsnachweis!
Zeitschriftenaufsatz | Veröffentlicht | Englisch
Autor
; ; ;
Abstract / Bemerkung
We present a detailed investigation of the potential of LEP2 to measure the (trilinear) couplings of the vector bosons, Z0W+ W- and gammaW+ W-, among one another. The restrictions imposed on non-standard trilinear couplings by symmetry requirements, thus excluding violent boson-loop divergences and a violent growth of tree amplitudes for vector-boson scattering, are discussed in detail. We elaborate on how to extract the W+/- spin-density matrix and the W+, W- spin correlations from future data. Various theoretically motivated fits to artificial ''data'' on e+ e- --> W+W- are carried out in order to evaluate the potential of LEP2 for, the measurement of trilinear vector boson couplings. We stress that a direct measurement of the couplings of the vector bosons with one another is indispensable for a verification of the basic SU(2)L X U(1)Y structure of the present electroweak theory. Such measurements at LEP2 improve indirect LEP1 bounds by factors which occasionally reach a full order of magnitude.
Erscheinungsjahr
Zeitschriftentitel
NUCLEAR PHYSICS B
Band
409
Zeitschriftennummer
1
Seite
22-68
ISSN
PUB-ID
Zitieren
BILENKY M, KNEUR JL, RENARD FM, Schildknecht D. TRILINEAR COUPLINGS AMONG THE ELECTROWEAK VECTOR BOSONS AND THEIR DETERMINATION AT LEP2. NUCLEAR PHYSICS B. 1993;409(1):22-68.
BILENKY, M., KNEUR, J. L., RENARD, F. M., & Schildknecht, D. (1993). TRILINEAR COUPLINGS AMONG THE ELECTROWEAK VECTOR BOSONS AND THEIR DETERMINATION AT LEP2. NUCLEAR PHYSICS B, 409(1), 22-68. doi:10.1016/0550-3213(93)90445-U
BILENKY, M., KNEUR, J. L., RENARD, F. M., and Schildknecht, D. (1993). TRILINEAR COUPLINGS AMONG THE ELECTROWEAK VECTOR BOSONS AND THEIR DETERMINATION AT LEP2. NUCLEAR PHYSICS B 409, 22-68.
BILENKY, M., et al., 1993. TRILINEAR COUPLINGS AMONG THE ELECTROWEAK VECTOR BOSONS AND THEIR DETERMINATION AT LEP2. NUCLEAR PHYSICS B, 409(1), p 22-68.
M. BILENKY, et al., “TRILINEAR COUPLINGS AMONG THE ELECTROWEAK VECTOR BOSONS AND THEIR DETERMINATION AT LEP2”, NUCLEAR PHYSICS B, vol. 409, 1993, pp. 22-68.
BILENKY, M., KNEUR, J.L., RENARD, F.M., Schildknecht, D.: TRILINEAR COUPLINGS AMONG THE ELECTROWEAK VECTOR BOSONS AND THEIR DETERMINATION AT LEP2. NUCLEAR PHYSICS B. 409, 22-68 (1993).
BILENKY, M, KNEUR, JL, RENARD, FM, and Schildknecht, Dieter. “TRILINEAR COUPLINGS AMONG THE ELECTROWEAK VECTOR BOSONS AND THEIR DETERMINATION AT LEP2”. NUCLEAR PHYSICS B 409.1 (1993): 22-68.
Open Data PUB
Web of Science
Dieser Datensatz im Web of Science®
Inspire: 353392
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2018-09-21 17:35:31
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https://georgia-james.com/find-the-center-x2-9y29/
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Find the Center x^2-9y^2=9
Find the standard form of the hyperbola.
Divide each term by to make the right side equal to one.
Simplify each term in the equation in order to set the right side equal to . The standard form of an ellipse or hyperbola requires the right side of the equation be .
This is the form of a hyperbola. Use this form to determine the values used to find vertices and asymptotes of the hyperbola.
Match the values in this hyperbola to those of the standard form. The variable represents the x-offset from the origin, represents the y-offset from origin, .
The center of a hyperbola follows the form of . Substitute in the values of and .
Find the Center x^2-9y^2=9
Need help with MATH HOMEWORK
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2022-09-28 00:58:01
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https://codereview.stackexchange.com/questions/60425/program-for-finding-fibonacci-primes/60434
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# Program for finding Fibonacci primes
I think it could have been designed with more object orientation. I don't like how one of my methods calls another from within the method, but I wasn't sure how to return the result because it is a loop.
Also is it ok to have all methods static, or should I be instantiating the classes?
If there is any other improvements please let me know, but these were my main concerns.
App.java:
public class App {
public static void main(String[] args) {
long startTime = System.currentTimeMillis();
Fibonacci.fibonacci();
long endTime = System.currentTimeMillis();
long totalTime = endTime - startTime;
System.out.println("****************************************\n");
System.out.println("Total Running Time: " + totalTime + "ms");
}
}
Fibonacci.class:
public class Fibonacci {
static void fibonacci() {
long i = 0;
long j = 1;
long k = 0;
while (i < 1E17) {
k = i + j;
i = j;
j = k;
Prime.prime(k);
}
}
}
Primes.java:
public class Prime {
static void prime(long number) {
boolean isPrime = false;
long end = (long) (Math.sqrt(number) + 1);
for (long i = 2; i <= end; i++) {
if (number % i == 0) {
isPrime = false;
break;
} else {
isPrime = true;
}
}
if (isPrime) {
System.out.println(number);
}
}
}
• There is an error in the program. Please check. – mass Nov 30 '16 at 6:51
Object Oriented
I wouldn't call your code object oriented. And yes, using static in too many places can be a hint that you are not using OOP correctly.
But your program is so small and specific that this isn't really a bad thing. If you actually have some extension in mind, a different approach might be better, but right now, I would leave it as it is.
But for example, lets say you plan to write a program in the future which prints every odd Fibonacci number, or every Fibonacci number dividable by 3. With your code, this might be harder to do.
If your approach was like this:
public class Fibonacci {
static void fibonacci(NumberCheck numberCheck) {
[...]
if (numberCheck.meetsContition(k)) {print(k)}
}
}
interface NumberCheck {
boolean meetsContition(int number);
}
public class Prime implements NumberCheck {
@Override
boolean meetsContition(int number) {
// check if number is prime, return true or false
}
}
public class Odd implements NumberCheck {
@Override
boolean meetsContition(int number) {
// check if number is odd, return true or false
}
}
It would be easily extendable. But as I said, if you are not planning on extending your code, you don't really need OOP in this case. I wouldn't even create the Fibonacci and Prime classes, they are more confusing than they are helpful, just put the methods in App.
Naming
prime should better be called isPrime, and I would find it easier to read if it then returned true or false (move the printing to fibonacci).
Other
I would pass an argument to fibonacci for up to which number it should run. Just hardcoding 1E17 is bad style.
The current design is not object-oriented, but why do you want object-orientation? Why would you need it?
Object-orientation is a software design paradigm, that helps people reason about software by applying structures that are familiar to them. This is the basic underlying principle. People often think about the world in terms of "things" that have "properties" or "features", and having these same structures in programs helps to understand them better.
A lot of nice features that goods software should have (like extensibility and maintainability) stem from much more general principles like modularity, loose coupling and single responsibility principle. Object-orientation supports and promotes these principles (like many other programming paradigms) but they're not the defining features of object-orientation.
Looking at your code, I think it is more important to separate the prime-check from the printing of the result (Single Responsibility Principle). This can easily be done by changing the method to boolean isPrime(Number). This method could easily live as a static method in a utility class, since its implementation is not likely going to be changed or extended.
The fact that the fibonacci method calls the prime check directly could also be improved (Tight Coupling). An improved design could see the Fibonacci sequence as an unlimited number generator. You could use the Iterator<Number> in Java (other languages have similar constructs) to model this.
class Fibonacci implements Iterator<Long> {
private long last = 0, next = 1;
public Long next() {
long current = next;
next += last;
last = current
return current;
}
public boolean hasNext() {return true;}
}
Now your main method can use the Fibonacci iterator/sequence to continuously generate the next number, use the utility method to check prime-ness and print accordingly. Note that stopping execution after a number of iterations is also the responsibility of the main method.
public class App {
public static void main(String[] args) {
long startTime = System.currentTimeMillis();
int max = Integer.parseInt(args[0]), i = 0;
Fibonacci fibonacci = new Fibonacci();
while (i++ < max) {
long number = fibonacci.next();
if (Prime.isPrime(number)) {
System.out.print(number);
System.out.print(" ");
}
}
long endTime = System.currentTimeMillis();
long totalTime = endTime - startTime;
System.out.println("****************************************\n");
System.out.println("Total Running Time: " + totalTime + "ms");
}
}
The big problem I see, is that your classes/methods are single use. Your class Prime can nothing but print. But in any bigger real program, you need the parts to cooperate somehow.
This printing destroy any flexibility. Imagine a tiny change like printing into a file. Impossible. Counting instead of printing. Impossible. Switching between counting and printing. Impossible.
Compare it to what Maarten Winkels wrote. His method boolean Prime.isPrime does exactly the right thing. Nicely reusable.
Sticking with the Single Responsibility Principle would prevent you from testing and printing in the same method. But before your master it, remember: A reusable method computing anything must return some result, or modify some data, or alike. Never print.
An efficiency comment.
The code wastes much time testing a primality of numbers which are known in advance to fail the test: a Fibonacci number with a composite index is composite. A primality test itself is quite suboptimal. These observations suggest a totally different approach:
1. Create a set of primes using any sieve you prefer.
2. Only test Fibonacci numbers with index belonging to that set (in fact, you may get away not even calculating the rest of them)
3. A primality test is just a set lookup.
• When it gets to large numbers there will be many many primes less or equal to that number. eg the 12th fibonacci prime is 99,194,853,094,755,497. The number of primes less than this is 2,602,986,161,967,491 so my set would have to be at least this long in order to check whether it is a prime or not. At 8 bytes for each long, the set would be (99194853094755497*8)/(1024^3) = 739059247GB in size. Is this right? – Jonny Shanahan Aug 19 '14 at 16:17
• Could you add a link to that Fibonacci index theorem? Without that, your answer can be easily misunderstood. – Roland Illig Dec 11 '16 at 10:16
• @JonnyShanahan: the 12th fibonacci prime is [17 digits]. The number of primes less than this is [16 digits] so my [set of primes] would have to be at least this long in order to [verify the 12th FP prime]. At 8 bytes for each long, the set would be (99194853094755497*8)/(1024^3) = 739059247GB in size. Is this right? not quite: every non-prime has an integer divisor smaller than its square-root - for the 12th Fibonacci prime, the set would need about 40 MBytes as a bit map. Then, there are heuristic primality tests. – greybeard Dec 11 '16 at 14:25
# Keep Concerns Separated
Your code structure conflates several things:
• Generating the Fibonacci sequence
• Checking if a number is prime or not
• Printing the numbers of interest
It's best to use a structure that keeps these concerns separated. You can then arrange them in a multitude of ways to accomplish different tasks.
For example, suppose you want to find the squares of Fibonacci primes, or you want to place the primes you find in a database so you can retrieve them later. Also, others have suggested algorithmic changes. All these changes will be easier to implement if your code is modular. But, more importantly, it allows the different parts to be reused.
# A Functional Approach
In this particular case, I think you would benefit from a paradigm shift from object-oriented programming to functional programming. There are varying definitions of functional programming. For our purposes here, we'll simply say that functional programming deals with the abstraction of composing functions (in contrast to the object-oriented approach, which deals with the abstraction of composing objects).
Note that this is purely a shift in our way of thinking about the problem. You can express any "object oriented" program in terms of functions and vice versa -- loosely speaking, objects and functions are isomorphic.
Here's how we can decompose this problem using functional principles:
• Generate an "infinite" stream of Fibonacci numbers
• Filter the stream of Fibonacci numbers to include only primes
• Print numbers from the filtered stream
You could implement all this yourself (c.f., the NumberCheck interface in Tim's answer and Java 8's Predicate interface, used below). However, we don't have to re-invent the wheel. There are multiple libraries for functional programming in Java, and Java 8 has added functional APIs to the standard. Here's one way we to map this to the functional programming abstractions provided in Java 8:
# Dealing with Large Numbers
The numbers of the Fibonacci sequence grow exponentially. It will not take long before long values are insufficient to compute Fibonacci numbers. To compute larger numbers, you will need to use an arbitrary-precision number type such as BigInteger.
# Algorithmic Improvements
There are several ways in which you can perform the computation more efficiently:
• Your prime checker requires $O(\sqrt{n})$ time, where $n$ is the number being checked. In the overall algorithm, though, $n$ grows exponentially. So checking the $k$th fibonacci number takes $O(2^n)$ time. Using a sieve, as suggested by vnp, will help reduce the constant factor, but will not help with the asymptotic complexity. Ultimately, you will have to resort to a probabilistic prime check as suggested by Danaj.
• As both vnp and Danaj point out, the $k$th Fibonacci number cannot be prime if $k$ is not also prime (excluding $k = 4$). Thus, we can structure our program as follows (modulo the case when $k = 4$ -- I leave that as an exercise for the reader):
• Generate a Stream of natural numbers
• Filter the natural numbers, producing a Stream of primes
• map each prime $k$ to the $k$th Fibonacci number
• Filter this stream once more for primes, producing a Stream of Fibonacci primes
• Print the Fibonacci primes
Note how we only need to change the way we generate Fibonacci numbers to compute the $k$th Fibonacci number directly instead of generating a Stream of the Fibonacci sequence. The rest is just making a few tweaks to the way we compose our pipeline of functions. Regardless of paradigm, this is the sort of modularity sought by good engineering principles.
• Since we are now calculating the $k$th Fibonacci number directly, we can use an $O(\log n)$ algorithm to calculate the Fibonacci numbers. See, e.g., matrix form and SICP Ex. 1.19.
• Excepting $k=4$, all prime $F_k$ have a prime $k$. If your prime function returned a boolean rather than printing the result, you could use this to quickly skip lots of candidates (testing primality on $k$ is cheap, but not so for $F_k$).
• There are faster primality tests which you'll probably have to use. Trial division is fast for small values but is exponential time in the size of the input. This isn't going to really work past the 12th Fibonacci prime ($F_{131}$ has 28 digits). On the other hand, get it working first is a good idea. You will probably end up with a probable prime test like BPSW or many random-base Miller-Rabin tests.
• Like you, I read vnp's answer (regarding sets) as useful for $k$ but not for $F_k$.
Once happy with what you have, you may find it entertaining to look at some other solutions, e.g. Haskell, Perl serial / parallel, PARI and Mathematica
• 18.2 seconds for 26 ($F_{9677}$)
• 4776 seconds for 32 ($F_{50833}$)
• 1.8 seconds for 26 ($F_{9677}$)
• 323 seconds for 32 ($F_{50833}$)
• 12009 seconds for 36 ($F_{148091}$)
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2019-12-07 07:50:06
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https://economics.stackexchange.com/questions/13931/what-is-the-difference-between-two-stage-least-squares-and-instrumental-variable/13933
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# What is the difference between two stage least squares and instrumental variable regression?
I'm doing independent study and I am having trouble understanding the difference between these two estimators.
I get that 2SLS is predicting the endogenous variable, and that instrumental variables are similar to proxy variables, but I don't get how one differs from the other.
2SLS estimators are IV estimators.
An IV estimator is the sample analog of the form: $\beta = \frac{Cov(Y, Z)}{Cov(X, Z)}$, where $Y$ is the outcome variable, $X$ is the endogenous variable, and $Z$ is the instrumental variable.
It can be shown that the 2SLS is of the above form. The advantage of 2SLS estimators over other IV estimators is that 2SLS can easily combine multiple instrumental variables, and it also makes including control variables easier.
The meaning of the words first
Some people use the word "IV estimator" to refer to any estimator that uses instrumental variables. To them, IV estimators contain 2SLS, LIML, k-class estimators, and others, so 2SLS is a special case of IV. For example, the title of Bekker's (1994, Econometrica) paper is "Alternative approximations to the distribution of instrumental variable estimators".
More traditional people mean by IV the particular instrumental variable estimator $(Z'X)^{-1}Z'y$ for the exactly identified case ($Z$ = instrument matrix, $X$ = regressor matrix, $y$ = regressand vector), and 2SLS is a generalization of IV to the overidentified case. But, as Paul says, 2SLS can be expressed as an IV estimator of this second sense because it is $(\hat{X}'X)^{-1} \hat{X}'y$, where $\hat{X} = Z(Z'Z)^{-1}Z'X$ is the instrument matrix.
I personally think it is very fine to leave the meaning of IV estimators ambiguous because the meaning is usually clear in the context and we need not rigorously distinguish them.
It seems to me that the sentence "2sls is predicting the endogenous variable" means the first stage regression of the endogenous regressor on the instrumental variables (to get $\hat{X}$). The expression "instrumental variables are similar to proxy variables" looks more casual. Proxy variables (e.g., IQ for ability) can be used to solve the endogeneity problem. Instrumental variables are another way of solving the endogeneity problem. In that sense they are "similar".
• In the exactly identified case, we assume each instrument has a correlation of 1 with a regressor: $Z(Z'Z)^{-1}Z'X = Z\ \impliedby\ (Z'Z)^{-1}Z'X = I$. This shows that 2SLS is equivalent to IV, up to the order of the instruments. If the instruments are not in the correct order, the projection $Z(Z'Z)^{-1}Z'X$ will re-order the variables so that $\hat X$ has a different ordering to $Z$ but the same as $X$. – ahorn Sep 19 at 12:03
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2019-11-13 18:31:23
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https://gamedev.stackexchange.com/questions/88466/problematic-cameraposition-eye-0-0-0-at-0-2-0-and-up-0-1-0
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# Problematic cameraposition (Eye = (0,0,0), at=(0,-2,0) and up = (0,1,0))?
I am taking a course in computergraphics and we talk a lot about OpenGL and the math you need to do everything OpenGL does "by hand". A Question which was asked in an old exam (I am preparing at the moment) was:
Why is the following Cameraposition considered problematic? eye = (0,0,0), at=(0,-2,0) and up = (0,1,0)
Is it because the eye-at = (0,2,0) and therefore the cross product of up x (eye-at) = (0,0,0) and that means, that no real transformation matrix can be constructed?
I found a post where someone asked a similiar question ( https://gamedev.stackexchange.com/a/45328/50476 ), but the explanation is somehow strange for me, because he says that he wants to calculate the cross product of the eye vector and the up vector. But there is no need for that, if you want to be able to calculate the transformation matrix?
• Yes... Just follow your nose. I mean, literally, point your nose ("at") at 0,-2,0 (say, South) and the top of your head ("up") at 0,1,0 (North). No solution! Even if "up" isn't 90 degrees from "at", as long as it's not in line with "at" (angle between them 0 or 180) is unambiguous enough. – david van brink Dec 10 '14 at 22:53
Well, that is the mathematical reason why it's problematic, but I'd prefer an analytical explanation.
A LookAt(pos, look, up) transform (you call it "cameraposition") is meant to represent a camera located at pos, pointing at look. However, with just pos and look, there are an infinite amount of possibilities for your camera, as you rotate it through the axis between pos and look.
Enter up. up is meant to disambiguate between the infinite cameras that can be placed at pos and pointing at look, by setting a vector to point up. In principle you need a vector orthogonal to the axis between pos and look, but in practice, any vector that you can use to disambiguate, and choose a rotation for your camera is acceptable.
If pos = (0, 0, 0), look = (0, -2, 0) and up = (0, 1, 0), You are placing the camera in the origin of the world and looking straight down. Now you need a vector to choose the rotation of that camera. Almost any vector would do, but (0, 1, 0) happens to be one of those that doesn't work. The vector is pointing straight up, is parallel to the axis between pos and look, and cannot be used to choose a rotation for the camera.
Any other vector where x != 0 or z != 0 would work though.
Is it because the eye-at = (0,2,0) and therefore the cross product of up x (eye-at) = (0,0,0) and that means, that no real transformation matrix can be constructed?
Exactly, the actual values in the resulting matrix is just the coordinates of the view direction (at-eye), up and right vectors next to each other;
result = [[right.x up.x view.x]
[right.y up.y view.y]
[right.z up.z view.z]]
They have to be orthogonal to each other so that's why the cross products need to happen. Some libraries provide a arbitrary up should the user supplied one be invalid.
• I have never seen a lookat-like function that doesn't compute a new up basis vector from the forward and right vectors. Using the user-supplied up directly is almost guaranteed to be non-orthogonal. It might be worth mentioning this process of two cross products to generate an orthogonal basis. – Lars Viklund Aug 9 '15 at 7:42
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2021-04-15 02:50:25
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https://www.acmicpc.net/problem/9899
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시간 제한메모리 제한제출정답맞힌 사람정답 비율
1 초 128 MB51125.000%
## 문제
Consider the following configuration of train tracks.
Tracks I, II, and III may hold train cars that can move in one go between Track I and Track III, and between Track II and Track III, but not between Track I and Track II. Cars cannot pass each other on a track in one go. Cars can move together in one go. In the situation depicted above, the cars G and A can move together in one go from Tack III to Track I, after which the sequence of cars on Track I is BFFGA. However, the car A cannot move alone in one go from Track III to Track I (because to do so it has to pass car G but this is not allowed). Each track is long enough to hold all cars.
Initially, a sequence of cars is on Track I, and Tracks II and III are empty. The goal is to move cars between Tracks I and III and between Tracks II and III, such that a desired sequence of cars, and no other cars, resides on Track II. The question to be answered by your program is: What is the smallest number of movements that achieves the desired sequence of cars, and no other cars, on Track II? Note that when two or more adjacent cars move together in one go, it counts as one single movement.
Let us say initially, the cars ABCD and E are on Track I in the order ABCDE. This means that the car A is furthest to the left, and car E is furthest to the right and closest to Track III. Let us say at the end, we want the sequence DBC on Track II. We can achieve this with four movements. First, we move the cars D and E together from Track I to Track III, then we move car D from Track III to Track II, then we move the cars B and C together from Track I to Track III, and finally, we move the cars B and C together from Track III to Track II. Figure 3 shows teh sequence of movements. The answer therefore is the number 4.
(a) Before first movement (b) After first movement (c) After second movement (d) After third movement (e) After fourth and final movement
Figure 3: Movements for example.
## 입력
The input consists of three lines. The first line contains two integers, separated with a blank character. The first integer i represents the initial number of cars on Track I, and the second number j represents the number of desired cars on Track II. The second line contains i capital letters, representing the initial sequence of cars on Track I. The third line contains j capital letters representing the desired sequence of cars on Track II.
You may assume that all letters in the second line are distinct, that all letters in the third line are distinct, and that every letter in the third line occurs in the second line, and that 0 < j < 7, 0 < i < 7.
## 출력
The output contains an integer, representing the minimal number of movements to achieve the desired sequence of cars in Track II.
## 예제 입력 1
5 3
ABCDE
DBC
## 예제 출력 1
4
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2022-08-14 12:48:17
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https://chem.libretexts.org/Courses/Sacramento_City_College/SCC%3A_CHEM_300_-_Beginning_Chemistry/SCC%3A_CHEM_300_-_Beginning_Chemistry_(Alviar-Agnew)/07%3A_Chemical_Reactions/7.07%3A_Writing_Chemical_Equations_for_Reactions_in_Solution-_Molecular%2C_Complete_Ionic%2C_and_Net_Ionic_Equations
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# 7.7: Writing Chemical Equations for Reactions in Solution- Molecular, Complete Ionic, and Net Ionic Equations
A typical precipitation reaction occurs when an aqueous solution of barium chloride is mixed with one containing sodium sulfate. The complete chemical equation can be written to describe what happens, and such an equation is useful in making chemical calculations.
$\underbrace{\ce{BaCl2(aq) + Na2SO4(aq) -> BaSO4(s) + 2NaCl(aq)}}_{\text{Complete Chemical Equation}}\label{1}$
However, Equation $$\ref{1}$$ does not really represent the microscopic particles (that is, the ions) present in the solution. Below is the complete ionic equation:
$\underbrace{\ce{Ba^{2+}(aq) + \overbrace{2Cl^{-}(aq)}^{spectator} + \overbrace{2Na^{+}(aq)}^{spectator} + SO4^{2-}(aq) -> BaSO4(s) + \overbrace{2Na^{+}(aq)}^{spectator} + \overbrace{Cl^{-}(aq)}}^{\text{spectator}}}_{\text{Complete Ionic Equation}}\label{2}$
Equation $$\ref{2}$$ is rather cumbersome and includes so many different ions that it may be confusing. In any case, we are often interested in the independent behavior of ions, not the specific compound from which they came. A precipitate of $$\ce{BaSO4(s)}$$ will form when any solution containing $$\ce{Ba^{2+}(aq)}$$ is mixed with any solution containing $$\ce{SO4^{2–}(aq)}$$ (provided concentrations are not extremely small). This happens independently of the $$\ce{Cl^{–}(aq)}$$ and $$\ce{Na^+(aq)}$$ ions in Equation $$\ref{2}$$. These ions are called spectator ions because they do not participate in the reaction. When we want to emphasize the independent behavior of ions, a net ionic equation is written, omitting the spectator ions. For precipitation of $$\ce{BaSO_4}$$ the net ionic equation is
$\underbrace{\ce{Ba^{2+}(aq) + SO4^{2-}(aq) -> BaSO4(s)}}_{\text{Net Ionic Equation}} \label{3}$
Example $$\PageIndex{1}$$
1. When a solution of $$\ce{AgNO3}$$ is added to a solution of $$\ce{CaCl2}$$, insoluble $$\ce{AgCl}$$ precipitates. Write three equations (complete chemical equation, complete ionic equation, and net ionic equation) that describe this process.
2. Write the balanced net ionic equation to describe any reaction that occurs when the solutions of $$\ce{Na2SO4}$$ and $$\ce{NH4I}$$ are mixed.
Solution
Equation Type Example $$\PageIndex{1a}$$ Example $$\PageIndex{1b}$$
Complete Chemical Equation
$$\ce{2AgNO3(aq) + CaCl2(aq) ->} \\ \ce{2AgCl(s) + Ca(NO3)2(aq)}$$
The proper states and formulas of all products are written and the chemical equation is balanced.
$$\ce{Na2SO4(aq) + NH4I2(aq) ->} \\ \ce{2NaI(aq) + (NH4)2SO4(aq)}$$
Both products are aqueous so there is no net ionic equation that can be written.
Complete Ionic Equation
$$\ce{2Ag^+(aq) + 2NO3^{-}(aq) + Ca^{2+}(aq) + Cl^{-}(aq) -> } \\ \ce{2AgCl(s) + Ca^{2+}(aq) + 2NO3^{-}(aq)}$$
AgCl is a solid so it does not break up into ions in solution.
Net Ionic Equation
$$\ce{Ag^+(aq) + Cl^{-} (aq) -> AgCl(s)}$$
All spectator ions are removed.
$$\ce{NaI}$$ and $$\ce{(NH4)2SO4}$$ are both soluble.
No net ionic equation
The occurrence or nonoccurrence of precipitates can be used to detect the presence or absence of various species in solution. A $$\ce{BaCl2}$$ solution, for instance, is often used as a test for the presence of $$\ce{SO4^{2–}(aq)}$$ ions. There are several insoluble salts of $$\ce{Ba}$$, but they all dissolve in dilute acid except for $$\ce{BaSO4}$$. Thus, if $$\ce{BaCl2}$$ solution is added to an unknown solution which has previously been acidified, the occurrence of a white precipitate is proof of the presence of the $$\ce{SO4^{2–}}$$ ion.
$$\ce{AgNO3}$$ solutions are often used in a similar way to test for halide ions. If $$\ce{AgNO3}$$ solution is added to an acidified unknown solution, a white precipitate indicates the presence of $$\ce{Cl^{–}}$$ ions, a cream-colored precipitate indicates the presence of $$\ce{Br^{–}}$$ ions, and a yellow precipitate indicates the presence of $$\ce{I^{–}}$$ ions (Figure $$\PageIndex{1}$$). Further tests can then be made to see whether perhaps a mixture of these ions is present. When $$\ce{AgNO_3}$$ is added to tap water, a white precipitate is almost always formed. The $$\ce{Cl^{–}}$$ ions in tap water usually come from the $$\ce{Cl2}$$ which is added to municipal water supplies to kill microorganisms.
Exercise $$\PageIndex{1}$$
Write balanced net ionic equations to describe any reaction that occurs when the following solutions are mixed.
1. $$\ce{K2CO3 + SrCl2}$$
2. $$\ce{FeSO4 + Ba(NO3)2 }$$
$\ce{Sr^{2+}(aq) + CO3^{2-} (aq) -> SrCO3 (s)} \nonumber$
$\ce{Ba^{2+}(aq) + SO4^{2-} (aq) -> Ba(SO4) (s)} \nonumber$
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2021-05-10 01:40:56
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https://de.maplesoft.com/support/help/maple/view.aspx?path=geom3d/parallelepiped
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parallelepiped - Maple Help
geom3d
parallelepiped
define a parallelepiped
Calling Sequence parallelepiped(pp, [d1, d2, d3])
Parameters
pp - name of the parallelepiped d1, d2, d3 - three directed segments having a common initial point
Description
• A parallelepiped is a polyhedron bounded by six parallelograms. It can be defined from three given directed segments having a common initial point.
• To access the information related to a parallelepiped pp, use the following function calls:
form(pp) returns the form of the geometric object (that is, $\mathrm{parallelepiped3d}$ if pp is a parallelepiped). See geom3d[form]. DefinedAs(pp) returns the list of three directed segments defining pp. See geom3d[DefinedAs]. detail(pp) returns a detailed description of the parallelepiped pp. See geom3d[detail].
• This function is part of the geom3d package, and so it can be used in the form parallelepiped(..) only after executing the command with(geom3d). However, it can always be accessed through the long form of the command by using geom3d[parallelepiped](..).
Examples
> $\mathrm{with}\left(\mathrm{geom3d}\right):$
Define four points $A$, $B$, $C$, and $E$.
> $\mathrm{point}\left(A,0,0,0\right),\mathrm{point}\left(B,4,0,0\right),\mathrm{point}\left(C,5,5,1\right),\mathrm{point}\left(E,0,2,5\right):$
Define three directed segments d1, d2, and d3 with initial point $A$ and end points $B$, $C$, and $E$ respectively.
> $\mathrm{dsegment}\left(\mathrm{d1},\left[A,B\right]\right),\mathrm{dsegment}\left(\mathrm{d2},\left[A,C\right]\right),\mathrm{dsegment}\left(\mathrm{d3},\left[A,E\right]\right):$
Use d1, d2, and d3 to define the parallelepiped pp.
> $\mathrm{parallelepiped}\left(\mathrm{pp},\left[\mathrm{d1},\mathrm{d2},\mathrm{d3}\right]\right)$
${\mathrm{pp}}$ (1)
> $\mathrm{form}\left(\mathrm{pp}\right)$
${\mathrm{parallelepiped3d}}$ (2)
> $\mathrm{DefinedAs}\left(\mathrm{pp}\right)$
$\left[{\mathrm{d1}}{,}{\mathrm{d2}}{,}{\mathrm{d3}}\right]$ (3)
> $\mathrm{detail}\left(\mathrm{pp}\right)$
$\begin{array}{ll}{\text{name of the object}}& {\mathrm{pp}}\\ {\text{form of the object}}& {\mathrm{parallelepiped3d}}\\ {\text{the 6 parallelogram faces of the object}}& \left[\left[\left[{0}{,}{0}{,}{0}\right]{,}\left[{4}{,}{0}{,}{0}\right]{,}\left[{9}{,}{5}{,}{1}\right]{,}\left[{5}{,}{5}{,}{1}\right]\right]{,}\left[\left[{0}{,}{2}{,}{5}\right]{,}\left[{4}{,}{2}{,}{5}\right]{,}\left[{9}{,}{7}{,}{6}\right]{,}\left[{5}{,}{7}{,}{6}\right]\right]{,}\left[\left[{0}{,}{0}{,}{0}\right]{,}\left[{4}{,}{0}{,}{0}\right]{,}\left[{4}{,}{2}{,}{5}\right]{,}\left[{0}{,}{2}{,}{5}\right]\right]{,}\left[\left[{4}{,}{0}{,}{0}\right]{,}\left[{9}{,}{5}{,}{1}\right]{,}\left[{9}{,}{7}{,}{6}\right]{,}\left[{4}{,}{2}{,}{5}\right]\right]{,}\left[\left[{5}{,}{5}{,}{1}\right]{,}\left[{9}{,}{5}{,}{1}\right]{,}\left[{9}{,}{7}{,}{6}\right]{,}\left[{5}{,}{7}{,}{6}\right]\right]{,}\left[\left[{0}{,}{0}{,}{0}\right]{,}\left[{5}{,}{5}{,}{1}\right]{,}\left[{5}{,}{7}{,}{6}\right]{,}\left[{0}{,}{2}{,}{5}\right]\right]\right]\\ {\text{coordinates of the 8 vertices}}& \left[\left[{0}{,}{0}{,}{0}\right]{,}\left[{4}{,}{0}{,}{0}\right]{,}\left[{5}{,}{5}{,}{1}\right]{,}\left[{9}{,}{5}{,}{1}\right]{,}\left[{0}{,}{2}{,}{5}\right]{,}\left[{4}{,}{2}{,}{5}\right]{,}\left[{5}{,}{7}{,}{6}\right]{,}\left[{9}{,}{7}{,}{6}\right]\right]\end{array}$ (4)
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2022-10-01 02:03:00
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https://www.physicsforums.com/threads/lagrange-with-two-constraints.905607/
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# Homework Help: Lagrange with Two Constraints
Tags:
1. Feb 26, 2017
### Kaura
1. The problem statement, all variables and given/known data
2. Relevant equations
Partials for main equation equal the respective partials of the constraints with their multipliers
3. The attempt at a solution
Basically I am checking to see if this is correct
I am pretty sure that 25/3 is the minimum but I am not sure how to find the maximum
The max an min at the bottom can be ignored or replaced with minimum
I have a lot to do today to prepare for midterms so any help would be much appreciated
2. Feb 26, 2017
### Ray Vickson
Your final solution looks OK, but I did not check the rest because I generally do not look at solutions given as posted images.
You should think about why your solution method does not give you a maximum.
Last edited: Feb 26, 2017
3. Feb 26, 2017
### Kaura
So is 25/3 the only extrema and a minimum?
4. Feb 26, 2017
### Ray Vickson
You tell me. But more importantly, what is the reason?
5. Feb 26, 2017
### Kaura
Yes? because the function is not bound and is continuous?
Last edited: Feb 26, 2017
6. Feb 26, 2017
### Ray Vickson
Right, and because the feasible region (the set of allowed $(x,y,z)$ values) is unbounded. We can find feasible points $(x,y,z)$ with $x,z \to -\infty,\: y \to +\infty$ (and opposite); and of course, $f \to +\infty$ for such points.
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2018-07-21 04:27:06
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https://physics.stackexchange.com/questions/631239/boundary-conditions-physical-wave-functions-and-domain-of-hamiltonian
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# Boundary conditions, physical wave-functions and domain of Hamiltonian
Context : In quantum mechanics, time evolution is described by a one-parameter unitary group, acting on the Hilbert space of states. Under Stone's theorem (with the right hypotheses), this group has a self-adjoint generator, which is called the Hamiltonian.
For a particle living in a 1D box, the Hilbert space is $$L^2([0,\ell])$$ (with $$\ell>0$$ the length of the box) and the Hamiltonian operator is : $$H = -\frac{\hbar^2}{2m}\frac{d}{d x^2} + V(x) \tag{1}$$
We also need to specify the domain on which $$H$$ is defined and self-adjoint. Now, it is pointed out here and in this P.SE post, that this is equivalent to fixing boundary conditions.
Then, the (unitary) time evolution operator is $$U(t) = e^{-iHt/\hbar}$$ and is well defined on the whole Hilbert space.
Questions:
• Concretely, how does changing the domain for $$H$$ change the time evolution operator $$U(t)$$ ?
• Presumably, $$\psi = 1/\sqrt{\ell} \in L^2([0,\ell])$$ is a valid wave-function, whichever boundary condition we choose, since it lives in the Hilbert space. How do boundary conditions determine its time evolution?
Here is the deal: canonical quantization forces your $$(1)$$ to be a quantum Hamiltonian. This operator drives (generates) time evolution iff it is self-adjoint. An operator $$A$$, if unbounded and defined on a (complex) separable Hilbert space $$\mathcal{H}$$, can be correctly defined only on a proper subset of $$\mathcal{H}$$ (called the maximal domain of $$A$$), if we require the operator to be closed. Self-adjoint operators are always closed, therefore their maximal domain is always proper: $$D(A)\subsetneq \mathcal{H}$$. This is basic stuff.
Come back to $$(1)$$. We want $$H$$ to be self-adjoint when seen as operator $$H:D(H)\rightarrow L^2 ([0,l])$$. For any well behaved real function $$V(x)$$, $$D(H) = D\left(\frac{d^2}{d x^2}\right)\subsetneq L^2 ([0,l])$$.
We can choose only one boundary condition for non-constant elements in $$L^2 ([0,l])$$, which renders $$H$$ self-adjoint on its maximal domain. So your first question is almost trivial: $$U(t)$$ exists only when $$H$$ is self-adjoint, which happens only in the presence of a particular boundary condition: $$\psi\in L^2 ([0,l]),~ \psi (0) = \psi (l)=0 \tag{2}$$ or the trivial (normalized) wavefunction: $$\psi$$ is constant, i.e. $$\psi (x) = \frac{\exp{i\alpha}}{\sqrt{l}},\alpha\in\mathbb{R} \tag{3}$$ As soon as you consider functions from the Hilbert space outside these two possible boundary conditions, then the Hamiltonian is no longer self-adjoint (not even symmetric, because you cannot make the boundary term vanish), so that $$U(t)$$ does not exist. Existence of constant wavefunctions is an artifact of using an unphysical restraining of motion in a box with "hard" walls. Usually PIB involve no dynamics at all ($$V(x) \equiv 0$$), case in which a constant wavefunction is trivially the $$0$$ vector, so that only option $$(2)$$ remains.
The second question gets an answer immediately: Since the constant function $$(3)$$ is a trivial solution to the spectral equation (energy spectrum = numeric value of $$V(x), x\in [0,1]$$), then there is no impact of choosing particular boundary conditions on the exact form of time evolution: $$U(t) = \exp (-i H(x)t /\hbar)$$ which acts trivially on a constant wavefunction, as a phase-factor containing the numeric value of the potential.
• I think a better example is to consider the operator densely defined on $L^2((0,l))$ (the open interval). You can impose periodic or infinite-well boundary conditions (by extending the domain) and get different time evolutions. You seem to be assuming that it is already defined on functions on the closed interval, so you only get one extension. – Keith McClary Apr 22 at 19:23
• Aren't $L^2([0,\ell])$ and $L^2((0,\ell))$ isometric ? (Since the value of $f\in L^2$ is not well defined) – SolubleFish Apr 23 at 7:54
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2021-07-27 08:16:00
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http://www.piping-designer.com/index.php/properties/dimensionless-numbers/171-reynolds-number?tmpl=component&print=1
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# Reynolds Number
Written by Jerry Ratzlaff on . Posted in Dimensionless Numbers
Reynolds number, abbreviated as Re, is a dimensionless number that measures the ratio of inertial forces (forces that remain at rest or in uniform motion) to viscosity forces (the resistance to flow).
## Reynolds Number Range
Laminar flow = up to Re = 2300
Transition flow = 2300 < Re < 4000
Turbulent flow = Re > 4000
## Formulas that use Reynolds Number
$$\large{ Re = \frac{ internal \; force }{ viscous \; force } }$$ $$\large{ Re = \frac{ \rho \; v \; l_c }{ \mu } }$$ $$\large{ Re = \frac{ v \; l_c }{ \nu } }$$ $$\large{ Re = \frac{ U \; l_c }{ \mu } }$$ $$\large{ Re = \frac{ \bar {v} \; d \; \rho}{ \mu } }$$ $$\large{ Re = \frac{ \bar {v} \; d }{ \nu } }$$ $$\large{ Re = \frac{ 4 \; Q }{ \pi \; d \; \bar {v} } }$$
### Where:
$$\large{ Re }$$ = Reynolds number
$$\large{ \bar {v} }$$ = average velocity
$$\large{ l_c }$$ = characteristic length or diameter of fluid flow
$$\large{ U }$$ = characteristic velocity
$$\large{ \rho }$$ (Greek symbol rho) = density of fluid
$$\large{ \mu }$$ (Greek symbol mu) = dynamic viscosity
$$\large{ \nu }$$ (Greek symbol nu) = kinematic viscosity
$$\large{ \pi }$$ = Pi
$$\large{ d }$$ = pipe inside diameter
$$\large{ v }$$ = velocity of fluid
$$\large{ Q }$$ = volumetric flow rate
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2020-05-28 08:19:59
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http://math.stackexchange.com/questions/57569/geometric-properties-of-a-d-dimensional-simplex-in-euclidean-space
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Geometric properties of a $d$-dimensional simplex in euclidean space
In school we have learned about objects in $2$-space and in $3$-space, with heavy emphasizes on the properties in $2$-space. My question can be formulated as follows:
What would we have learned in school, if the geomtry lessons didn't essentially restrict to the geometry of simplices in the euclidean plane, but fully generalized these inspections for $d$-dimensional simplices?
Whereas knowledge on the geometry of a triangle is taken for granted, I admit I don't know about corresponding results for a tetrahedron, (e.g.: What is the sum of the angles between faces?) not to speak of the higher dimensional analogues.
Whereas this is elementary, I don't think this is completely trivial. Do you know articles or other resources which develop the geometric theory of $d$-simplices in the elementary way I described?
-
I guess the thing is that three dimensions are already vastly more complicated than two dimensions. One instance of this is Hilbert's third problem which you might find interesting. – t.b. Aug 15 '11 at 11:27
My note "Heron-Like Results for Tetrahedral Volume" (daylateanddollarshort.com/math/pdfs/heron4tet.pdf)discusses some aspects of tetrahedra --such as Laws (plural!) of Cosines for faces and dihedral angles-- that echo properties of triangles. Higher-dimensional analogues can get messy, but at least the Pythagorean Theorem is nice everywhere: for a "right-corner" $d$-simplex, the square of the content of the hypotenuse-cell is equal to the sum of the squares of the contents of the leg-cells. ($H^2 = L_1^2 + L_2^2 + \cdots + L_d^2$) – Blue Oct 14 '11 at 16:17
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2015-11-29 19:53:14
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https://julesh.com/2018/04/02/the-pre-history-of-open-games/
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# The pre-history of open games
I feel that having Compositional game theory accepted for publication marks the end of the first chapter for me, and marks open games as a proper research topic. I want to record how open games came to be, told through the story of this paper, which took almost 3 years from writing to acceptance. (That’s roughly the same amount of time as the Higher Order Decisions/Games duo, although they definitely felt longer. Their story can wait for another blog post.)
I was a PhD student with Paulo Oliva, original tasked with extending higher order sequential games to simultaneous games. By 2014 we had achieved this using multi-valued selection functions, but this led to the question of unifying the single-valued and multi-valued approaches. This is something I still want to do, but there’s some surprisingly serious barriers.
Motivated by this, and hearing about the need for a new foundation of mathematical economics from Viktor Winschel, in late 2014 I was explicitly thinking about the question “How do you make game theory compositional?” Everybody implicitly or explicitly uses von Neumann’s models of extensive form or normal form games, which are quite bad for this purpose (although some people have tried composing them, with varying amounts of success). I was mainly looking for inspiration from concurrency theory and game semantics.
One of my ideas was to generalise extensive form games from trees to event structures. I was unaware of the paper Equilibria of concurrent games on event structures, which was published earlier in 2014. I think that paper has several problems game-theoretically such as its naive treatment of nondeterminism, but is a good place to start. If I had known about it back then, open games would probably have never existed. Fortunately I didn’t, because open games are more strongly compositional.
Another closely related thing I was thinking about was games on series-parallel (or N-free) posets. This primed me into thinking about monoidal categories. Later I would like to come back and tie up these loose ends via categorical presentations of these concurrency models, such as this paper introduced to me by Pawel Sobocinski.
Anyway, between January and April 2015 I was a visiting student in Mannheim’s department of economics, spending every day with Viktor Winschel and Philipp Zahn and sometimes Evguenia Shprits. Other than trying to push selection functions further, I was still thinking hard about compositional game theory.
There was no ‘aha!’ moment when open games sprang into being. (This is one reason that I still find it so hard to explain them.) Inspired by Dusko Pavlovic’s paper, I tried to make a category whose objects were sets and whose morphisms $X \to Y$ are pieces of games that can observe a state in $X$ and output a new state in $Y$. From the first attempt, these game-processes carried a set $\Sigma$ of strategy profiles and a play function $\Sigma \times X \to Y$, both of which survived unchanged into open games. This is the only part that I got right first time, and still the only part that I think is intuitive.
Beyond that, everything was very different. I was already using the Haskell interpreter GHCi to type-check and test many definitions by brute force. I wrote a report, dated February 17, 2015, called “String diagrams for game theory: a (very) preliminary report” which I have made available here. Section 14 implies that I’d been playing around in Haskell for over 2 weeks by that point, although I don’t remember it.
At this time, ‘pregames’ had a sideput $R$ that composed only by cartesian product (like strategy profiles), and what became the counit was a noticeably non-compositional operator that was only defined on pregames with domain $1$. I also now think that the graphical language would take a lot more work to formalise properly. Despite the problems, most of the philosophical benefits of open games are already in this paper, and example 4 survived essentially unchanged all the way into the published version of Compositional game theory. It also contains the phrase ‘open games’ which later replaced ‘pregames’ as the name.
Viktor sent my report to several of his contacts in computer science departments, of which only Neil Ghani responded, and enthusiastically at that.
As far as I can remember, I had the idea the contravariant $R$ and $S$ ports, to make outcomes compositional, soon after this. As far as I can remember, there followed another week of intense wrangling with GHCi, type-checking and testing many possible definitions. At some point I started narrowing down to a few remaining possibilities, after which I would declare the problem impossible. I worked through them in decreasing order of how likely they were to work out.
At the end of one day I had narrowed down to all but the last possibility, which I thought was the least likely. (I have no way to remember other definitions I tried around this time.) At the end of the day Viktor, Philipp and me were in the Irish pub in Mannheim, where we often went after work, and I was quite depressed because I thought my idea wouldn’t work. (Clearly I already realised the significance of 4-variant open games, before having a working definition.) I still haven’t been able to live this down, because the remaining thing I tried the next morning turned out to be the correct definition of open games.
I wrote this up very quickly as String diagrams for game theory, and submitted it to MFPS 2015, where it was rejected mostly for being too preliminary. Although I still called them ‘pregames’, the full definition of open games appeared in this paper. The only difference was that the best response function was written as an ‘individual rationality relation’ equivalent to just remembering the fixpoints of best response, i.e. the Nash equilibria. This is a very minor difference, and I don’t think best response is the last word on the matter anyway.
I thought (probably correctly) that my writing style left a lot to be desired, so the next thing I did was recruit Neil as a coauthor. He mostly rewrote my paper, which became A compositional approach to economic game theory. I don’t remember clearly what happened around this time, but I think we took our time with it, and Neil submitted it as an invited publication to a special issue. I think it was under review for a long time (maybe a year) before it was rejected (technically major revisions, which is a politer way of saying the same thing) — as an invited submission this is quite a dubious achievement.
By this time it was late 2017, I was a postdoc in Oxford, and the paper had been renamed to Compositional game theory and had gained Viktor and Philipp as coauthors. I want to be clear about this, in case anybody is looking around the different versions and wondering about the changes of authorship. The mathematical definition of open games was due to me, and the first version of the paper was written solely by me. But it was directly motivated by discussions with them, and on reflection I should have understood that it was impossible to disentangle it from the context of our discussions. By 2017 they were both working on various extensions and applications of open games, and both felt that their early contributions were not recognised. I agreed, and to make everything unambiguous they both worked heavily on the rewrite for the LiCS 2018 submission, still called Compositional game theory but otherwise with no text in common with the previous version.
I have to thank Jamie Vicary for telling me in no uncertain terms that I should submit the paper to LiCS. After attending LiCS in 2014 (an earlier version of Dialectica categories and games with bidding was rejected from it, admittedly for a serious error, and somehow I missed or forgot the paper on games on event structures I mentioned earlier) I was left with the impression that such a big and powerful conference (to the point where you almost need a publication or two there) isn’t healthy for the subject, and I became determined not to play everyone’s game. This lasted until half way through my first postdoc, when the threat of job applications caught up with me and I realised that an unfavourable Nash equilibrium is still a Nash equilibrium, and I was harming myself by deviating unilaterally.
## 1 thought on “The pre-history of open games”
1. […] time to jump forward in time again. It’s 2015 and I write down the play/coplay functions of open games, and their composition law. For a fixed strategy, an open […]
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2021-10-22 06:31:54
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http://mathhelpforum.com/new-users/213246-entropy-change-relation-number-lost-bits.html
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entropy change relation to the number of lost bits
can we use entropy change value to define the number of bits of information that are lost for and , or and xor gates?What is the number of bits lost due and, or,x xor gates?Thanks much in advance!!!
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2017-08-17 14:49:43
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https://www.techwhiff.com/issue/donna-bought-6-cds-that-were-each-the-same-price-including--670192
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# Donna bought 6 CDs that were each the same price. Including sales tax, she paid a total of $84.60 . Of that total$4.20, was tax. What was the price of each CD before tax?
1 answer
###### Question:
Donna bought 6 CDs that were each the same price. Including sales tax, she paid a total of $84.60 . Of that total$4.20, was tax. What was the price of each CD before tax?
## Answers
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It is one of the sources of livelihood many Filipinos todayA.) AnimalB.) FishC.) CowD.) PoultryPakisagot sa may alam po..Wag na po kayo sumagot kung hindi nyo alam.Thanks Po...
2 answers
### Which choice provides the best evidence that this story is written from a first- person point of view? a. Pronouns such as he, she, and they are used. b. The story tells about something that happened in the past. c. The story includes a quotation from one of the characters. d. The narrator is a character in the story.
Which choice provides the best evidence that this story is written from a first- person point of view? a. Pronouns such as he, she, and they are used. b. The story tells about something that happened in the past. c. The story includes a quotation from one of the characters. d. The narrator is a char...
1 answer
### The two triangles are similar. What is the value of x? Enter your answer in the box. x = ??
The two triangles are similar. What is the value of x? Enter your answer in the box. x = ??...
1 answer
### Representative Government Why is it important in the U.S.?
Representative Government Why is it important in the U.S.?...
1 answer
### I can’t figure this out! I don’t really know if I’m supposed to use the vertices that are on the coordinate plane or something else, I need help. My question is, What’s the area and the perimeter of the polygon????
I can’t figure this out! I don’t really know if I’m supposed to use the vertices that are on the coordinate plane or something else, I need help. My question is, What’s the area and the perimeter of the polygon????...
1 answer
### An interest group that gives money collected from members to political candidates or parties is called a Lobbyists
An interest group that gives money collected from members to political candidates or parties is called a Lobbyists...
1 answer
### What does it tell you if there is a large distance between the dots on a piece of ticker tape?
what does it tell you if there is a large distance between the dots on a piece of ticker tape?...
1 answer
### Where was heath ledger born?
Where was heath ledger born?...
1 answer
### Jim has three times as many comic and Charles. Charles has 2/3 as many books as Bob. Bob has 27 books. How many comic books dose Jim have?
Jim has three times as many comic and Charles. Charles has 2/3 as many books as Bob. Bob has 27 books. How many comic books dose Jim have?...
2 answers
### Describe conformity in a simple way the meaning of it.
describe conformity in a simple way the meaning of it....
1 answer
### Do the odd numbers please !!
do the odd numbers please !!...
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2023-04-01 20:37:45
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https://edoc.unibas.ch/51180/
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# Modeling Gain-Loss Asymmetries in Risky Choice: The Critical Role of Probability Weighting
Pachur, Thorsten and Kellen, David. (2013) Modeling Gain-Loss Asymmetries in Risky Choice: The Critical Role of Probability Weighting. In: Proceedings of the 35th Annual Conference of the Cognitive Science Society, 1. pp. 3205-3210.
Full text not available from this repository.
Official URL: http://edoc.unibas.ch/51180/
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2021-06-23 06:44:46
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https://en.wikibooks.org/wiki/Octave_Programming_Tutorial/Loops_and_conditions
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# Octave Programming Tutorial/Loops and conditions
Loops are used to repeat a block of code for a known or unknown number of times, depending on the type of loop. Using loops, you will draw some nice pictures of fractals and shapes drawn with random dots.
## The for loop
We use for loops to repeat a block of code for a list of known values. As an example, we'll calculate the mean of a list of values. The mean is calculated from
${\displaystyle {\overline {x}}={\frac {1}{n}}\sum _{i=1}^{n}x_{i}.}$
We set up a vector with some values
octave:1> x = [1.2, 6.3, 7.8, 3.6];
and calculate the mean with
octave:2> sum = 0;
octave:3> for entry = x,
octave:4> sum = sum + entry;
octave:5> end;
octave:6> x_mean = sum / length(x)
Line 2: Set sum equal to 0.
Line 3: For each value in x, assign it to entry.
Line 4: Increment sum by entry.
Line 5: Ends the for loop when there are no more members of x.
Line 6: Assign the final value of sum divided by the length of x to x_mean.
TO DO: get a better example and explain the code.
In general, we write a for loop as
for variable = vector
...
end
The ... represents the block of code that is executed exactly once for each value inside the vector.
### Example: The Sierpinski triangle
The Sierpinski triangle is a fractal that can be generated with a very simple algorithm.
1. Start on a vertex of an equilateral triangle.
2. Select a vertex of the triangle at random.
3. Move to the point halfway between where you are now and the selected vertex.
4. Repeat from step 2.
Plotting the points that you visit by following this procedure, generates the following picture.
You can download the code that generates this fractal from [2shared.com]. Note that this code uses one very simple for loop to generate the fractal:
for i = 1:N
...
end
### Exercises
1. Write a script that sums the first N integers. You can check your result with the formula ${\displaystyle {\frac {1}{2}}N(N+1)}$.
2. Write a script that does the same thing as the linspace function. It should start at some value, xstart, stop at xstop and create a vector that contains N values evenly spaced from xstart to xstop. You can use the zeros function to create a zero-filled vector of the right size. Use help zeros to find out how the function works.
## The while loop
The while loop also executes a block of code more than once but stops based on a logical condition. For example
x = 1.0;
while x < 1000
disp(x);
x = x*2;
endwhile
will multiply x by 2 until its value exceeds 1000. Here, x < 1000 is the condition of the loop. As long as the condition holds (is true), the loop will continue executing. As soon as it is false, the loop terminates and the first instruction after the loop is executed.
The general form of a while loop is
while condition
...
endwhile
### Exercise
1. Write a script that calculates the smallest positive integer, n, such that ${\displaystyle a^{n}\geq b}$ for some real numbers a and b. (Meaning, find the smallest power of a that is at least b.) Using the log function is considered cheating.
### Example: The Mandelbrot fractal
The Mandelbrot set is another fractal and is generated by checking how long it takes a complex number to become large. For each complex number, c,
1. Start with ${\displaystyle z_{0}=0}$.
2. Let ${\displaystyle z_{i}=z_{i-1}^{2}+c\quad \forall i=1,2,\ldots }$
3. Find the first i such that ${\displaystyle |z_{i}|>2}$.
We record all of these i values and assign a colour to each of them. This is used to generate an image like this one.
You can download the code that generates this fractal from Mandelbrot.m. Note that there is a while loop (inside some for loops) that tests whether the complex number z has modulus less than 2:
while (count < maxcount) & (abs(z) < 2)
...
endwhile
The first condition in the while loop checks that we do not perform too many iterations. For some values of c the iteration will go on forever if we let it.
## The do...until statement
These loops are very similar to while loops in that they keep executing based on whether a given condition is true or false. There are however some important difference between while and do...until loops.
1. while loops have their conditions at the beginning of the loop;
do...until loops have theirs at the end.
2. while loops repeat as long as the condition is true;
do...until loops continue as long as theirs is false.
3. while will execute 0 or more times (because the condition is at the beginning);
do...until loops will execute 1 or more times (since the condition is at the end).
The general form of a do...until loop is
do
...
until condition
### Exercise
Write a script that calculates the greatest common divisor (GCD) of two positive integers. You can do this using Euclid's algorithm.
### Challenge
Write a script that generates random number pairs (a, b) that are distributed uniformly
1. over the disc ${\displaystyle \left\{(x,y)|x^{2}+y^{2}\leq 1\right\}}$ (the first image below);
2. as in the second image below
File:Octave uniform random circle.png File:Octave uniform random challenge.png
## The break and continue statements
Sometimes it is necessary to stop a loop somewhere in the middle of its execution or to move on to the next value in a for loop without executing the rest of the loop code for the current value. This is where the break and continue statements are useful.
The following code demonstrates how the break statement works.
total = 0;
while true
x = input('Value to add (enter 0 to stop): ');
if x == 0
break;
endif
total = total+x;
disp(['Total: ', num2str(total)]);
endwhile
Without the break statement, the loop would keep executing forever since the condition of the while loop is always true. The break allows you to jump past the end of the loop (to the statement after the endwhile).
The break statement can be used in any loop: for, while or do...until.
The continue statement also jumps from the inside of a loop but returns to the beginning of the loop rather than going to the end. In a
1. for loop, the next value inside the vector will be assigned to the for variable (if there are any left) and the loop restarted with that value;
2. while loop, the condition at the beginning of the loop will be retested and the loop continued if it is still true;
3. do...until loop, the condition at the end of the loop will be tested and the loop continued from the beginning if it is still false.
As an example, the following code will fill the lower triangular part of a square matrix with 1s and the rest with 0s.
N = 5;
A = zeros(N); % Create an N x N matrix filled with 0s
for row = 1:N
for column = 1:N
if column > row
continue;
endif
A(row, column) = 1;
endfor
endfor
disp(A);
Note that the inner for skips (continues) over the code that assigns a 1 to an entry of A whenever the column index is greater than the row index.
## The if statement
The general form of the if statement is
if condition1
...
elseif condition2
...
else
...
endif
If condition1 evaluates to true, the statements in the block immediately following the if are executed. If condition1 is false, the next condition (condition2 in the elseif) is checked and its statements executed if it is true. You can have as many elseif statements as you like. The final set of statements, after the else, is executed if all of the conditions evaluate to false. Note that the elseif and else parts of the if statement are optional.
The following are all valid if statements:
% Take the log of the absolute value of x
if x > 0
y = log(x);
elseif x < 0
y = log(-x);
else
disp("Cannot take the log of zero.");
endif
x = input("Enter a value: ");
if x > 0
disp("The number is positive");
endif
if x < 0
disp("The number is negative");
endif
if x == 0
disp("The number is zero");
endif
### Example: The fractal fern
This algorithm is not quite complete. Have a look at the .m file available from http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?objectId=4372&objectType=file.
The image to the right can be generated with the following algorithm:
1. Let x1 and y1 be random values between 0 and 1.
2. Choose one of the linear transformations below to calculate (xi+1, yi+1) from (xi, yi):
1. xi+1 = 0
yi+1 = 0.16yi
2. xi+1 = 0.20xi − 0.26yi
yi+1 = 0.23xi + 0.22yi + 1.6
3. xi+1 = −0.15xi + 0.28yi
yi+1 = 0.26xi + 0.24yi + 0.44
4. xi+1 = 0.85xi + 0.04yi
yi+1 = −0.04xi + 0.85yi + 1.6
The first transformation is chosen if probability 0.01, the second and third with probability 0.07 each and the fourth with probability 0.85.
3. Calculate these values for i up to at least 10,000.
You can download the code that generates this fractal as fracfern.m (this is disabled for now).
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2017-06-28 19:31:15
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http://www.physicsforums.com/showthread.php?p=4252217
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# FORTRAN in linux..read file problems
by jelanier
P: 40 I wrote a simple FORTRAN program to show my read problem. This works fine in windows. On the Linux machine I always get this eof error when I open a file and read. This means that every program I have written doesn't work :) The error is line 12 EOF. What is the problem? (I am using GFORTRAN in linux) program read_write implicit none !reads data from a file called input.dat integer :: i real a(10) !single dimension array real b(10) open(10,file='input.dat') do i = 1,10 read(10,*) a(i) !this is line 12 b(i) = a(i)**1.3 end do close(10) open(12,file='output.dat') do i = 1,10 write (12,*) a(i),b(i) end do close(12) end program read_write oh, the input file is simply: 1 2 3 4 5 6 7 8 9 10 Thanks, Jim
Mentor P: 11,628 The program may be looking for input.dat in a different directory (folder) from where it actually is. Try specifying the complete path to the file.
P: 40
Quote by jtbell The program may be looking for input.dat in a different directory (folder) from where it actually is. Try specifying the complete path to the file.
Nice try, but did not fix it. Same error. BTW I have everything in the same directory.
Jim
Emeritus Sci Advisor HW Helper Thanks PF Gold P: 6,334 FORTRAN in linux..read file problems Is output.dat a new file or one which already exists? If it is new, I would add STATUS = 'NEW' to the open command.
P: 40
Quote by SteamKing Is output.dat a new file or one which already exists? If it is new, I would add STATUS = 'NEW' to the open command.
The output file is fine. If I internally specify the input data it will always create a new output file.
IOW..I can always write files, I just can't read files.
Engineering Sci Advisor HW Helper Thanks P: 6,959 When you do open(10,file='input.dat') if the file input.dat doesn't exist in the directory where Fortran expected to find it, it will create a new empty file. Reading from that will (obviosuly) give you an EOF error. Do a search of your file system for "input.dat" files and delete any empty (zero length) ones that should't be there. Then change the statement to open(10,file='input.dat',status='old') That will fail if Fortran it can't find the "real" input.dat file. Usually you don't need the "status" option for an output file, because you want to overwrite an existing file if it already exists, or create a new one if it doesn't exist, and that's what happens by default.
P: 40 I found a solution. This Linux GFORTRAN compiler handles files differently than the g77 or g95 for windows. I added a $D,$A (CR,LF) at the end of the file. It works now. FWIW..I am using a Raspberry Pi with Debian. Thanks everyone. Jim
P: 873 I seem to recall a problem like this. I don't remember if dos2unix/unix2dos kind of thing had something to do with it...but it certainly had something to do with the end-of-file character being right after the last entry...so, if you went to the very end and press and re-saved the file, the problem goes away. For example, if the original file looked like this: 12.3EOL 23.4EOL 34.5EOF If wouldn't work, but if it looked like this: 12.3EOL 23.4EOL 34.5EOL EOF Then, if would work. I noticed that such condition could happen depending depending on the editor that you are using to enter the data; for example, if I use Nedit and type the data in and leave the EOF right after the last entry, Nedit automatically increases the number of line in the file and moves the EOF by itself to the next line; but, if I use something like Notepad++, it leaves the data the way I typed it. my 2 cents.
Engineering Sci Advisor HW Helper Thanks P: 6,959 It's so long since I've seen a text editor that let you create a file with an "unterminated" last line, I forgot about that problem! But hey, one of the design goals of Unix was NOT to protect people from their own stupidity - not "what you see is what you get" but "what you got was all you deserved"
P: 40
Thanks for the reply. I have seen this before with different compilers. They all seem to handle CR LF differently. A few test programs were run and the solution was found.
Thanks again,
Jim
Quote by gsal I seem to recall a problem like this. I don't remember if dos2unix/unix2dos kind of thing had something to do with it...but it certainly had something to do with the end-of-file character being right after the last entry...so, if you went to the very end and press and re-saved the file, the problem goes away. For example, if the original file looked like this: 12.3EOL 23.4EOL 34.5EOF If wouldn't work, but if it looked like this: 12.3EOL 23.4EOL 34.5EOL EOF Then, if would work. I noticed that such condition could happen depending depending on the editor that you are using to enter the data; for example, if I use Nedit and type the data in and leave the EOF right after the last entry, Nedit automatically increases the number of line in the file and moves the EOF by itself to the next line; but, if I use something like Notepad++, it leaves the data the way I typed it. my 2 cents.
P: 40
Quote by AlephZero It's so long since I've seen a text editor that let you create a file with an "unterminated" last line, I forgot about that problem! But hey, one of the design goals of Unix was NOT to protect people from their own stupidity - not "what you see is what you get" but "what you got was all you deserved"
No problem! I am writing a compiler that compiles "what you meant to do" hehe
Thanks,
Jim
Mentor
P: 21,214
Quote by jelanier Thanks for the reply. I have seen this before with different compilers. They all seem to handle CR LF differently. A few test programs were run and the solution was found.
Operating systems handle ends of lines differently. IIRC, Windows adds a <CR> <LF> pair at the end of a line, while Unix and Linux add only a <CR> character.
P: 40
Quote by Mark44 Operating systems handle ends of lines differently. IIRC, Windows adds a pair at the end of a line, while Unix and Linux add only a character.
That has not been my experience. The linux text editor I use only places a LF ($0A). I saved the file with no "enter" at the end of the last line, and again with enter at the end. The one with no enter, has nothing after the last character. The one with "enter" has only a LF ($0A) after the last character.
see attachment. (I used Leafpad in Debian Linux for this test)
Thanks,
Jim
Attached Thumbnails
P: 873 As people develop their own editors, they can do whatever they want regardless of operating system and/or cater to both; in particular, if they are developing a multi-platform text editor....all you have to do is go to the settings and pick how you want your lines terminated: Windows or Unix style.
Related Discussions Programming & Computer Science 20 Programming & Computer Science 4 Programming & Computer Science 4 Programming & Computer Science 5 Programming & Computer Science 5
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2014-07-31 23:48:57
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https://brilliant.org/discussions/thread/gravityyour-views/
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# Gravity. Your views
You are most welcome to give suggestions to improve my questions..................
Note by Sravanth Chebrolu
5 years, 5 months ago
This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.
When posting on Brilliant:
• Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
• Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
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• Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.
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@Sravanth Chebrolu Thanks,A very nice set.
I really enjoyed solving your questions,i solved all the questions,feeling awsome. Looking for more sets by you.Keep posting.
- 4 years, 11 months ago
Awesome! Have you made similar sets for other topics as well ?
People like you make brilliant an awesome place to learn . I am enjoying this set a lot. Please keep posting such questions, they are interesting!
- 3 years ago
Thanks a lot! (No, this is the only set I've made)
I'm happy that you liked the problems, but I haven't been active lately so I couldn't continue posting. I'll be back soon and I'll keep posting.
If you would like questions of some select topics please leave a comment below, I'd try posting problems on them. Do check my profile to find other problems of mine, stay tuned for more!
- 3 years ago
You have provided awesome questions for Mechanics. I will enjoy solving some Thermodynamics and Magnetism problems. It'll be awesome if you could provide links to such sets. Anyways, you should make some more sets.
Have you solved some of my sets and questions?
- 3 years ago
Thanks! Sure you would... I am afraid I havent made any other sets, but I'll be making more if them soon.
No, I'll try when I find time :)
- 3 years ago
Don't worry and be afraid friend. :)
- 3 years ago
They are amazing...... I learnt a lot about gravity and the twists in the questions. They are quite brain teasing also !! Well..... What else can I say. The questions are as brilliant and amazing as the same way u are....
- 5 years, 5 months ago
well, thank you Skanda................ Any suggestions????????????
- 5 years, 5 months ago
The question named Gravity slope forces has incorrect answer. Work done by force will be equal to change in potential energy. hence 1 + 2 will be 2mglsin30... please correct me if i am incorrect somewhere
- 5 years, 3 months ago
The mistake you've done is, you've missed out the "Friction" Case into calculation. We know, "mu"=tan(theta). So, "mu" becomes tan(30)=(1/sqrt3). Then the WORK for lifting up the block will be ((98+98)(3))=588 Joules Itself. Then, as we have lifted the block up a HEIGHT of (3/2), So, the increase in it's potential energy will be mg(3/2)=294 Joules. Then The sum becomes 588+294=882 Joules which is the correct answer.
- 5 years, 3 months ago
but mu=tantheta is only valid when it is the limiting case of sliding. Please refer standard texts. Also there is not mention of friction in the question.
- 5 years, 3 months ago
Please see my solution for the same.
- 5 years, 3 months ago
The problem " Gravity Niagara Falls This Time " has the exact answer 526588.2353 kg(per minute). Because, mgh = (5000)(746)(100/85)(60). As you've said g=10 & h=50, we get m= 526588.2353 kg(per minute). Your answer is 527000. Why? It is a Bit Far from the exact answer. If we post the answer to the nearest integer, the answer is very clearly 526588 kg(per minute). Kindly tell, where am I wrong? Shouldn't the answer be more exact? Kindly notice this. I hope you will also get the answer 526588 kg(per minute), NOT 527000 which is far away from the correct one.
- 5 years, 3 months ago
Thanks for writing in sir! I am extremely sorry for not mentioning to round off your answer, it is my mistake.
I'm sorry for my mistake, please reply and give your views
- 5 years, 3 months ago
No problem. No need to sorry ... That happens ....... After all, we all are human .... And, please never call me Sir ... I am just a student like you and learning new things regularly ..... By the way, your this set "GRAVITY" was really creative and praiseworthy... Please keep on posting problems like this in future ! Thanks a lot for your knowledge sharing .....
- 5 years, 3 months ago
Thank you, very much I respect your comment sincerely, thanks for liking my set and forgiving me.
The question in discussion was posted long before when I was very new to this website and committed such mistake, in future I hope I will not do such things, thank you!
- 5 years, 3 months ago
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2020-08-11 22:45:46
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https://mpickering.github.io/ide/posts/2020-05-08-state-of-haskell-ide.html
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## The State of Haskell IDEs
Posted on May 8, 2020 by Luke Lau
It is an exciting time for Haskell tooling. As many might be aware, the past year has seen a number of significant changes to the ecosystem, with one of the most noticeable ones being the marriage of ghcide and haskell-ide-engine. We now have contributors from both projects working towards a unified vision of a language server, the haskell-language-server, which aims to be the de-facto IDE for veteran and newcomer Haskellers alike: A full-fledged LSP server that provides diagnostics, code completion, navigation and more, works with both your Cabal and Stack projects, and scales from tiny scripts all the way up to huge codebases like GHC.
haskell-language-server does not do this on its own however. It builds upon a whole ecosystem of tools to drive all of the underlying IDE features. How they all interconnect can be a bit overwhelming at first, so this post will break it down and take a look at them individually.
### ghcide
Powering the language server under the hood is ghcide. Based on tooling built for DAML, it is the core piece of infrastructure that talks to GHC to parse and typecheck your code. One of its many clever innovations is the use of the Shake build system to keep an in-memory cache of modules, file contents and other computations (e.g. code completions). Tooling built on top of it can then query it to get responsive, up-to-date information about the code it is working with. ghcide is also a language server itself, so if you need a lightweight IDE without any fancy trimmings then it will slot right in with any LSP client.
### hie-bios
In order for ghcide to set up the GHC session, it needs to know what set of flags to pass to it. Unfortunately, this is not just as simple as -Wall -O1 — if you ever run cabal build -v you will find that there are loads of flags passed to GHC, a lot of them related to whatever packages your project depends on. hie-bios takes care of this by querying the underlying build tool, such as Stack, Cabal or Hadrian, delegating it the work of figuring out the flags and building any package dependencies that might be needed. By specifying a hie.yaml file in your project’s root directory, you can specify one or more cradles, where each cradle represents some component to build with a specific build tool.
### cabal-helper
You can leave out the hie.yaml file, and hie-bios will try its best to infer which components to build with which tools. However this can get fairly complicated and hairy quickly. haskell-ide-engine and haskell-language-server use cabal-helper to query more information about your project to help with this.
haskell-lsp provides the transport between the client and the server using the Language Server Protocol. It keeps track of a lot of bookkeeping within the protocol, like request IDs and client/server capabilities, and also provides a virtual file system that mirrors edits coming in from the text editor, before they have saved the actually document. Having this mirror is pretty useful for external tools that need to be run on physical files rather than in-memory text buffers. Its sister library, haskell-lsp-types, provides type definitions for the actual specification, so if you want to do your own thing you don’t need to rewrite the data types and parsing all over again.
### lsp-test
lsp-test is a testing framework for LSP servers, used by ghcide, HIE and haskell-language-server. It acts as a language client that can be programmed to send messages to servers, and assert that the right messages are received back. It can also be used to recreate certain scenarios: useful for hunting down memory leaks.
### GHC .hie files
A lot of the work on ghcide and haskell-ide-engine has driven new features and functionality upstream into GHC. One such example is .hie files. These are generated with the -fwrite-ide-flag during compilation, and like a .hi file they contain additional information about some compiled module. However .hie files contain lots of information specifically useful for tooling, such as the type of expressions or where things are defined, hence the acronym for haskell information extended — not to be confused with haskell-ide-engine! Work is underway to use these files in ghcide to provide much more accurate code navigation, completion and type definitions.
The haskell-ide-engine is a language server that faithfully served as a focal point for a whole suite of tools. It’s been a relatively long-running project: It predates the existence of LSP! It originally used ghc-mod as its backend before switching to hie-bios, and it provides a bunch of logic for extracting code completion and symbols etc. out of the GHC API that eventually got absorbed into ghcide. It also has a plugin system which allows external tools to easily interface with LSP. So built into HIE, Floskell, Ormolu and Brittany can provide formatting whilst GHC, Liquid Haskell and HLint provide diagnostics, all through the same interface.
haskell-language-server now aims to concentrate the efforts behind ghcide and haskell-ide-engine. It uses the powerful core of ghcide and HIE’s approach of plugins to integrate an ecosystem worth of tools. Eventually there will be enough tools integrated that users will be able to configure what tools they want to use for each job. Floskell for formatting, or Ormolu? And more importantly, because it builds upon so many components, haskell-language-server will receive any improvements made downstream. This division of labour allows contributors to focus on the individual problems that need tackled, whilst benefiting the whole ecosystem.
Ultimately this means that haskell-ide-engine is being sunset and users should eventually move to haskell-language-server when it is ready. ghcide will continue to be developed and will serve as the underlying backend that powers haskell-language-server.
### Looking forward
We are now entering the renaissance of Haskell tooling. This summer there are 3 Google Summer of Code projects and a Tweag open source fellowship all working on tooling, as well as the continued efforts of many contributors.
Fendor is working on supporting compilation of multiple home-packages at once within GHC. In short this will allow tooling to work with multiple components inside a package simultaneously. Luke Lau (that’s me) is improving the implicit discovery of cradles in hie-bios by connecting together the Cabal show-build-info command, which will give a much more reliable Cabal setup in the absence of hie.yaml files. Zubin Duggal will be focusing on the haskell-language-server, fleshing out its features and taking advantage of GHC’s .hie files. And Michalis Pardalos is integrating OpenTelemetry with the language servers, so that we can instrument and profile how they perform on the vast heterogeneous array of LSP clients that they may be used with.
By the end of the summer we will have built a robust language server which works on any Haskell project of any size and built with any build system.
There are a lot of exciting projects in the pipeline, and we will be posting about them here every Friday. In the meantime, come chat with us over at #haskell-ide-engine on Freenode, clone some projects and help us build the ultimate Haskell IDE.
Index
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2020-08-15 07:58:06
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https://economics.stackexchange.com/questions/44005/why-are-cost-functions-often-assumed-to-be-convex-in-microeconomics/44019
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# Why are cost functions often assumed to be convex in microeconomics?
Why are cost functions typically assumed to be convex in producer theory of (introductory) microeconomics?
For me this goes against the intuition of economies of scale. There are fixed costs (FC) which contribute to concavity of the cost function. There are also variable costs (VC) which may be concave, linear or convex. If we are on the concave part of VC, total costs (TC) must also be concave due to both FC and VC being concave. If we are in the linear part of VC, TC are again concave due to the concavity of FC. And if we are in the convex part of VC, TC may be either concave, linear or convex depending on the relative influence/weight of FC and VC on/in TC. However, even in the case where TC is convex, the producer does not have to operate that way. It can rather operate multiple copies of its production facility each at the level where TC is concave or linear to ensure the TC added over all production facilities is never convex.*,** This makes the assumption of convex costs suspect for me.
I do see one reason why convexity could occur, though. It is if resources are becoming scarce and the producer is big enough to influence the prices in the input markets. However, the producers are assumed to be small in perfect competition, yet their cost functions are assumed to be convex. This appears contradictory to me. So what am I failing to see?
*The fact that FC are incurred with each copy of the production facility might or might not make this a poor strategy depending on the relative weight of FC and VC.
**I think I borrowed the idea for this argument from Varian "Microeconomic Analysis". In 3rd edition, Section 5.2 "The geometry of costs" p. 68 it says:
In the long run all costs are variable costs; in such circumstances increasing average costs seems unreasonable since a firm could always replicate its production process. Hence, the reasonable long-run possibilities should be either constant or decreasing average costs.
The cost function is also shown to be concave in the subsequent section 5.4 "Factor prices and cost functions".
Edit: Thank you for all the great answers! It seems we can have different plausible stories with opposite implications. So far it seems one can plausibly argue for both convex and concave costs. The crux of the matter becomes the assumptions needed to make one story more plausible than the other. Thus the question is, what are the assumptions taken to make convex costs plausible (and concave costs implausible) in introductory microeconomics?
• If $c$ is your cost, it and you pick two points $x \neq y$, it is not unreasonable to suppose that the cost of $tx+(1-t)y$ (with $t \in [0,1]$) can be no greater than the cost of $t$ 'units' of $x$ combined with $(1-t)$ 'units' of $y$. That is, $c(tx+(1-t)y) \le t c(x)+(1-t)c(y)$. May 18 '21 at 3:47
• @copper.hat, that would go against the idea of economies of scale and consequently I find it questionable. May 18 '21 at 6:06
• Economies of scale do not say that bigger is better, though. They just say there's some optimal point (which changes with all sorts of variables) where the economy is highest - smaller and bigger is less economical. And even that is assuming you get all the resources you need for the same prices, including labour costs. And even that's still simplified, since you can have many valleys and hills on the economies of scale curve - it goes up and down, up and down... May 19 '21 at 5:57
• @Luaan, that may well be so, but the argument outlined in my post suggests otherwise, thus the question. May 19 '21 at 10:40
There are several reasons:
1. Didactic Reasons: Other users seem to have missed it but in your question you specify you are talking about "(introductory) microeconomics" [emphasis mine].
Well the most prosaic answer is simply that it is much easier to solve cost minimization, or various other models when costs are assumed to be convex.
This in itself is sufficient reason to construct problems with convex cost functions in introductory microeconomic courses. Demand and supply are not linear, yet in most textbooks and introductory problem they will be assumed to be linear. In addition, in real life demand can be sometimes even upward sloping if a good is a Giffen good, and supply can actually be downward sloping (e.g. some labor supply in some special cases depending on people's preference between consumption and leisure). Yet introductory textbooks typically show downward sloping demand and upward sloping supply (e.g. see Mankiw Principles of Economics that discusses these concepts but only briefly, or more narrowly micro introductory books such as Frank Microeconomics & Behavior).
This is to a great degree for didactic reasons. It is much better for students to first master basics with simple models and when it comes to learning about costs having nicely behaved convex cost functions with single minimum makes learning easier than having to teach cost minimization with concave cost curves. Hence, even if empirically most cost curves would be concave not convex it would be very bad teaching practice to start with concave functions (or just go for full blown realism where cost functions might be piecewise, have different concavity/convexity at different points, be ill defined somewhere etc).
2. Because of Decreasing Returns to Scale - This was covered in great detail by Bayesian, but let me add more arguments and also rebuff some of your arguments in the question.
First, it is not unreasonable to assume that costs are convex in a long-run. In a world of scarcity firm cannot forever increase its demand for factors of production without affecting costs of these factors or inputs as well, their prices will rise eventually (ceteris paribus). We have crystal clear evidence that wages rise in tight labor markets, or that generally speaking shift in demand to the right (ceteris paribus) rises prices. You argue that in perfect competition models firms are assumed to be small, but that is not a good argument in this case. This is because firms are assumed to be too small in terms of their output being able to affect market price of their output so price of output can be taken as given (See Frank Microeconomics and Behavior pp 337). Perfect competition does not require price of inputs to be taken as given. In fact, firm might operate on perfectly competitive market while facing just monopolistically competitive factor market (where the firm is consumer not producer).
Next, you argue that thanks to fixed costs one firms could just continuously invest in a new factories, but this argument should be false. A fix cost by definition cannot vary with output. If firm increases output by building new factory, the cost of factory ceases to be fixed costs. In fact fixed costs primarily exist in short-run as in a long-run most costs are variable (see Mankiw Principles of economics pp 260). In a long-run as you try to build more and more factories you run into the same problems of scarcity of land, capital and labor and thus bid up their prices. In fact this is nicely visualized and explained in the Mankiw textbook with the picture below:
Empirically, we observe that many industries have decreasing returns to scale (although constant returns to scale are common as well), and increasing returns to scale are rare (although not completely uncommon). See for example: Basu & Fernald, 1997; Gao & Kehrig 2017.
Introductory texts by their nature will not deal with specific cases but more general ones. Most introductory textbooks again do not spend too much time on Giffen goods not just because modeling them would be difficult for 101 students but also because they are not very often seen (although, I am not claiming non-convex cost functions are as rare as Giffen goods).
1. On the Aesthetics: I think Giskard raises a valid point that there are probably many economists who assume convex costs just for mathematical elegance. However:
• I think Giskard slightly exaggerates the problem and is bit too cynical about it. For sure there are economists who value mathematical elegance uber ales, but there is increasing trend in share of empirical papers (see Angrist et al 2017), even in microeconomics, and I think that a reasonable non-cynical explanation for the small share of micro empirical papers is that until very recently there was always lack of good micro data (in addition this is also due to breakdown, you can see the share of industrial organization empirical papers (that also heavily use cost functions) is quite high).
• Empirically, most industries do not exhibit increasing returns to scale. While non-convex functions are definitely real (especially along some points of cost curve), empirical evidence does show that decreasing returns to scale (although constant returns to scale as well) are quite common (e.g. see Basu & Fernald, 1997; Gao & Kehrig 2017), but I think Giskard has definitely valid point that some modelers will ignore empirics for sake of mathematical elegance.
• Lastly, but not least, I think mathematical elegance can explain why such assumption features heavily in some published theoretical work, I don't think it can explain why it is featured in introductory micro texts. Is really quadratic cost function $$c=q^2$$ mathematically elegant? I don't think so but that is probably the most commonly used cost function you will ever see in intro texts.
Regarding the Varian quote. Varian on page 67 states that he will first cover situation with fixed factor costs and later move to variable factor costs. Hence, unless I am misreading Varian I think the statement on the page 68 is made under assumption of constant factor prices. However, the explanation above by Mankiw does not assume that.
• Very helpful, thank you. So you would object my quotation of Varian by pointing to the picture from Mankiw? Fair enough, it looks sensible. My discussion of fixed costs was sloppy indeed. I do not think the idea I am trying to convey is dead on arrival, but I should clearly work on its formulation. May 17 '21 at 16:23
• @RichardHardy I would have to read more context of that, I am hesitant to argue with someone as well known as Varian, but I think it could be typo because to me it seems reasonable that would imply that in long run costs are either constant or increasing not decreasing. However, now seeing that quote I must admit that impostor syndrome kicks in and I am bit confused, I have Varians textbook I will have look at the passage and chapter to see what he means.
– 1muflon1
May 17 '21 at 16:30
• I do not think it is a typo, as it is discussed quite extensively and Varian points out it may appear surprising (as it did for you). May 17 '21 at 16:31
• @RichardHardy Well, he is not wrong there I softened the language in my answer about prima facie being false, I will definitely have closer look at that passage
– 1muflon1
May 17 '21 at 16:33
• @RichardHardy I think then he reuses the graphs, because I double checked the title and the book I took it from is principles of economics... I guess this is nasty feature of the US textbook market, you have so much mandatory overlapping textbooks that often even cover verbatim the same stuff and then students end up paying on all those additional textbooks :(
– 1muflon1
May 18 '21 at 15:07
Theoretically, the cost function is a result of a cost minimization problem with a given production technology. Convex/linear/concave costs are a result of decreasing/constant/increasing returns to scale. The thinking behind convex costs is the idea of decreasing marginal product of your input goods for production.
As an example for the kind of thinking behind a convex cost function: If you want to produce one widget, you can do it with the 3 most skilled workers in town. If you want to produce two widgets, you can do it with the 7 most skilled workers in town because the 4 additional ones are slower. Alternatively, all workers have the same productivity but first you take the cheapest and the next ones would only do the job for more money. Alternatively, you consider hours worked: A worker can produce one good in three hours, but the second one takes four hours because working is exhausting. Similarly, the first hours are paid on regular contract wherease extra-hours need extra compensation. Alternatively, you need wood for production. For the first goods you can chop wood in your own forest, but once you need more you need to find additional more expensive sources. And so on.
Remember that the supply curve is the increasing part of the marginal cost curve. The supply curve in Econ 101 is upward sloping because of the above intuition. It might be that there are increasing returns to scale, e.g. because workers can divide jobs and there are gains from specialization. Eventually, however, we assume that those gains come to an end at some point as marginal returns diminish.
Next, and this is not a good reason, note that a monopolist optimally produces a quantity such that marginal revenue - marginal cost = 0. Convex costs ensure that this is in fact a maximum.
• It seems we can have different plausible stories with opposite implications. My interest is in finding why the plausible story of convex cost is more convincing than the plausible story of concave costs. I am willing to take additional assumptions to achieve that, and the choice of assumptions seems crucial. Among what you wrote, It might be that there are increasing returns to scale, e.g. because workers can divide jobs and there are gains from specialization. Eventually, however, we assume that those gains come to an end at some point as marginal returns diminish seems to be about it. May 17 '21 at 14:41
• Yes, I find it reasonable that such gains dry up. Your argument seems to be that instead of one big team where there specialization gains dried up, you can make several small teams/small factories does not seem to scale up because recources are scarce. You can't copy the more skilled workers which you would hire first and you cannot copy the easy to get oil/coal. At some point you need to hire less skilled workers and drill deeper to get oil/coal. May 17 '21 at 14:49
• Very well. These are precisely the assumptions I am looking for! I wonder if there are more, or if there is an explicit set of them (e.g. minimal sufficient set) somewhere. There has to be something about the aggregate in addition, I think, since under perfect competition a small producer is not supposed to have an effect on the input markets (like being able to exhaust them to a degree that would affect input prices). May 17 '21 at 14:50
• For such discussions about the fundamentals, it is always best to open the bible again. Have a look at MWG Section 5.D "geometry of the cost function." May 17 '21 at 14:57
• I read it once, and what I found was a discussion of multiple shapes of cost functions without paying much attention to how they arise. Yes, there were some hints but only for some cases. Unfortunately, I could not find a discussion relevant to this thread. I found something more interesting in Varian's "Microeconomic Analysis"; see my edit. May 17 '21 at 15:42
If the cost function is globally concave in output $$y$$, then
• the profit function is convex in $$y$$ and the optimal (profit maximizing) output is not characterized by the equality between price and marginal cost, so price taker firms have an optimal output level that is either 0 or tends to infinity
• the profit is negative at least for low levels of output (if $$c'(0)>p$$)
Such a concavity assumption will have difficulties to explain why about 60% of firms produce less than 5% of total output.
For these reasons, the cost functions are probably not concave (globally), unless for firms with strong market power... Instead it is quite plausible that the cost function is locally convex and exhibits nonconvexities here and there.
• Thank you. The second bullet point is obviously correct, isn't it? The first bullet point seems intuitively correct, too, as virtually all companies try to expand production as long as there is demand for it and the level of production does not cause the price to fall too much. It is uncommon to see a producer of a commodity saying, well, we should not expand our production any more because we have reached a sweet spot. (I am not talking about monopolies but rather perfect competition and settings close to it.) May 18 '21 at 6:04
• Regarding why about 60% of firms produce less than 5% of total output, I think we may need to look for the answer elsewhere than in the cost function: (1) the markets together with their participants are never in equilibrium but on their way there, and the conditions keep changing so that the equilbrium is constantly moving; (2) there are young companies that are growing and have not reached their optimal production level yet; (3) there is market power (thus not perfect competition) etc. ect. May 18 '21 at 6:34
Increasing and convex costs are a result of decreasing returns to scale. These are mainly due to the limited availability of (local) input factors. Other contributing factors are the decline of management efficiency of large-scale production, the imperfection of internal supervision and control mechanisms, and more complex information transmission.
• I have made an argument for increasing returns to scale. (Regarding decline of management efficiency of large-scale production, the imperfection of internal supervision and control mechanisms, and more complex information transmission, why not split your factory into multiple smaller copies to avoid that?) If the argument is not faulty and the producer is not big enough to affect the market prices of inputs, then I do not find your argument convincing. Please let me know where you think I am mistaken. May 17 '21 at 13:42
• Within a single factory you typically have increasing marginal productivity, so you add wokers and machines until you reach the optimal factory size. Then, if you want to further expand output, you need to set up a second factory, where you repeat the process. When you have multiple factories, you need managers for each one, and the supervision/control/information transmission problems kick in. So n factories are more than n times as costly to run than a single one. May 17 '21 at 14:22
• Then you split the company into multiple one-factory companies. The idea is never to choose an inefficient large entity when better efficiency can be achieved by a number of smaller entities. In other words, always use the most efficient technology. A rational actor would naturally choose that, especially given that the efficient technology is readily available as it has been implemented on a smaller scale / in a smaller number of entities already. (It is not I who came up with that, I read it somewhere a while ago.) May 17 '21 at 14:44
• This does not work as a solution to the problem. Multiple companies would compete against each other - unless you somehow integrate them into a "supercompany" acting as a single unit and maximizing the sum of company profits. But then your supervision/control/information problems are back again. May 18 '21 at 7:08
• Thank you. The textbook examples that I encountered had both convex costs and perfect competition, and the contradiction bugged me. In realistic situations, I agree things can be very different. May 19 '21 at 17:53
In my very limited empirical experience it seemed that cost functions were in fact non-convex for most output levels in the few industries I looked at. Allocating costs to exact parts of a process is very difficult, but marginal costs were generally assumed to be constant, with some jumps as capacity constraints were reached.
The theorems in microeconomics/general equilibrium theory that deal with the existence of solutions to profit maximization problems, the existence of competitive equilibria and Pareto-efficiency of these equilibria are well-liked for their mathematical elegance. However they rely on a bunch of convexity/concavity assumptions. (The branch of math used is convex analysis.)
Hence these assumptions are dictated more by the desire for elegant theoretical solutions rather than empirical knowledge.
Note that there are many possible rationalizations for why cost functions may be convex, some (interesting ones) are outlined in the other answers. I would argue that these are mostly rationalizations of the assumption, not proof of its empirical validity. To be fair, I also do not provide empirical proof.
• This has been my feeling, too, but I do not trust it. I am cautious to dismiss the basic microeconomic theory. People must have had reasonably convincing arguments besides mathematical elegance to make them widely accepted. Or is it too idealistic on my part to think this way? Also, I am trying to see how this is supposed to work at least in theory if not in practice. There seems to be some trouble with my understanding of the former let alone the latter on which tend I agree with you. May 17 '21 at 13:43
• @RichardHardy I am not the right person to turn to right now for this sort of advice. I recently decided to leave the discipline, in part due to similar frustrations. In my discussions with other economists the varied answers I received were 1. "of course it is just a model, still it is useful" (I was not convinced by the reasoning on usefulness) 2. "of course it is a bad model, but publish or perish" and 3. "who cares if it is empirically valid? I like math!" May 17 '21 at 13:49
• I am sorry to hear that. There definitely are cases like you describe. I hope they do not dominate generally, but they may surely plague many. In any case, your help and critical approach is appreciated (surely more broadly than at Economics SE). May 17 '21 at 13:59
I would intuit the following: consumer utility is defined as a function as $$U=U(C,L)$$ where $$C$$ is consumption and $$L$$ is leisure. We normally assume that this function is concave in both arguments. Given a fixed time endowment, leisure becomes more and more valuable the lesser you have of it (consequence of concavity+ Inada conditions).
In general equilibrium, labour demand has to equal labour supply. If a firm wants to increase production from $$Q_{1}$$ to $$Q_{2}$$, it will have to incentivize workers by paying higher wages- which will increase at an increasing rate given the concavity of the utility function defined over leisure.
• That is a nice example of the phenomenon mentioned in the last paragraph of the OP. It applies directly for a producer that is big enough to affect the price of labour. What about a smaller producer though? (Maybe this is already in the notion of general equilibrium or something? Since my knowledge of microeconomics is very rusty and has never been deep, I cannot tell.) May 17 '21 at 12:39
• (-1) How about companies that are big enough to hire several people, working for monthly salaries rather than an hourly wage? I hear this business model is widespread, and the cost function seem unaffected by labor supply function of individual workers. May 17 '21 at 13:27
• @RichardHardy I will write a more detailed answer if I find the time today- but essentially, in many models, labour is assumed to be perfectly mobile across firms. Given perfect mobility, the size of the firm does not matter- there is only one wage across firms. For your firm to incentivize the marginal worker to come work to increase your own production, you would have to pay higher than the prevailing market wage. May 17 '21 at 13:30
• Last comment was by me, not Hardy. The theoretical model you describe seems ill-fited to reality. I do not doubt its inner mathematical consistency. May 17 '21 at 13:31
• @Giskard I see what you mean. I would also agree that this may not reflect reality accurately. Of course, one could build models of monopsony power, segmented labor markets, labor market frictions etc. to reflect reality better. The above was just one reason that came to mind regarding the convexity of cost functions. May 17 '21 at 14:41
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2022-01-18 10:58:27
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https://tex.stackexchange.com/questions/394442/package-babel-error-unknown-language-option
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# Package Babel error, unknown language option [closed]
Today I updated my operating system to Ubuntu 14.04 and now I run into the following problem:
\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage[english]{babel}
\begin{document}
This is a MINIMUM WORKING EXAMPLE.
\end{document}
gives the error message:
! LaTeX Error: Unknown option 'english' for package 'babel'. See the LaTeX
manual or LaTeX Companion for explanation.
I am using Texmaker and this seems to happen for all the different language options, even though Texlive is fully installed. Thank you for your help.
Regards Michael
## closed as off-topic by Andrew Swann, Stefan Pinnow, siracusa, TeXnician, dexteritasSep 7 '18 at 10:09
• This question does not fall within the scope of TeX, LaTeX or related typesetting systems as defined in the help center.
If this question can be reworded to fit the rules in the help center, please edit the question.
• Welcome to TeX.SX! Can you show what's the output of kpsewhich english.ldf from the terminal? – egreg Oct 3 '17 at 21:08
• /usr/share/texlive/texmf-dist/tex/generic/babel-english/english.ldf – Michael Scheitz Oct 3 '17 at 21:12
• OK. Can you find the version number of babel.sty in the log file? It's right at the top. – egreg Oct 3 '17 at 21:13
• Babel <3.9h> and hyphenation patterns for 78 languages loaded. – Michael Scheitz Oct 3 '17 at 21:25
• I'm voting to close this question as off-topic because it was solved by updating the distribution and cleaning out the auxiliary files – Andrew Swann Sep 7 '18 at 7:25
My solution: Create a file named babel-english.sty. You may leave its contents empty. Put the file in the same folder as your main *.tex document. Discard its existing *.aux and *.synctex.gz files. Then re-compile your *.tex document.
As best as I can determine, when babel loads with default language english it looks for package babel-english. Even though babel-english is installed, it has only data files, not a *.sty file. So, babel cannot find it. When you make a fake babel-english.sty file available, then babel proceeds normally.
You may also create folder (texmf-local)/text/generic/babel-english and place the fake file there, then update your file name database (on Ubuntu, command line mktexlsr).
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2019-10-22 11:20:33
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https://research.chalmers.se/publication/504626
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# Pure type systems with judgemental equality Artikel i vetenskaplig tidskrift, 2006
In a typing system, there are two approaches that may be taken to the notion of equality. One can use some external relation of convertibility defined on the terms of the grammar, such as $\beta$-convertibility or $\beta \eta$-convertibility; or one can introduce a judgement form for equality into the rules of the typing system itself. For quite some time, it has been an open problem whether the two systems produced by these two choices are equivalent. This problem is essentially the problem of proving that the Subject Reduction property holds in the system with judgemental equality. In this paper, we shall prove that the equivalence holds for all functional Pure Type Systems (PTSs). The proof essentially consists of proving the Church-Rosser Theorem for a typed version of parallel one-step reduction. This method should generalise easily to many typing systems which satisfy the Uniqueness of Types property.
type theory
pure type systems
## Författare
Chalmers, Data- och informationsteknik, Datavetenskap
#### Journal of Functional Programming
0956-7968 (ISSN) 1469-7653 (eISSN)
Vol. 16 2 219-246
#### Ämneskategorier
Algebra och logik
Datavetenskap (datalogi)
#### Styrkeområden
Informations- och kommunikationsteknik
#### Fundament
Grundläggande vetenskaper
#### DOI
10.1017/S0956796805005770
2018-08-23
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2019-10-16 02:46:38
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https://www.scielo.br/j/cr/a/3rfzgB4V8G9Mp9S37TFrwFh/?lang=en
|
ABSTRACT:
The harvesting process is a current challenge for the commercial production of microalgae because the biomass is diluted in the culture medium. Several methods have been proposed to harvest microalgae cells, but there is not a consensus about the optimum method for such application. Herein, the methods based on sedimentation, flocculation, and centrifugation were evaluated on the recovery of Chlorella sorokiniana BR001 cultivated in a low-nitrogen medium. C. sorokiniana BR001 was cultivated using a low-nitrogen medium to trigger the accumulation of neutral lipids and neutral carbohydrates. The biomass of C. sorokiniana BR001 cultivated in a low-nitrogen medium showed a total lipid content of 1.9 times higher (23.8 ± 4.5%) when compared to the biomass produced in a high-nitrogen medium (12.3 ± 1.2%). In addition, the biomass of the BR001 strain cultivated in a low-nitrogen medium showed a high content of neutral carbohydrates (52.1 ± 1.5%). The natural sedimentation-based process was evaluated using a sedimentation column, and it was concluded that C. sorokiniana BR001 is a non-flocculent strain. Therefore, it was evaluated the effect of different concentrations of ferric sulfate (0.005 to 1 g L-1) or aluminum sulfate (0.025 to 0.83 g L-1) on the flocculation process of C. sorokiniana BR001, but high doses of flocculant agents were required for an efficient harvest of biomass. It was evaluated the centrifugation at low speed (300 to 3,000 g) as well, and it was possible to conclude that this process was the most adequate to harvest the non-flocculent strain C. sorokiniana BR001.
Key words:
microalgae; ferric sulfate; aluminum sulfate; sedimentation; centrifugation
RESUMO:
Palavras-chave:
microalgas; sulfato de ferro; sulfato de alumínio; sedimentação; centrifugação
INTRODUCTION:
Harvesting of microalgal biomass is considered a bottleneck in algae farms because the biomass is generally diluted in the medium (0.5 to 4 kg of dry weight per m-3), and many microalgae with biotechnological potential are planktonic (i.e. free-floating) organisms that show density values similar to water (TIRON et al., 2017TIRON, O. et al. Overcoming microalgae harvesting barrier by activated algae granules. Scientific Reports, Dec. 2017. v.7, n.1, p.4646. Available from: <Available from: http://dx.doi.org/10.1038/s41598-017-05027-3 >. Accessed: Jan. 19, 2020. doi: 10.1038/s41598-017-05027-3.
http://dx.doi.org/10.1038/s41598-017-050...
). Microalgal cultures are considered stable systems because the surface of microalgal cells presents negative charges that repel other cells, and microalgae are generally found in a dispersed state (SINGH & PATIDAR, 2018SINGH, G. et al. Microalgae harvesting techniques: a review. Journal of Environmental Management, Jul. 2018. v.217, p.499-508. Available from: <Available from: http://dx.doi.org/10.1016/j.jenvman.2018.04.010 >. Accessed: Jan. 18, 2020. doi: 10.1016/j.jenvman.2018.04.010.
http://dx.doi.org/10.1016/j.jenvman.2018...
).
Harvesting of microalgae biomass requires costly and complex processes that can reach up to 30% of the total costs of production (FASAEI et al., 2018FASAEI, F. et al. Techno-economic evaluation of microalgae harvesting and dewatering systems. Algal Research, Apr. 2018. v.31, p.347-362. Available from: <Available from: http://dx.doi.org/10.1016/j.algal.2017.11.038 >. Accessed: Feb. 04, 2020. doi: 10.1016/j.algal.2017.11.038.
http://dx.doi.org/10.1016/j.algal.2017.1...
). Different methods to harvest microalgal cells have been proposed for a large number of species (TAPARIA et al., 2016TAPARIA, T. et al. Developments and challenges in biodiesel production from microalgae: a review. Biotechnology and Applied Biochemistry, Oct. 2016. v.63, n.5, p.715-726. Available from: <Available from: http://dx.doi.org/10.1002/bab.1412 >. Accessed: Feb. 15, 2020. doi: 10.1002/bab.1412.
http://dx.doi.org/10.1002/bab.1412...
). Sedimentation shows low operational costs when compared to other methods of biomass harvest (FASAEI et al., 2018FASAEI, F. et al. Techno-economic evaluation of microalgae harvesting and dewatering systems. Algal Research, Apr. 2018. v.31, p.347-362. Available from: <Available from: http://dx.doi.org/10.1016/j.algal.2017.11.038 >. Accessed: Feb. 04, 2020. doi: 10.1016/j.algal.2017.11.038.
http://dx.doi.org/10.1016/j.algal.2017.1...
), but the slowness of this process may be a problem for microalgae with a fast metabolism. Catabolism reactions may occur during the harvest process leading to undesired changes in the biochemical composition of the microalgae before their extraction.
To overcome the slow settling of non-flocculent microalgae strains, the use of flocculants have been proposed as a promising and cheap alternative to improve the harvest processes (WAN et al., 2015WAN, C. et al. Current progress and future prospect of microalgal biomass harvest using various flocculation technologies. Bioresource Technology, May 2015. v.184, p.251-257. Available from: <Available from: http://dx.doi.org/10.1016/j.biortech.2014.11.081 >. Accessed: Feb. 03, 2020. doi: 10.1016/j.biortech.2014.11.081.
http://dx.doi.org/10.1016/j.biortech.201...
). Chemical flocculation is widely used in industries for water treatment (VANDAMME; FOUBERT; MUYLAERT, 2013VANDAMME, D. et al. Flocculation as a low-cost method for harvesting microalgae for bulk biomass production. Trends in Biotechnology, Apr. 2013. v.31, n.4, p.233-239. Available from: <Available from: http://dx.doi.org/10.1016/j.tibtech.2012.12.005 >. Accessed: Feb. 21, 2020. doi: 10.1016/j.tibtech.2012.12.005.
http://dx.doi.org/10.1016/j.tibtech.2012...
), and different chemical flocculant agents have been successfully used in the harvest of several microalgal strains (WAN et al., 2015). Flocculation is also used as a secondary harvesting method to shorten the duration of the primary harvesting process (e.g. centrifugation) and increase the maximum cell recovery rate (KNUCKEY et al., 2006KNUCKEY, R. M. et al. Production of microalgal concentrates by flocculation and their assessment as aquaculture feeds. Aquacultural Engineering, Oct. 2006. v.35, n.3, p.300-313. Available from: <Available from: http://dx.doi.org/10.1016/j.aquaeng.2006.04.001 >. Accessed: Jan. 24, 2020. doi: 10.1016/j.aquaeng.2006.04.001.
http://dx.doi.org/10.1016/j.aquaeng.2006...
).
Centrifuges are a robust alternative to process large volumes of microalgae culture in a short time (SPOLAORE et al., 2006SPOLAORE, P. et al. Commercial applications of microalgae. Journal of Bioscience and Bioengineering, Feb. 2006. v.101, n.2, p.87-96. Available from: <Available from: http://dx.doi.org/10.1263/jbb.101.87 >. Accessed: Feb. 05, 2020. doi: 10.1263/jbb.101.87.
http://dx.doi.org/10.1263/jbb.101.87...
). Many types of centrifuges are commercially available (e.g. disc stacked centrifuge and scroll centrifuge), and the equipment can be readily incorporated in microalgal downstream processes. Centrifuges diminish or abolish the use of chemical flocculant agents which are not desired in some specific applications, like the use of microalgae as food and feed.
Despite the several harvest methods proposed in the literature, it is unlikely to determine an optimum harvesting method for all microalgae strains. Indeed, it is expected that the method and conditions of biomass harvesting should be specific for each microalgal strain. Chlorella is currently the second most commercially-produced microalga, and it has been considered a promising feedstock for advanced biofuels production (FALCONÍ et al., 2021FALCONÍ, J. H. H. et al. Strain screening and ozone pretreatment for algae farming in wastewaters from sugarcane ethanol biorefinery. Journal of Cleaner Production, Feb. 2021, v.282. Available from: <Available from: http://dx.doi.org/10.1016/j.jclepro.2020.124522 >. Accessed: Mar. 01, 2021. doi: 10.1016/j.jclepro.2020.124522.
http://dx.doi.org/10.1016/j.jclepro.2020...
; LIU & CHEN, 2014LIU, J. et al. Biology and industrial applications of Chlorella: advances and prospects. Advances in biochemical engineering/biotechnology, Dec. 2014, v.123, p.1-35. Available from: <Available from: http://dx.doi.org/10.1007/10_2014_286 >. Accessed: Feb. 05, 2020. doi: 10.1007/10_2014_286.
http://dx.doi.org/10.1007/10_2014_286...
; ROCHA et al., 2017ROCHA, R. P. et al. Exploring the metabolic and physiological diversity of native microalgal strains (Chlorophyta) isolated from tropical freshwater reservoirs. Algal Research, Dec. 2017. v.28, p.139-150. Available from: <Available from: http://dx.doi.org/10.1016/j.algal.2017.10.021 >. Accessed: Jan. 24, 2020. doi: 10.1016/j.algal.2017.10.021.
http://dx.doi.org/10.1016/j.algal.2017.1...
). Specifically, the strain C. sorokiniana BR001 shows a fast growth synthetic media in comparison to other Chlorophyta strains isolated from Brazilian freshwater reservoirs (ROCHA et al., 2017), and it is considered a promising strain for the treatment of wastewaters from sugarcane ethanol biorefinery which are largely produced in Brazil (FALCONÍ et al., 2020).
Although Chlorella has been used at a commercial scale and novel algae farming application have been proposed, the harvesting process requires investigation because the self-flocculation is a trait observed only in some strains of the genus Chlorella (ALAM et al., 2014ALAM, M. A. et al. Characterization of the flocculating agent from the spontaneously flocculating microalga Chlorella vulgaris JSC-7. Journal of Bioscience and Bioengineering, Jul. 2014. v.118, n.1, p.29-33. Available from: <Available from: http://dx.doi.org/10.1016/j.jbiosc.2013.12.021 >. Accessed: Jan. 17, 2020. doi: 10.1016/j.jbiosc.2013.12.021.
http://dx.doi.org/10.1016/j.jbiosc.2013....
; ESCAPA et al., 2015ESCAPA, C. et al. Nutrients and pharmaceuticals removal from wastewater by culture and harvesting of Chlorella sorokiniana. Bioresource Technology, Jun. 2015. v.185, p.276-284. Available from: <Available from: http://dx.doi.org/10.1016/j.biortech.2015.03.004 >. Accessed: Feb. 03, 2020. doi: 10.1016/j.biortech.2015.03.004.
http://dx.doi.org/10.1016/j.biortech.201...
; RAS et al., 2011RAS, M. et al. Experimental study on a coupled process of production and anaerobic digestion of Chlorella vulgaris. Bioresource Technology, Jan. 2011. v.102, n.1, p.200-206. Available from: <Available from: http://dx.doi.org/10.1016/j.biortech.2010.06.146 >. Accessed: Feb. 09, 2020. doi: 10.1016/j.biortech.2010.06.146.
http://dx.doi.org/10.1016/j.biortech.201...
). Previous studies showed the efficiency of different methods on the harvest of Chlorella cultivated in rich-nitrogen media (AHMAD et al., 2014AHMAD, A. L. et al. Comparison of harvesting methods for microalgae Chlorella sp. and its potential use as a biodiesel feedstock. Environmental Technology, Sep. 2014. v.35, n.17, p.2244-2253. Available from: <Available from: http://dx.doi.org/10.1080/09593330.2014.900117 >. Accessed: Feb. 02, 2020. doi: 10.1080/09593330.2014.900117.
http://dx.doi.org/10.1080/09593330.2014....
; NGUYEN et al., 2014NGUYEN, T. D. P. et al. Harvesting Chlorella vulgaris by natural increase in pH: effect of medium composition. Environmental Technology, Jun. 2014. v.35, n.11, p.1378-1388. Available from: <Available from: http://dx.doi.org/10.1080/09593330.2013.868531 >. Accessed: Jan. 19, 2020. doi: 10.1080/09593330.2013.868531.
http://dx.doi.org/10.1080/09593330.2013....
). However, little is known about the harvesting of Chlorella cells cultivated in a low-nitrogen medium (ILLMAN; SCRAGG; SHALES, 2000ILLMAN, A. M. et al. Increase in Chlorella strains calorific values when grown in low nitrogen medium. Enzyme and Microbial Technology, Nov. 2000. v.27, n.8, p.631-635. Available from: <Available from: http://dx.doi.org/10.1016/S0141-0229(00)00266-0 >. Accessed: Jan. 25, 2020. doi: 10.1016/S0141-0229(00)00266-0.
http://dx.doi.org/10.1016/S0141-0229(00)...
). The main objective of this study was to determine the best method of biomass harvesting for a specific Chlorella strain cultivated in a low-nitrogen medium. The methods of sedimentation, centrifugation, and flocculation were evaluated on the harvesting of C. sorokiniana BR001 cultivated in a low-nitrogen medium. Algae farming using low-nitrogen media is largely adopted as a strategy to trigger the accumulation of neutral lipids and neutral carbohydrates (LIU & CHEN, 2014LIU, J. et al. Biology and industrial applications of Chlorella: advances and prospects. Advances in biochemical engineering/biotechnology, Dec. 2014, v.123, p.1-35. Available from: <Available from: http://dx.doi.org/10.1007/10_2014_286 >. Accessed: Feb. 05, 2020. doi: 10.1007/10_2014_286.
http://dx.doi.org/10.1007/10_2014_286...
).
The strain C. sorokiniana BR001 was first cultivated in rich- and low-nitrogen media for evaluation of the accumulation of C-rich biochemical classes (i.e. total lipids and total neutral carbohydrates). Then, the different methods of biomass harvesting were evaluated on the harvesting of C. sorokiniana BR001 cultivated in a low-nitrogen medium. It was evaluated the natural sedimentation to evaluate if of C. sorokiniana BR001 presents the self-flocculation phenotype. A careful evaluation of flocculant agents was performed because their optimum dosage may vary one order of magnitude for different microalgae (DEMIR et al., 2020). Different centrifugation speeds and times were evaluated because centrifuges will be common equipment in algae farms and biorefineries as they are required in biorefining processes (AMORIM et al., 2020AMORIM, M. L. et al. Extraction of proteins from the microalga Scenedesmus obliquus BR003 followed by lipid extraction of the wet deproteinized biomass using hexane and ethyl acetate. Bioresource Technology, Jul. 2020. v.307. Available from: <Available from: http://dx.doi.org/10.1016/j.biortech.2020.123190 >. Accessed: Aug. 02, 2020. doi: 10.1016/j.biortech.2020.123190.
http://dx.doi.org/10.1016/j.biortech.202...
).
MATERIALS AND METHODS:
Strain and growth conditions
C. sorokiniana BR001 was obtained from the Collection of Microalgae of the Department of Plant Biology, Universidade Federal de Viçosa (Minas Gerais, Brazil). The BR001 strain was maintained in a rich-nitrogen medium for Chlorella ellipsoidea (WATANABE, 1960WATANABE, A. List of algal strains in collection at the Institute of Applied Microbiology, University of Tokyo. The Journal of General and Applied Microbiology, 1960. v.6, n.4, p.283-292. Available from: <Available from: http://dx.doi.org/10.2323/jgam.6.283 >. Accessed: Jan. 15, 2020. doi: 10.2323/jgam.6.283.
http://dx.doi.org/10.2323/jgam.6.283...
).
Cultivation of C. sorokiniana BR001 in rich- and low-nitrogen media
The BR001 strain was cultivated in 2 L photobioreactors containing 1.6 L of the low-nitrogen medium proposed by ILLMAN et al. (2000ILLMAN, A. M. et al. Increase in Chlorella strains calorific values when grown in low nitrogen medium. Enzyme and Microbial Technology, Nov. 2000. v.27, n.8, p.631-635. Available from: <Available from: http://dx.doi.org/10.1016/S0141-0229(00)00266-0 >. Accessed: Jan. 25, 2020. doi: 10.1016/S0141-0229(00)00266-0.
http://dx.doi.org/10.1016/S0141-0229(00)...
) or the rich-nitrogen medium for Chlorella ellipsoidea (WATANABE, 1960WATANABE, A. List of algal strains in collection at the Institute of Applied Microbiology, University of Tokyo. The Journal of General and Applied Microbiology, 1960. v.6, n.4, p.283-292. Available from: <Available from: http://dx.doi.org/10.2323/jgam.6.283 >. Accessed: Jan. 15, 2020. doi: 10.2323/jgam.6.283.
http://dx.doi.org/10.2323/jgam.6.283...
). Photobioreactors were maintained in photoautotrophic growth conditions at 25 ± 2 ºC, 16/8 h photoperiod (light/dark cycle), and irradiance at bench height of 83 µmols photons m-2 s-1 obtained using 40-watt daylight fluorescent lamps. A diaphragm pump was used to provide mixing for cultivations in flasks. Cultures of C. sorokiniana BR001 were collected on day 14, and the biomass was harvested by centrifugation (20,000 g for 20 min), freeze-dried and stored at -20 ºC. Freeze-dried biomass was used for the determination of total neutral carbohydrates based on the phenol-sulfuric acid method (CRAIGIE & HELLEBUST, 1978CRAIGIE, J. S. et al. Handbook of phycological methods: physiological and biochemical methods - volume 2. 1st. ed. Cambridge: Cambridge University Press, 1978. ), and the determination of total lipids was performed according to the Bligh and Dyer method (BLIGH & DYER, 1959BLIGH, E. G. et al. A rapid method of total lipid extraction and purification. Canadian Journal of Biochemistry and Physiology, Aug. 1959. v.37, n.8, p.911-917. Available from: <Available from: http://dx.doi.org/10.1139/o59-099 >. Accessed: Feb. 03, 2020. doi: 10.1139/o59-099.
http://dx.doi.org/10.1139/o59-099...
; ZHU, 2002ZHU, M. Extraction of lipids from Mortierella alpina and enrichment of arachidonic acid from the fungal lipids. Bioresource Technology, Aug. 2002. v.84, n.1, p.93-95. Available from: <Available from: http://dx.doi.org/10.1016/S0960-8524(02)00028-7 >. Accessed: Feb. 09, 2020. doi: 10.1016/S0960-8524(02)00028-7.
http://dx.doi.org/10.1016/S0960-8524(02)...
).
Cultivation of C. sorokiniana BR001 for evaluation of the harvesting methods
The BR001 strain was cultivated in 20 L photobioreactors containing 16 L of low-nitrogen medium proposed by ILLMAN et al. (2000ILLMAN, A. M. et al. Increase in Chlorella strains calorific values when grown in low nitrogen medium. Enzyme and Microbial Technology, Nov. 2000. v.27, n.8, p.631-635. Available from: <Available from: http://dx.doi.org/10.1016/S0141-0229(00)00266-0 >. Accessed: Jan. 25, 2020. doi: 10.1016/S0141-0229(00)00266-0.
http://dx.doi.org/10.1016/S0141-0229(00)...
). Photobioreactors were maintained in the aforementioned photoautotrophic growth conditions. Samples of C. sorokiniana BR001 culture were collected on day 17 for evaluation of the following methods of biomass recovery: sedimentation, flocculation, and centrifugation. An independent microalgae cultivation was carried out for each biomass harvesting method evaluated in this study. The harvesting methods were evaluated in quadruplicate.
Biomass harvest by sedimentation
Natural sedimentation of C. sorokiniana BR001 was evaluated using an acrylic sedimentation column with a diameter of 0.1 m and a height of 1 m. The sedimentation column was filled with a culture of C. sorokiniana BR001, and the cell suspension was homogenized using a rod for 1 min to ensure its uniform distribution along the column. Then, 10 mL of samples were collected from top to bottom of the column using the column scale as reference (0, 20, 40, 60 and 80 cm) in different times (0, 30, 180, 240, 300 and 360 min).
Optical density at 670 nm of the samples was determined using a UV-Vis spectrophotometer. Biomass dry weight was determined according to a standard curve correlating the optical density against different dry weights of the C. sorokiniana BR001. Recovery efficiency was calculated according to equation 1.
$Recoveryefficiency\left(%\right)=\frac{massofmicroalgarecoverd×100}{massofmicroalgainitialculture}$ (1)
Biomass harvest by flocculation
Flocculation of C. sorokiniana BR001 biomass was performed using ferric sulfate or aluminum sulfate. The culture of C. sorokiniana BR001 was poured into a 500 mL beaker and the flocculant was added. The beaker was placed in the jar test apparatus and maintained for 10 seconds at 160 rpm and 25 ºC, then the rotation was reduced to 20 rpm and kept for more 5 min. The jar test apparatus is the equipment used for the uniform stirring of multiple samples for the evaluation of different types and doses of flocculant. The maximum speed achieved by the jar test apparatus was 160 rpm (velocity gradient of about 340 s-1). Rotation of the jar test apparatus was turned off and samples were taken at different times (15, 30 and 60 min) during the flocculation process for determination of the recovery efficiency (Equation 1).
The following concentrations of ferric sulfate were used (g L-1): 0; 0.005; 0.01; 0.025; 0.05; 0.1; 0.17; 0.25; 0.33; 0.5 and 1. The concentrations of aluminum sulfate used where (g L-1): 0; 0.025; 0.05; 0.083; 0.17; 0.25; 0.33; 0.42; 0.5; 0.67 and 0.83. Those optimum concentrations of flocculants were previously determined in preliminary tests. pH of the flocculent solutions was adjusted to 6 using 0.1 M L-1 NaOH prior the test.
Biomass harvest by centrifugation
Centrifugation of the culture of C. sorokiniana BR001 was performed at room temperature using five different speeds (300; 600; 1,400; 2,200 and 3,000 g) and times (15, 30, 60, 120 and 180 min). After the centrifugation samples of the upper phase were taken for estimation of the recovery efficiency (Equation 1).
Statistical analysis
The experiment was performed in a completely randomized factorial delineation. The results of the cultivation of C. sorokiniana BR001 in rich- and low-nitrogen media were submitted to analysis of variance, and means were compared by Duncan’s test at a 5% significance level. Results of biomass harvest by sedimentation were evaluated by response surface methodology, and the results of biomass harvest by flocculation and centrifugation were submitted to non-linear regression analysis. The results of this study are presented as mean ± standard deviation.
RESULTS AND DISCUSSION:
The strain C. sorokiniana BR001 cultivated in a low-nitrogen medium showed a content of total lipids 1.9 times higher (23.8 ± 4.5% in dry weight basis, DW) when compared to the cultivation with a rich-nitrogen medium (12.3 ± 1.2% DW). Cultivation using a low-nitrogen medium also allowed a significantly higher (P-value < 0.05) content of total neutral carbohydrates of (52.1 ± 1.5% DW) in comparison to the biomass produced using a rich-nitrogen medium (48.3 ± 3.3% DW). The high content of C-rich molecules suggests that the BR001 is a promising strain for advanced biofuels production (e.g. biodiesel and bioethanol). Thus, the evaluation of harvesting methods was evaluated using a culture of C. sorokiniana BR001 produced using a low-nitrogen medium.
Sedimentation is a low-cost process to harvest microalgae biomass. However, microalgae cell densities are generally similar to water density (MILLEDGE & HEAVEN, 2013MILLEDGE, J. J. et al. A review of the harvesting of micro-algae for biofuel production. Reviews in Environmental Science and Bio/Technology, Jun. 2013. v.12, n.2, p.165-178. Available from: <Available from: http://dx.doi.org/10.1007/s11157-012-9301-z >. Accessed: Jan. 20, 2020. doi: 10.1007/s11157-012-9301-z.
http://dx.doi.org/10.1007/s11157-012-930...
). The microalgal cells separate from the medium during the sedimentation process due to gravitation forces, but the similar density of microalgae and medium results in a slow separation (MILLEDGE & HEAVEN, 2013MILLEDGE, J. J. et al. A review of the harvesting of micro-algae for biofuel production. Reviews in Environmental Science and Bio/Technology, Jun. 2013. v.12, n.2, p.165-178. Available from: <Available from: http://dx.doi.org/10.1007/s11157-012-9301-z >. Accessed: Jan. 20, 2020. doi: 10.1007/s11157-012-9301-z.
http://dx.doi.org/10.1007/s11157-012-930...
). Media also show a density similar to the water since few grams of nutrients are added to them; for example, the low-nitrogen medium contains 99.4% (w w-1) of water in its composition (ILLMAN; SCRAGG; SHALES, 2000ILLMAN, A. M. et al. Increase in Chlorella strains calorific values when grown in low nitrogen medium. Enzyme and Microbial Technology, Nov. 2000. v.27, n.8, p.631-635. Available from: <Available from: http://dx.doi.org/10.1016/S0141-0229(00)00266-0 >. Accessed: Jan. 25, 2020. doi: 10.1016/S0141-0229(00)00266-0.
http://dx.doi.org/10.1016/S0141-0229(00)...
). Therefore, the efficiency of the sedimentation process was evaluated in C. sorokiniana BR001 cultivated under nitrogen starvation condition because self-flocculation is a trait observed only in some strains of the genus Chorella (ALAM et al., 2014ALAM, M. A. et al. Characterization of the flocculating agent from the spontaneously flocculating microalga Chlorella vulgaris JSC-7. Journal of Bioscience and Bioengineering, Jul. 2014. v.118, n.1, p.29-33. Available from: <Available from: http://dx.doi.org/10.1016/j.jbiosc.2013.12.021 >. Accessed: Jan. 17, 2020. doi: 10.1016/j.jbiosc.2013.12.021.
http://dx.doi.org/10.1016/j.jbiosc.2013....
; ESCAPA et al., 2015ESCAPA, C. et al. Nutrients and pharmaceuticals removal from wastewater by culture and harvesting of Chlorella sorokiniana. Bioresource Technology, Jun. 2015. v.185, p.276-284. Available from: <Available from: http://dx.doi.org/10.1016/j.biortech.2015.03.004 >. Accessed: Feb. 03, 2020. doi: 10.1016/j.biortech.2015.03.004.
http://dx.doi.org/10.1016/j.biortech.201...
; RAS et al., 2011RAS, M. et al. Experimental study on a coupled process of production and anaerobic digestion of Chlorella vulgaris. Bioresource Technology, Jan. 2011. v.102, n.1, p.200-206. Available from: <Available from: http://dx.doi.org/10.1016/j.biortech.2010.06.146 >. Accessed: Feb. 09, 2020. doi: 10.1016/j.biortech.2010.06.146.
http://dx.doi.org/10.1016/j.biortech.201...
). The sedimentation was evaluated using a response surface methodology, and the results showed that the recovery efficiency increased along the top to middle regions of the sedimentation column (Figure 1A). The highest recovery efficiencies were observed on the top of the column (i.e. 0 cm) and after 300 min of sedimentation (Figure 1A). However, the sedimentation process was slow and inefficient to harvest the C. sorokiniana BR001 biomass, and it was possible to recover only 30% of the biomass after 350 min (Figure 1A). These results clearly show that C. sorokiniana BR001 is not a self-flocculent strain.
Figure 1
Effect of different methods on the recovery efficiency of the biomass Chlorella sorokiniana BR001 cultivated under a nitrogen starvation condition. (A) Effect of the sedimentation process using different heights (top to bottom) and times in a sedimentation column. (B) Effect of different harvesting times and dosages of aluminum sulfate and (C) ferric sulfate. (D) Effect of the centrifugation process using different speeds and times.
A study showed that C. vulgaris JSC-7 is a self-flocculent strain and cell wall-associated polysaccharides containing a phosphodiester functional group might play an important role in the flocculent phenotype (ALAM et al., 2014ALAM, M. A. et al. Characterization of the flocculating agent from the spontaneously flocculating microalga Chlorella vulgaris JSC-7. Journal of Bioscience and Bioengineering, Jul. 2014. v.118, n.1, p.29-33. Available from: <Available from: http://dx.doi.org/10.1016/j.jbiosc.2013.12.021 >. Accessed: Jan. 17, 2020. doi: 10.1016/j.jbiosc.2013.12.021.
http://dx.doi.org/10.1016/j.jbiosc.2013....
). Self-flocculation of a C. sorokiniana strain was observed when this microalga was cultivated in swine manure wastewater and medium BG11 at the very high pH of 12 (ZHANG & CHEN, 2015ZHANG, B. et al. Effect of different organic matters on flocculation of Chlorella sorokiniana and optimization of flocculation conditions in swine manure wastewater. Bioresource Technology, Sep. 2015. v.192, p.774-780. Available from: <Available from: http://dx.doi.org/10.1016/j.biortech.2015.06.068 >. Accessed: Feb. 02, 2020. doi: 10.1016/j.biortech.2015.06.068.
http://dx.doi.org/10.1016/j.biortech.201...
). However, the self-flocculation of C. sorokiniana was not observed at pH 7 (ESCAPA et al., 2015ESCAPA, C. et al. Nutrients and pharmaceuticals removal from wastewater by culture and harvesting of Chlorella sorokiniana. Bioresource Technology, Jun. 2015. v.185, p.276-284. Available from: <Available from: http://dx.doi.org/10.1016/j.biortech.2015.03.004 >. Accessed: Feb. 03, 2020. doi: 10.1016/j.biortech.2015.03.004.
http://dx.doi.org/10.1016/j.biortech.201...
; XU; PURTON; BAGANZ, 2013XU, Y. et al. Chitosan flocculation to aid the harvesting of the microalga Chlorella sorokiniana. Bioresource Technology, Feb. 2013. v.129, p.296-301. Available from: <Available from: http://dx.doi.org/10.1016/j.biortech.2012.11.068 >. Accessed: Jan. 29, 2020. doi: 10.1016/j.biortech.2012.11.068.
http://dx.doi.org/10.1016/j.biortech.201...
; ZHANG & CHEN, 2015ZHANG, B. et al. Effect of different organic matters on flocculation of Chlorella sorokiniana and optimization of flocculation conditions in swine manure wastewater. Bioresource Technology, Sep. 2015. v.192, p.774-780. Available from: <Available from: http://dx.doi.org/10.1016/j.biortech.2015.06.068 >. Accessed: Feb. 02, 2020. doi: 10.1016/j.biortech.2015.06.068.
http://dx.doi.org/10.1016/j.biortech.201...
). Those results suggest that some C. vulgaris strains but not C. sorokiniana are able to self-flocculate at different values of pH. Moreover, flocculation using pH 12 requires high consumption of alkali, especially if the microalgal biomass shows buffering capacity, which might limit the adoption of this strategy in commercial algae farms.
The development of a fast process to harvest microalgae biomass produced in open cultivation systems is necessary to avoid contamination by fast-growing heterotrophic microorganisms that are unavoidably present in cultures produced in open cultivation systems, and changes in the biomass composition like the catabolism of carbohydrates and lipids. For that reason, flocculating agents can be used to promote the aggregation of microalgae cells and increase sedimentation rates (MILLEDGE & HEAVEN, 2013MILLEDGE, J. J. et al. A review of the harvesting of micro-algae for biofuel production. Reviews in Environmental Science and Bio/Technology, Jun. 2013. v.12, n.2, p.165-178. Available from: <Available from: http://dx.doi.org/10.1007/s11157-012-9301-z >. Accessed: Jan. 20, 2020. doi: 10.1007/s11157-012-9301-z.
http://dx.doi.org/10.1007/s11157-012-930...
). A detailed evaluation of flocculating agents is required because the type and dosage of the flocculation agent, medium composition, and microalgae species play an important role in the flocculation process (GRIMA et al., 2003GRIMA, E. M. et al. Recovery of microalgal biomass and metabolites: process options and economics. Biotechnology Advances, Jan. 2003. v.20, n.7-8, p.491-515. Available from: <Available from: http://dx.doi.org/10.1016/S0734-9750(02)00050-2 >. Accessed: Feb. 03, 2020. doi: 10.1016/S0734-9750(02)00050-2.
http://dx.doi.org/10.1016/S0734-9750(02)...
).
Herein, the flocculating agents aluminum sulfate and iron sulfate were evaluated on the sedimentation process of the non-flocculent C. sorokiniana BR001 using non-linear regression models that showed high coefficients of determination (R2 ≥ 0.92) (Figures 1B and 1C). Aluminum sulfate and iron sulfate were considered some of the best flocculating agents to harvest Chlorella cells (PAPAZI et al., 2010PAPAZI, A. et al. Harvesting Chlorella minutissima using cell coagulants. Journal of Applied Phycology, Jun. 2010. v.22, n.3, p.349-355. Available from: <Available from: http://dx.doi.org/10.1007/s10811-009-9465-2 >. Accessed: Feb. 14, 2020. doi: 10.1007/s10811-009-9465-2.
http://dx.doi.org/10.1007/s10811-009-946...
), and they resulted in higher efficiency recoveries of C. sorokiniana BR001 in comparison to the sedimentation process (Figures 1A to 1C). It was possible to recover more than 80% of the biomass using 0.5 g L-1 of aluminum sulfate and iron sulfate (Figures 1B and 1C). Aluminum sulfate and iron sulfate also reduced the duration of the process of biomass harvest, and it was possible to achieve high biomass recovery efficiencies after 15 min (Figures 1B and 1C).
According to the non-linear regression models, the flocculant dosage was the most important parameter to achieve high recovery efficiencies (Figures 1B and 1C). Both flocculating agents showed little differences in the recovery rates of BR001 biomass (Figures 1B and 1C). Interestingly, the different harvesting times evaluated in this study also showed little effect on the maximum recovery of biomass (Figures 1B and 1C). However, the flocculating dosage of 0.5 g L-1 resulted in a satisfactory biomass recovery and higher dosages showed little effect on the biomass recovery (Figures 1B and 1C). For instance, iron sulfate dosages of 0.5 g L-1 and 1 g L-1 resulted in recovery efficiencies of 81.2% and 85.1% after 15 min, respectively (Figure 1C). These results are in agreement with a previous study that showed that increasing the dosage of aluminum chloride induced the flocculation of C. sorokiniana (ZHANG & CHEN, 2015ZHANG, B. et al. Effect of different organic matters on flocculation of Chlorella sorokiniana and optimization of flocculation conditions in swine manure wastewater. Bioresource Technology, Sep. 2015. v.192, p.774-780. Available from: <Available from: http://dx.doi.org/10.1016/j.biortech.2015.06.068 >. Accessed: Feb. 02, 2020. doi: 10.1016/j.biortech.2015.06.068.
http://dx.doi.org/10.1016/j.biortech.201...
), and the optimum doses observed herein are in agreement with a previous study that evaluated the harvest of C. minutissima (PAPAZI; MAKRIDIS; DIVANACH, 2010PAPAZI, A. et al. Harvesting Chlorella minutissima using cell coagulants. Journal of Applied Phycology, Jun. 2010. v.22, n.3, p.349-355. Available from: <Available from: http://dx.doi.org/10.1007/s10811-009-9465-2 >. Accessed: Feb. 14, 2020. doi: 10.1007/s10811-009-9465-2.
http://dx.doi.org/10.1007/s10811-009-946...
).
ZHANG & CHEN (2015ZHANG, B. et al. Effect of different organic matters on flocculation of Chlorella sorokiniana and optimization of flocculation conditions in swine manure wastewater. Bioresource Technology, Sep. 2015. v.192, p.774-780. Available from: <Available from: http://dx.doi.org/10.1016/j.biortech.2015.06.068 >. Accessed: Feb. 02, 2020. doi: 10.1016/j.biortech.2015.06.068.
http://dx.doi.org/10.1016/j.biortech.201...
) showed that the optimum dosage of the flocculant varies according to the composition of the medium and pH. Low levels of aluminum chloride (e.g. 10 mg L-1) resulted in efficient flocculation of C. sorokiniana cultivated in medium BG11 (ZHANG & CHEN, 2015). In this current study, the use of 10 mg L-1 iron sulfate and 25 mg L-1 aluminum sulfate did not result in efficient flocculation of C. sorokiniana BR001 cultivated in a low-nitrogen medium (Figures 1C and 1D). Indeed, the low-nitrogen medium (ILLMAN; SCRAGG; SHALES, 2000ILLMAN, A. M. et al. Increase in Chlorella strains calorific values when grown in low nitrogen medium. Enzyme and Microbial Technology, Nov. 2000. v.27, n.8, p.631-635. Available from: <Available from: http://dx.doi.org/10.1016/S0141-0229(00)00266-0 >. Accessed: Jan. 25, 2020. doi: 10.1016/S0141-0229(00)00266-0.
http://dx.doi.org/10.1016/S0141-0229(00)...
) contains 3.7 times more nutrients (i.e. 6.3 g L-1) than the medium BG11 (i.e. 1.7 g L-1) (ANDERSEN, 2005ANDERSEN, R. A. Algal culturing techniques. 1st. ed. Amsterdam: Elsevier, 2005.). These different compositions of media are possibly related to the different efficiency recoveries observed in these studies.
Centrifugation is considered an efficient process to harvest microalgae biomass (BOROWITZKA & MOHEIMANI, 2013BOROWITZKA, M. A. et al. Algae for biofuels and energy. Dordrecht: Springer Netherlands, 2013. v.5. Available from: <Available from: http://dx.doi.org/10.1007/978-94-007-5479-9 >. Accessed: Jan. 21, 2020. doi: 10.1007/978-94-007-5479-9.
http://dx.doi.org/10.1007/978-94-007-547...
). Moreover, centrifugation can also be used in combination with other processes like flocculation, sedimentation, and filtration to develop a cheap and efficient process (BOROWITZKA & MOHEIMANI, 2013BOROWITZKA, M. A. et al. Algae for biofuels and energy. Dordrecht: Springer Netherlands, 2013. v.5. Available from: <Available from: http://dx.doi.org/10.1007/978-94-007-5479-9 >. Accessed: Jan. 21, 2020. doi: 10.1007/978-94-007-5479-9.
http://dx.doi.org/10.1007/978-94-007-547...
). However, previous studies did not evaluate the use of centrifuges to harvest the biomass of C. sorokiniana (XU; PURTON; BAGANZ, 2013XU, Y. et al. Chitosan flocculation to aid the harvesting of the microalga Chlorella sorokiniana. Bioresource Technology, Feb. 2013. v.129, p.296-301. Available from: <Available from: http://dx.doi.org/10.1016/j.biortech.2012.11.068 >. Accessed: Jan. 29, 2020. doi: 10.1016/j.biortech.2012.11.068.
http://dx.doi.org/10.1016/j.biortech.201...
; ZHANG & CHEN, 2015ZHANG, B. et al. Effect of different organic matters on flocculation of Chlorella sorokiniana and optimization of flocculation conditions in swine manure wastewater. Bioresource Technology, Sep. 2015. v.192, p.774-780. Available from: <Available from: http://dx.doi.org/10.1016/j.biortech.2015.06.068 >. Accessed: Feb. 02, 2020. doi: 10.1016/j.biortech.2015.06.068.
http://dx.doi.org/10.1016/j.biortech.201...
). High costs associated with the use of centrifuges can be reduced with a proper adjustment of the centrifugation process and the use of more efficient and low-cost centrifuge models (BOROWITZKA & MOHEIMANI, 2013BOROWITZKA, M. A. et al. Algae for biofuels and energy. Dordrecht: Springer Netherlands, 2013. v.5. Available from: <Available from: http://dx.doi.org/10.1007/978-94-007-5479-9 >. Accessed: Jan. 21, 2020. doi: 10.1007/978-94-007-5479-9.
http://dx.doi.org/10.1007/978-94-007-547...
). Thus, the effect of different centrifugation speeds and times harvest of C. sorokiniana BR001 cultivated in a low-nitrogen medium was evaluated in detail using non-linear regression models that showed high coefficients of determination (R2 > 0.99) (Figure 1D).
High recovery efficiencies were observed using centrifugation in comparison to the sedimentation and flocculation processes (Figure 1). It was possible to achieve high recovery efficiencies in this study using low centrifugal forces (e.g. 600 g) that are easily achieved by most of the industrial centrifuges. These results suggest that a robust and expensive centrifuge is not necessary to harvest the cells of C. sorokiniana BR001 cultivated in the low-nitrogen medium. High centrifuge speeds clearly improved the recovery efficiency using the different centrifugation times evaluated herein (Figure 1D). On the other hand, the centrifuge speed of 300 g was inefficient to harvest the biomass of C. sorokiniana BR001, and these recovery efficiencies were similar to those observed in the sedimentation process that resulted in a recovery efficiency lower than 40% (Figures 1A and 1D). However, centrifugation was much faster than the sedimentation process which increases the productivity of algae farms. Increasing the centrifuge speed to 600 g resulted in a significant increase in the biomass recovery, even using the shortest time of centrifugation evaluated in this study (Figure 1D). A remarkable advantage of centrifuges is the abolishing or reduction of the demand for flocculating agents that are potential contaminants for the biomass and water sources.
CONCLUSION:
The free sedimentation-based process does not result in an efficient harvest of the biomass of the non-flocculent strain Chlorella sorokiniana BR001 cultivated in a low-nitrogen medium. Conversely, the inclusion of ferric sulfate or aluminum sulfate in the sedimentation-based process allows recovery efficiencies higher than 80% in less than one hour, but a high concentration of these flocculent agents is necessary to achieve adequate recovery efficiencies. Centrifugation presents high recovery efficiency, and the centrifugation speed at 600 g can harvest more than 90% of the C. sorokiniana BR001 biomass in 5 min. Therefore, centrifuge-based methods are the best alternative to harvest the biomass of the non-flocculent strain Chlorella sorokiniana BR001 cultivated in a low-nitrogen medium.
ACKNOWLEDGEMENTS
We are thankful to the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq, grant 307147/2015-0). JS was supported by a fellowship from CNPq - Brazil (process: 155994/2018-2).
REFERENCES
• CR-2020-0293.R2
• Editors: Leandro Souza da Silva Gustavo Brunetto
Publication Dates
• Publication in this collection
26 July 2021
• Date of issue
2022
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What is the value of a ?
(1) a ^2 = b^2
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03 Apr 2013, 09:48
What is the value of a ?
(1) a ^2 = b^2. Clearly insufficient. But from this statement $$b^2-a^2=0$$ --> $$(b-a)(b+a)=0$$ --> $$b-a=0$$ or $$b+a=0$$.
(2) b − a = −12. Also clearly insufficient.
(1)+(2) Since from (2) $$b-a=-12\neq{0}$$, then from (1) $$b+a=0$$. So, we have two equations: $$b-a=-12$$ and $$b+a=0$$. Solving gives $$a=6$$ and $$b=-6$$. Sufficient.
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03 Apr 2013, 10:01
Thanks Bunuel....your explanation is much more easier than Kaplan's...
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Re: What is the value of a ? [#permalink]
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09 Apr 2013, 22:37
What is the value of a ?
1$$.a^2$$ = $$b^2$$
$$|a|=|b|$$ so or $$a=b$$ or $$a=-b$$, we have no value of b. Not sufficient
2.b - a = -12
Clearly not sufficient.
1+2
$$a-b=12$$, so from statement 1 we can deduce that a=-b ( it cannot be a=b because a-b=b-b=0 and not 12).
$$-b-b=12,b=-6$$ and $$a=6$$. C
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Re: What is the value of a ? [#permalink]
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09 Apr 2013, 23:24
subhendu009 wrote:
What is the value of a ?
1$$.a^2$$ = $$b^2$$
2.b - a = -12
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From F.S 1, we have (a-b)(a+b) = 0. Insufficient.
From F.S 2, we have b-a = -12. Insufficient.
Taking both together, we know that (a-b) is not equal to zero. Thus, (a+b) = 0, and we can get the value for a. Sufficient.
C.
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# gnuplot
Copyright (C) 1986 - 1993, 1998 Thomas Williams, Colin Kelley
Permission to use, copy, and distribute this software and its documentation for any purpose with or without fee is hereby granted, provided that the above copyright notice appear in all copies and that both that copyright notice and this permission notice appear in supporting documentation.
Permission to modify the software is granted, but not the right to distribute the complete modified source code. Modifications are to be distributed as patches to the released version. Permission to distribute binaries produced by compiling modified sources is granted, provided you
1. distribute the corresponding source modifications from the
released version in the form of a patch file along with the binaries,
in addition to the base release version number,
3. provide your name and address as the primary contact for the
support of your modified version, and
4. retain our contact information in regard to use of the base
software.
Permission to distribute the released version of the source code along with corresponding source modifications in the form of a patch file is granted with same provisions 2 through 4 for binary distributions.
This software is provided "as is" without express or implied warranty to the extent permitted by applicable law.
AUTHORS
Original Software:
Thomas Williams, Colin Kelley.
Gnuplot 2.0 additions:
Russell Lang, Dave Kotz, John Campbell.
Gnuplot 3.0 additions:
Gershon Elber and many others.
# Introduction
gnuplot is a command-driven interactive function and data plotting program. It is case sensitive (commands and function names written in lowercase are not the same as those written in CAPS). All command names may be abbreviated as long as the abbreviation is not ambiguous. Any number of commands may appear on a line (with the exception that load or call must be the final command), separated by semicolons (;). Strings are indicated with quotes. They may be either single or double quotation marks, e.g.,
load "filename"
cd 'dir'
although there are some subtle differences (see syntax for more details).
Any command-line arguments are assumed to be names of files containing gnuplot commands, with the exception of standard X11 arguments, which are processed first. Each file is loaded with the load command, in the order specified. gnuplot exits after the last file is processed. When no load files are named, gnuplot enters into an interactive mode. The special filename "-" is used to denote standard input. See "help batch/interactive" for more details.
Many gnuplot commands have multiple options. These options must appear in the proper order, although unwanted ones may be omitted in most cases. Thus if the entire command is "command a b c", then "command a c" will probably work, but "command c a" will fail.
Commands may extend over several input lines by ending each line but the last with a backslash (\). The backslash must be the _last_ character on each line. The effect is as if the backslash and newline were not there. That is, no white space is implied, nor is a comment terminated. Therefore, commenting out a continued line comments out the entire command (see comment). But note that if an error occurs somewhere on a multi-line command, the parser may not be able to locate precisely where the error is and in that case will not necessarily point to the correct line.
In this document, curly braces ({}) denote optional arguments and a vertical bar (|) separates mutually exclusive choices. gnuplot keywords or help topics are indicated by backquotes or boldface (where available). Angle brackets (<>) are used to mark replaceable tokens. In many cases, a default value of the token will be taken for optional arguments if the token is omitted, but these cases are not always denoted with braces around the angle brackets.
For on-line help on any topic, type help followed by the name of the topic or just help or ? to get a menu of available topics.
The new gnuplot user should begin by reading about plotting (if on-line, type help plotting). Simple Plots Demo
# Seeking-assistance
There is a mailing list for gnuplot users. Note, however, that the newsgroup
comp.graphics.apps.gnuplot
is identical to the mailing list (they both carry the same set of messages). We prefer that you read the messages through the newsgroup rather than subscribing to the mailing list. Administrative requests should be sent to
majordomo@dartmouth.edu
Send a message with the body (not the subject) consisting of the single word "help" (without the quotes) for more details.
The address for mailing to list members is:
info-gnuplot@dartmouth.edu
Bug reports and code contributions should be mailed to:
bug-gnuplot@dartmouth.edu
The list of those interested in beta-test versions is:
info-gnuplot-beta@dartmouth.edu
There is also a World Wide Web page with up-to-date information, including known bugs:
http://www.cs.dartmouth.edu/gnuplot_info.html
Before seeking help, please check the FAQ (Frequently Asked Questions) list. If you do not have a copy of the FAQ, you may request a copy by email from the Majordomo address above, ftp a copy from
ftp://ftp.ucc.ie/pub/gnuplot/faq,
ftp://ftp.gnuplot.vt.edu/pub/gnuplot/faq,
or see the WWW gnuplot page.
When posting a question, please include full details of the version of gnuplot, the machine, and operating system you are using. A _small_ script demonstrating the problem may be useful. Function plots are preferable to datafile plots. If email-ing to info-gnuplot, please state whether or not you are subscribed to the list, so that users who use news will know to email a reply to you. There is a form for such postings on the WWW site.
# What's New in version 3.7
Gnuplot version 3.7 contains many new features. This section gives a partial list and links to the new items in no particular order.
1. fit f(x) 'file' via uses the Marquardt-Levenberg method to fit data. (This is only slightly different from the gnufit patch available for 3.5.)
2. Greatly expanded using command. See plot using.
3. set timefmt allows for the use of dates as input and output for time series plots. See Time/Date data and timedat.dem.
4. Multiline labels and font selection in some drivers.
5. Minor (unlabeled) tics. See set mxtics.
6. key options for moving the key box in the page (and even outside of the plot), putting a title on it and a box around it, and more. See set key.
7. Multiplots on a single logical page with set multiplot.
8. Enhanced postscript driver with super/subscripts and font changes. (This was a separate driver (enhpost) that was available as a patch for 3.5.)
9. Second axes: use the top and right axes independently of the bottom and left, both for plotting and labels. See plot.
10. Special datafile names '-' and "". See plot special-filenames.
11. Additional coordinate systems for labels and arrows. See coordinates.
12. set size can try to plot with a specified aspect ratio.
13. set missing now treats missing data correctly.
14. The call command: load with arguments.
15. More flexible range commands with reverse and writeback keywords.
16. set encoding for multi-lingual encoding.
17. New x11 driver with persistent and multiple windows.
18. New plotting styles: xerrorbars, histeps, financebars and more. See set style.
19. New tic label formats, including "%l %L" which uses the mantissa and exponents to a given base for labels. See set format.
20. New drivers, including cgm for inclusion into MS-Office applications and gif for serving plots to the WEB.
21. Smoothing and spline-fitting options for plot. See plot smooth.
22. set margin and set origin give much better control over where a graph appears on the page.
23. set border now controls each border individually.
24. The new commands if and reread allow command loops.
25. Point styles and sizes, line types and widths can be specified on the plot command. Line types and widths can also be specified for grids, borders, tics and arrows. See plot with. Furthermore these types may be combined and stored for further use. See set linestyle.
26. Text (labels, tic labels, and the time stamp) can be written vertically by those terminals capable of doing so.
# Batch/Interactive Operation
gnuplot may be executed in either batch or interactive modes, and the two may even be mixed together on many systems.
Any command-line arguments are assumed to be names of files containing gnuplot commands (with the exception of standard X11 arguments, which are processed first). Each file is loaded with the load command, in the order specified. gnuplot exits after the last file is processed. When no load files are named, gnuplot enters into an interactive mode. The special filename "-" is used to denote standard input.
Both the exit and quit commands terminate the current command file and load the next one, until all have been processed.
Examples:
To launch an interactive session:
gnuplot
To launch a batch session using two command files "input1" and "input2":
gnuplot input1 input2
To launch an interactive session after an initialization file "header" and followed by another command file "trailer":
gnuplot header - trailer
# Command-line-editing
Command-line editing is supported by the Unix, Atari, VMS, MS-DOS and OS/2 versions of gnuplot. Also, a history mechanism allows previous commands to be edited and re-executed. After the command line has been edited, a newline or carriage return will enter the entire line without regard to where the cursor is positioned.
(The readline function in gnuplot is not the same as the readline used in GNU Bash and GNU Emacs. If the GNU version is desired, it may be selected instead of the gnuplot version at compile time.)
The editing commands are as follows:
Line-editing:
^B moves back a single character.
^F moves forward a single character.
^A moves to the beginning of the line.
^E moves to the end of the line.
^H and DEL delete the previous character.
^D deletes the current character.
^K deletes from current position to the end of line.
^L,^R redraws line in case it gets trashed.
^U deletes the entire line.
^W deletes the last word.
History:
^P moves back through history.
^N moves forward through history.
On the IBM PC, the use of a TSR program such as DOSEDIT or CED may be desired for line editing. The default makefile assumes that this is the case; by default gnuplot will be compiled with no line-editing capability. If you want to use gnuplot's line editing, set READLINE in the makefile and add readline.obj to the link file. The following arrow keys may be used on the IBM PC and Atari versions if readline is used:
Left Arrow - same as ^B.
Right Arrow - same as ^F.
Ctrl Left Arrow - same as ^A.
Ctrl Right Arrow - same as ^E.
Up Arrow - same as ^P.
Down Arrow - same as ^N.
Undo - same as ^L.
Home - same as ^A.
Ctrl Home - same as ^E.
Esc - same as ^U.
Help - help plus return.
Ctrl Help - help .
Comments are supported as follows: a # may appear in most places in a line and gnuplot will ignore the rest of the line. It will not have this effect inside quotes, inside numbers (including complex numbers), inside command substitutions, etc. In short, it works anywhere it makes sense to work.
# Coordinates
The commands set arrow, set key, and set label allow you to draw something at an arbitrary position on the graph. This position is specified by the syntax:
{<system>} <x>, {<system>} <y> {,{<system>} <z>}
Each <system> can either be first, second, graph or screen.
first places the x, y, or z coordinate in the system defined by the left and bottom axes; second places it in the system defined by the second axes (top and right); graph specifies the area within the axes---0,0 is bottom left and 1,1 is top right (for splot, 0,0,0 is bottom left of plotting area; use negative z to get to the base---see set ticslevel); and screen specifies the screen area (the entire area---not just the portion selected by set size), with 0,0 at bottom left and 1,1 at top right.
If the coordinate system for x is not specified, first is used. If the system for y is not specified, the one used for x is adopted.
If one (or more) axis is timeseries, the appropriate coordinate should be given as a quoted time string according to the timefmt format string. See set xdata and set timefmt. gnuplot will also accept an integer expression, which will be interpreted as seconds from 1 January 2000.
# Environment
A number of shell environment variables are understood by gnuplot. None of these are required, but may be useful.
If GNUTERM is defined, it is used as the name of the terminal type to be used. This overrides any terminal type sensed by gnuplot on start-up, but is itself overridden by the .gnuplot (or equivalent) start-up file (see start-up) and, of course, by later explicit changes.
On Unix, AmigaOS, AtariTOS, MS-DOS and OS/2, GNUHELP may be defined to be the pathname of the HELP file (gnuplot.gih).
On VMS, the logical name GNUPLOT$HELP should be defined as the name of the help library for gnuplot. The gnuplot help can be put inside any system help library, allowing access to help from both within and outside gnuplot if desired. On Unix, HOME is used as the name of a directory to search for a .gnuplot file if none is found in the current directory. On AmigaOS, AtariTOS, MS-DOS and OS/2, gnuplot is used. On VMS, SYS$LOGIN: is used. See help start-up.
On Unix, PAGER is used as an output filter for help messages.
On Unix, AtariTOS and AmigaOS, SHELL is used for the shell command. On MS-DOS and OS/2, COMSPEC is used for the shell command.
On MS-DOS, if the BGI or Watcom interface is used, PCTRM is used to tell the maximum resolution supported by your monitor by setting it to S<max. horizontal resolution>. E.g. if your monitor's maximum resolution is 800x600, then use:
set PCTRM=S800
If PCTRM is not set, standard VGA is used.
FIT_SCRIPT may be used to specify a gnuplot command to be executed when a fit is interrupted---see fit. FIT_LOG specifies the filename of the logfile maintained by fit.
# Expressions
In general, any mathematical expression accepted by C, FORTRAN, Pascal, or BASIC is valid. The precedence of these operators is determined by the specifications of the C programming language. White space (spaces and tabs) is ignored inside expressions.
Complex constants are expressed as {<real>,<imag>}, where <real> and <imag> must be numerical constants. For example, {3,2} represents 3 + 2i; {0,1} represents 'i' itself. The curly braces are explicitly required here.
Note that gnuplot uses both "real" and "integer" arithmetic, like FORTRAN and C. Integers are entered as "1", "-10", etc; reals as "1.0", "-10.0", "1e1", 3.5e-1, etc. The most important difference between the two forms is in division: division of integers truncates: 5/2 = 2; division of reals does not: 5.0/2.0 = 2.5. In mixed expressions, integers are "promoted" to reals before evaluation: 5/2e0 = 2.5. The result of division of a negative integer by a positive one may vary among compilers. Try a test like "print -5/2" to determine if your system chooses -2 or -3 as the answer.
The real and imaginary parts of complex expressions are always real, whatever the form in which they are entered: in {3,2} the "3" and "2" are reals, not integers.
## Functions
The functions in gnuplot are the same as the corresponding functions in the Unix math library, except that all functions accept integer, real, and complex arguments, unless otherwise noted.
For those functions that accept or return angles that may be given in either degrees or radians (sin(x), cos(x), tan(x), asin(x), acos(x), atan(x), atan2(x) and arg(z)), the unit may be selected by set angles, which defaults to radians.
### abs
The abs(x) function returns the absolute value of its argument. The returned value is of the same type as the argument.
For complex arguments, abs(x) is defined as the length of x in the complex plane [i.e., sqrt(real(x)**2 + imag(x)**2) ].
### acosh
The acosh(x) function returns the inverse hyperbolic cosine of its argument in radians.
### asin
The asin(x) function returns the arc sin (inverse sin) of its argument. asin returns its argument in radians or degrees, as selected by set angles.
### asinh
The asinh(x) function returns the inverse hyperbolic sin of its argument in radians.
### atanh
The atanh(x) function returns the inverse hyperbolic tangent of its argument in radians.
### besj0
The besj0(x) function returns the j0th Bessel function of its argument. besj0 expects its argument to be in radians.
### besj1
The besj1(x) function returns the j1st Bessel function of its argument. besj1 expects its argument to be in radians.
### besy0
The besy0 function returns the y0th Bessel function of its argument. besy0 expects its argument to be in radians.
### besy1
The besy1(x) function returns the y1st Bessel function of its argument. besy1 expects its argument to be in radians.
### ceil
The ceil(x) function returns the smallest integer that is not less than its argument. For complex numbers, ceil returns the smallest integer not less than the real part of its argument.
### cosh
The cosh(x) function returns the hyperbolic cosine of its argument. cosh expects its argument to be in radians.
### erf
The erf(x) function returns the error function of the real part of its argument. If the argument is a complex value, the imaginary component is ignored.
### erfc
The erfc(x) function returns 1.0 - the error function of the real part of its argument. If the argument is a complex value, the imaginary component is ignored.
### exp
The exp(x) function returns the exponential function of its argument (e raised to the power of its argument). On some implementations (notably suns), exp(-x) returns undefined for very large x. A user-defined function like safe(x) = x<-100 ? 0 : exp(x) might prove useful in these cases.
### floor
The floor(x) function returns the largest integer not greater than its argument. For complex numbers, floor returns the largest integer not greater than the real part of its argument.
### gamma
The gamma(x) function returns the gamma function of the real part of its argument. For integer n, gamma(n+1) = n!. If the argument is a complex value, the imaginary component is ignored.
### ibeta
The ibeta(p,q,x) function returns the incomplete beta function of the real parts of its arguments. p, q > 0 and x in [0:1]. If the arguments are complex, the imaginary components are ignored.
### inverf
The inverf(x) function returns the inverse error function of the real part of its argument.
### igamma
The igamma(a,x) function returns the incomplete gamma function of the real parts of its arguments. a > 0 and x >= 0. If the arguments are complex, the imaginary components are ignored.
### imag
The imag(x) function returns the imaginary part of its argument as a real number.
### invnorm
The invnorm(x) function returns the inverse normal distribution function of the real part of its argument.
### int
The int(x) function returns the integer part of its argument, truncated toward zero.
### lgamma
The lgamma(x) function returns the natural logarithm of the gamma function of the real part of its argument. If the argument is a complex value, the imaginary component is ignored.
### log
The log(x) function returns the natural logarithm (base e) of its argument.
### log10
The log10(x) function returns the logarithm (base 10) of its argument.
### norm
The norm(x) function returns the normal distribution function (or Gaussian) of the real part of its argument.
### rand
The rand(x) function returns a pseudo random number in the interval [0:1] using the real part of its argument as a seed. If seed < 0, the sequence is (re)initialized. If the argument is a complex value, the imaginary component is ignored.
### real
The real(x) function returns the real part of its argument.
### sgn
The sgn(x) function returns 1 if its argument is positive, -1 if its argument is negative, and 0 if its argument is 0. If the argument is a complex value, the imaginary component is ignored.
### sinh
The sinh(x) function returns the hyperbolic sine of its argument. sinh expects its argument to be in radians.
### sqrt
The sqrt(x) function returns the square root of its argument.
### tanh
The tanh(x) function returns the hyperbolic tangent of its argument. tanh expects its argument to be in radians.
A few additional functions are also available.
### column
column(x) may be used only in expressions as part of using manipulations to fits or datafile plots. See plot datafile using.
### tm_hour
The tm_hour function interprets its argument as a time, in seconds from 1 Jan 2000. It returns the hour (an integer in the range 0--23) as a real.
### tm_mday
The tm_mday function interprets its argument as a time, in seconds from 1 Jan 2000. It returns the day of the month (an integer in the range 1--31) as a real.
### tm_min
The tm_min function interprets its argument as a time, in seconds from 1 Jan 2000. It returns the minute (an integer in the range 0--59) as a real.
### tm_mon
The tm_mon function interprets its argument as a time, in seconds from 1 Jan 2000. It returns the month (an integer in the range 1--12) as a real.
### tm_sec
The tm_sec function interprets its argument as a time, in seconds from 1 Jan 2000. It returns the second (an integer in the range 0--59) as a real.
### tm_wday
The tm_wday function interprets its argument as a time, in seconds from 1 Jan 2000. It returns the day of the week (an integer in the range 1--7) as a real.
### tm_yday
The tm_yday function interprets its argument as a time, in seconds from 1 Jan 2000. It returns the day of the year (an integer in the range 1--366) as a real.
### tm_year
The tm_year function interprets its argument as a time, in seconds from 1 Jan 2000. It returns the year (an integer) as a real.
### valid
valid(x) may be used only in expressions as part of using manipulations to fits or datafile plots. See plot datafile using. Use of functions and complex variables for airfoils
## Operators
The operators in gnuplot are the same as the corresponding operators in the C programming language, except that all operators accept integer, real, and complex arguments, unless otherwise noted. The ** operator (exponentiation) is supported, as in FORTRAN.
Parentheses may be used to change order of evaluation.
### Unary
The following is a list of all the unary operators and their usages:
Symbol Example Explanation
- -a unary minus
+ +a unary plus (no-operation)
~ ~a * one's complement
! !a * logical negation
! a! * factorial
3 * call arg/column during using manipulation
(*) Starred explanations indicate that the operator requires an integer argument.
Operator precedence is the same as in Fortran and C. As in those languages, parentheses may be used to change the order of operation. Thus -2**2 = -4, but (-2)**2 = 4.
The factorial operator returns a real number to allow a greater range.
### Binary
The following is a list of all the binary operators and their usages:
Symbol Example Explanation
** a**b exponentiation
* a*b multiplication
/ a/b division
% a%b * modulo
- a-b subtraction
== a==b equality
!= a!=b inequality
< a<b less than
<= a<=b less than or equal to
> a>b greater than
>= a>=b greater than or equal to
& a&b * bitwise AND
^ a^b * bitwise exclusive OR
| a|b * bitwise inclusive OR
&& a&&b * logical AND
|| a||b * logical OR
(*) Starred explanations indicate that the operator requires integer arguments.
Logical AND (&&) and OR (||) short-circuit the way they do in C. That is, the second && operand is not evaluated if the first is false; the second || operand is not evaluated if the first is true.
### Ternary
There is a single ternary operator:
Symbol Example Explanation
?: a?b:c ternary operation
The ternary operator behaves as it does in C. The first argument (a), which must be an integer, is evaluated. If it is true (non-zero), the second argument (b) is evaluated and returned; otherwise the third argument (c) is evaluated and returned.
The ternary operator is very useful both in constructing piecewise functions and in plotting points only when certain conditions are met.
Examples:
Plot a function that is to equal sin(x) for 0 <= x < 1, 1/x for 1 <= x < 2, and undefined elsewhere:
f(x) = 0<=x && x<1 ? sin(x) : 1<=x && x<2 ? 1/x : 1/0
plot f(x)
Note that gnuplot quietly ignores undefined values, so the final branch of the function (1/0) will produce no plottable points. Note also that f(x) will be plotted as a continuous function across the discontinuity if a line style is used. To plot it discontinuously, create separate functions for the two pieces. (Parametric functions are also useful for this purpose.)
For data in a file, plot the average of the data in columns 2 and 3 against the datum in column 1, but only if the datum in column 4 is non-negative:
plot 'file' using 1:( $4<0 ? 1/0 : ($2+$3)/2 ) Please see plot data-file using for an explanation of the using syntax. ## User-defined User-defined function syntax: <func-name>( <dummy1> {,<dummy2>} ... {,<dummy5>} ) = <expression> where <expression> is defined in terms of <dummy1> through <dummy5>. User-defined variable syntax: <variable-name> = <constant-expression> Examples: w = 2 q = floor(tan(pi/2 - 0.1)) f(x) = sin(w*x) sinc(x) = sin(pi*x)/(pi*x) delta(t) = (t == 0) ramp(t) = (t > 0) ? t : 0 min(a,b) = (a < b) ? a : b comb(n,k) = n!/(k!*(n-k)!) len3d(x,y,z) = sqrt(x*x+y*y+z*z) plot f(x) = sin(x*a), a = 0.2, f(x), a = 0.4, f(x) Note that the variable pi is already defined. But it is in no way magic; you may redefine it to be whatever you like. Valid names are the same as in most programming languages: they must begin with a letter, but subsequent characters may be letters, digits, "$", or "_". Note, however, that the fit mechanism uses several variables with names that begin "FIT_". It is safest to avoid using such names. "FIT_LIMIT", however, is one that you may wish to redefine. See the documentation on fit for details.
See show functions, show variables, and fit.
# Glossary
Throughout this document an attempt has been made to maintain consistency of nomenclature. This cannot be wholly successful because as gnuplot has evolved over time, certain command and keyword names have been adopted that preclude such perfection. This section contains explanations of the way some of these terms are used.
A "page" or "screen" is the entire area addressable by gnuplot. On a monitor, it is the full screen; on a plotter, it is a single sheet of paper.
A screen may contain one or more "plots". A plot is defined by an abscissa and an ordinate, although these need not actually appear on it, as well as the margins and any text written therein.
A plot contains one "graph". A graph is defined by an abscissa and an ordinate, although these need not actually appear on it.
A graph may contain one or more "lines". A line is a single function or data set. "Line" is also a plotting style. The word will also be used in sense "a line of text". Presumably the context will remove any ambiguity.
The lines on a graph may have individual names. These may be listed together with a sample of the plotting style used to represent them in the "key", sometimes also called the "legend".
The word "title" occurs with multiple meanings in gnuplot. In this document, it will always be preceded by the adjective "plot", "line", or "key" to differentiate among them.
A graph may have up to four labelled axes. Various commands have the name of an axis built into their names, such as set xlabel. Other commands have one or more axis names as options, such as set logscale xy. The names of the four axes for these usages are "x" for the axis along the bottom border of the plot, "y" for the left border, "x2" for the top border, and "y2" for the right border. "z" also occurs in commands used with 3-d plotting.
When discussing data files, the term "record" will be resurrected and used to denote a single line of text in the file, that is, the characters between newline or end-of-record characters. A "point" is the datum extracted from a single record. A "datablock" is a set of points from consecutive records, delimited by blank records. A line, when referred to in the context of a data file, is a subset of a datablock.
# Plotting
There are three gnuplot commands which actually create a plot: plot, splot and replot. plot generates 2-d plots, splot generates 3-d plots (actually 2-d projections, of course), and replot appends its arguments to the previous plot or splot and executes the modified command.
Much of the general information about plotting can be found in the discussion of plot; information specific to 3-d can be found in the splot section.
plot operates in either rectangular or polar coordinates -- see set polar for details of the latter. splot operates only in rectangular coordinates, but the set mapping command allows for a few other coordinate systems to be treated. In addition, the using option allows both plot and splot to treat almost any coordinate system you'd care to define.
splot can plot surfaces and contours in addition to points and/or lines. In addition to splot, see set isosamples for information about defining the grid for a 3-d function; splot datafile for information about the requisite file structure for 3-d data values; and set contour and set cntrparam for information about contours.
# Start-up
When gnuplot is run, it looks for an initialization file to load. This file is called .gnuplot on Unix and AmigaOS systems, and GNUPLOT.INI on other systems. If this file is not found in the current directory, the program will look for it in the home directory (under AmigaOS, Atari(single)TOS, MS-DOS and OS/2, the environment variable gnuplot should contain the name of this directory). Note: if NOCWDRC is defined during the installation, gnuplot will not read from the current directory.
If the initialization file is found, gnuplot executes the commands in it. These may be any legal gnuplot commands, but typically they are limited to setting the terminal and defining frequently-used functions or variables.
# Substitution
Newlines in the output produced by the spawned command are replaced with blanks.
Command-line substitution can be used anywhere on the gnuplot command line.
Example:
This will run the program leastsq and replace leastsq (including backquotes) on the command line with its output:
f(x) = leastsq
or, in VMS
f(x) = run leastsq
# Syntax
The general rules of syntax and punctuation in gnuplot are that keywords and options are order-dependent. Options and any accompanying parameters are separated by spaces whereas lists and coordinates are separated by commas. Ranges are separated by colons and enclosed in brackets [], text and file names are enclosed in quotes, and a few miscellaneous things are enclosed in parentheses. Braces {} are used for a few special purposes.
Commas are used to separate coordinates on the set commands arrow, key, and label; the list of variables being fitted (the list after the via keyword on the fit command); lists of discrete contours or the loop parameters which specify them on the set cntrparam command; the arguments of the set commands dgrid3d, dummy, isosamples, offsets, origin, samples, size, time, and view; lists of tics or the loop parameters which specify them; the offsets for titles and axis labels; parametric functions to be used to calculate the x, y, and z coordinates on the plot, replot and splot commands; and the complete sets of keywords specifying individual plots (data sets or functions) on the plot, replot and splot commands.
Parentheses are used to delimit sets of explicit tics (as opposed to loop parameters) and to indicate computations in the using filter of the fit, plot, replot and splot commands.
(Parentheses and commas are also used as usual in function notation.)
Brackets are used to delimit ranges, whether they are given on set, plot or splot commands.
Colons are used to separate extrema in range specifications (whether they are given on set, plot or splot commands) and to separate entries in the using filter of the plot, replot, splot and fit commands.
Semicolons are used to separate commands given on a single command line.
Braces are used in text to be specially processed by some terminals, like postscript. They are also used to denote complex numbers: {3,2} = 3 + 2i.
Text may be enclosed in single- or double-quotes. Backslash processing of sequences like \n (newline) and \345 (octal character code) is performed for double-quoted strings, but not for single-quoted strings.
The justification is the same for each line of a multi-line string. Thus the center-justified string
"This is the first line of text.\nThis is the second line."
will produce
This is the first line of text.
This is the second line.
but
'This is the first line of text.\nThis is the second line.'
will produce
This is the first line of text.\nThis is the second line.
Filenames may be entered with either single- or double-quotes. In this manual the command examples generally single-quote filenames and double-quote other string tokens for clarity.
At present you should not embed \n inside {} when using the enhanced option of the postscript terminal.
The EEPIC, Imagen, Uniplex, LaTeX, and TPIC drivers allow a newline to be specified by \\ in a single-quoted string or \\\\ in a double-quoted string.
Back-quotes are used to enclose system commands for substitution.
# Time/Date data
gnuplot supports the use of time and/or date information as input data. This feature is activated by the commands set xdata time, set ydata time, etc.
Internally all times and dates are converted to the number of seconds from the year 2000. The command set timefmt defines the format for all inputs: data files, ranges, tics, label positions---in short, anything that accepts a data value must receive it in this format. Since only one input format can be in force at a given time, all time/date quantities being input at the same time must be presented in the same format. Thus if both x and y data in a file are time/date, they must be in the same format.
The conversion to and from seconds assumes Universal Time (which is the same as Greenwich Standard Time). There is no provision for changing the time zone or for daylight savings. If all your data refer to the same time zone (and are all either daylight or standard) you don't need to worry about these things. But if the absolute time is crucial for your application, you'll need to convert to UT yourself.
Commands like show xrange will re-interpret the integer according to timefmt. If you change timefmt, and then show the quantity again, it will be displayed in the new timefmt. For that matter, if you give the deactivation command (like set xdata), the quantity will be shown in its numerical form.
The command set format defines the format that will be used for tic labels, whether or not the specified axis is time/date.
If time/date information is to be plotted from a file, the using option _must_ be used on the plot or splot command. These commands simply use white space to separate columns, but white space may be embedded within the time/date string. If you use tabs as a separator, some trial-and-error may be necessary to discover how your system treats them.
The following example demonstrates time/date plotting.
Suppose the file "data" contains records like
03/21/95 10:00 6.02e23
This file can be plotted by
set xdata time
set timefmt "%m/%d/%y"
set xrange ["03/21/95":"03/22/95"]
set format x "%m/%d"
set timefmt "%m/%d/%y %H:%M"
plot "data" using 1:3
which will produce xtic labels that look like "03/21".
See the descriptions of each command for more details.
# Commands
This section lists the commands acceptable to gnuplot in alphabetical order. Printed versions of this document contain all commands; on-line versions may not be complete. Indeed, on some systems there may be no commands at all listed under this heading.
Note that in most cases unambiguous abbreviations for command names and their options are permissible, i.e., "p f(x) w l" instead of "plot f(x) with lines".
In the syntax descriptions, braces ({}) denote optional arguments and a vertical bar (|) separates mutually exclusive choices.
# cd
The cd command changes the working directory.
Syntax:
cd '<directory-name>'
The directory name must be enclosed in quotes.
Examples:
cd 'subdir'
cd ".."
DOS users _must_ use single-quotes---backslash [\] has special significance inside double-quotes. For example,
cd "c:\newdata"
fails, but
cd 'c:\newdata'
works as expected.
# call
The call command _must_ be the last command on a multi-command line.
Syntax:
call "<input-file>" <parameter-0> <parm-1> ... <parm-9>
The name of the input file must be enclosed in quotes, and it is recommended that parameters are similarly enclosed in quotes (future versions of gnuplot may treat quoted and unquoted arguments differently).
Example:
If the file 'calltest.gp' contains the line:
print "p0=$0 p1=$1 p2=$2 p3=$3 p4=$4 p5=$5 p6=$6 p7=x$7x"
entering the command:
call 'calltest.gp' "abcd" 1.2 + "'quoted'" -- "$2" will display: p0=abcd p1=1.2 p2=+ p3='quoted' p4=- p5=- p6=$2 p7=xx
NOTE: there is a clash in syntax with the datafile using callback operator. Use n or column(n) to access column n from a datafile inside a called datafile plot. # clear The clear command erases the current screen or output device as specified by set output. This usually generates a formfeed on hardcopy devices. Use set terminal to set the device type. For some terminals clear erases only the portion of the plotting surface defined by set size, so for these it can be used in conjunction with set multiplot to create an inset. Example: set multiplot plot sin(x) set origin 0.5,0.5 set size 0.4,0.4 clear plot cos(x) set nomultiplot Please see set multiplot, set size, and set origin for details of these commands. # exit The commands exit and quit and the END-OF-FILE character will exit the current gnuplot command file and load the next one. See "help batch/interactive" for more details. Each of these commands will clear the output device (as does the clear command) before exiting. # fit The fit command can fit a user-defined function to a set of data points (x,y) or (x,y,z), using an implementation of the nonlinear least-squares (NLLS) Marquardt-Levenberg algorithm. Any user-defined variable occurring in the function body may serve as a fit parameter, but the return type of the function must be real. Syntax: fit {[xrange] {[yrange]}} <function> '<datafile>' {datafile-modifiers} via '<parameter file>' | <var1>{,<var2>,...} Ranges may be specified to temporarily limit the data which is to be fitted; any out-of-range data points are ignored. The syntax is [{dummy_variable=}{<min>}{:<max>}], <function> is any valid gnuplot expression, although it is usual to use a previously user-defined function of the form f(x) or f(x,y). <datafile> is treated as in the plot command. All the plot datafile modifiers (using, every,...) except smooth are applicable to fit. See plot datafile. The default data formats for fitting functions with a single independent variable, y=f(x), are {x:}y or x:y:s; those formats can be changed with the datafile using qualifier. The third item, (a column number or an expression), if present, is interpreted as the standard deviation of the corresponding y value and is used to compute a weight for the datum, 1/s**2. Otherwise, all data points are weighted equally, with a weight of one. To fit a function with two independent variables, z=f(x,y), the required format is using with four items, x:y:z:s. The complete format must be given---no default columns are assumed for a missing token. Weights for each data point are evaluated from 's' as above. If error estimates are not available, a constant value can be specified as a constant expression (see plot datafile using), e.g., using 1:2:3:(1). Multiple datasets may be simultaneously fit with functions of one independent variable by making y a 'pseudo-variable', e.g., the dataline number, and fitting as two independent variables. See fit multibranch. The via qualifier specifies which parameters are to be adjusted, either directly, or by referencing a parameter file. Examples: f(x) = a*x**2 + b*x + c g(x,y) = a*x**2 + b*y**2 + c*x*y FIT_LIMIT = 1e-6 fit f(x) 'measured.dat' via 'start.par' fit f(x) 'measured.dat' using 3:(7-5) via 'start.par' fit f(x) './data/trash.dat' using 1:2:3 via a, b, c fit g(x,y) 'surface.dat' using 1:2:3:(1) via a, b, c After each iteration step, detailed information about the current state of the fit is written to the display. The same information about the initial and final states is written to a log file, "fit.log". This file is always appended to, so as to not lose any previous fit history; it should be deleted or renamed as desired. The fit may be interrupted by pressing Ctrl-C (any key but Ctrl-C under MSDOS and Atari Multitasking Systems). After the current iteration completes, you have the option to (1) stop the fit and accept the current parameter values, (2) continue the fit, (3) execute a gnuplot command as specified by the environment variable FIT_SCRIPT. The default for FIT_SCRIPT is replot, so if you had previously plotted both the data and the fitting function in one graph, you can display the current state of the fit. Once fit has finished, the update command may be used to store final values in a file for subsequent use as a parameter file. See update for details. ## adjustable parameters There are two ways that via can specify the parameters to be adjusted, either directly on the command line or indirectly, by referencing a parameter file. The two use different means to set initial values. Adjustable parameters can be specified by a comma-separated list of variable names after the via keyword. Any variable that is not already defined is is created with an initial value of 1.0. However, the fit is more likely to converge rapidly if the variables have been previously declared with more appropriate starting values. In a parameter file, each parameter to be varied and a corresponding initial value are specified, one per line, in the form varname = value Comments, marked by '#', and blank lines are permissible. The special form varname = value # FIXED means that the variable is treated as a 'fixed parameter', initialized by the parameter file, but not adjusted by fit. For clarity, it may be useful to designate variables as fixed parameters so that their values are reported by fit. The keyword # FIXED has to appear in exactly this form. ## beginner's guide fit is used to find a set of parameters that 'best' fits your data to your user-defined function. The fit is judged on the basis of the the sum of the squared differences or 'residuals' (SSR) between the input data points and the function values, evaluated at the same places. This quantity is often called 'chisquare' (i.e., the Greek letter chi, to the power of 2). The algorithm attempts to minimize SSR, or more precisely, WSSR, as the residuals are 'weighted' by the input data errors (or 1.0) before being squared; see fit error_estimates for details. That's why it is called 'least-squares fitting'. Let's look at an example to see what is meant by 'non-linear', but first we had better go over some terms. Here it is convenient to use z as the dependent variable for user-defined functions of either one independent variable, z=f(x), or two independent variables, z=f(x,y). A parameter is a user-defined variable that fit will adjust, i.e., an unknown quantity in the function declaration. Linearity/non-linearity refers to the relationship of the dependent variable, z, to the parameters which fit is adjusting, not of z to the independent variables, x and/or y. (To be technical, the second {and higher} derivatives of the fitting function with respect to the parameters are zero for a linear least-squares problem). For linear least-squares (LLS), the user-defined function will be a sum of simple functions, not involving any parameters, each multiplied by one parameter. NLLS handles more complicated functions in which parameters can be used in a large number of ways. An example that illustrates the difference between linear and nonlinear least-squares is the Fourier series. One member may be written as z=a*sin(c*x) + b*cos(c*x). If a and b are the unknown parameters and c is constant, then estimating values of the parameters is a linear least-squares problem. However, if c is an unknown parameter, the problem is nonlinear. In the linear case, parameter values can be determined by comparatively simple linear algebra, in one direct step. However LLS is a special case which is also solved along with more general NLLS problems by the iterative procedure that gnuplot uses. fit attempts to find the minimum by doing a search. Each step (iteration) calculates WSSR with a new set of parameter values. The Marquardt-Levenberg algorithm selects the parameter values for the next iteration. The process continues until a preset criterium is met, either (1) the fit has "converged" (the relative change in WSSR is less than FIT_LIMIT), or (2) it reaches a preset iteration count limit, FIT_MAXITER (see fit control variables). The fit may also be interrupted and subsequently halted from the keyboard (see fit). Often the function to be fitted will be based on a model (or theory) that attempts to describe or predict the behaviour of the data. Then fit can be used to find values for the free parameters of the model, to determine how well the data fits the model, and to estimate an error range for each parameter. See fit error_estimates. Alternatively, in curve-fitting, functions are selected independent of a model (on the basis of experience as to which are likely to describe the trend of the data with the desired resolution and a minimum number of parameters*functions.) The fit solution then provides an analytic representation of the curve. However, if all you really want is a smooth curve through your data points, the smooth option to plot may be what you've been looking for rather than fit. ## error estimates In fit, the term "error" is used in two different contexts, data error estimates and parameter error estimates. Data error estimates are used to calculate the relative weight of each data point when determining the weighted sum of squared residuals, WSSR or chisquare. They can affect the parameter estimates, since they determine how much influence the deviation of each data point from the fitted function has on the final values. Some of the fit output information, including the parameter error estimates, is more meaningful if accurate data error estimates have been provided. The 'statistical overview' describes some of the fit output and gives some background for the 'practical guidelines'. ### statistical overview The theory of non-linear least-squares (NLLS) is generally described in terms of a normal distribution of errors, that is, the input data is assumed to be a sample from a population having a given mean and a Gaussian (normal) distribution about the mean with a given standard deviation. For a sample of sufficiently large size, and knowing the population standard deviation, one can use the statistics of the chisquare distribution to describe a "goodness of fit" by looking at the variable often called "chisquare". Here, it is sufficient to say that a reduced chisquare (chisquare/degrees of freedom, where degrees of freedom is the number of datapoints less the number of parameters being fitted) of 1.0 is an indication that the weighted sum of squared deviations between the fitted function and the data points is the same as that expected for a random sample from a population characterized by the function with the current value of the parameters and the given standard deviations. If the standard deviation for the population is not constant, as in counting statistics where variance = counts, then each point should be individually weighted when comparing the observed sum of deviations and the expected sum of deviations. At the conclusion fit reports 'stdfit', the standard deviation of the fit, which is the rms of the residuals, and the variance of the residuals, also called 'reduced chisquare' when the data points are weighted. The number of degrees of freedom (the number of data points minus the number of fitted parameters) is used in these estimates because the parameters used in calculating the residuals of the datapoints were obtained from the same data. To estimate confidence levels for the parameters, one can use the minimum chisquare obtained from the fit and chisquare statistics to determine the value of chisquare corresponding to the desired confidence level, but considerably more calculation is required to determine the combinations of parameters which produce such values. Rather than determine confidence intervals, fit reports parameter error estimates which are readily obtained from the variance-covariance matrix after the final iteration. By convention, these estimates are called "standard errors" or "asymptotic standard errors", since they are calculated in the same way as the standard errors (standard deviation of each parameter) of a linear least-squares problem, even though the statistical conditions for designating the quantity calculated to be a standard deviation are not generally valid for the NLLS problem. The asymptotic standard errors are generally over-optimistic and should not be used for determining confidence levels, but are useful for qualitative purposes. The final solution also produces a correlation matrix, which gives an indication of the correlation of parameters in the region of the solution; if one parameter is changed, increasing chisquare, does changing another compensate? The main diagonal elements, autocorrelation, are all 1; if all parameters were independent, all other elements would be nearly 0. Two variables which completely compensate each other would have an off-diagonal element of unit magnitude, with a sign depending on whether the relation is proportional or inversely proportional. The smaller the magnitudes of the off-diagonal elements, the closer the estimates of the standard deviation of each parameter would be to the asymptotic standard error. ### practical guidelines If you have a basis for assigning weights to each data point, doing so lets you make use of additional knowledge about your measurements, e.g., take into account that some points may be more reliable than others. That may affect the final values of the parameters. Weighting the data provides a basis for interpreting the additional fit output after the last iteration. Even if you weight each point equally, estimating an average standard deviation rather than using a weight of 1 makes WSSR a dimensionless variable, as chisquare is by definition. Each fit iteration will display information which can be used to evaluate the progress of the fit. (An '*' indicates that it did not find a smaller WSSR and is trying again.) The 'sum of squares of residuals', also called 'chisquare', is the WSSR between the data and your fitted function; fit has minimized that. At this stage, with weighted data, chisquare is expected to approach the number of degrees of freedom (data points minus parameters). The WSSR can be used to calculate the reduced chisquare (WSSR/ndf) or stdfit, the standard deviation of the fit, sqrt(WSSR/ndf). Both of these are reported for the final WSSR. If the data are unweighted, stdfit is the rms value of the deviation of the data from the fitted function, in user units. If you supplied valid data errors, the number of data points is large enough, and the model is correct, the reduced chisquare should be about unity. (For details, look up the 'chi-squared distribution' in your favourite statistics reference.) If so, there are additional tests, beyond the scope of this overview, for determining how well the model fits the data. A reduced chisquare much larger than 1.0 may be due to incorrect data error estimates, data errors not normally distributed, systematic measurement errors, 'outliers', or an incorrect model function. A plot of the residuals, e.g., plot 'datafile' using 1:(2-f(1)), may help to show any systematic trends. Plotting both the data points and the function may help to suggest another model. Similarly, a reduced chisquare less than 1.0 indicates WSSR is less than that expected for a random sample from the function with normally distributed errors. The data error estimates may be too large, the statistical assumptions may not be justified, or the model function may be too general, fitting fluctuations in a particular sample in addition to the underlying trends. In the latter case, a simpler function may be more appropriate. You'll have to get used to both fit and the kind of problems you apply it to before you can relate the standard errors to some more practical estimates of parameter uncertainties or evaluate the significance of the correlation matrix. Note that fit, in common with most NLLS implementations, minimizes the weighted sum of squared distances (y-f(x))**2. It does not provide any means to account for "errors" in the values of x, only in y. Also, any "outliers" (data points outside the normal distribution of the model) will have an exaggerated effect on the solution. ## fit controlling There are a number of gnuplot variables that can be defined to affect fit. Those which can be defined once gnuplot is running are listed under 'control_variables' while those defined before starting gnuplot are listed under 'environment_variables'. ### control variables The default epsilon limit (1e-5) may be changed by declaring a value for FIT_LIMIT When the sum of squared residuals changes between two iteration steps by a factor less than this number (epsilon), the fit is considered to have 'converged'. The maximum number of iterations may be limited by declaring a value for FIT_MAXITER A value of 0 (or not defining it at all) means that there is no limit. If you need even more control about the algorithm, and know the Marquardt-Levenberg algorithm well, there are some more variables to influence it. The startup value of lambda is normally calculated automatically from the ML-matrix, but if you want to, you may provide your own one with FIT_START_LAMBDA Specifying FIT_START_LAMBDA as zero or less will re-enable the automatic selection. The variable FIT_LAMBDA_FACTOR gives the factor by which lambda is increased or decreased whenever the chi-squared target function increased or decreased significantly. Setting FIT_LAMBDA_FACTOR to zero re-enables the default factor of 10.0. Oher variables with the FIT_ prefix may be added to fit, so it is safer not to use that prefix for user-defined variables. The variables FIT_SKIP and FIT_INDEX were used by earlier releases of gnuplot with a 'fit' patch called gnufit and are no longer available. The datafile every modifier provides the functionality of FIT_SKIP. FIT_INDEX was used for multi-branch fitting, but multi-branch fitting of one independent variable is now done as a pseudo-3D fit in which the second independent variable and using are used to specify the branch. See fit multi-branch. ### environment variables The environment variables must be defined before gnuplot is executed; how to do so depends on your operating system. FIT_LOG changes the name (and/or path) of the file to which the fit log will be written from the default of "fit.log" in the working directory. FIT_SCRIPT specifies a command that may be executed after an user interrupt. The default is replot, but a plot or load command may be useful to display a plot customized to highlight the progress of the fit. ## multi-branch In multi-branch fitting, multiple data sets can be simultaneously fit with functions of one independent variable having common parameters by minimizing the total WSSR. The function and parameters (branch) for each data set are selected by using a 'pseudo-variable', e.g., either the dataline number (a 'column' index of -1) or the datafile index (-2), as the second independent variable. Example: Given two exponential decays of the form, z=f(x), each describing a different data set but having a common decay time, estimate the values of the parameters. If the datafile has the format x:z:s, then f(x,y) = (y==0) ? a*exp(-x/tau) : b*exp(-x/tau) fit f(x,y) 'datafile' using 1:-1:2:3 via a, b, tau For a more complicated example, see the file "hexa.fnc" used by the "fit.dem" demo. Appropriate weighting may be required since unit weights may cause one branch to predominate if there is a difference in the scale of the dependent variable. Fitting each branch separately, using the multi-branch solution as initial values, may give an indication as to the relative effect of each branch on the joint solution. ## starting values Nonlinear fitting is not guaranteed to converge to the global optimum (the solution with the smallest sum of squared residuals, SSR), and can get stuck at a local minimum. The routine has no way to determine that; it is up to you to judge whether this has happened. fit may, and often will get "lost" if started far from a solution, where SSR is large and changing slowly as the parameters are varied, or it may reach a numerically unstable region (e.g., too large a number causing a floating point overflow) which results in an "undefined value" message or gnuplot halting. To improve the chances of finding the global optimum, you should set the starting values at least roughly in the vicinity of the solution, e.g., within an order of magnitude, if possible. The closer your starting values are to the solution, the less chance of stopping at another minimum. One way to find starting values is to plot data and the fitting function on the same graph and change parameter values and replot until reasonable similarity is reached. The same plot is also useful to check whether the fit stopped at a minimum with a poor fit. Of course, a reasonably good fit is not proof there is not a "better" fit (in either a statistical sense, characterized by an improved goodness-of-fit criterion, or a physical sense, with a solution more consistent with the model.) Depending on the problem, it may be desirable to fit with various sets of starting values, covering a reasonable range for each parameter. ## tips Here are some tips to keep in mind to get the most out of fit. They're not very organized, so you'll have to read them several times until their essence has sunk in. The two forms of the via argument to fit serve two largely distinct purposes. The via "file" form is best used for (possibly unattended) batch operation, where you just supply the startup values in a file and can later use update to copy the results back into another (or the same) parameter file. The via var1, var2, ... form is best used interactively, where the command history mechanism may be used to edit the list of parameters to be fitted or to supply new startup values for the next try. This is particularly useful for hard problems, where a direct fit to all parameters at once won't work without good starting values. To find such, you can iterate several times, fitting only some of the parameters, until the values are close enough to the goal that the final fit to all parameters at once will work. Make sure that there is no mutual dependency among parameters of the function you are fitting. For example, don't try to fit a*exp(x+b), because a*exp(x+b)=a*exp(b)*exp(x). Instead, fit either a*exp(x) or exp(x+b). A technical issue: the parameters must not be too different in magnitude. The larger the ratio of the largest and the smallest absolute parameter values, the slower the fit will converge. If the ratio is close to or above the inverse of the machine floating point precision, it may take next to forever to converge, or refuse to converge at all. You will have to adapt your function to avoid this, e.g., replace 'parameter' by '1e9*parameter' in the function definition, and divide the starting value by 1e9. If you can write your function as a linear combination of simple functions weighted by the parameters to be fitted, by all means do so. That helps a lot, because the problem is no longer nonlinear and should converge with only a small number of iterations, perhaps just one. Some prescriptions for analysing data, given in practical experimentation courses, may have you first fit some functions to your data, perhaps in a multi-step process of accounting for several aspects of the underlying theory one by one, and then extract the information you really wanted from the fitting parameters of those functions. With fit, this may often be done in one step by writing the model function directly in terms of the desired parameters. Transforming data can also quite often be avoided, though sometimes at the cost of a more difficult fit problem. If you think this contradicts the previous paragraph about simplifying the fit function, you are correct. A "singular matrix" message indicates that this implementation of the Marquardt-Levenberg algorithm can't calculate parameter values for the next iteration. Try different starting values, writing the function in another form, or a simpler function. Finally, a nice quote from the manual of another fitting package (fudgit), that kind of summarizes all these issues: "Nonlinear fitting is an art!" # help The help command displays on-line help. To specify information on a particular topic use the syntax: help {<topic>} If <topic> is not specified, a short message is printed about gnuplot. After help for the requested topic is given, a menu of subtopics is given; help for a subtopic may be requested by typing its name, extending the help request. After that subtopic has been printed, the request may be extended again or you may go back one level to the previous topic. Eventually, the gnuplot command line will return. If a question mark (?) is given as the topic, the list of topics currently available is printed on the screen. # if The if command allows commands to be executed conditionally. Syntax: if (<condition>) <command-line> <condition> will be evaluated. If it is true (non-zero), then the command(s) of the <command-line> will be executed. If <condition> is false (zero), then the entire <command-line> is ignored. Note that use of ; to allow multiple commands on the same line will _not_ end the conditionalized commands. Examples: pi=3 if (pi!=acos(-1)) print "?Fixing pi!"; pi=acos(-1); print pi will display: ?Fixing pi! 3.14159265358979 but if (1==2) print "Never see this"; print "Or this either" will not display anything. See reread for an example of how if and reread can be used together to perform a loop. # load The load command executes each line of the specified input file as if it had been typed in interactively. Files created by the save command can later be loaded. Any text file containing valid commands can be created and then executed by the load command. Files being loaded may themselves contain load or call commands. See comment for information about comments in commands. To load with arguments, see call. The load command _must_ be the last command on a multi-command line. Syntax: load "<input-file>" The name of the input file must be enclosed in quotes. The special filename "-" may be used to load commands from standard input. This allows a gnuplot command file to accept some commands from standard input. Please see "help batch/interactive" for more details. Examples: load 'work.gnu' load "func.dat" The load command is performed implicitly on any file names given as arguments to gnuplot. These are loaded in the order specified, and then gnuplot exits. # pause Syntax: pause <time> {"<string>"} <time> may be any integer constant or expression. Choosing -1 will wait until a carriage return is hit, zero (0) won't pause at all, and a positive integer will wait the specified number of seconds. pause 0 is synonymous with print. Note: Since pause communicates with the operating system rather than the graphics, it may behave differently with different device drivers (depending upon how text and graphics are mixed). Examples: pause -1 # Wait until a carriage return is hit pause 3 # Wait three seconds pause -1 "Hit return to continue" pause 10 "Isn't this pretty? It's a cubic spline." # plot plot is the primary command for drawing plots with gnuplot. It creates plots of functions and data in many, many ways. plot is used to draw 2-d functions and data; splot draws 2-d projections of 3-d surfaces and data. plot and splot contain many common features; see splot for differences. Note specifically that splot's binary and matrix options do not exist for plot. Syntax: plot {<ranges>} {<function> | {"<datafile>" {datafile-modifiers}}} {axes <axes>} {<title-spec>} {with <style>} {, {definitions,} <function> ...} where either a <function> or the name of a data file enclosed in quotes is supplied. A function is a mathematical expression or a pair of mathematical expressions in parametric mode. The expressions may be defined completely or in part earlier in the stream of gnuplot commands (see user-defined). It is also possible to define functions and parameters on the plot command itself. This is done merely by isolating them from other items with commas. There are four possible sets of axes available; the keyword <axes> is used to select the axes for which a particular line should be scaled. x1y1 refers to the axes on the bottom and left; x2y2 to those on the top and right; x1y2 to those on the bottom and right; and x2y1 to those on the top and left. Ranges specified on the plot command apply only to the first set of axes (bottom left). Examples: plot sin(x) plot f(x) = sin(x*a), a = .2, f(x), a = .4, f(x) plot [t=1:10] [-pi:pi*2] tan(t), \ "data.1" using (tan(2)):(3/4) smooth csplines \ axes x1y2 notitle with lines 5 ## data-file Syntax: plot '<file_name>' {index <index list>} {every <every list>} {thru <thru expression>} {using <using list>} {smooth <option>} The modifiers index, every, thru, using, and smooth are discussed separately. In brief, index selects which data sets in a multi-data-set file are to be plotted, every specifies which points within a single data set are to be plotted, using determines how the columns within a single record are to be interpreted (thru is a special case of using), and smooth allows for simple interpolation and approximation. ('splot' has a similar syntax, but does not support the smooth and thru options.) Data files should contain at least one data point per record (using can select one data point from the record). Records beginning with # (and also with ! on VMS) will be treated as comments and ignored. Each data point represents an (x,y) pair. For plots with error bars (see set style errorbars), each data point is (x,y,ydelta), (x,y,ylow,yhigh), (x,y,xdelta), (x,y,xlow,xhigh), or (x,y,xlow,xhigh,ylow,yhigh). In all cases, the numbers on each record of a data file must be separated by white space (one or more blanks or tabs), unless a format specifier is provided by the using option. This white space divides each record into columns. Data may be written in exponential format with the exponent preceded by the letter e, E, d, D, q, or Q. Only one column (the y value) need be provided. If x is omitted, gnuplot provides integer values starting at 0. In datafiles, blank records (records with no characters other than blanks and a newline and/or carriage return) are significant---pairs of blank records separate indexes (see plot datafile index). Data separated by double blank records are treated as if they were in separate data files. Single blank records designate discontinuities in a plot; no line will join points separated by a blank records (if they are plotted with a line style). If autoscaling has been enabled (set autoscale), the axes are automatically extended to include all datapoints, with a whole number of tic marks if tics are being drawn. This has two consequences: i) For splot, the corner of the surface may not coincide with the corner of the base. In this case, no vertical line is drawn. ii) When plotting data with the same x range on a dual-axis graph, the x coordinates may not coincide if the x2tics are not being drawn. This is because the x axis has been autoextended to a whole number of tics, but the x2 axis has not. The following example illustrates the problem: reset; plot '-', '-' 1 1 19 19 e 1 1 19 19 e ### every The every keyword allows a periodic sampling of a data set to be plotted. Syntax: plot 'file' every {<point_incr>} {:{<block_incr>} {:{<start_point>} {:{<start_block>} {:{<end_point>} {:<end_block>}}}}} The data points to be plotted are selected according to a loop from <start_point> to <end_point> with increment <point_incr> and the blocks according to a loop from <start_block> to <end_block> with increment <block_incr>. The first datum in each block is numbered '0', as is the first block in the file. Note that records containing unplottable information are counted. Any of the numbers can be omitted; the increments default to unity, the start values to the first point or block, and the end values to the last point or block. If every is not specified, all points in all lines are plotted. Examples: every :::3::3 # selects just the fourth block ('0' is first) every :::::9 # selects the first 10 blocks every 2:2 # selects every other point in every other block every ::5::15 # selects points 5 through 15 in each block Simple Plot Demos , Non-parametric splot demos , and Parametric splot demos. ### example datafile This example plots the data in the file "population.dat" and a theoretical curve: pop(x) = 103*exp((1965-x)/10) plot [1960:1990] 'population.dat', pop(x) The file "population.dat" might contain: # Gnu population in Antarctica since 1965 1965 103 1970 55 1975 34 1980 24 1985 10 ### index The index keyword allows only some of the data sets in a multi-data-set file to be plotted. Syntax: plot 'file' index <m>{{:<n>}:<p>} Data sets are separated by pairs of blank records. index <m> selects only set <m>; index <m>:<n> selects sets in the range <m> to <n>; and index <m>:<n>:<p> selects indices <m>, <m>+<p>, <m>+2<p>, etc., but stopping at <n>. Following C indexing, the index 0 is assigned to the first data set in the file. Specifying too large an index results in an error message. If index is not specified, all sets are plotted as a single data set. Example: plot 'file' index 4:5 splot with indices demo. ### smooth gnuplot includes a few general-purpose routines for interpolation and approximation of data; these are grouped under the smooth option. More sophisticated data processing may be performed by preprocessing the data externally or by using fit with an appropriate model. Syntax: smooth {unique | csplines | acsplines | bezier | sbezier} unique plots the data after making them monotonic. Each of the other routines uses the data to determine the coefficients of a continuous curve between the endpoints of the data. This curve is then plotted in the same manner as a function, that is, by finding its value at uniform intervals along the abscissa (see set samples) and connecting these points with straight line segments (if a line style is chosen). If autoscale is in effect, the ranges will be computed such that the plotted curve lies within the borders of the graph. If too few points are available to allow the selected option to be applied, an error message is produced. The minimum number is one for unique, four for acsplines, and three for the others. The smooth options have no effect on function plots. #### acsplines The acsplines option approximates the data with a "natural smoothing spline". After the data are made monotonic in x (see smooth unique), a curve is piecewise constructed from segments of cubic polynomials whose coefficients are found by the weighting the data points; the weights are taken from the third column in the data file. That default can be modified by the third entry in the using list, e.g., plot 'data-file' using 1:2:(1.0) smooth acsplines Qualitatively, the absolute magnitude of the weights determines the number of segments used to construct the curve. If the weights are large, the effect of each datum is large and the curve approaches that produced by connecting consecutive points with natural cubic splines. If the weights are small, the curve is composed of fewer segments and thus is smoother; the limiting case is the single segment produced by a weighted linear least squares fit to all the data. The smoothing weight can be expressed in terms of errors as a statistical weight for a point divided by a "smoothing factor" for the curve so that (standard) errors in the file can be used as smoothing weights. Example: sw(x,S)=1/(x*x*S) plot 'data_file' using 1:2:(sw(3,100)) smooth acsplines #### bezier The bezier option approximates the data with a Bezier curve of degree n (the number of data points) that connects the endpoints. #### csplines #### sbezier The sbezier option first renders the data monotonic (unique) and then applies the bezier algorithm. #### unique ### special-filenames A special filename of '-' specifies that the data are inline; i.e., they follow the command. Only the data follow the command; plot options like filters, titles, and line styles remain on the 'plot' command line. This is similar to << in unix shell script, and DECK in VMS DCL. The data are entered as though they are being read from a file, one data point per record. The letter "e" at the start of the first column terminates data entry. The using option can be applied to these data---using it to filter them through a function might make sense, but selecting columns probably doesn't! '-' is intended for situations where it is useful to have data and commands together, e.g., when gnuplot is run as a sub-process of some front-end application. Some of the demos, for example, might use this feature. While plot options such as index and every are recognized, their use forces you to enter data that won't be used. For example, while plot '-' index 0, '-' index 1 2 4 6 10 12 14 e 2 4 6 10 12 14 e does indeed work, plot '-', '-' 2 4 6 e 10 12 14 e is a lot easier to type. If you use '-' with replot, you may need to enter the data more than once (see replot). A blank filename ('') specifies that the previous filename should be reused. This can be useful with things like plot 'a/very/long/filename' using 1:2, '' using 1:3, '' using 1:4 (If you use both '-' and '' on the same plot command, you'll need to have two sets of inline data, as in the example above.) On some computer systems with a popen function (Unix), the datafile can be piped through a shell command by starting the file name with a '<'. For example, pop(x) = 103*exp(-x/10) plot "< awk '{print 1-1965, 2}' population.dat", pop(x) would plot the same information as the first population example but with years since 1965 as the x axis. If you want to execute this example, you have to delete all comments from the data file above or substitute the following command for the first part of the command above (the part up to the comma): plot "< awk '0 !~ /^#/ {print 1-1965, 2}' population.dat" While this approach is most flexible, it is possible to achieve simple filtering with the using or thru keywords. ### thru The thru function is provided for backward compatibility. Syntax: plot 'file' thru f(x) It is equivalent to: plot 'file' using 1:(f(2)) While the latter appears more complex, it is much more flexible. The more natural plot 'file' thru f(y) also works (i.e. you can use y as the dummy variable). thru is parsed for splot and fit but has no effect. ### using The most common datafile modifier is using. Syntax: plot 'file' using {<entry> {:<entry> {:<entry> ...}}} {'format'} If a format is specified, each datafile record is read using the C library's 'scanf' function, with the specified format string. Otherwise the record is read and broken into columns at spaces or tabs. A format cannot be specified if time-format data is being used (this must be done by set data time). The resulting array of data is then sorted into columns according to the entries. Each <entry> may be a simple column number, which selects the datum, an expression enclosed in parentheses, or empty. The expression can use 1 to access the first item read, 2 for the second item, and so on. It can also use column(x) and valid(x) where x is an arbitrary expression resulting in an integer. column(x) returns the x'th datum; valid(x) tests that the datum in the x'th column is a valid number. A column number of 0 generates a number increasing (from zero) with each point, and is reset upon encountering two blank records. A column number of -1 gives the dataline number, which starts at 0, increments at single blank records, and is reset at double blank records. A column number of -2 gives the index number, which is incremented only when two blank records are found. An empty <entry> will default to its order in the list of entries. For example, using ::4 is interpreted as using 1:2:4. N.B.---the call command also uses 's as a special character. See call for details about how to include a column number in a call argument list. If the using list has but a single entry, that <entry> will be used for y and the data point number is used for x; for example, "plot 'file' using 1" is identical to "plot 'file' using 0:1". If the using list has two entries, these will be used for x and y. Additional entries are usually errors in x and/or y. See set style for details about plotting styles that make use of error information, and fit for use of error information in curve fitting. 'scanf' accepts several numerical specifications but gnuplot requires all inputs to be double-precision floating-point variables, so lf is the only permissible specifier. 'scanf' expects to see white space---a blank, tab ("\t"), newline ("\n"), or formfeed ("\f")---between numbers; anything else in the input stream must be explicitly skipped. Note that the use of "\t", "\n", or "\f" or requires use of double-quotes rather than single-quotes. Examples: This creates a plot of the sum of the 2nd and 3rd data against the first: (The format string specifies comma- rather than space-separated columns.) plot 'file' using 1:(2+3) '%lf,%lf,%lf' In this example the data are read from the file "MyData" using a more complicated format: plot 'MyData' using "%*lf%lf%*20[^\n]%lf" The meaning of this format is: %*lf ignore a number %lf read a double-precision number (x by default) %*20[^\n] ignore 20 non-newline characters %lf read a double-precision number (y by default) One trick is to use the ternary ?: operator to filter data: plot 'file' using 1:(3>10 ? 2 : 1/0) which plots the datum in column two against that in column one provided the datum in column three exceeds ten. 1/0 is undefined; gnuplot quietly ignores undefined points, so unsuitable points are suppressed. In fact, you can use a constant expression for the column number, provided it doesn't start with an opening parenthesis; constructs like using 0+(complicated expression) can be used. The crucial point is that the expression is evaluated once if it doesn't start with a left parenthesis, or once for each data point read if it does. If timeseries data are being used, the time can span multiple columns. The starting column should be specified. Note that the spaces within the time must be included when calculating starting columns for other data. E.g., if the first element on a line is a time with an embedded space, the y value should be specified as column three. It should be noted that plot 'file', plot 'file' using 1:2, and plot 'file' using (1):(2) can be subtly different: 1) if file has some lines with one column and some with two, the first will invent x values when they are missing, the second will quietly ignore the lines with one column, and the third will store an undefined value for lines with one point (so that in a plot with lines, no line joins points across the bad point); 2) if a line contains text at the first column, the first will abort the plot on an error, but the second and third should quietly skip the garbage. In fact, it is often possible to plot a file with lots of lines of garbage at the top simply by specifying plot 'file' using 1:2 However, if you want to leave text in your data files, it is safer to put the comment character (#) in the first column of the text lines. Feeble using demos. ## errorbars Error bars are supported for 2-d data file plots by reading one to four additional columns (or using entries); these additional values are used in different ways by the various errorbar styles. In the default situation, gnuplot expects to see three, four, or six numbers on each line of the data file---either (x, y, ydelta), (x, y, ylow, yhigh), (x, y, xdelta), (x, y, xlow, xhigh), (x, y, xdelta, ydelta), or (x, y, xlow, xhigh, ylow, yhigh). The x coordinate must be specified. The order of the numbers must be exactly as given above, though the using qualifier can manipulate the order and provide values for missing columns. For example, plot 'file' with errorbars plot 'file' using 1:2:(sqrt(1)) with xerrorbars plot 'file' using 1:2:(1-3):(1+3):4:5 with xyerrorbars The last example is for a file containing an unsupported combination of relative x and absolute y errors. The using entry generates absolute x min and max from the relative error. The y error bar is a vertical line plotted from (x, ylow) to (x, yhigh). If ydelta is specified instead of ylow and yhigh, ylow = y - ydelta and yhigh = y + ydelta are derived. If there are only two numbers on the record, yhigh and ylow are both set to y. The x error bar is a horizontal line computed in the same fashion. To get lines plotted between the data points, plot the data file twice, once with errorbars and once with lines (but remember to use the notitle option on one to avoid two entries in the key). The error bars have crossbars at each end unless set bar is used (see set bar for details). If autoscaling is on, the ranges will be adjusted to include the error bars. Errorbar demos. See plot using, plot with, and set style for more information. ## parametric When in parametric mode (set parametric) mathematical expressions must be given in pairs for plot and in triplets for splot. Examples: plot sin(t),t**2 splot cos(u)*cos(v),cos(u)*sin(v),sin(u) Data files are plotted as before, except any preceding parametric function must be fully specified before a data file is given as a plot. In other words, the x parametric function (sin(t) above) and the y parametric function (t**2 above) must not be interrupted with any modifiers or data functions; doing so will generate a syntax error stating that the parametric function is not fully specified. Other modifiers, such as with and title, may be specified only after the parametric function has been completed: plot sin(t),t**2 title 'Parametric example' with linespoints Parametric Mode Demos. ## ranges The optional ranges specify the region of the graph that will be displayed. Syntax: [{<dummy-var>=}{{<min>}:{<max>}}] [{{<min>}:{<max>}}] The first form applies to the independent variable (xrange or trange, if in parametric mode). The second form applies to the dependent variable yrange (and xrange, too, if in parametric mode). <dummy-var> is a new name for the independent variable. (The defaults may be changed with set dummy.) The optional <min> and <max> terms can be constant expressions or *. In non-parametric mode, the order in which ranges must be given is xrange and yrange. In parametric mode, the order for the plot command is trange, xrange, and yrange. The following plot command shows setting the trange to [-pi:pi], the xrange to [-1.3:1.3] and the yrange to [-1:1] for the duration of the graph: plot [-pi:pi] [-1.3:1.3] [-1:1] sin(t),t**2 Note that the x2range and y2range cannot be specified here---set x2range and set y2range must be used. Ranges are interpreted in the order listed above for the appropriate mode. Once all those needed are specified, no further ones must be listed, but unneeded ones cannot be skipped---use an empty range [] as a placeholder. * can be used to allow autoscaling of either of min and max. See also set autoscale. Ranges specified on the plot or splot command line affect only that graph; use the set xrange, set yrange, etc., commands to change the default ranges for future graphs. With time data, you must provide the range (in the same manner as the time appears in the datafile) within quotes. gnuplot uses the timefmt string to read the value---see set timefmt. Examples: This uses the current ranges: plot cos(x) This sets the x range only: plot [-10:30] sin(pi*x)/(pi*x) This is the same, but uses t as the dummy-variable: plot [t = -10 :30] sin(pi*t)/(pi*t) This sets both the x and y ranges: plot [-pi:pi] [-3:3] tan(x), 1/x This sets only the y range, and turns off autoscaling on both axes: plot [ ] [-2:sin(5)*-8] sin(x)**besj0(x) This sets xmax and ymin only: plot [:200] [-pi:] exp(sin(x)) This sets the x range for a timeseries: set timefmt "%d/%m/%y %H:%M" plot ["1/6/93 12:00":"5/6/93 12:00"] 'timedata.dat' ## title A line title for each function and data set appears in the key, accompanied by a sample of the line and/or symbol used to represent it. It can be changed by using the title option. Syntax: title "<title>" | notitle where <title> is the new title of the line and must be enclosed in quotes. The quotes will not be shown in the key. A special character may be given as a backslash followed by its octal value ("\345"). The tab character "\t" is understood. Note that backslash processing occurs only for strings enclosed in double quotes---use single quotes to prevent such processing. The newline character "\n" is not processed in key entries in either type of string. The line title and sample can be omitted from the key by using the keyword notitle. A null title (title '') is equivalent to notitle. If only the sample is wanted, use one or more blanks (title ' '). By default the line title is the function or file name as it appears on the plot command. If it is a file name, any datafile modifiers specified will be included in the default title. The layout of the key itself (position, title justification, etc.) can be controlled by set key. Please see set key for details. Examples: This plots y=x with the title 'x': plot x This plots x squared with title "x^2" and file "data.1" with title "measured data": plot x**2 title "x^2", 'data.1' t "measured data" This puts an untitled circular border around a polar graph: set polar; plot my_function(t), 1 notitle ## with Functions and data may be displayed in one of a large number of styles. The with keyword provides the means of selection. Syntax: with <style> { {linestyle | ls <line_style>} | {{linetype | lt <line_type>} {linewidth | lw <line_width>} {pointtype | pt <point_type>} {pointsize | ps <point_size>}} } where <style> is either lines, points, linespoints, impulses, dots, steps, fsteps, histeps, errorbars, xerrorbars, yerrorbars, xyerrorbars, boxes, boxerrorbars, boxxyerrorbars, financebars, candlesticks or vector. Some of these styles require additional information. See set style <style> for details of each style. Default styles are chosen with the set function style and set data style commands. By default, each function and data file will use a different line type and point type, up to the maximum number of available types. All terminal drivers support at least six different point types, and re-use them, in order, if more are required. The LaTeX driver supplies an additional six point types (all variants of a circle), and thus will only repeat after 12 curves are plotted with points. The PostScript drivers (postscript) supplies a total of 64. If you wish to choose the line or point type for a single plot, <line_type> and <point_type> may be specified. These are positive integer constants (or expressions) that specify the line type and point type to be used for the plot. Use test to display the types available for your terminal. You may also scale the line width and point size for a plot by using <line_width> and <point_size>, which are specified relative to the default values for each terminal. The pointsize may also be altered globally---see set pointsize for details. But note that both <point_size> as set here and as set by set pointsize multiply the default point size---their effects are not cumulative. That is, set pointsize 2; plot x w p ps 3 will use points three times default size, not six. If you have defined specific line type/width and point type/size combinations with set linestyle, one of these may be selected by setting <line_style> to the index of the desired style. The keywords may be abbreviated as indicated. Note that the linewidth and pointsize options are not supported by all terminals. Examples: This plots sin(x) with impulses: plot sin(x) with impulses This plots x with points, x**2 with the default: plot x*y w points, x**2 + y**2 This plots tan(x) with the default function style, file "data.1" with lines: plot [ ] [-2:5] tan(x), 'data.1' with l This plots "leastsq.dat" with impulses: plot 'leastsq.dat' w i This plots the data file "population" with boxes: plot 'population' with boxes This plots "exper.dat" with errorbars and lines connecting the points (errorbars require three or four columns): plot 'exper.dat' w lines, 'exper.dat' notitle w errorbars This plots sin(x) and cos(x) with linespoints, using the same line type but different point types: plot sin(x) with linesp lt 1 pt 3, cos(x) with linesp lt 1 pt 4 This plots file "data" with points of type 3 and twice usual size: plot 'data' with points pointtype 3 pointsize 2 This plots two data sets with lines differing only by weight: plot 'd1' t "good" w l lt 2 lw 3, 'd2' t "bad" w l lt 2 lw 1 See set style to change the default styles. Styles demos. # print The print command prints the value of <expression> to the screen. It is synonymous with pause 0. <expression> may be anything that gnuplot can evaluate that produces a number, or it can be a string. Syntax: print <expression> {, <expression>, ...} See expressions. # pwd The pwd command prints the name of the working directory to the screen. # quit The exit and quit commands and END-OF-FILE character will exit gnuplot. Each of these commands will clear the output device (as does the clear command) before exiting. # replot The replot command without arguments repeats the last plot or splot command. This can be useful for viewing a plot with different set options, or when generating the same plot for several devices. Arguments specified after a replot command will be added onto the last plot or splot command (with an implied ',' separator) before it is repeated. replot accepts the same arguments as the plot and splot commands except that ranges cannot be specified. Thus you can use replot to plot a function against the second axes if the previous command was plot but not if it was splot, and similarly you can use replot to add a plot from a binary file only if the previous command was splot. N.B.---use of plot '-' ; ... ; replot is not recommended. gnuplot does not store the inline data internally, so since replot appends new information to the previous plot and then executes the modified command, the '-' from the initial plot will expect to read inline data again. Note that replot does not work in multiplot mode, since it reproduces only the last plot rather than the entire screen. See also command-line-editing for ways to edit the last plot (splot) command. # reread The reread command causes the current gnuplot command file, as specified by a load command or on the command line, to be reset to its starting point before further commands are read from it. This essentially implements an endless loop of the commands from the beginning of the command file to the reread command. (But this is not necessarily a disaster---reread can be very useful when used in conjunction with if. See if for details.) The reread command has no effect if input from standard input. Examples: Suppose the file "looper" contains the commands a=a+1 plot sin(x*a) pause -1 if(a<5) reread and from within gnuplot you submit the commands a=0 load 'looper' The result will be four plots (separated by the pause message). Suppose the file "data" contains six columns of numbers with a total yrange from 0 to 10; the first is x and the next are five different functions of x. Suppose also that the file "plotter" contains the commands c_p = c_p+1 plot "0" using 1:c_p with lines linetype c_p if(c_p < n_p) reread and from within gnuplot you submit the commands n_p=6 c_p=1 set nokey set yrange [0:10] set multiplot call 'plotter' 'data' set nomultiplot The result is a single graph consisting of five plots. The yrange must be set explicitly to guarantee that the five separate graphs (drawn on top of each other in multiplot mode) will have exactly the same axes. The linetype must be specified; otherwise all the plots would be drawn with the same type. Reread Animation Demo # reset The reset command causes all options that can be set with the set command to take on their default values. The only exceptions are that the terminal set with set term and the output file set with set output are left unchanged. This command is useful, e.g., to restore the default settings at the end of a command file, or to return to a defined state after lots of settings have been changed within a command file. Please refer to the set command to see the default values that the various options take. # save The save command saves user-defined functions, variables, set options, or all three, plus the last plot (splot) command to the specified file. Syntax: save {<option>} '<filename>' where <option> is functions, variables or set. If no option is used, gnuplot saves functions, variables, set options and the last plot (splot) command. saved files are written in text format and may be read by the load command. The filename must be enclosed in quotes. Examples: save 'work.gnu' save functions 'func.dat' save var 'var.dat' save set 'options.dat' # set-show The show command shows their settings; show all shows all the settings. If a variable contains time/date data, show will display it according to the format currently defined by set timefmt, even if that was not in effect when the variable was initially defined. ## angles By default, gnuplot assumes the independent variable in polar graphs is in units of radians. If set angles degrees is specified before set polar, then the default range is [0:360] and the independent variable has units of degrees. This is particularly useful for plots of data files. The angle setting also applies to 3-d mapping as set via the set mapping command. Syntax: set angles {degrees | radians} show angles The angle specified in set grid polar is also read and displayed in the units specified by set angles. set angles also affects the arguments of the machine-defined functions sin(x), cos(x) and tan(x), and the outputs of asin(x), acos(x), atan(x), atan2(x), and arg(x). It has no effect on the arguments of hyperbolic functions or Bessel functions. However, the output arguments of inverse hyperbolic functions of complex arguments are affected; if these functions are used, set angles radians must be in effect to maintain consistency between input and output arguments. x={1.0,0.1} set angles radians y=sinh(x) print y #prints {1.16933, 0.154051} print asinh(y) #prints {1.0, 0.1} but set angles degrees y=sinh(x) print y #prints {1.16933, 0.154051} print asinh(y) #prints {57.29578, 5.729578} Polar plot using set angles. ## arrow Arbitrary arrows can be placed on a plot using the set arrow command. Syntax: set arrow {<tag>} {from <position>} {to <position>} {{no}head} { {linestyle | ls <line_style>} | {linetype | lt <line_type>} {linewidth | lw <line_width} } set noarrow {<tag>} show arrow <tag> is an integer that identifies the arrow. If no tag is given, the lowest unused tag value is assigned automatically. The tag can be used to delete or change a specific arrow. To change any attribute of an existing arrow, use the set arrow command with the appropriate tag and specify the parts of the arrow to be changed. The <position>s are specified by either x,y or x,y,z, and may be preceded by first, second, graph, or screen to select the coordinate system. Unspecified coordinates default to 0. The endpoints can be specified in one of four coordinate systems---first or second axes, graph or screen. See coordinates for details. A coordinate system specifier does not carry over from the "from" position to the "to" position. Arrows outside the screen boundaries are permitted but may cause device errors. Specifying nohead produces an arrow drawn without a head---a line segment. This gives you yet another way to draw a line segment on the plot. By default, arrows have heads. The line style may be selected from a user-defined list of line styles (see set linestyle) or may be defined here by providing values for <line_type> (an index from the default list of styles) and/or <line_width> (which is a multiplier for the default width). Note, however, that if a user-defined line style has been selected, its properties (type and width) cannot be altered merely by issuing another set arrow command with the appropriate index and lt or lw. Examples: To set an arrow pointing from the origin to (1,2) with user-defined style 5, use: set arrow to 1,2 ls 5 To set an arrow from bottom left of plotting area to (-5,5,3), and tag the arrow number 3, use: set arrow 3 from graph 0,0 to -5,5,3 To change the preceding arrow to end at 1,1,1, without an arrow head and double its width, use: set arrow 3 to 1,1,1 nohead lw 2 To draw a vertical line from the bottom to the top of the graph at x=3, use: set arrow from 3, graph 0 to 3, graph 1 nohead To delete arrow number 2, use: set noarrow 2 To delete all arrows, use: set noarrow To show all arrows (in tag order), use: show arrow Arrows Demos. ## autoscale Autoscaling may be set individually on the x, y or z axis or globally on all axes. The default is to autoscale all axes. Syntax: set autoscale {<axes>{min|max}} set noautoscale {<axes>{min|max}} show autoscale where <axes> is either x, y, z, x2, y2 or xy. A keyword with min or max appended (this cannot be done with xy) tells gnuplot to autoscale just the minimum or maximum of that axis. If no keyword is given, all axes are autoscaled. When autoscaling, the axis range is automatically computed and the dependent axis (y for a plot and z for splot) is scaled to include the range of the function or data being plotted. If autoscaling of the dependent axis (y or z) is not set, the current y or z range is used. Autoscaling the independent variables (x for plot and x,y for splot) is a request to set the domain to match any data file being plotted. If there are no data files, autoscaling an independent variable has no effect. In other words, in the absence of a data file, functions alone do not affect the x range (or the y range if plotting z = f(x,y)). Please see set xrange for additional information about ranges. The behavior of autoscaling remains consistent in parametric mode, (see set parametric). However, there are more dependent variables and hence more control over x, y, and z axis scales. In parametric mode, the independent or dummy variable is t for plots and u,v for splots. autoscale in parametric mode, then, controls all ranges (t, u, v, x, y, and z) and allows x, y, and z to be fully autoscaled. Autoscaling works the same way for polar mode as it does for parametric mode for plot, with the extension that in polar mode set dummy can be used to change the independent variable from t (see set dummy). When tics are displayed on second axes but no plot has been specified for those axes, x2range and y2range are inherited from xrange and yrange. This is done _before_ xrange and yrange are autoextended to a whole number of tics, which can cause unexpected results. Examples: This sets autoscaling of the y axis (other axes are not affected): set autoscale y This sets autoscaling only for the minimum of the y axis (the maximum of the y axis and the other axes are not affected): set autoscale ymin This sets autoscaling of the x and y axes: set autoscale xy This sets autoscaling of the x, y, z, x2 and y2 axes: set autoscale This disables autoscaling of the x, y, z, x2 and y2 axes: set noautoscale This disables autoscaling of the z axis only: set noautoscale z ### parametric mode When in parametric mode (set parametric), the xrange is as fully scalable as the y range. In other words, in parametric mode the x axis can be automatically scaled to fit the range of the parametric function that is being plotted. Of course, the y axis can also be automatically scaled just as in the non-parametric case. If autoscaling on the x axis is not set, the current x range is used. Data files are plotted the same in parametric and non-parametric mode. However, there is a difference in mixed function and data plots: in non-parametric mode with autoscaled x, the x range of the datafile controls the x range of the functions; in parametric mode it has no influence. For completeness a last command set autoscale t is accepted. However, the effect of this "scaling" is very minor. When gnuplot determines that the t range would be empty, it makes a small adjustment if autoscaling is true. Otherwise, gnuplot gives an error. Such behavior may, in fact, not be very useful and the command set autoscale t is certainly questionable. splot extends the above ideas as you would expect. If autoscaling is set, then x, y, and z ranges are computed and each axis scaled to fit the resulting data. ### polar mode When in polar mode (set polar), the xrange and the yrange are both found from the polar coordinates, and thus they can both be automatically scaled. In other words, in polar mode both the x and y axes can be automatically scaled to fit the ranges of the polar function that is being plotted. When plotting functions in polar mode, the rrange may be autoscaled. When plotting data files in polar mode, the trange may also be autoscaled. Note that if the trange is contained within one quadrant, autoscaling will produce a polar plot of only that single quadrant. Explicitly setting one or two ranges but not others may lead to unexpected results. See polar demos ## bar The set bar command controls the tics at the ends of errorbars. Syntax: set bar {small | large | <size>} show bar small is a synonym for 0.0, and large for 1.0. The default is 1.0 if no size is given. ## bmargin ## border Syntax: set border {<integer> { {linestyle | ls <line_style>} | {linetype | lt <line_type> } {linewidth | lw <line_width>} } } set noborder show border The borders are encoded in a 12-bit integer: the bottom four bits control the border for plot and the sides of the base for splot; The next four bits control the verticals in splot; the top four bits control the edges on top of the splot. In detail, the <integer> should be the sum of the appropriate entries from the following table: plot border splot splot Side splot base verticals top bottom (south) 1 16 256 left (west) 2 32 512 top (north) 4 64 1024 right (east) 8 128 2048 The default is 31, which is all four sides for plot, and base and z axis for splot. Using the optional <line_style>, <line_type> and <line_width> specifiers, the way the border lines are drawn can be influenced (limited by what the current terminal driver supports). By default, the border is drawn with twice the usual linewidth. The <line_width> specifier scales this default value; for example, set border 15 lw 2 will produce a border with four times the usual linewidth. Various axes or combinations of axes may be added together in the command. To have tics on edges other than bottom and left, disable the usual tics and enable the second axes. Examples: Draw all borders: set border Draw only the SOUTHWEST borders: set border 3 Draw a complete box around a splot: set border 4095 Draw a partial box, omitting the front vertical: set border 127+256+512 Draw only the NORTHEAST borders: set noxtics; set noytics; set x2tics; set y2tics; set border 12 ## boxwidth Syntax: set boxwidth {<width>} show boxwidth If a data file is plotted without the width being specified in the third, fourth, or fifth column (or using entry), or if a function is plotted, the width of each box is set by the set boxwidth command. (If a width is given both in the file and by the set boxwidth command, the one in the file is used.) If the width is not specified in one of these ways, the width of each box will be calculated automatically so that it touches the adjacent boxes. In a four-column data set, the fourth column will be interpreted as the box width unless the width is set to -2.0, in which case the width will be calculated automatically. See set style boxerrorbars for more details. To set the box width to automatic use the command set boxwidth or, for four-column data, set boxwidth -2 The same effect can be achieved with the using keyword in plot: plot 'file' using 1:2:3:4:(-2) ## clabel gnuplot will vary the linetype used for each contour level when clabel is set. When this option on (the default), a legend labels each linestyle with the z level it represents. It is not possible at present to separate the contour labels from the surface key. Syntax: set clabel {'<format>'} set noclabel show clabel The default for the format string is %8.3g, which gives three decimal places. This may produce poor label alignment if the key is altered from its default configuration. The first contour linetype, or only contour linetype when clabel is off, is the surface linetype +1; contour points are the same style as surface points. See also set contour. ## clip gnuplot can clip data points and lines that are near the boundaries of a graph. Syntax: set clip <clip-type> set noclip <clip-type> show clip Three clip types are supported by gnuplot: points, one, and two. One, two, or all three clip types may be active for a single graph. The points clip type forces gnuplot to clip (actually, not plot at all) data points that fall within but too close to the boundaries. This is done so that large symbols used for points will not extend outside the boundary lines. Without clipping points near the boundaries, the plot may look bad. Adjusting the x and y ranges may give similar results. Setting the one clip type causes gnuplot to draw a line segment which has only one of its two endpoints within the graph. Only the in-range portion of the line is drawn. The alternative is to not draw any portion of the line segment. Some lines may have both endpoints out of range, but pass through the graph. Setting the two clip-type allows the visible portion of these lines to be drawn. In no case is a line drawn outside the graph. The defaults are noclip points, clip one, and noclip two. To check the state of all forms of clipping, use show clip For backward compatibility with older versions, the following forms are also permitted: set clip set noclip set clip is synonymous with set clip points; set noclip turns off all three types of clipping. ## cntrparam set cntrparam controls the generation of contours and their smoothness for a contour plot. show contour displays current settings of cntrparam as well as contour. Syntax: set cntrparam { {linear | cubicspline | bspline} { points <n>} { order <n> } { levels auto {<n>} | <n> | discrete <z1> {,<z2>{,<z3>...}} | incremental <start>, <incr> {,<end>} } } show contour This command has two functions. First, it sets the values of z for which contour points are to be determined (by linear interpolation between data points or function isosamples.) Second, it controls the way contours are drawn between the points determined to be of equal z. <n> should be an integral constant expression and <z1>, <z2> ... any constant expressions. The parameters are: linear, cubicspline, bspline---Controls type of approximation or interpolation. If linear, then straight line segments connect points of equal z magnitude. If cubicspline, then piecewise-linear contours are interpolated between the same equal z points to form somewhat smoother contours, but which may undulate. If bspline, a guaranteed-smoother curve is drawn, which only approximates the position of the points of equal-z. points---Eventually all drawings are done with piecewise-linear strokes. This number controls the number of line segments used to approximate the bspline or cubicspline curve. Number of cubicspline or bspline segments (strokes) = points * number of linear segments. order---Order of the bspline approximation to be used. The bigger this order is, the smoother the resulting contour. (Of course, higher order bspline curves will move further away from the original piecewise linear data.) This option is relevant for bspline mode only. Allowed values are integers in the range from 2 (linear) to 10. levels--- Selection of contour levels, controlled by auto (default), discrete, incremental, and <n>, number of contour levels, limited to MAX_DISCRETE_LEVELS as defined in plot.h (30 is standard.) For auto, <n> specifies a nominal number of levels; the actual number will be adjusted to give simple labels. If the surface is bounded by zmin and zmax, contours will be generated at integer multiples of dz between zmin and zmax, where dz is 1, 2, or 5 times some power of ten (like the step between two tic marks). For levels discrete, contours will be generated at z = <z1>, <z2> ... as specified; the number of discrete levels sets the number of contour levels. In discrete mode, any set cntrparms levels <n> are ignored. For incremental, contours are generated at values of z beginning at <start> and increasing by <increment>, until the number of contours is reached. <end> is used to determine the number of contour levels, which will be changed by any subsequent set cntrparam levels <n>. If the command set cntrparam is given without any arguments specified, the defaults are used: linear, 5 points, order 4, 5 auto levels. Examples: set cntrparam bspline set cntrparam points 7 set cntrparam order 10 To select levels automatically, 5 if the level increment criteria are met: set cntrparam levels auto 5 To specify discrete levels at .1, .37, and .9: set cntrparam levels discrete .1,1/exp(1),.9 To specify levels from 0 to 4 with increment 1: set cntrparam levels incremental 0,1,4 To set the number of levels to 10 (changing an incremental end or possibly the number of auto levels): set cntrparam levels 10 To set the start and increment while retaining the number of levels: set cntrparam levels incremental 100,50 See also set contour for control of where the contours are drawn, and set clabel for control of the format of the contour labels and linetypes. Contours Demo and contours with User Defined Levels. ## contour Syntax: set contour {base | surface | both} set nocontour show contour The three options specify where to draw the contours: base draws the contours on the grid base where the x/ytics are placed, surface draws the contours on the surfaces themselves, and both draws the contours on both the base and the surface. If no option is provided, the default is base. See also set cntrparam for the parameters that affect the drawing of contours, and set clabel for control of labelling of the contours. The surface can be switched off (see set surface), giving a contour-only graph. Though it is possible to use set size to enlarge the plot to fill the screen, more control over the output format can be obtained by writing the contour information to a file, and rereading it as a 2-d datafile plot: set nosurface set contour set cntrparam ... set term table set out 'filename' splot ... set out # contour info now in filename set term <whatever> plot 'filename' In order to draw contours, the data should be organized as "grid data". In such a file all the points for a single y-isoline are listed, then all the points for the next y-isoline, and so on. A single blank line (a line containing no characters other than blank spaces and a carriage return and/or a line feed) separates one y-isoline from the next. See also splot datafile. If contours are desired from non-grid data, set dgrid3d can be used to create an appropriate grid. See set dgrid3d for more information. Contours Demo and contours with User Defined Levels. ## data style The set data style command changes the default plotting style for data plots. Syntax: set data style <style-choice> show data style See set style for the choices. If no choice is given, the choices are listed. show data style shows the current default data plotting style. ## dgrid3d The set dgrid3d command enables, and can set parameters for, non-grid to grid data mapping. Syntax: set dgrid3d {<row_size>} {,{<col_size>} {,<norm>}} set nodgrid3d show dgrid3d By default dgrid3d is disabled. When enabled, 3-d data read from a file are always treated as a scattered data set. A grid with dimensions derived from a bounding box of the scattered data and size as specified by the row/col_size parameters is created for plotting and contouring. The grid is equally spaced in x (rows) and in y (columns); the z values are computed as weighted averages of the scattered points' z values. The third parameter, norm, controls the weighting: Each data point is weighted inversely by its distance from the grid point raised to the norm power. (Actually, the weights are given by the inverse of dx^norm + dy^norm, where dx and dy are the components of the separation of the grid point from each data point. For some norms that are powers of two, specifically 4, 8, and 16, the computation is optimized by using the Euclidean distance in the weight calculation, (dx^2+dx^2)^norm/2. However, any non-negative integer can be used.) The closer the data point is to a grid point, the more effect it has on that grid point and the larger the value of norm the less effect more distant data points have on that grid point. (The z values are found by weighting all data points, not by interpolating between nearby data points; also edge effects may produce unexpected and/or undesired results. In some cases, small norm values produce a grid point reflecting the average of distant data points rather than a local average, while large values of norm may produce "steps" with several grid points having the same value as the closest data point, rather than making a smooth transition between adjacent data points. Some areas of a grid may be filled by extrapolation, to an arbitrary boundary condition. The variables are not normalized; consequently the units used for x and y will affect the relative weights of points in the x and y directions.) Examples: set dgrid3d 10,10,1 # defaults set dgrid3d ,,4 The first specifies that a grid of size 10 by 10 is to be constructed using a norm value of 1 in the weight computation. The second only modifies the norm, changing it to 4. Dgrid3d Demo. ## dummy The set dummy command changes the default dummy variable names. Syntax: set dummy {<dummy-var>} {,<dummy-var>} show dummy By default, gnuplot assumes that the independent, or "dummy", variable for the plot command is "t" if in parametric or polar mode, or "x" otherwise. Similarly the independent variables for the splot command are "u" and "v" in parametric mode (splot cannot be used in polar mode), or "x" and "y" otherwise. It may be more convenient to call a dummy variable by a more physically meaningful or conventional name. For example, when plotting time functions: set dummy t plot sin(t), cos(t) At least one dummy variable must be set on the command; set dummy by itself will generate an error message. Examples: set dummy u,v set dummy ,s The second example sets the second variable to s. ## encoding The set encoding command selects a character encoding. Valid values are default, which tells a terminal to use its default; iso_8859_1 (known in the PostScript world as ISO-Latin1), which is used on many Unix workstations and with MS-Windows; cp850, for OS/2; and cp437, for MS-DOS. Syntax: set encoding {<value>} show encoding Note that encoding is not supported by all terminal drivers and that the device must be able to produce the desired non-standard characters. ## format The format of the tic-mark labels can be set with the set format command. Syntax: set format {<axes>} {"<format-string>"} set format {<axes>} {'<format-string>'} show format Newline (\n) is accepted in the format string. Use double-quotes rather than single-quotes to enable such interpretation. See also syntax. The default format for both axes is "%g", but other formats such as "%.2f" or "%3.0em" are often desirable. Anything accepted by 'printf' when given a double precision number, and accepted by the terminal, will work. Some other options have been added. If the format string looks like a floating point format, then gnuplot tries to construct a reasonable format. Characters not preceded by "%" are printed verbatim. Thus you can include spaces and labels in your format string, such as "%g m", which will put " m" after each number. If you want "%" itself, double it: "%g %%". See also set xtics for more information about tic labels. See demo. ### format specifiers The acceptable formats (if not in time/date mode) are: Format Explanation %f floating point notation %e or %E exponential notation; an "e" or "E" before the power %g or %G the shorter of %e (or %E) and %f %x or %X hex %o or %O octal %t mantissa to base 10 %l mantissa to base of current logscale %s mantissa to base of current logscale; scientific power %T power to base 10 %L power to base of current logscale %S scientific power %c character replacement for scientific power %P multiple of pi A 'scientific' power is one such that the exponent is a multiple of three. Character replacement of scientific powers ("%c") has been implemented for powers in the range -18 to +18. For numbers outside of this range the format reverts to exponential. Other acceptable modifiers (which come after the "%" but before the format specifier) are "-", which left-justifies the number; "+", which forces all numbers to be explicitly signed; "#", which places a decimal point after floats that have only zeroes following the decimal point; a positive integer, which defines the field width; "0" (the digit, not the letter) immediately preceding the field width, which indicates that leading zeroes are to be used instead of leading blanks; and a decimal point followed by a non-negative integer, which defines the precision (the minimum number of digits of an integer, or the number of digits following the decimal point of a float). Some releases of 'printf' may not support all of these modifiers but may also support others; in case of doubt, check the appropriate documentation and then experiment. Examples: set format y "%t"; set ytics (5,10) # "5.0" and "1.0" set format y "%s"; set ytics (500,1000) # "500" and "1.0" set format y "+-12.3f"; set ytics(12345) # "+12345.000 " set format y "%.2t*10^%+03T"; set ytic(12345)# "1.23*10^+04" set format y "%s*10^{%S}"; set ytic(12345) # "12.345*10^{3}" set format y "%s %cg"; set ytic(12345) # "12.345 kg" set format y "%.0P pi"; set ytic(6.283185) # "2 pi" set format y "%.0P%%"; set ytic(50) # "50%" set log y 2; set format y '%l'; set ytics (1,2,3) #displays "1.0", "1.0" and "1.5" (since 3 is 1.5 * 2^1) There are some problem cases that arise when numbers like 9.999 are printed with a format that requires both rounding and a power. If the data type for the axis is time/date, the format string must contain valid codes for the 'strftime' function (outside of gnuplot, type "man strftime"). See set timefmt for a list of the allowed input format codes. ### time/date specifiers In time/date mode, the acceptable formats are: Format Explanation %a abbreviated name of day of the week %A full name of day of the week %b or %h abbreviated name of the month %B full name of the month %d day of the month, 1--31 %D shorthand for "%m/%d/%y" %H or %k hour, 0--24 %I or %l hour, 0--12 %j day of the year, 1--366 %m month, 1--12 %M minute, 0--60 %p "am" or "pm" %r shorthand for "%I:%M:%S %p" %R shorthand for %H:%M" %S second, 0--60 %T shorthand for "%H:%M:%S" %U week of the year (week starts on Sunday) %w day of the week, 0--6 (Sunday = 0) %W week of the year (week starts on Monday) %y year, 0-99 %Y year, 4-digit Except for the non-numerical formats, these may be preceded by a "0" ("zero", not "oh") to pad the field length with leading zeroes, and a positive digit, to define the minimum field width (which will be overridden if the specified width is not large enough to contain the number). There is a 24-character limit to the length of the printed text; longer strings will be truncated. Examples: Suppose the text is "76/12/25 23:11:11". Then set format x # defaults to "12/25/76" \n "23:11" set format x "%A, %d %b %Y" # "Saturday, 25 Dec 1976" set format x "%r %d" # "11:11:11 pm 12/25/76" Suppose the text is "98/07/06 05:04:03". Then set format x "%1y/%2m/%3d %01H:%02M:%03S" # "98/ 7/ 6 5:04:003" ## function style The set function style command changes the default plotting style for function plots. Syntax: set function style <style-choice> show function style See set style for the choices. If no choice is given, the choices are listed. show function style shows the current default function plotting style. ## functions The show functions command lists all user-defined functions and their definitions. Syntax: show functions ## grid The set grid command allows grid lines to be drawn on the plot. Syntax: set grid {{no}{m}xtics} {{no}{m}ytics} {{no}{m}ztics} {{no}{m}x2tics} {{no}{m}y2tics} {polar {<angle>}} { {linestyle <major_linestyle>} | {linetype | lt <major_linetype>} {linewidth | lw <major_linewidth>} { , {linestyle | ls <minor_linestyle>} | {linetype | lt <minor_linetype>} {linewidth | lw <minor_linewidth>} } } set nogrid show grid The grid can be enabled and disabled for the major and/or minor tic marks on any axis, and the linetype and linewidth can be specified for major and minor grid lines, also via a predefined linestyle, as far as the active terminal driver supports this. Additionally, a polar grid can be selected for 2-d plots---circles are drawn to intersect the selected tics, and radial lines are drawn at definable intervals. (The interval is given in degrees or radians ,depending on the set angles setting.) Note that a polar grid is no longer automatically generated in polar mode. The pertinent tics must be enabled before set grid can draw them; gnuplot will quietly ignore instructions to draw grid lines at non-existent tics, but they will appear if the tics are subsequently enabled. If no linetype is specified for the minor gridlines, the same linetype as the major gridlines is used. The default polar angle is 30 degrees. By default, grid lines are drawn with half the usual linewidth. The major and minor linewidth specifiers scale this default value; for example, set grid lw .5 will draw grid lines with one quarter the usual linewidth. Z grid lines are drawn on the back of the plot. This looks better if a partial box is drawn around the plot---see set border. ## hidden3d The set hidden3d command enables hidden line removal for surface plotting (see splot). Some optional features of the underlying algorithm can also be controlled using this command. Syntax: set hidden3d {defaults} | { {{offset <offset>} | {nooffset}} {trianglepattern <bitpattern>} {{undefined <level>} | {noundefined}} {{no}altdiagonal} {{no}bentover} } set nohidden3d show hidden3d In contrast to the usual display in gnuplot, hidden line removal actually treats the given function or data grids as real surfaces that can't be seen through, so parts behind the surface will be hidden by it. For this to be possible, the surface needs to have 'grid structure' (see splot datafile about this), and it has to be drawn with lines or with linespoints. When hidden3d is set, both the hidden portion of the surface and possibly its contours drawn on the base (see set contour) as well as the grid will be hidden. Each surface has its hidden parts removed with respect to itself and to other surfaces, if more than one surface is plotted. Contours drawn on the surface (set contour surface) don't work. Labels and arrows are always visible and are unaffected. The key is also never hidden by the surface. Functions are evaluated at isoline intersections. The algorithm interpolates linearly between function points or data points when determining the visible line segments. This means that the appearance of a function may be different when plotted with hidden3d than when plotted with nohidden3d because in the latter case functions are evaluated at each sample. Please see set samples and set isosamples for discussion of the difference. The algorithm used to remove the hidden parts of the surfaces has some additional features controllable by this command. Specifying defaults will set them all to their default settings, as detailed below. If defaults is not given, only explicitly specified options will be influenced: all others will keep their previous values, so you can turn on/off hidden line removal via set {no}hidden3d, without modifying the set of options you chose. The first option, offset, influences the linestyle used for lines on the 'back' side. Normally, they are drawn in a linestyle one index number higher than the one used for the front, to make the two sides of the surface distinguishable. You can specify a different line style offset to add instead of the default 1, by offset <offset>. Option nooffset stands for offset 0, making the two sides of the surface use the same linestyle. Next comes the option trianglepattern <bitpattern>. <bitpattern> must be a number between 0 and 7, interpreted as a bit pattern. Each bit determines the visibility of one edge of the triangles each surface is split up into. Bit 0 is for the 'horizontal' edges of the grid, Bit 1 for the 'vertical' ones, and Bit 2 for the diagonals that split each cell of the original grid into two triangles. The default pattern is 3, making all horizontal and vertical lines visible, but not the diagonals. You may want to choose 7 to see those diagonals as well. The undefined <level> option lets you decide what the algorithm is to do with data points that are undefined (missing data, or undefined function values), or exceed the given x-, y- or z-ranges. Such points can either be plotted nevertheless, or taken out of the input data set. All surface elements touching a point that is taken out will be taken out as well, thus creating a hole in the surface. If <level> = 3, equivalent to option noundefined, no points will be thrown away at all. This may produce all kinds of problems elsewhere, so you should avoid this. <level> = 2 will throw away undefined points, but keep the out-of-range ones. <level> = 1, the default, will get rid of out-of-range points as well. By specifying noaltdiagonal, you can override the default handling of a special case can occur if undefined is active (i.e. <level> is not 3). Each cell of the grid-structured input surface will be divided in two triangles along one of its diagonals. Normally, all these diagonals have the same orientation relative to the grid. If exactly one of the four cell corners is excluded by the undefined handler, and this is on the usual diagonal, both triangles will be excluded. However if the default setting of altdiagonal is active, the other diagonal will be chosen for this cell instead, minimizing the size of the hole in the surface. The bentover option controls what happens to another special case, this time in conjunction with the trianglepattern. For rather crumply surfaces, it can happen that the two triangles a surface cell is divided into are seen from opposite sides (i.e. the original quadrangle is 'bent over'), as illustrated in the following ASCII art: C----B original quadrangle: A--B displayed quadrangle: |\ | ("set view 0,0") | /| ("set view 75,75" perhaps) | \ | |/ | | \ | C--D | \| A D If the diagonal edges of the surface cells aren't generally made visible by bit 2 of the <bitpattern> there, the edge CB above wouldn't be drawn at all, normally, making the resulting display hard to understand. Therefore, the default option of bentover will turn it visible in this case. If you don't want that, you may choose nobentover instead. Hidden Line Removal Demo and Complex Hidden Line Demo. ## isosamples The isoline density (grid) for plotting functions as surfaces may be changed by the set isosamples command. Syntax: set isosamples <iso_1> {,<iso_2>} show isosamples Each function surface plot will have <iso_1> iso-u lines and <iso_2> iso-v lines. If you only specify <iso_1>, <iso_2> will be set to the same value as <iso_1>. By default, sampling is set to 10 isolines per u or v axis. A higher sampling rate will produce more accurate plots, but will take longer. These parameters have no effect on data file plotting. An isoline is a curve parameterized by one of the surface parameters while the other surface parameter is fixed. Isolines provide a simple means to display a surface. By fixing the u parameter of surface s(u,v), the iso-u lines of the form c(v) = s(u0,v) are produced, and by fixing the v parameter, the iso-v lines of the form c(u) = s(u,v0) are produced. When a function surface plot is being done without the removal of hidden lines, set samples controls the number of points sampled along each isoline; see set samples and set hidden3d. The contour algorithm assumes that a function sample occurs at each isoline intersection, so change in samples as well as isosamples may be desired when changing the resolution of a function surface/contour. ## key The set key enables a key (or legend) describing plots on a plot. The contents of the key, i.e., the names given to each plotted data set and function and samples of the lines and/or symbols used to represent them, are determined by the title and with options of the {s}plot command. Please see plot title and plot with for more information. Syntax: set key { left | right | top | bottom | outside | below | <position>} {Left | Right} {{no}reverse} {samplen <sample_length>} {spacing <vertical_spacing>} {width <width_increment>} {title "<text>"} {{no}box { {linestyle | ls <line_style>} | {linetype | lt <line_type>} {linewidth | lw <line_width>}}} set nokey show key By default the key is placed in the upper right corner of the graph. The keywords left, right, top, bottom, outside and below may be used to place the key in the other corners inside the graph or to the right (outside) or below the graph. They may be given alone or combined. Justification of the labels within the key is controlled by Left or Right (default is Right). The text and sample can be reversed (reverse) and a box can be drawn around the key (box {...}) in a specified linetype and linewidth, or a user-defined linestyle. Note that not all terminal drivers support linewidth selection, though. The length of the sample line can be controlled by samplen. The sample length is computed as the sum of the tic length and <sample_length> times the character width. samplen also affects the positions of point samples in the key since these are drawn at the midpoint of the sample line, even if it is not drawn. <sample_length> must be an integer. The vertical spacing between lines is controlled by spacing. The spacing is set equal to the product of the pointsize, the vertical tic size, and <vertical_spacing>. The program will guarantee that the vertical spacing is no smaller than the character height. The <width_increment> is a number of character widths to be added to or subtracted from the length of the string. This is useful only when you are putting a box around the key and you are using control characters in the text. gnuplot simply counts the number of characters in the string when computing the box width; this allows you to correct it. A title can be put on the key (title "<text>")---see also syntax for the distinction between text in single- or double-quotes. The key title uses the same justification as do the plot titles. The defaults for set key are right, top, Right, noreverse, samplen 4, spacing 1.25, title "", and nobox. The default <linetype> is the same as that used for the plot borders. Entering set key with no options returns the key to its default configuration. The <position> can be a simple x,y,z as in previous versions, but these can be preceded by one of four keywords (first, second, graph, screen) which selects the coordinate system in which the position is specified. See coordinates for more details. The key is drawn as a sequence of lines, with one plot described on each line. On the right-hand side (or the left-hand side, if reverse is selected) of each line is a representation that attempts to mimic the way the curve is plotted. On the other side of each line is the text description (the line title), obtained from the plot command. The lines are vertically arranged so that an imaginary straight line divides the left- and right-hand sides of the key. It is the coordinates of the top of this line that are specified with the set key command. In a plot, only the x and y coordinates are used to specify the line position. For a splot, x, y and z are all used as a 3-d location mapped using the same mapping as the graph itself to form the required 2-d screen position of the imaginary line. Some or all of the key may be outside of the graph boundary, although this may interfere with other labels and may cause an error on some devices. If you use the keywords outside or below, gnuplot makes space for the keys and the graph becomes smaller. Putting keys outside to the right, they occupy as few columns as possible, and putting them below, as many columns as possible (depending of the length of the labels), thus stealing as little space from the graph as possible. When using the TeX or PostScript drivers, or similar drivers where formatting information is embedded in the string, gnuplot is unable to calculate correctly the width of the string for key positioning. If the key is to be positioned at the left, it may be convenient to use the combination set key left Left reverse. The box and gap in the grid will be the width of the literal string. If splot is being used to draw contours, the contour labels will be listed in the key. If the alignment of these labels is poor or a different number of decimal places is desired, the label format can be specified. See set clabel for details. Examples: This places the key at the default location: set key This disables the key: set nokey This places a key at coordinates 2,3.5,2 in the default (first) coordinate system: set key 2,3.5,2 This places the key below the graph: set key below This places the key in the bottom left corner, left-justifies the text, gives it a title, and draws a box around it in linetype 3: set key left bottom Left title 'Legend' box 3 ## label Arbitrary labels can be placed on the plot using the set label command. Syntax: set label {<tag>} {"<label_text>"} {at <position>} {<justification>} {{no}rotate} {font "<name><,size>"} set nolabel {<tag>} show label The tag is an integer that is used to identify the label. If no <tag> is given, the lowest unused tag value is assigned automatically. The tag can be used to delete or modify a specific label. To change any attribute of an existing label, use the set label command with the appropriate tag, and specify the parts of the label to be changed. By default, the text is placed flush left against the point x,y,z. To adjust the way the label is positioned with respect to the point x,y,z, add the parameter <justification>, which may be left, right or center, indicating that the point is to be at the left, right or center of the text. Labels outside the plotted boundaries are permitted but may interfere with axis labels or other text. If rotate is given, the label is written vertically (if the terminal can do so, of course). If one (or more) axis is timeseries, the appropriate coordinate should be given as a quoted time string according to the timefmt format string. See set xdata and set timefmt. The EEPIC, Imagen, LaTeX, and TPIC drivers allow \\ in a string to specify a newline. Examples: To set a label at (1,2) to "y=x", use: set label "y=x" at 1,2 To set a Sigma of size 24, from the Symbol font set, at the center of the graph, use: set label "S" at graph 0.5,0.5 center font "Symbol,24" To set a label "y=x^2" with the right of the text at (2,3,4), and tag the label as number 3, use: set label 3 "y=x^2" at 2,3,4 right To change the preceding label to center justification, use: set label 3 center To delete label number 2, use: set nolabel 2 To delete all labels, use: set nolabel To show all labels (in tag order), use: show label To set a label on a graph with a timeseries on the x axis, use, for example: set timefmt "%d/%m/%y,%H:%M" set label "Harvest" at "25/8/93",1 ## linestyle Each terminal has a default set of line and point types, which can be seen by using the command test. set linestyle defines a set of line types and widths and point types and sizes so that you can refer to them later by an index instead of repeating all the information at each invocation. Syntax: set linestyle <index> {linetype | lt <line_type>} {linewidth | lw <line_width>} {pointtype | pt <point_type>} {pointsize | ps <point_size>} set nolinestyle show linestyle The line and point types are taken from the default types for the terminal currently in use. The line width and point size are multipliers for the default width and size (but note that <point_size> here is unaffected by the multiplier given on 'set pointsize'). The defaults for the line and point types is the index. The defaults for the width and size are both unity. Linestyles created by this mechanism do not replace the default styles; both may be used. Not all terminals support the linewidth and pointsize features; if not supported, the option will be ignored. Note that this feature is not completely implemented; linestyles defined by this mechanism may be used with 'plot', 'splot', 'replot', and 'set arrow', but not by other commands that allow the default index to be used, such as 'set grid'. Example: Suppose that the default lines for indices 1, 2, and 3 are red, green, and blue, respectively, and the default point shapes for the same indices are a square, a cross, and a triangle, respectively. Then set linestyle 1 lt 2 lw 2 pt 3 ps 0.5 defines a new linestyle that is green and twice the default width and a new pointstyle that is a half-sized triangle. The commands set function style lines plot f(x) lt 3, g(x) ls 1 will create a plot of f(x) using the default blue line and a plot of g(x) using the user-defined wide green line. Similarly the commands set function style linespoints plot p(x) lt 1 pt 3, q(x) ls 1 will create a plot of f(x) using the default triangles connected by a red line and q(x) using small triangles connected by a green line. ## lmargin ## locale The locale setting determines the language with which {x,y,z}{d,m}tics will write the days and months. Syntax: set locale {"<locale>"} <locale> may be any language designation acceptable to your installation. See your system documentation for the available options. The default value is determined from the LANG environment variable. ## logscale Log scaling may be set on the x, y, z, x2 and/or y2 axes. Syntax: set logscale <axes> <base> set nologscale <axes> show logscale where <axes> may be any combinations of x, y, and z, in any order, or x2 or y2 and where <base> is the base of the log scaling. If <base> is not given, then 10 is assumed. If <axes> is not given, then all axes are assumed. set nologscale turns off log scaling for the specified axes. Examples: To enable log scaling in both x and z axes: set logscale xz To enable scaling log base 2 of the y axis: set logscale y 2 To disable z axis log scaling: set nologscale z ## mapping If data are provided to splot in spherical or cylindrical coordinates, the set mapping command should be used to instruct gnuplot how to interpret them. Syntax: set mapping {cartesian | spherical | cylindrical} A cartesian coordinate system is used by default. For a spherical coordinate system, the data occupy two or three columns (or using entries). The first two are interpreted as the polar and azimuthal angles theta and phi (in the units specified by set angles). The radius r is taken from the third column if there is one, or is set to unity if there is no third column. The mapping is: x = r * cos(theta) * cos(phi) y = r * sin(theta) * cos(phi) z = r * sin(phi) Note that this is a "geographic" spherical system, rather than a "polar" one. For a cylindrical coordinate system, the data again occupy two or three columns. The first two are interpreted as theta (in the units specified by set angles) and z. The radius is either taken from the third column or set to unity, as in the spherical case. The mapping is: x = r * cos(theta) y = r * sin(theta) z = z The effects of mapping can be duplicated with the using filter on the splot command, but mapping may be more convenient if many data files are to be processed. However even if mapping is used, using may still be necessary if the data in the file are not in the required order. mapping has no effect on plot. Mapping Demos. ## margin The computed margins can be overridden by the set margin commands. show margin shows the current settings. Syntax: set bmargin {<margin>} set lmargin {<margin>} set rmargin {<margin>} set tmargin {<margin>} show margin Normally the margins of a plot are automatically calculated based on tics, tic labels, axis labels, the plot title, the timestamp and the size of the key if it is outside the borders. If, however, tics are attached to the axes (set xtics axis, for example), neither the tics themselves nor their labels will be included in either the margin calculation or the calculation of the positions of other text to be written in the margin. This can lead to tic labels overwriting other text if the axis is very close to the border. ## missing The set missing command allows you to tell gnuplot what character is used in a data file to denote missing data. Syntax: set missing {"<character>"} show missing Example: set missing "?" would mean that, when plotting a file containing 1 1 2 ? 3 2 the middle line would be ignored. There is no default character for missing. ## multiplot The command set multiplot places gnuplot in the multiplot mode, in which several plots are placed on the same page, window, or screen. Syntax: set multiplot set nomultiplot For some terminals, no plot is displayed until the command set nomultiplot is given, which causes the entire page to be drawn and then returns gnuplot to its normal single-plot mode. For other terminals, each separate plot command produces a plot, but the screen may not be cleared between plots. Any labels or arrows that have been defined will be drawn for each plot according to the current size and origin (unless their coordinates are defined in the screen system). Just about everything else that can be set is applied to each plot, too. If you want something to appear only once on the page, for instance a single time stamp, you'll need to put a set time/set notime pair around one of the plot, splot or replot commands within the set multiplot/set nomultiplot block. The commands set origin and set size must be used to correctly position each plot; see set origin and set size for details of their usage. Example: set size 0.7,0.7 set origin 0.1,0.1 set multiplot set size 0.4,0.4 set origin 0.1,0.1 plot sin(x) set size 0.2,0.2 set origin 0.5,0.5 plot cos(x) set nomultiplot displays a plot of cos(x) stacked above a plot of sin(x). Note the initial set size and set origin. While these are not always required, their inclusion is recommended. Some terminal drivers require that bounding box information be available before any plots can be made, and the form given above guarantees that the bounding box will include the entire plot array rather than just the bounding box of the first plot. set size and set origin refer to the entire plotting area used for each plot. If you want to have the axes themselves line up, you can guarantee that the margins are the same size with the set margin commands. See set margin for their use. Note that the margin settings are absolute, in character units, so the appearance of the graph in the remaining space will depend on the screen size of the display device, e.g., perhaps quite different on a video display and a printer. See demo. ## mx2tics ## mxtics Minor tic marks along the x axis are controlled by set mxtics. They can be turned off with set nomxtics. Similar commands control minor tics along the other axes. Syntax: set mxtics {<freq> | default} set nomxtics show mxtics <freq> is the number of sub-intervals (NOT the number of minor tics) between major tics (ten is the default for a linear axis, so there are nine minor tics between major tics). Selecting default will return the number of minor ticks to its default value. If the axis is logarithmic, the number of sub-intervals will be set to a reasonable number by default (based upon the length of a decade). This will be overridden if <freq> is given. However the usual minor tics (2, 3, ..., 8, 9 between 1 and 10, for example) are obtained by setting <freq> to 10, even though there are but nine sub-intervals. Minor tics can be used only with uniformly spaced major tics. Since major tics can be placed arbitrarily by set {x|x2|y|y2|z}tics, minor tics cannot be used if major tics are explicitly set. By default, minor tics are off for linear axes and on for logarithmic axes. They inherit the settings for axis|border and {no}mirror specified for the major tics. Please see set xtics for information about these. ## my2tics ## mytics ## mztics ## offsets Offsets provide a mechanism to put a boundary around the data inside of an autoscaled graph. Syntax: set offsets <left>, <right>, <top>, <bottom> set nooffsets show offsets Each offset may be a constant or an expression. Each defaults to 0. Left and right offsets are given in units of the x axis, top and bottom offsets in units of the y axis. A positive offset expands the graph in the specified direction, e.g., a positive bottom offset makes ymin more negative. Negative offsets, while permitted, can have unexpected interactions with autoscaling and clipping. Example: set offsets 0, 0, 2, 2 plot sin(x) This graph of sin(x) will have a y range [-3:3] because the function will be autoscaled to [-1:1] and the vertical offsets are each two. ## origin Syntax: set origin <x-origin>,<y-origin> ## output By default, screens are displayed to the standard output. The set output command redirects the display to the specified file or device. Syntax: set output {"<filename>"} show output MSDOS users should note that the \ character has special significance in double-quoted strings, so single-quotes should be used for filenames in different directories. When both set terminal and set output are used together, it is safest to give set terminal first, because some terminals set a flag which is needed in some operating systems. This would be the case, for example, if the operating system needs to know whether or not a file is to be formatted in order to open it properly. On machines with popen functions (Unix), output can be piped through a shell command if the first non-whitespace character of the filename is '|'. For instance, set output "|lpr -Plaser filename" set output "|lp -dlaser filename" On MSDOS machines, set output "PRN" will direct the output to the default printer. On VMS, output can be sent directly to any spooled device. It is also possible to send the output to DECnet transparent tasks, which allows some flexibility. ## parametric The set parametric command changes the meaning of plot (splot) from normal functions to parametric functions. The command set noparametric restores the plotting style to normal, single-valued expression plotting. Syntax: set parametric set noparametric show parametric For 2-d plotting, a parametric function is determined by a pair of parametric functions operating on a parameter. An example of a 2-d parametric function would be plot sin(t),cos(t), which draws a circle (if the aspect ratio is set correctly---see set size). gnuplot will display an error message if both functions are not provided for a parametric plot. For 3-d plotting, the surface is described as x=f(u,v), y=g(u,v), z=h(u,v). Therefore a triplet of functions is required. An example of a 3-d parametric function would be cos(u)*cos(v),cos(u)*sin(v),sin(u), which draws a sphere. gnuplot will display an error message if all three functions are not provided for a parametric splot. The total set of possible plots is a superset of the simple f(x) style plots, since the two functions can describe the x and y values to be computed separately. In fact, plots of the type t,f(t) are equivalent to those produced with f(x) because the x values are computed using the identity function. Similarly, 3-d plots of the type u,v,f(u,v) are equivalent to f(x,y). Note that the order the parametric functions are specified is xfunction, yfunction (and zfunction) and that each operates over the common parametric domain. Also, the set parametric function implies a new range of values. Whereas the normal f(x) and f(x,y) style plotting assume an xrange and yrange (and zrange), the parametric mode additionally specifies a trange, urange, and vrange. These ranges may be set directly with set trange, set urange, and set vrange, or by specifying the range on the plot or splot commands. Currently the default range for these parametric variables is [-5:5]. Setting the ranges to something more meaningful is expected. ## pointsize The set pointsize command scales the size of the points used in plots. Syntax: set pointsize <multiplier> show pointsize The default is a multiplier of 1.0. Larger pointsizes may be useful to make points more visible in bitmapped graphics. The pointsize of a single plot may be changed on the plot command. See plot with for details. Please note that the pointsize setting is not supported by all terminal types. ## polar The set polar command changes the meaning of the plot from rectangular coordinates to polar coordinates. Syntax: set polar set nopolar show polar There have been changes made to polar mode in version 3.7, so that scripts for gnuplot versions 3.5 and earlier will require modification. The main change is that the dummy variable t is used for the angle so that the x and y ranges can be controlled independently. Other changes are: 1) tics are no longer put along the zero axes automatically ---use set xtics axis nomirror; set ytics axis nomirror; 2) the grid, if selected, is not automatically polar ---use set grid polar; 3) the grid is not labelled with angles ---use set label as necessary. In polar coordinates, the dummy variable (t) is an angle. The default range of t is [0:2*pi], or, if degree units have been selected, to [0:360] (see set angles). The command set nopolar changes the meaning of the plot back to the default rectangular coordinate system. The set polar command is not supported for splots. See the set mapping command for similar functionality for splots. While in polar coordinates the meaning of an expression in t is really r = f(t), where t is an angle of rotation. The trange controls the domain (the angle) of the function, and the x and y ranges control the range of the graph in the x and y directions. Each of these ranges, as well as the rrange, may be autoscaled or set explicitly. See set xrange for details of all the set range commands. Example: set polar plot t*sin(t) plot [-2*pi:2*pi] [-3:3] [-3:3] t*sin(t) The first plot uses the default polar angular domain of 0 to 2*pi. The radius and the size of the graph are scaled automatically. The second plot expands the domain, and restricts the size of the graph to [-3:3] in both directions. You may want to set size square to have gnuplot try to make the aspect ratio equal to unity, so that circles look circular. Polar demos Polar Data Plot. ## rmargin ## rrange ## samples The sampling rate of functions, or for interpolating data, may be changed by the set samples command. Syntax: set samples <samples_1> {,<samples_2>} show samples When a 2-d graph is being done, only the value of <samples_1> is relevant. When a surface plot is being done without the removal of hidden lines, the value of samples specifies the number of samples that are to be evaluated for the isolines. Each iso-v line will have <sample_1> samples and each iso-u line will have <sample_2> samples. If you only specify <samples_1>, <samples_2> will be set to the same value as <samples_1>. See also set isosamples. ## size The set size command scales the displayed size of the plot. Syntax: set size {{no}square | ratio <r> | noratio} {<xscale>,<yscale>} show size The <xscale> and <yscale> values are the scaling factors for the size of the plot, which includes the graph and the margins. ratio causes gnuplot to try to create a graph with an aspect ratio of <r> (the ratio of the y-axis length to the x-axis length) within the portion of the plot specified by <xscale> and <yscale>. The meaning of a negative value for <r> is different. If <r>=-1, gnuplot tries to set the scales so that the unit has the same length on both the x and y axes (suitable for geographical data, for instance). If <r>=-2, the unit on y has twice the length of the unit on x, and so on. The success of gnuplot in producing the requested aspect ratio depends on the terminal selected. The graph area will be the largest rectangle of aspect ratio <r> that will fit into the specified portion of the output (leaving adequate margins, of course). square is a synonym for ratio 1. Both noratio and nosquare return the graph to the default aspect ratio of the terminal, but do not return <xscale> or <yscale> to their default values (1.0). ratio and square have no effect on 3-d plots. set size is relative to the default size, which differs from terminal to terminal. Since gnuplot fills as much of the available plotting area as possible by default, it is safer to use set size to decrease the size of a plot than to increase it. See set terminal for the default sizes. On some terminals, changing the size of the plot will result in text being misplaced. Examples: To set the size to normal size use: set size 1,1 To make the graph half size and square use: set size square 0.5,0.5 To make the graph twice as high as wide use: set size ratio 2 ## style Default styles are chosen with the set function style and set data style commands. See plot with for information about how to override the default plotting style for individual functions and data sets. Syntax: set function style <style> set data style <style> show function style show data style The types used for all line and point styles (i.e., solid, dash-dot, color, etc. for lines; circles, squares, crosses, etc. for points) will be either those specified on the plot or splot command or will be chosen sequentially from the types available to the terminal in use. Use the command test to see what is available. None of the styles requiring more than two columns of information (e.g., errorbars) can be used with splots or function plots. Neither boxes nor any of the steps styles can be used with splots. If an inappropriate style is specified, it will be changed to points. For 2-d data with more than two columns, gnuplot is picky about the allowed errorbar styles. The using option on the plot command can be used to set up the correct columns for the style you want. (In this discussion, "column" will be used to refer both to a column in the data file and an entry in the using list.) For three columns, only xerrorbars, yerrorbars (or errorbars), boxes, and boxerrorbars are allowed. If another plot style is used, the style will be changed to yerrorbars. The boxerrorbars style will calculate the boxwidth automatically. For four columns, only xerrorbars, yerrorbars (or errorbars), xyerrorbars, boxxyerrorbars, and boxerrorbars are allowed. An illegal style will be changed to yerrorbars. Five-column data allow only the boxerrorbars, financebars, and candlesticks styles. (The last two of these are primarily used for plots of financial prices.) An illegal style will be changed to boxerrorbars before plotting. Six- and seven-column data only allow the xyerrorbars and boxxyerrorbars styles. Illegal styles will be changed to xyerrorbars before plotting. For more information about error bars, please see plot errorbars. ### boxerrorbars The boxerrorbars style is only relevant to 2-d data plotting. It is a combination of the boxes and yerrorbars styles. The boxwidth will come from the fourth column if the y errors are in the form of "ydelta" and the boxwidth was not previously set equal to -2.0 (set boxwidth -2.0) or from the fifth column if the y errors are in the form of "ylow yhigh". The special case boxwidth = -2.0 is for four-column data with y errors in the form "ylow yhigh". In this case the boxwidth will be calculated so that each box touches the adjacent boxes. The width will also be calculated in cases where three-column data are used. The box height is determined from the y error in the same way as it is for the yerrorbars style---either from y-ydelta to y+ydelta or from ylow to yhigh, depending on how many data columns are provided. See Demo. ### boxes The boxes style is only relevant to 2-d plotting. It draws a box centered about the given x coordinate from the x axis (not the graph border) to the given y coordinate. The width of the box is obtained in one of three ways. If it is a data plot and the data file has a third column, this will be used to set the width of the box. If not, if a width has been set using the set boxwidth command, this will be used. If neither of these is available, the width of each box will be calculated automatically so that it touches the adjacent boxes. ### boxxyerrorbars The box width and height are determined from the x and y errors in the same way as they are for the xyerrorbars style---either from xlow to xhigh and from ylow to yhigh, or from x-xdelta to x+xdelta and from y-ydelta to y+ydelta , depending on how many data columns are provided. ### candlesticks ### dots The dots style plots a tiny dot at each point; this is useful for scatter plots with many points. ### financebars ### fsteps ### histeps The histeps style is only relevant to 2-d plotting. It is intended for plotting histograms. Y-values are assumed to be centered at the x-values; the point at x1 is represented as a horizontal line from ((x0+x1)/2,y1) to ((x1+x2)/2,y1). The lines representing the end points are extended so that the step is centered on at x. Adjacent points are connected by a vertical line at their average x, that is, from ((x1+x2)/2,y1) to ((x1+x2)/2,y2). If autoscale is in effect, it selects the xrange from the data rather than the steps, so the end points will appear only half as wide as the others. See demo. histeps is only a plotting style; gnuplot does not have the ability to create bins and determine their population from some data set. ### impulses ### lines The lines style connects adjacent points with straight line segments. ### linespoints The linespoints style does both lines and points, that is, it draws a small symbol at each point and then connects adjacent points with straight line segments. The command set pointsize may be used to change the size of the points. See set pointsize for its usage. linespoints may be abbreviated lp. ### points ### steps ### vector The vector style draws a vector from (x,y) to (x+xdelta,y+ydelta). Thus it requires four columns of data. It also draws a small arrowhead at the end of the vector. The vector style is still experimental: it doesn't get clipped properly and other things may also be wrong with it. Use it at your own risk. ### xerrorbars The xerrorbars style is only relevant to 2-d data plots. xerrorbars is like dots, except that a horizontal error bar is also drawn. At each point (x,y), a line is drawn from (xlow,y) to (xhigh,y) or from (x-xdelta,y) to (x+xdelta,y), depending on how many data columns are provided. A tic mark is placed at the ends of the error bar (unless set bar is used---see set bar for details). ### xyerrorbars The xyerrorbars style is only relevant to 2-d data plots. xyerrorbars is like dots, except that horizontal and vertical error bars are also drawn. At each point (x,y), lines are drawn from (x,y-ydelta) to (x,y+ydelta) and from (x-xdelta,y) to (x+xdelta,y) or from (x,ylow) to (x,yhigh) and from (xlow,y) to (xhigh,y), depending upon the number of data columns provided. A tic mark is placed at the ends of the error bar (unless set bar is used---see set bar for details). If data are provided in an unsupported mixed form, the using filter on the plot command should be used to set up the appropriate form. For example, if the data are of the form (x,y,xdelta,ylow,yhigh), then you can use plot 'data' using 1:2:(1-3),(1+3),4,5 with xyerrorbars ### yerrorbars The yerrorbars (or errorbars) style is only relevant to 2-d data plots. yerrorbars is like dots, except that a vertical error bar is also drawn. At each point (x,y), a line is drawn from (x,y-ydelta) to (x,y+ydelta) or from (x,ylow) to (x,yhigh), depending on how many data columns are provided. A tic mark is placed at the ends of the error bar (unless set bar is used---see set bar for details). See demo. ## surface Syntax: set surface set nosurface show surface The surface is drawn with the style specifed by with, or else the appropriate style, data or function. Whenever set nosurface is issued, splot will not draw points or lines corresponding to the function or data file points. Contours may be still be drawn on the surface, depending on the set contour option. set nosurface; set contour base is useful for displaying contours on the grid base. See also set contour. ## Terminal Types ## terminal gnuplot supports many different graphics devices. Use set terminal to tell gnuplot what kind of output to generate. Use set output to redirect that output to a file or device. Syntax: set terminal {<terminal-type>} show terminal If <terminal-type> is omitted, gnuplot will list the available terminal types. <terminal-type> may be abbreviated. If both set terminal and set output are used together, it is safest to give set terminal first, because some terminals set a flag which is needed in some operating systems. Several terminals have additional options. For example, see dumb, iris4d, hpljii or postscript. This document may describe drivers that are not available to you because they were not installed, or it may not describe all the drivers that are available to you, depending on its output format. ### aed767 The aed512 and aed767 terminal drivers support AED graphics terminals. The two drivers differ only in their horizontal ranges, which are 512 and 768 pixels, respectively. Their vertical range is 575 pixels. There are no options for these drivers. ### aifm Several options may be set in aifm---the Adobe Illustrator 3.0+ driver. Syntax: set terminal aifm {<color>} {"<fontname>"} {<fontsize>} <color> is either color or monochrome; "<fontname>" is the name of a valid PostScript font; <fontsize> is the size of the font in PostScript points, before scaling by the set size command. Selecting default sets all options to their default values: monochrome, "Helvetica", and 14pt. Since AI does not really support multiple pages, multiple graphs will be drawn directly on top of one another. However, each graph will be grouped individually, making it easy to separate them inside AI (just pick them up and move them). Examples: set term aifm set term aifm 22 set size 0.7,1.4; set term aifm color "Times-Roman" 14 ### amiga The amiga terminal, for Commodore Amiga computers, allows the user to plot either to a screen (default), or, if Kickstart 3.0 or higher is installed, to a window on the current public screen. The font and its size can also be selected. Syntax: set terminal amiga {screen | window} {"<fontname>"} {<fontsize>} The default font is 8-point "topaz". The screen option uses a virtual screen, so it is possible that the graph will be larger than the screen. ### apollo The apollo terminal driver supports the Apollo Graphics Primitive Resource with rescaling after window resizing. It has no options. If a fixed-size window is desired, the gpr terminal may be used instead. ### atari ST (via AES) The atari terminal has options to set the character size and the screen colors. Syntax: set terminal atari {<fontsize>} {<col0> <col1> ... <col15.} The character size must appear if any colors are to be specified. Each of the (up to 16) colors is given as a three-digit hex number, where the digits represent RED, GREEN and BLUE (in that order). The range of 0--15 is scaled to whatever color range the screen actually has. On a normal ST screen, odd and even intensities are the same. Examples: set terminal atari 4 # use small (6x6) font set terminal atari 6 0 # set monochrome screen to white on black set terminal atari 13 0 fff f00 f0 f ff f0f # set first seven colors to black, white, green, blue, # cyan, purple, and yellow and use large font (8x16). Additionally, if an environment variable GNUCOLORS exists, its contents are interpreted as an options string, but an explicit terminal option takes precedence. ### atari ST (via VDI) The vdi terminal is the same as the atari terminal, except that it sends output to the screen via the VDI and not into AES-Windows. The vdi terminal has options to set the character size and the screen colors. Syntax: set terminal vdi {<fontsize>} {<col0> <col1> ... <col15.} The character size must appear if any colors are to be specified. Each of the (up to 16) colors is given as a three-digit hex number, where the digits represent RED, GREEN and BLUE (in that order). The range of 0--15 is scaled to whatever color range the screen actually has. On a normal ST screen, odd and even intensities are the same. Examples: set terminal vdi 4 # use small (6x6) font set terminal vdi 6 0 # set monochrome screen to white on black set terminal vdi 13 0 fff f00 f0 f ff f0f # set first seven colors to black, white, green, blue, # cyan, purple, and yellow and use large font (8x16). Additionally, if an environment variable GNUCOLORS exists, its contents are interpreted as an options string, but an explicit terminal option takes precedence. ### be gnuplot provides the be terminal type for use with X servers. This terminal type is set automatically at startup if the DISPLAY environment variable is set, if the TERM environment variable is set to xterm, or if the -display command line option is used. Syntax: set terminal be {reset} {<n>} Multiple plot windows are supported: set terminal be <n> directs the output to plot window number n. If n>0, the terminal number will be appended to the window title and the icon will be labeled gplt <n>. The active window may distinguished by a change in cursor (from default to crosshair.) Plot windows remain open even when the gnuplot driver is changed to a different device. A plot window can be closed by pressing the letter q while that window has input focus, or by choosing close from a window manager menu. All plot windows can be closed by specifying reset, which actually terminates the subprocess which maintains the windows (unless -persist was specified). Plot windows will automatically be closed at the end of the session unless the -persist option was given. The size or aspect ratio of a plot may be changed by resizing the gnuplot window. Linewidths and pointsizes may be changed from within gnuplot with set linestyle. For terminal type be, gnuplot accepts (when initialized) the standard X Toolkit options and resources such as geometry, font, and name from the command line arguments or a configuration file. See the X(1) man page (or its equivalent) for a description of such options. A number of other gnuplot options are available for the be terminal. These may be specified either as command-line options when gnuplot is invoked or as resources in the configuration file "/.Xdefaults". They are set upon initialization and cannot be altered during a gnuplot session. #### command-line_options In addition to the X Toolkit options, the following options may be specified on the command line when starting gnuplot or as resources in your ".Xdefaults" file: -clear requests that the window be cleared momentarily before a new plot is displayed. -gray requests grayscale rendering on grayscale or color displays. (Grayscale displays receive monochrome rendering by default.) -mono forces monochrome rendering on color displays. -persist plot windows survive after main gnuplot program exits -raise raise plot window after each plot -noraise do not raise plot window after each plot -tvtwm requests that geometry specifications for position of the window be made relative to the currently displayed portion of the virtual root. The options are shown above in their command-line syntax. When entered as resources in ".Xdefaults", they require a different syntax. Example: gnuplot*gray: on gnuplot also provides a command line option (-pointsize <v>) and a resource, gnuplot*pointsize: <v>, to control the size of points plotted with the points plotting style. The value v is a real number (greater than 0 and less than or equal to ten) used as a scaling factor for point sizes. For example, -pointsize 2 uses points twice the default size, and -pointsize 0.5 uses points half the normal size. #### monochome_options For monochrome displays, gnuplot does not honor foreground or background colors. The default is black-on-white. -rv or gnuplot*reverseVideo: on requests white-on-black. #### color_resources For color displays, gnuplot honors the following resources (shown here with their default values) or the greyscale resources. The values may be color names as listed in the BE rgb.txt file on your system, hexadecimal RGB color specifications (see BE documentation), or a color name followed by a comma and an intensity value from 0 to 1. For example, blue, 0.5 means a half intensity blue. gnuplot*background: white gnuplot*textColor: black gnuplot*borderColor: black gnuplot*axisColor: black gnuplot*line1Color: red gnuplot*line2Color: green gnuplot*line3Color: blue gnuplot*line4Color: magenta gnuplot*line5Color: cyan gnuplot*line6Color: sienna gnuplot*line7Color: orange gnuplot*line8Color: coral The command-line syntax for these is, for example, Example: gnuplot -background coral #### grayscale_resources When -gray is selected, gnuplot honors the following resources for grayscale or color displays (shown here with their default values). Note that the default background is black. gnuplot*background: black gnuplot*textGray: white gnuplot*borderGray: gray50 gnuplot*axisGray: gray50 gnuplot*line1Gray: gray100 gnuplot*line2Gray: gray60 gnuplot*line3Gray: gray80 gnuplot*line4Gray: gray40 gnuplot*line5Gray: gray90 gnuplot*line6Gray: gray50 gnuplot*line7Gray: gray70 gnuplot*line8Gray: gray30 #### line_resources gnuplot honors the following resources for setting the width (in pixels) of plot lines (shown here with their default values.) 0 or 1 means a minimal width line of 1 pixel width. A value of 2 or 3 may improve the appearance of some plots. gnuplot*borderWidth: 2 gnuplot*axisWidth: 0 gnuplot*line1Width: 0 gnuplot*line2Width: 0 gnuplot*line3Width: 0 gnuplot*line4Width: 0 gnuplot*line5Width: 0 gnuplot*line6Width: 0 gnuplot*line7Width: 0 gnuplot*line8Width: 0 gnuplot honors the following resources for setting the dash style used for plotting lines. 0 means a solid line. A two-digit number jk (j and k are >= 1 and <= 9) means a dashed line with a repeated pattern of j pixels on followed by k pixels off. For example, '16' is a "dotted" line with one pixel on followed by six pixels off. More elaborate on/off patterns can be specified with a four-digit value. For example, '4441' is four on, four off, four on, one off. The default values shown below are for monochrome displays or monochrome rendering on color or grayscale displays. For color displays, the default for each is 0 (solid line) except for axisDashes which defaults to a '16' dotted line. gnuplot*borderDashes: 0 gnuplot*axisDashes: 16 gnuplot*line1Dashes: 0 gnuplot*line2Dashes: 42 gnuplot*line3Dashes: 13 gnuplot*line4Dashes: 44 gnuplot*line5Dashes: 15 gnuplot*line6Dashes: 4441 gnuplot*line7Dashes: 42 gnuplot*line8Dashes: 13 ### cgi The cgi and hcgi terminal drivers support SCO CGI drivers. hcgi is for printers; the environment variable CGIPRNT must be set. cgi may be used for either a display or hardcopy; if the environment variable CGIDISP is set, then that display is used. Otherwise CGIPRNT is used. These terminals have no options. ### cgm The cgm terminal generates a Computer Graphics Metafile. This file format is a subset of the ANSI X3.122-1986 standard entitled "Computer Graphics - Metafile for the Storage and Transfer of Picture Description Information". Several options may be set in cgm. Syntax: set terminal cgm {<mode>} {<color>} {<rotation>} {solid | dashed} {width <plot_width>} {linewidth <line_width>} {"<font>"} {<fontsize>} where <mode> is landscape, portrait, or default; <color> is either color or monochrome; <rotation> is either rotate or norotate; solid draws all curves with solid lines, overriding any dashed patterns; <plot_width> is the width of the page in points; <line_width> is the line width in points; <font> is the name of a font; and <fontsize> is the size of the font in points. By default, cgm uses rotated text for the Y axis label. The first six options can be in any order. Selecting default sets all options to their default values. Examples: set terminal cgm landscape color rotate dashed width 432 \ linewidth 1 'Arial Bold' 12 # defaults set terminal cgm 14 linewidth 2 14 # wider lines & larger font set terminal cgm portrait 'Times Roman Italic' 12 set terminal cgm color solid # no pesky dashes! #### font The first part of a Computer Graphics Metafile, the metafile description, includes a font table. In the picture body, a font is designated by an index into this table. By default, this terminal generates a table with the following fonts: Arial Arial Italic Arial Bold Arial Bold Italic Times Roman Times Roman Italic Times Roman Bold Times Roman Bold Italic Helvetica Roman Case is not distinct, but the modifiers must appear in the above order (that is, not 'Arial Italic Bold'). 'Arial Bold' is the default font. You may also specify a font name which does not appear in the default font table. In that case, a new font table is constructed with the specified font as its only entry. You must ensure that the spelling, capitalization, and spacing of the name are appropriate for the application that will read the CGM file. #### fontsize Fonts are scaled assuming the page is 6 inches wide. If the size command is used to change the aspect ratio of the page or the CGM file is converted to a different width (e.g. it is imported into a document in which the margins are not 6 inches apart), the resulting font sizes will be different. To change the assumed width, use the width option. #### linewidth #### rotate The norotate option may be used to disable text rotation. For example, the CGM input filter for Word for Windows 6.0c can accept rotated text, but the DRAW editor within Word cannot. If you edit a graph (for example, to label a curve), all rotated text is restored to horizontal. The Y axis label will then extend beyond the clip boundary. With norotate, the Y axis label starts in a less attractive location, but the page can be edited without damage. The rotate option confirms the default behavior. #### solid The solid option may be used to disable dashed line styles in the plots. This is useful when color is enabled and the dashing of the lines detracts from the appearance of the plot. The dashed option confirms the default behavior, which gives a different dash pattern to each curve. #### size Default size of a CGM page is 32599 units wide and 23457 units high for landscape, or 23457 units wide by 32599 units high for portrait. #### width set terminal cgm width 432 # default set terminal cgm width 6*72 # same as above set terminal cgm width 10/2.54*72 # 10 cm wide #### winword6 The default font table was chosen to match, where possible, the default font assignments made by the Computer Graphics Metafile input filter for Microsoft Word 6.0c, although the filter makes available only 'Arial' and 'Times Roman' fonts and their bold and/or italic variants. Other fonts such as 'Helvetica' and 'Roman' are not available. If the CGM file includes a font table, the filter mostly ignores it. However, it changes certain font assignments so that they disagree with the table. As a workaround, the winword6 option deletes the font table from the CGM file. In this case, the filter makes predictable font assignments. 'Arial Bold' is correctly assigned even with the font table present, which is one reason it was chosen as the default. winword6 disables the color tables for a similar reason---with the color table included, Microsoft Word displays black for color 7. ### corel The corel terminal driver supports CorelDraw. Syntax: set terminal corel { default | {monochrome | color {<fontname> {"<fontsize>" {<xsize> <ysize> {<linewidth> }}}}} where the fontsize and linewidth are specified in points and the sizes in inches. The defaults are monochrome, "SwitzerlandLight", 22, 8.2, 10 and 1.2. ### debug This terminal is provided to allow for the debugging of gnuplot. It is likely to be of use only for users who are modifying the source code. ### svga The svga terminal driver supports PCs with SVGA graphics. It can only be be used if it is compiled with DJGPP. Its only option is the font. Syntax: set terminal svga {"<fontname>"} ### dumb The dumb terminal driver has an optional size specification and trailing linefeed control. Syntax: set terminal dumb {[no]feed} {<xsize> <ysize>} where <xsize> and <ysize> set the size of the dumb terminals. Default is 79 by 24. The last newline is printed only if feed is enabled. Examples: set term dumb nofeed set term dumb 79 49 # VGA screen---why would anyone do that? ### dxf The dxf terminal driver creates pictures that can be imported into AutoCad (Release 10.x). It has no options of its own, but some features of its plots may be modified by other means. The default size is 120x80 AutoCad units, which can be changed by set size. dxf uses seven colors (white, red, yellow, green, cyan, blue and magenta), which can be changed only by modifying the source file. If a black-and-white plotting device is used, the colors are mapped to differing line thicknesses. See the description of the AutoCad print/plot command. ### dxy800a This terminal driver supports the Roland DXY800A plotter. It has no options. ### eepic The output of this terminal is intended for use with the "eepic.sty" macro package for LaTeX. To use it, you need "eepic.sty", "epic.sty" and a printer driver that supports the "tpic" \specials. If your printer driver doesn't support those \specials, "eepicemu.sty" will enable you to use some of them. Although dotted and dashed lines are possible with eepic and are tempting, they do not work well for high-sample-rate curves, fusing the dashes all together into a solid line. For now, the eepic driver creates only solid lines. There is another gnuplot driver (tpic) that supports dashed lines, but it cannot be used if your DVI driver doesn't support "tpic" \specials. All drivers for LaTeX offer a special way of controlling text positioning: If any text string begins with '{', you also need to include a '}' at the end of the text, and the whole text will be centered both horizontally and vertically by LaTeX. --- If the text string begins with '[', you need to continue it with: a position specification (up to two out of t,b,l,r), ']{', the text itself, and finally, '}'. The text itself may be anything LaTeX can typeset as an LR-box. \rule{}{}'s may help for best positioning. The eepic terminal has no options. Examples: About label positioning: Use gnuplot defaults (mostly sensible, but sometimes not really best): set title '\LaTeX\ -- \gamma ' Force centering both horizontally and vertically: set label '{\LaTeX\ -- \gamma }' at 0,0 Specify own positioning (top here): set xlabel '[t]{\LaTeX\ -- \gamma }' The other label -- account for long ticlabels: set ylabel '[r]{\LaTeX\ -- \gamma \rule{7mm}{0pt}' ### emxvga The emxvga, emxvesa and vgal terminal drivers support PCs with SVGA, vesa SVGA and VGA graphics boards, respectively. They are intended to be compiled with "emx-gcc" under either DOS or OS/2. They also need VESA and SVGAKIT maintained by Johannes Martin (JMARTIN@GOOFY.ZDV.UNI-MAINZ.DE) with additions by David J. Liu (liu@phri.nyu.edu). Syntax: set terminal emxvga set terminal emxvesa {vesa-mode} set terminal vgal The only option is the vesa mode for emxvesa, which defaults to G640x480x256. ### epson-180dpi This driver supports a family of Epson printers and derivatives. epson-180dpi and epson-60dpi are drivers for Epson LQ-style 24-pin printers with resolutions of 180 and 60 dots per inch, respectively. epson-lx800 is a generic 9-pin driver appropriate for printers like the Epson LX-800, the Star NL-10 and NX-1000, the PROPRINTER, and so forth. nec-cp6 is generix 24-pin driver that can be used for printers like the NEC CP6 and the Epson LQ-800. The okidata driver supports the 9-pin OKIDATA 320/321 Standard printers. The starc driver is for the Star Color Printer. The tandy-60dpi driver is for the Tandy DMP-130 series of 9-pin, 60-dpi printers. Only nec-cp6 has any options. Syntax: set terminal nec-cp6 {monochrome | colour | draft} which defaults to monochrome. With each of these drivers, a binary copy is required on a PC to print. Do not use print---use instead copy file /b lpt1:. ### excl The excl terminal driver supports Talaris printers such as the EXCL Laser printer and the 1590. It has no options. ### hercules These drivers supports PC monitors with autodetected graphics boards. They can be used only when compiled with Zortech C/C++. None have options. ### fig The fig terminal device generates output in the Fig graphics language. Syntax: set terminal fig {monochrome | color} {small | big} {pointsmax <max_points>} {landscape | portrait} {metric | inches} {fontsize <fsize>} {size <xsize> <ysize>} {thickness <units>} {depth <layer>} monochrome and color determine whether the picture is black-and-white or color. small and big produce a 5x3 or 8x5 inch graph in the default landscape mode and 3x5 or 5x8 inches in portrait mode. <max_points> sets the maximum number of points per polyline. Default units for editing with "xfig" may be metric or inches. fontsize sets the size of the text font to <fsize> points. size sets (overrides) the size of the drawing area to <xsize>*<ysize> in units of inches or centimeters depending on the inches or metric setting in effect. depth sets the default depth layer for all lines and text. The default depth is 10 to leave room for adding material with "xfig" on top of the plot. thickness sets the default line thickness, which is 1 if not specified. Overriding the thickness can be achieved by adding a multiple of 100 to the to the linetype value for a plot command. In a similar way the depth of plot elements (with respect to the default depth) can be controlled by adding a multiple of 1000 to <linetype>. The depth is then <layer> + <linetype>/1000 and the thickness is (<linetype>%1000)/100 or, if that is zero, the default line thickness. Additional point-plot symbols are also available with the fig driver. The symbols can be used through pointtype values % 100 above 50, with different fill intensities controlled by <pointtype> % 5 and outlines in black (for <pointtype> % 10 < 5) or in the current color. Available symbols are 50 - 59: circles 60 - 69: squares 70 - 79: diamonds 80 - 89: upwards triangles 90 - 99: downwards triangles The size of these symbols is linked to the font size. The depth of symbols is by default one less than the depth for lines to achieve nice error bars. If <pointtype> is above 1000, the depth is <layer> + <pointtype>/1000-1. If <pointtype>%1000 is above 100, the fill color is (<pointtype>%1000)/100-1. Available fill colors are (from 1 to 9): black, blue, green, cyan, red, magenta, yellow, white and dark blue (in monochrome mode: black for 1 to 6 and white for 7 to 9). See plot with for details of <linetype> and <pointtype>. The big option is a substitute for the bfig terminal in earlier versions, which is no longer supported. Examples: set terminal fig monochrome small pointsmax 1000 # defaults plot 'file.dat' with points linetype 102 pointtype 759 would produce circles with a blue outline of width 1 and yellow fill color. plot 'file.dat' using 1:2:3 with err linetype 1 pointtype 554 would produce errorbars with black lines and circles filled red. These circles are one layer above the lines (at depth 9 by default). To plot the error bars on top of the circles use plot 'file.dat' using 1:2:3 with err linetype 1 pointtype 2554 ### jpeg The jpeg terminal driver generates output in JPEG format. It uses Thomas Boutell's gd library, which is available from http://www.boutell.com/gd/ By default, the jpeg terminal driver uses a shared Web-friendy palette. Syntax: set terminal jpeg {transparent} {interlace} {tiny | small | medium | large | giant} {size <x>,<y>} {<color0> <color1> <color2> ...} transparent instructs the driver to generate transparent JPEGs. The first color will be the transparent one. interlace instructs the driver to generate interlaced JPEGs. The choice of fonts is tiny (5x8 pixels), small (6x12 pixels), medium (7x13 Bold), large (8x16) or giant (9x15 pixels) Each color must be of the form 'xrrggbb', where x is the literal character 'x' and 'rrggbb' are the red, green and blue components in hex. For example, 'x00ff00' is green. The background color is set first, then the border colors, then the X & Y axis colors, then the plotting colors. The maximum number of colors that can be set is 256. Examples: set terminal jpeg small size 640,480 \ xffffff x000000 x404040 \ xff0000 xffa500 x66cdaa xcdb5cd \ xadd8e6 x0000ff xdda0dd x9500d3 # defaults which uses white for the non-transparent background, black for borders, gray for the axes, and red, orange, medium aquamarine, thistle 3, light blue, blue, plum and dark violet for eight plotting colors. set terminal jpeg transparent xffffff \ x000000 x202020 x404040 x606060 \ x808080 xA0A0A0 xC0C0C0 xE0E0E0 \ which uses white for the transparent background, black for borders, dark gray for axes, and a gray-scale for the six plotting colors. The page size is 640x480 pixels. The jpeg driver can create either color or monochromatic output, but you have no control over which is produced. The current version of the jpeg driver does not support animated JPEGs. ### unixplot Syntax: set terminal unixplot {"<fontname>"} {<fontsize>} which defaults to 10-point "Courier". There is a non-GNU version of the unixplot driver which cannot be compiled unless this version is left out. ### gpic The gpic terminal driver generates GPIC graphs in the Free Software Foundations's "groff" package. The default size is 5 x 3 inches. The only option is the origin, which defaults to (0,0). Syntax: set terminal gpic {<x> <y>} where x and y are in inches. A simple graph can be formatted using groff -p -mpic -Tps file.pic > file.ps. The output from pic can be pipe-lined into eqn, so it is possible to put complex functions in a graph with the set label and set {x/y}label commands. For instance, set ylab '@space 0 int from 0 to x alpha ( t ) roman d t@' will label the y axis with a nice integral if formatted with the command: gpic filename.pic | geqn -d@@ -Tps | groff -m[macro-package] -Tps > filename.ps Figures made this way can be scaled to fit into a document. The pic language is easy to understand, so the graphs can be edited by hand if need be. All co-ordinates in the pic-file produced by gnuplot are given as x+gnuplotx and y+gnuploty. By default x and y are given the value 0. If this line is removed with an editor in a number of files, one can put several graphs in one figure like this (default size is 5.0x3.0 inches): .PS 8.0 x=0;y=3 copy "figa.pic" x=5;y=3 copy "figb.pic" x=0;y=0 copy "figc.pic" x=5;y=0 copy "figd.pic" .PE This will produce an 8-inch-wide figure with four graphs in two rows on top of each other. One can also achieve the same thing by the command set terminal gpic x y for example, using .PS 6.0 copy "trig.pic" .PE ### gpr The gpr terminal driver supports the Apollo Graphics Primitive Resource for a fixed-size window. It has no options. If a variable window size is desired, use the apollo terminal instead. ### grass The grass terminal driver gives gnuplot capabilities to users of the GRASS geographic information system. Contact grassp-list@moon.cecer.army.mil for more information. Pages are written to the current frame of the GRASS Graphics Window. There are no options. ### hp2648 The hp2648 terminal driver supports the Hewlett Packard HP2647 and HP2648. It has no options. ### hp2623a The hp2623a terminal driver supports the Hewlett Packard HP2623A. It has no options. ### hp500c The hp500c terminal driver supports the Hewlett Packard HP DeskJet 500c. It has options for resolution and compression. Syntax: set terminal hp500c {<res>} {<comp>} where res can be 75, 100, 150 or 300 dots per inch and comp can be "rle", or "tiff". Any other inputs are replaced by the defaults, which are 75 dpi and no compression. Rasterization at the higher resolutions may require a large amount of memory. ### hpgl The hpgl driver produces HPGL output for devices like the HP7475A plotter. There are two options which can be set---the number of pens and "eject", which tells the plotter to eject a page when done. The default is to use 6 pens and not to eject the page when done. Syntax: set terminal hpgl {<number_of_pens>} {eject} The selection set terminal hpgl 8 eject is equivalent to the previous hp7550 terminal, and the selection set terminal hpgl 4 is equivalent to the previous hp7580b terminal. The pcl5 driver supports the Hewlett-Packard Laserjet III. It actually uses HPGL-2, but there is a name conflict among the terminal devices. It has several options Syntax: set terminal pcl5 {<mode>} {<font>} {<fontsize>} where <mode> is landscape, or portrait, <font> is stick, univers, or cg_times, and <fontsize> is the size in points. With pcl5 international characters are handled by the printer; you just put the appropriate 8-bit character codes into the text strings. You don't need to bother with set encoding. HPGL graphics can be imported by many software packages. ### hpljii The hpljii terminal driver supports the HP Laserjet Series II printer. The hpdj driver supports the HP DeskJet 500 printer. These drivers allow a choice of resolutions. Syntax: set terminal hpljii | hpdj {<res>} where res may be 75, 100, 150 or 300 dots per inch; the default is 75. Rasterization at the higher resolutions may require a large amount of memory. The hp500c terminal is similar to hpdj; hp500c additionally supports color and compression. ### hppj The hppj terminal driver supports the HP PaintJet and HP3630 printers. The only option is the choice of font. Syntax: set terminal hppj {FNT5X9 | FNT9X17 | FNT13X25} with the middle-sized font (FNT9X17) being the default. ### imagen The imagen terminal driver supports Imagen laser printers. It is capable of placing multiple graphs on a single page. Syntax: set terminal imagen {<fontsize>} {portrait | landscape} {[<horiz>,<vert>]} where fontsize defaults to 12 points and the layout defaults to landscape. <horiz> and <vert> are the number of graphs in the horizontal and vertical directions; these default to unity. Example: set terminal imagen portrait [2,3] puts six graphs on the page in three rows of two in portrait orientation. ### iris4d The iris4d terminal driver supports Silicon Graphics IRIS 4D computers. Its only option is 8- or 24-bit color depth. The default is 8. Syntax: set terminal iris4d {8 | 24} The color depth is not really a choice -- the value appropriate for the hardware should be selected. When using 24-bit mode, the colors can be directly specified via the file .gnuplot_iris4d that is searched in the current directory and then in the home directory specified by the HOME environment variable. This file holds RGB values for the background, border, labels and nine plotting colors, in that order. For example, here is a file containing the default colors: 85 85 85 Background (dark gray) 0 0 0 Boundary (black) 170 0 170 Labeling (magenta) 85 255 255 Plot Color 1 (light cyan) 170 0 0 Plot Color 2 (red) 0 170 0 Plot Color 3 (green) 255 85 255 Plot Color 4 (light magenta) 255 255 85 Plot Color 5 (yellow) 255 85 85 Plot Color 6 (light red) 85 255 85 Plot Color 7 (light green) 0 170 170 Plot Color 8 (cyan) 170 170 0 Plot Color 9 (brown) This file must have exactly 12 lines of RGB triples. No empty lines are allowed, and anything after the third number on a line is ignored. ### kyo The kyo and prescribe terminal drivers support the Kyocera laser printer. The only difference between the two is that kyo uses "Helvetica" whereas prescribe uses "Courier". There are no options. ### latex The latex and emtex drivers allow two options. Syntax: set terminal latex | emtex {courier | roman | default} {<fontsize>} fontsize may be any size you specify. The default is for the plot to inherit its font setting from the embedding document. Unless your driver is capable of building fonts at any size (e.g. dvips), stick to the standard 10, 11 and 12 point sizes. METAFONT users beware: METAFONT does not like odd sizes. All drivers for LaTeX offer a special way of controlling text positioning: If any text string begins with '{', you also need to include a '}' at the end of the text, and the whole text will be centered both horizontally and vertically. If the text string begins with '[', you need to follow this with a position specification (up to two out of t,b,l,r), ']{', the text itself, and finally '}'. The text itself may be anything LaTeX can typeset as an LR-box. '\rule{}{}'s may help for best positioning. Points, among other things, are drawn using the LaTeX commands "\Diamond" and "\Box". These commands no longer belong to the LaTeX2e core; they are included in the latexsym package, which is part of the base distribution and thus part of any LaTeX implementation. Please do not forget to use this package. Points are drawn with the LaTex commands \Diamond and \Box. These commands do no longer belong to the LaTeX2e core, but are included in the latexsym-package in the base distribution, and are hence part of all LaTeX implementations. Please do not forget to use this package. Examples: About label positioning: Use gnuplot defaults (mostly sensible, but sometimes not really best): set title '\LaTeX\ -- \gamma ' Force centering both horizontally and vertically: set label '{\LaTeX\ -- \gamma }' at 0,0 Specify own positioning (top here): set xlabel '[t]{\LaTeX\ -- \gamma }' The other label -- account for long ticlabels: set ylabel '[r]{\LaTeX\ -- \gamma \rule{7mm}{0pt}' ### linux The linux driver has no additional options to specify. It looks at the environment variable GSVGAMODE for the default mode; if not set, it uses 1024x768x256 as default mode or, if that is not possible, 640x480x16 (standard VGA). ### macintosh Several options may be set in the 'macintosh' driver. Syntax: set terminal macintosh {singlewin | multiwin} {vertical | novertical} {size <width>, <height> | default} 'singlewin' limits the output to a single window and is useful for animations. 'multiwin' allows multiple windows. 'vertical' is only valid under the gx option. With this option, rotated text be drawn vertically. novertical turns this option off. size <width>, <height> overrides the graph size set in the preferences dialog until it is cleared with either 'set term mac size default' or 'set term mac default'. 'set term mac size default' sets the window size settings to those set in the preferences dialog. 'set term mac default' sets all options to their default values. Default values: nogx, multiwin, novertical. If you generate graphs under the multiwin option and then switch to singlewin, the next plot command will cause one more window to be created. This new window will be reused as long as singlewin is in effect. If you switch back to multiwin, generate some graphs, and then switch to singlewin again, the orginal 'singlewin' window will be resused if it is still open. Otherwise a new 'singlewin' window will be created. The 'singlewin' window is not numbered. ### mf The mf terminal driver creates a input file to the METAFONT program. Thus a figure may be used in the TeX document in the same way as is a character. To use a picture in a document, the METAFONT program must be run with the output file from gnuplot as input. Thus, the user needs a basic knowledge of the font creating process and the procedure for including a new font in a document. However, if the METAFONT program is set up properly at the local site, an unexperienced user could perform the operation without much trouble. The text support is based on a METAFONT character set. Currently the Computer Modern Roman font set is input, but the user is in principal free to chose whatever fonts he or she needs. The METAFONT source files for the chosen font must be available. Each character is stored in a separate picture variable in METAFONT. These variables may be manipulated (rotated, scaled etc.) when characters are needed. The drawback is the interpretation time in the METAFONT program. On some machines (i.e. PC) the limited amount of memory available may also cause problems if too many pictures are stored. The mf terminal has no options. #### METAFONT Instructions - Set your terminal to METAFONT: set terminal mf - Select an output-file, e.g.: set output "myfigures.mf" - Create your pictures. Each picture will generate a separate character. Its default size will be 5*3 inches. You can change the size by saying set size 0.5,0.5 or whatever fraction of the default size you want to have. - Generate a TFM and GF file by running METAFONT on the output of gnuplot. Since the picture is quite large (5*3 in), you will have to use a version of METAFONT that has a value of at least 150000 for memmax. On Unix systems these are conventionally installed under the name bigmf. For the following assume that the command virmf stands for a big version of METAFONT. For example: - Invoke METAFONT: virmf '&plain' - Select the output device: At the METAFONT prompt ('*') type: \mode:=CanonCX; % or whatever printer you use - Optionally select a magnification: mag:=1; % or whatever you wish - Input the gnuplot-file: input myfigures.mf On a typical Unix machine there will usually be a script called "mf" that executes virmf '&plain', so you probably can substitute mf for virmf &plain. This will generate two files: mfput.tfm and mfput.$gf (where$ indicates the resolution of your device). The above can be conveniently achieved by typing everything on the command line, e.g.: virmf '&plain' '\mode:=CanonCX; mag:=1; input myfigures.mf' In this case the output files will be named myfigures.tfm and myfigures.300gf.
- Generate a PK file from the GF file using gftopk:
gftopk myfigures.300gf myfigures.300pk
The name of the output file for gftopk depends on the DVI driver you use. Ask your local TeX administrator about the naming conventions. Next, either install the TFM and PK files in the appropriate directories, or set your environment variables properly. Usually this involves setting TEXFONTS to include the current directory and doing the same thing for the environment variable that your DVI driver uses (no standard name here...). This step is necessary so that TeX will find the font metric file and your DVI driver will find the PK file.
- To include your pictures in your document you have to tell TeX the font:
\font\gnufigs=myfigures
Each picture you made is stored in a single character. The first picture is character 0, the second is character 1, and so on... After doing the above step, you can use the pictures just like any other characters. Therefore, to place pictures 1 and 2 centered in your document, all you have to do is:
\centerline{\gnufigs\char0}
\centerline{\gnufigs\char1}
in plain TeX. For LaTeX you can, of course, use the picture environment and place the picture wherever you wish by using the \makebox and \put macros.
This conversion saves you a lot of time once you have generated the font; TeX handles the pictures as characters and uses minimal time to place them, and the documents you make change more often than the pictures do. It also saves a lot of TeX memory. One last advantage of using the METAFONT driver is that the DVI file really remains device independent, because no \special commands are used as in the eepic and tpic drivers.
### mp
The mp driver produces output intended to be input to the Metapost program. Running Metapost on the file creates EPS files containing the plots. By default, Metapost passes all text through TeX. This has the advantage of allowing essentially any TeX symbols in titles and labels.
The mp terminal is selected with a command of the form
set term mp {color} {solid} {notex} {mag <magsize>} {"<name>"} {<size>}
The option color causes lines to be drawn in color (on a printer or display that supports it), monochrome (or nothing) selects black lines. The option solid draws solid lines, while dashed (or nothing) selects lines with different patterns of dashes. If solid is selected but color is not, nearly all lines will be identical. This may occasionally be useful, so it is allowed.
The option notex bypasses TeX entirely, therefore no TeX code can be used in labels under this option. This is intended for use on old plot files or files that make frequent use of common characters like $and % that require special handling in TeX. Changing font sizes in TeX has no effect on the size of mathematics, and there is no foolproof way to make such a change, except by globally setting a magnification factor. This is the purpose of the magnification option. It must be followed by a scaling factor. All text (NOT the graphs) will be scaled by this factor. Use this if you have math that you want at some size other than the default 10pt. Unfortunately, all math will be the same size, but see the discussion below on editing the MP output. mag will also work under notex but there seems no point in using it as the font size option (below) works as well. A name in quotes selects the font that will be used when no explicit font is given in a set label or set title. A name recognized by TeX (a TFM file exists) must be used. The default is "cmr10" unless notex is selected, then it is "pcrr8r" (Courier). Even under notex, a TFM file is needed by Metapost. The file pcrr8r.tfm is the name given to Courier in LaTeX's psnfss package. If you change the font from the notex default, choose a font that matches the ASCII encoding at least in the range 32-126. cmtt10 almost works, but it has a nonblank character in position 32 (space). The size can be any number between 5.0 and 99.99. If it is omitted, 10.0 is used. It is advisable to use magstep sizes: 10 times an integer or half-integer power of 1.2, rounded to two decimals, because those are the most available sizes of fonts in TeX systems. All the options are optional. If font information is given, it must be at the end, with size (if present) last. The size is needed to select a size for the font, even if the font name includes size information. For example, set term mp "cmtt12" selects cmtt12 shrunk to the default size 10. This is probably not what you want or you would have used cmtt10. The following common ascii characters need special treatment in TeX: $, &, #, %, _; |, <, >; ^, ~, \, {, and }
The five characters $, #, &, _, and % can simply be escaped, e.g., \$. The three characters <, >, and | can be wrapped in math mode, e.g., $<$. The remainder require some TeX work-arounds. Any good book on TeX will give some guidance.
If you type your labels inside double quotes, backslashes in TeX code need to be escaped (doubled). Using single quotes will avoid having to do this, but then you cannot use \n for line breaks. As of this writing, version 3.7 of gnuplot processess titles given in a plot command differently than in other places, and backslashes in TeX commands need to be doubled regardless of the style of quotes.
Metapost pictures are typically used in TeX documents. Metapost deals with fonts pretty much the same way TeX does, which is different from most other document preparation programs. If the picture is included in a LaTeX document using the graphics package, or in a plainTeX document via epsf.tex, and then converted to PostScript with dvips (or other dvi-to-ps converter), the text in the plot will usually be handled correctly. However, the text may not appear if you send the Metapost output as-is to a PostScript interpreter.
#### Metapost Instructions
- Set your terminal to Metapost, e.g.:
set terminal mp mono "cmtt12" 12
- Select an output-file, e.g.:
set output "figure.mp"
- Create your pictures. Each plot (or multiplot group) will generate a separate Metapost beginfig...endfig group. Its default size will be 5 by 3 inches. You can change the size by saying set size 0.5,0.5 or whatever fraction of the default size you want to have.
- Quit gnuplot.
- Generate EPS files by running Metapost on the output of gnuplot:
mpost figure.mp OR mp figure.mp
The name of the Metapost program depends on the system, typically mpost for a Unix machine and mp on many others. Metapost will generate one EPS file for each picture.
- To include your pictures in your document you can use the graphics package in LaTeX or epsf.tex in plainTeX:
\usepackage{graphics} % LaTeX
\input epsf.tex % plainTeX
If you use a driver other than dvips for converting TeX DVI output to PS, you may need to add the following line in your LaTeX document:
\DeclareGraphicsRule{*}{eps}{*}{}
Each picture you made is in a separate file. The first picture is in, e.g., figure.0, the second in figure.1, and so on.... To place the third picture in your document, for example, all you have to do is:
\includegraphics{figure.2} % LaTeX
\epsfbox{figure.2} % plainTeX
The advantage, if any, of the mp terminal over a postscript terminal is editable output. Considerable effort went into making this output as clean as possible. For those knowledgeable in the Metapost language, the default line types and colors can be changed by editing the arrays lt[] and col[]. The choice of solid vs dashed lines, and color vs black lines can be change by changing the values assigned to the booleans dashedlines and colorlines. If the default tex option was in effect, global changes to the text of labels can be achieved by editing the vebatimtex...etex block. In particular, a LaTeX preamble can be added if desired, and then LaTeX's built-in size changing commands can be used for maximum flexibility. Be sure to set the appropriate MP configuration variable to force Metapost to run LaTeX instead of plainTeX.
### mgr
The mgr terminal driver supports the Mgr Window system. It has no options.
### mif
The mif terminal driver produces Frame Maker MIF format version 3.00. It plots in MIF Frames with the size 15*10 cm, and plot primitives with the same pen will be grouped in the same MIF group. Plot primitives in a gnuplot page will be plotted in a MIF Frame, and several MIF Frames are collected in one large MIF Frame. The MIF font used for text is "Times".
Several options may be set in the MIF 3.00 driver.
Syntax:
set terminal mif {colour | monochrome} {polyline | vectors}
{help | ?}
colour plots lines with line types >= 0 in colour (MIF sep. 2--7) and monochrome plots all line types in black (MIF sep. 0). polyline plots curves as continuous curves and vectors plots curves as collections of vectors. help and ? print online help on standard error output---both print a short description of the usage; help also lists the options;
Examples:
set term mif colour polylines # defaults
set term mif # defaults
set term mif vectors
set term mif help
### mtos
The mtos terminal has no options. It sends data via a pipe to an external program called GPCLIENT. It runs under MULTITOS, Magic 3.x, MagicMAC. and MiNT. If you cannot find GPCLIENT, than mail to dirk@lstm.uni-erlangen.de.
### next
Several options may be set in the next driver.
Syntax:
set terminal next {<mode>} {<type> } {<color>} {<dashed>}
{"<fontname>"} {<fontsize>} title {"<newtitle>"}
where <mode> is default, which sets all options to their defaults; <type> is either new or old, where old invokes the old single window; <color> is either color or monochrome; <dashed> is either solid or dashed; "<fontname>" is the name of a valid PostScript font; <fontsize> is the size of the font in PostScript points; and <title> is the title for the GnuTerm window. Defaults are new, monochrome, dashed, "Helvetica", 14pt.
Examples:
set term next default
set term next 22
set term next color "Times-Roman" 14
set term next color "Helvetica" 12 title "MyPlot"
set term next old
Pointsizes may be changed with set linestyle.
### next
Several options may be set in the next driver.
Syntax:
set terminal next {<mode>} {<type> } {<color>} {<dashed>}
{"<fontname>"} {<fontsize>} title {"<newtitle>"}
where <mode> is default, which sets all options to their defaults; <type> is either new or old, where old invokes the old single window; <color> is either color or monochrome; <dashed> is either solid or dashed; "<fontname>" is the name of a valid PostScript font; <fontsize> is the size of the font in PostScript points; and <title> is the title for the GnuTerm window. Defaults are new, monochrome, dashed, "Helvetica", 14pt.
Examples:
set term next default
set term next 22
set term next color "Times-Roman" 14
set term next color "Helvetica" 12 title "MyPlot"
set term next old
Pointsizes may be changed with set linestyle.
### pbm
Several options may be set in the pbm terminal---the driver for PBMplus.
Syntax:
set terminal pbm {<fontsize>} {<mode>}
The output of the pbm driver depends upon <mode>: monochrome produces a portable bitmap (one bit per pixel), gray a portable graymap (three bits per pixel) and color a portable pixmap (color, four bits per pixel).
The output of this driver can be used with Jef Poskanzer's excellent PBMPLUS package, which provides programs to convert the above PBMPLUS formats to GIF, TIFF, MacPaint, Macintosh PICT, PCX, X11 bitmap and many others. PBMPLUS may be obtained from ftp.x.org. The relevant files have names that begin with "netpbm-1mar1994.p1"; they reside in /contrib/utilities. The package can probably also be obtained from one of the many sites that mirrors ftp.x.org.
Examples:
set terminal pbm small monochrome # defaults
set size 2,2; set terminal pbm color medium
### dospc
The dospc terminal driver supports PCs with arbitrary graphics boards, which will be automatically detected. It should be used only if you are not using the gcc or Zortec C/C++ compilers.
### pm
Syntax:
set terminal pm {server {n}} {persist} {widelines} {enhanced} {"title"}
If persist is specified, each graph appears in its own window and all windows remain open after gnuplot exits. If server is specified, all graphs appear in the same window, which remains open when gnuplot exits. This option takes an optional numerical argument which specifies an instance of the server process. Thus multiple server windows can be in use at the same time.
If widelines is specified, all plots will be drawn with wide lines. If enhanced is specified, sub- and superscripts and multiple fonts are enabled using the same syntax as the enhanced postscript option (see set terminal postscript enhanced for details). Font names for the basic PostScript fonts may be abbreviated to single letters.
If title is specified, it will be used as the title of the plot window. It will also be used as the name of the server instance, and will override the optional numerical argument.
Linewidths may be changed with set linestyle.
### png
The png terminal driver supports Portable Network Graphics. To compile it, you will need the third-party libraries "libpng" and "zlib"; both are available at ftp://ftp.uu.net/graphics/png. png has two options.
Syntax:
set terminal png {small | medium | large}
{monochrome | gray | color}
The defaults are small (fontsize) and monochrome. Default size of the output is 640*480 pixel.
### postscript
Several options may be set in the postscript driver.
Syntax:
set terminal postscript {<mode>} {enhanced | noenhanced}
{color | monochrome} {solid | dashed}
{<duplexing>}
{"<fontname>"} {<fontsize>}
where <mode> is landscape, portrait, eps or default; solid draws all plots with solid lines, overriding any dashed patterns; <duplexing> is defaultplex, simplex or duplex ("duplexing" in PostScript is the ability of the printer to print on both sides of the same page---don't set this if your printer can't do it); enhanced activates the "enhanced PostScript" features (subscripts, superscripts and mixed fonts); "<fontname>" is the name of a valid PostScript font; and <fontsize> is the size of the font in PostScript points.
default mode sets all options to their defaults: landscape, monochrome, dashed, defaultplex, noenhanced, "Helvetica" and 14pt.
Default size of a PostScript plot is 10 inches wide and 7 inches high.
eps mode generates EPS (Encapsulated PostScript) output, which is just regular PostScript with some additional lines that allow the file to be imported into a variety of other applications. (The added lines are PostScript comment lines, so the file may still be printed by itself.) To get EPS output, use the eps mode and make only one plot per file. In eps mode the whole plot, including the fonts, is reduced to half of the default size.
Examples:
set terminal postscript default # old postscript
set terminal postscript enhanced # old enhpost
set terminal postscript landscape 22 # old psbig
set terminal postscript eps 14 # old epsf1
set terminal postscript eps 22 # old epsf2
set size 0.7,1.4; set term post portrait color "Times-Roman" 14
Linewidths and pointsizes may be changed with set linestyle.
The postscript driver supports about 70 distinct pointtypes, selectable through the pointtype option on plot and set linestyle.
Several possibly useful files about gnuplot's PostScript are included in the /docs/ps subdirectory of the gnuplot distribution and at the distribution sites. These are "ps_symbols.gpi" (a gnuplot command file that, when executed, creates the file "ps_symbols.ps" which shows all the symbols available through the postscript terminal), "ps_guide.ps" (a PostScript file that contains a summary of the enhanced syntax and a page showing what the octal codes produce with text and symbol fonts) and "ps_file.doc" (a text file that contains a discussion of the organization of a PostScript file written by gnuplot).
A PostScript file is editable, so once gnuplot has created one, you are free to modify it to your heart's desire. See the "editing postscript" section for some hints.
#### enhanced postscript
Control Examples Explanation
^ a^x superscript
_ a_x subscript
@ @x or a@^b_c phantom box (occupies no width)
& &{space} inserts space of specified length
Braces can be used to place multiple-character text where a single character is expected (e.g., 2^{10}). To change the font and/or size, use the full form: {/[fontname][=fontsize | *fontscale] text}. Thus {/Symbol=20 G} is a 20-point GAMMA) and {/*0.75 K} is a K at three-quarters of whatever fontsize is currently in effect. (The '/' character MUST be the first character after the '{'.)
If the encoding vector has been changed by set encoding, the default encoding vector can be used instead by following the slash with a dash. This is unnecessary if you use the Symbol font, however---since /Symbol uses its own encoding vector, gnuplot will not apply any other encoding vector to it.
The phantom box is useful for a@^b_c to align superscripts and subscripts but does not work well for overwriting an accent on a letter. (To do the latter, it is much better to use set encoding iso_8859_1 to change to the ISO Latin-1 encoding vector, which contains a large variety of letters with accents or other diacritical marks.) Since the box is non-spacing, it is sensible to put the shorter of the subscript or superscript in the box (that is, after the @).
Space equal in length to a string can be inserted using the '&' character. Thus
'abc&{def}ghi'
would produce
'abc ghi'.
You can access special symbols numerically by specifying \character-code (in octal), e.g., {/Symbol \245} is the symbol for infinity.
You can escape control characters using \, e.g., \\, \{, and so on.
But be aware that strings in double-quotes are parsed differently than those enclosed in single-quotes. The major difference is that backslashes may need to be doubled when in double-quoted strings.
Examples (these are hard to describe in words---try them!):
set xlabel 'Time (10^6 {/Symbol m}s)'
set title '{/Symbol=18 \362@_{/=9.6 0}^{/=12 x}} \
{/Helvetica e^{-{/Symbol m}^2/2} d}{/Symbol m}'
The file "ps_guide.ps" in the /docs/ps subdirectory of the gnuplot source distribution contains more examples of the enhanced syntax.
#### editing postscript
The PostScript language is a very complex language---far too complex to describe in any detail in this document. Nevertheless there are some things in a PostScript file written by gnuplot that can be changed without risk of introducing fatal errors into the file.
For example, the PostScript statement "/Color true def" (written into the file in response to the command set terminal postscript color), may be altered in an obvious way to generate a black-and-white version of a plot. Similarly line colors, text colors, line weights and symbol sizes can also be altered in straight-forward ways. Text (titles and labels) can be edited to correct misspellings or to change fonts. Anything can be repositioned, and of course anything can be added or deleted, but modifications such as these may require deeper knowledge of the PostScript language.
The organization of a PostScript file written by gnuplot is discussed in the text file "ps_file.doc" in the /docs/ps subdirectory.
### pslatex and pstex
The pslatex and pstex drivers generate output for further processing by LaTeX and TeX, respectively. Figures generated by pstex can be included in any plain-based format (including LaTeX).
Syntax:
set terminal pslatex | |pstex {<color>} {<dashed>} {<rotate>}
{auxfile} {<font_size>}
<color> is either color or monochrome. <rotate> is either rotate or norotate and determines if the y-axis label is rotated. <font_size> is used to scale the font from its usual size.
If auxfile is specified, it directs the driver to put the PostScript commands into an auxiliary file instead of directly into the LaTeX file. This is useful if your pictures are large enough that dvips cannot handle them. The name of the auxiliary PostScript file is derived from the name of the TeX file given on the set output command; it is determined by replacing the trailing .tex (actually just the final extent in the file name) with .ps in the output file name, or, if the TeX file has no extension, .ps is appended. Remember to close the file before leaving gnuplot.
All drivers for LaTeX offer a special way of controlling text positioning: If any text string begins with '{', you also need to include a '}' at the end of the text, and the whole text will be centered both horizontally and vertically by LaTeX. --- If the text string begins with '[', you need to continue it with: a position specification (up to two out of t,b,l,r), ']{', the text itself, and finally, '}'. The text itself may be anything LaTeX can typeset as an LR-box. \rule{}{}'s may help for best positioning.
Examples:
set term pslatex monochrome dashed rotate # set to defaults
To write the PostScript commands into the file "foo.ps":
set term pslatex auxfile
set output "foo.tex"; plot ...: set output
About label positioning: Use gnuplot defaults (mostly sensible, but sometimes not really best):
set title '\LaTeX\ -- $\gamma$'
Force centering both horizontally and vertically:
set label '{\LaTeX\ -- $\gamma$}' at 0,0
Specify own positioning (top here):
set xlabel '[t]{\LaTeX\ -- $\gamma$}'
The other label -- account for long ticlabels:
set ylabel '[r]{\LaTeX\ -- $\gamma$\rule{7mm}{0pt}'
Linewidths and pointsizes may be changed with set linestyle.
### pstricks
The pstricks driver is intended for use with the "pstricks.sty" macro package for LaTeX. It is an alternative to the eepic and latex drivers. You need "pstricks.sty", and, of course, a printer that understands PostScript, or a converter such as Ghostscript.
PSTricks is available via anonymous ftp from the /pub directory at Princeton.EDU. This driver definitely does not come close to using the full capability of the PSTricks package.
Syntax:
set terminal pstricks {hacktext | nohacktext} {unit | nounit}
The first option invokes an ugly hack that gives nicer numbers; the second has to do with plot scaling. The defaults are hacktext and nounit.
### qms
The qms terminal driver supports the QMS/QUIC Laser printer, the Talaris 1200 and others. It has no options.
### regis
The regis terminal device generates output in the REGIS graphics language. It has the option of using 4 (the default) or 16 colors.
Syntax:
set terminal regis {4 | 16}
### rgip
The rgip and uniplex terminal drivers support RGIP metafiles. They can combine several graphs on a single page, but only one page is allowed in a given output file.
Syntax:
set terminal rgip | uniplex {portrait | landscape}
{[<horiz>,<vert>]} {<fontsize>}
permissible values for the font size are in the range 1--8, with the default being 1. The default layout is landscape. Graphs are placed on the page in a horizxvert grid, which defaults to [1,1].
Example:
set terminal uniplex portrait [2,3]
puts six graphs on a page in three rows of two in portrait orientation.
### sun
The sun terminal driver supports the SunView window system. It has no options.
### tek410x
The tek410x terminal driver supports the 410x and 420x family of Tektronix terminals. It has no options.
### table
Instead of producing a graph, the table terminal prints out the points on which a graph would be based, i.e., the results of processing the plot or splot command, in a multicolumn ASCII table of X Y {Z} R values. The character R takes on one of three values: "i" if the point is in the active range, "o" if it is out-of-range, or "u" if it is undefined. The data format is determined by the format of the axis labels (see set format).
For those times when you want the numbers, you can display them on the screen or save them to a file. This can be useful if you want to generate contours and then save them for further use, perhaps for plotting with plot; see set contour for an example. The same method can be used to save interpolated data (see set samples and set dgrid3d).
### tek40
This family of terminal drivers supports a variety of VT-like terminals. tek40xx supports Tektronix 4010 and others as well as most TEK emulators; vttek supports VT-like tek40xx terminal emulators; kc-tek40xx supports MS-DOS Kermit Tek4010 terminal emulators in color: km-tek40xx supports them in monochrome; selanar supports Selanar graphics; and bitgraph supports BBN Bitgraph terminals. None have any options.
### texdraw
The texdraw terminal driver supports the LaTeX texdraw environment. It is intended for use with "texdraw.sty" and "texdraw.tex" in the texdraw package.
It has no options.
### tgif
Tgif is an X11-based drawing tool---it has nothing to do with GIF.
The tgif driver supports different pointsizes (with set pointsize), different label fonts and font sizes (e.g. set label "Hallo" at x,y font "Helvetica,34") and multiple graphs on the page. The proportions of the axes are not changed.
Syntax:
set terminal tgif {portrait | landscape} {<[x,y]>}
{solid | dashed}
{"<fontname>"} {<fontsize>}
where <[x,y]> specifies the number of graphs in the x and y directions on the page, "<fontname>" is the name of a valid PostScript font, and <fontsize> specifies the size of the PostScript font. Defaults are portrait, [1,1], dashed, "Helvetica", and 18.
The solid option is usually prefered if lines are colored, as they often are in the editor. Hardcopy will be black-and-white, so dashed should be chosen for that.
Multiplot is implemented in two different ways.
The first multiplot implementation is the standard gnuplot multiplot feature:
set terminal tgif
set output "file.obj"
set multiplot
set origin x01,y01
set size xs,ys
plot ...
...
set origin x02,y02
plot ...
set nomultiplot
See set multiplot for further information.
The second version is the [x,y] option for the driver itself. The advantage of this implementation is that everything is scaled and placed automatically without the need for setting origins and sizes; the graphs keep their natural x/y proportions of 3/2 (or whatever is fixed by set size).
If both multiplot methods are selected, the standard method is chosen and a warning message is given.
Examples of single plots (or standard multiplot):
set terminal tgif # defaults
set terminal tgif "Times-Roman" 24
set terminal tgif landscape
set terminal tgif landscape solid
Examples using the built-in multiplot mechanism:
set terminal tgif portrait [2,4] # portrait; 2 plots in the x-
# and 4 in the y-direction
set terminal tgif [1,2] # portrait; 1 plot in the x-
# and 2 in the y-direction
set terminal tgif landscape [3,3] # landscape; 3 plots in both
# directions
### tkcanvas
This terminal driver generates Tk canvas widget commands based on Tcl/Tk (default) or Perl. To use it, rebuild gnuplot (after uncommenting or inserting the appropriate line in "term.h"), then
gnuplot> set term tkcanvas {perltk} {interactive}
gnuplot> set output 'plot.file'
After invoking "wish", execute the following sequence of Tcl/Tk commands:
% source plot.file
% canvas .c
% pack .c
% gnuplot .c
Or, for Perl/Tk use a program like this:
use Tk;
my $top = MainWindow->new; my$c = $top->Canvas;$c->pack();
do "plot.pl";
gnuplot->($c); MainLoop; The code generated by gnuplot creates a procedure called "gnuplot" that takes the name of a canvas as its argument. When the procedure is called, it clears the canvas, finds the size of the canvas and draws the plot in it, scaled to fit. For 2-dimensional plotting (plot) two additional procedures are defined: "gnuplot_plotarea" will return a list containing the borders of the plotting area "xleft, xright, ytop, ybot" in canvas screen coordinates, while the ranges of the two axes "x1min, x1max, y1min, y1max, x2min, x2max, y2min, y2max" in plot coordinates can be obtained calling "gnuplot_axisranges". If the "interactive" option is specified, mouse clicking on a line segment will print the coordinates of its midpoint to stdout. Advanced actions can happen instead if the user supplies a procedure named "user_gnuplot_coordinates", which takes the following arguments: "win id x1s y1s x2s y2s x1e y1e x2e y2e x1m y1m x2m y2m", the name of the canvas and the id of the line segment followed by the coordinates of its start and end point in the two possible axis ranges; the coordinates of the midpoint are only filled for logarithmic axes. The current version of tkcanvas supports neither multiplot nor replot. ### tpic The tpic terminal driver supports the LaTeX picture environment with tpic \specials. It is an alternative to the latex and eepic terminal drivers. Options are the point size, line width, and dot-dash interval. Syntax: set terminal tpic <pointsize> <linewidth> <interval> where pointsize and linewidth are integers in milli-inches and interval is a float in inches. If a non-positive value is specified, the default is chosen: pointsize = 40, linewidth = 6, interval = 0.1. All drivers for LaTeX offer a special way of controlling text positioning: If any text string begins with '{', you also need to include a '}' at the end of the text, and the whole text will be centered both horizontally and vertically by LaTeX. --- If the text string begins with '[', you need to continue it with: a position specification (up to two out of t,b,l,r), ']{', the text itself, and finally, '}'. The text itself may be anything LaTeX can typeset as an LR-box. \rule{}{}'s may help for best positioning. Examples: About label positioning: Use gnuplot defaults (mostly sensible, but sometimes not really best): set title '\LaTeX\ --$ \gamma $' Force centering both horizontally and vertically: set label '{\LaTeX\ --$ \gamma $}' at 0,0 Specify own positioning (top here): set xlabel '[t]{\LaTeX\ --$ \gamma $}' The other label -- account for long ticlabels: set ylabel '[r]{\LaTeX\ --$ \gamma \rule{7mm}{0pt}' ### unixpc The unixpc terminal driver supports AT&T 3b1 and AT&T 7300 Unix PC. It has no options. ### unixplot The unixplot terminal driver generates output in the Unix "plot" graphics language. It has no options. This terminal cannot be compiled if the GNU version of plot is to be used; in that case, use the gnugraph terminal instead. ### vx384 The vx384 terminal driver supports the Vectrix 384 and Tandy color printers. It has no options. ### VWS The VWS terminal driver supports the VAX Windowing System. It has no options. It will sense the display type (monochrome, gray scale, or color.) All line styles are plotted as solid lines. ### windows Three options may be set in the windows terminal driver. Syntax: set terminal windows {<color>} {"<fontname>"} {<fontsize>} where <color> is either color or monochrome, "<fontname>" is the name of a valid Windows font, and <fontsize> is the size of the font in points. The Windows version normally terminates immediately as soon as the end of any files given as command line arguments is reached (i.e. in non-interactive mode). It will also not show the text-window at all, in this mode, only the plot. By giving the optional argument /noend or -noend, you can disable this behaviour. #### graph-menu The gnuplot graph window has the following options on a pop-up menu accessed by pressing the right mouse button or selecting Options from the system menu: Bring to Top when checked brings the graph window to the top after every plot. Color when checked enables color linestyles. When unchecked it forces monochrome linestyles. Copy to Clipboard copies a bitmap and a Metafile picture. Background... sets the window background color. Choose Font... selects the font used in the graphics window. Line Styles... allows customization of the line colors and styles. Update wgnuplot.ini saves the current window locations, window sizes, text window font, text window font size, graph window font, graph window font size, background color and linestyles to the initialization file WGNUPLOT.INI. #### printing In order of preference, graphs may be be printed in the following ways. 1. Use the gnuplot command set terminal to select a printer and set output to redirect output to a file. 2. Select the Print... command from the gnuplot graph window. An extra command screendump does this from the text window. 3. If set output "PRN" is used, output will go to a temporary file. When you exit from gnuplot or when you change the output with another set output command, a dialog box will appear for you to select a printer port. If you choose OK, the output will be printed on the selected port, passing unmodified through the print manager. It is possible to accidentally (or deliberately) send printer output meant for one printer to an incompatible printer. #### text-menu The gnuplot text window has the following options on a pop-up menu accessed by pressing the right mouse button or selecting Options from the system menu: Copy to Clipboard copies marked text to the clipboard. Paste copies text from the clipboard as if typed by the user. Choose Font... selects the font used in the text window. System Colors when selected makes the text window honor the System Colors set using the Control Panel. When unselected, text is black or blue on a white background. Update wgnuplot.ini saves the current text window location, text window size, text window font and text window font size to the initialisation file WGNUPLOT.INI. MENU BAR If the menu file WGNUPLOT.MNU is found in the same directory as WGNUPLOT.EXE, then the menu specified in WGNUPLOT.MNU will be loaded. Menu commands: [Menu] starts a new menu with the name on the following line. [EndMenu] ends the current menu. [--] inserts a horizontal menu separator. [|] inserts a vertical menu separator. [Button] puts the next macro on a push button instead of a menu. Macros take two lines with the macro name (menu entry) on the first line and the macro on the second line. Leading spaces are ignored. Macro commands: [INPUT] --- Input string with prompt terminated by [EOS] or {ENTER} [EOS] --- End Of String terminator. Generates no output. [OPEN] --- Get name of file to open from list box, with title of list box terminated by [EOS], followed by default filename terminated by [EOS] or {ENTER}. This uses COMMDLG.DLL from Windows 3.1. [SAVE] --- Get name of file to save. Similar to [OPEN] Macro character substitutions: {ENTER} --- Carriage Return '\r' {TAB} --- Tab '\011' {ESC} --- Escape '\033' {^A} --- '\001' ... {^_} --- '\031' Macros are limited to 256 characters after expansion. #### wgnuplot.ini Windows gnuplot will read some of its options from the [WGNUPLOT] section of WGNUPLOT.INI in the Windows directory. A sample WGNUPLOT.INI file: [WGNUPLOT] TextOrigin=0 0 TextSize=640 150 TextFont=Terminal,9 GraphOrigin=0 150 GraphSize=640 330 GraphFont=Arial,10 GraphColor=1 GraphToTop=1 GraphBackground=255 255 255 Border=0 0 0 0 0 Axis=192 192 192 2 2 Line1=0 0 255 0 0 Line2=0 255 0 0 1 Line3=255 0 0 0 2 Line4=255 0 255 0 3 Line5=0 0 128 0 4 The GraphFont entry specifies the font name and size in points. The five numbers given in the Border, Axis and Line entries are the Red intensity (0--255), Green intensity, Blue intensity, Color Linestyle and Mono Linestyle. Linestyles are 0=SOLID, 1=DASH, 2=DOT, 3=DASHDOT, 4=DASHDOTDOT. In the sample WGNUPLOT.INI file above, Line 2 is a green solid line in color mode, or a dashed line in monochrome mode. The default line width is 1 pixel. If Linestyle is negative, it specifies the width of a SOLID line in pixels. Line1 and any linestyle used with the points style must be SOLID with unit width. #### windows3.0 Windows 3.1 is preferred, but WGNUPLOT will run under Windows 3.0 with the following restrictions: 1. COMMDLG.DLL and SHELL.DLL (available with Windows 3.1 or Borland C++ 3.1) must be in the windows directory. 2. WGNUPLOT.HLP produced by Borland C++ 3.1 is in Windows 3.1 format. You need to use the WINHELP.EXE supplied with Borland C++ 3.1. 3. It will not run in real mode due to lack of memory. 4. TrueType fonts are not available in the graph window. 5. Drag-drop does not work. ### x11 gnuplot provides the x11 terminal type for use with X servers. This terminal type is set automatically at startup if the DISPLAY environment variable is set, if the TERM environment variable is set to xterm, or if the -display command line option is used. Syntax: set terminal x11 {reset} {<n>} Multiple plot windows are supported: set terminal x11 <n> directs the output to plot window number n. If n>0, the terminal number will be appended to the window title and the icon will be labeled gplt <n>. The active window may distinguished by a change in cursor (from default to crosshair.) Plot windows remain open even when the gnuplot driver is changed to a different device. A plot window can be closed by pressing the letter q while that window has input focus, or by choosing close from a window manager menu. All plot windows can be closed by specifying reset, which actually terminates the subprocess which maintains the windows (unless -persist was specified). Plot windows will automatically be closed at the end of the session unless the -persist option was given. The size or aspect ratio of a plot may be changed by resizing the gnuplot window. Linewidths and pointsizes may be changed from within gnuplot with set linestyle. For terminal type x11, gnuplot accepts (when initialized) the standard X Toolkit options and resources such as geometry, font, and name from the command line arguments or a configuration file. See the X(1) man page (or its equivalent) for a description of such options. A number of other gnuplot options are available for the x11 terminal. These may be specified either as command-line options when gnuplot is invoked or as resources in the configuration file "/.Xdefaults". They are set upon initialization and cannot be altered during a gnuplot session. #### command-line_options In addition to the X Toolkit options, the following options may be specified on the command line when starting gnuplot or as resources in your ".Xdefaults" file: -clear requests that the window be cleared momentarily before a new plot is displayed. -gray requests grayscale rendering on grayscale or color displays. (Grayscale displays receive monochrome rendering by default.) -mono forces monochrome rendering on color displays. -persist plot windows survive after main gnuplot program exits -raise raise plot window after each plot -noraise do not raise plot window after each plot -tvtwm requests that geometry specifications for position of the window be made relative to the currently displayed portion of the virtual root. The options are shown above in their command-line syntax. When entered as resources in ".Xdefaults", they require a different syntax. Example: gnuplot*gray: on gnuplot also provides a command line option (-pointsize <v>) and a resource, gnuplot*pointsize: <v>, to control the size of points plotted with the points plotting style. The value v is a real number (greater than 0 and less than or equal to ten) used as a scaling factor for point sizes. For example, -pointsize 2 uses points twice the default size, and -pointsize 0.5 uses points half the normal size. #### monochome_options For monochrome displays, gnuplot does not honor foreground or background colors. The default is black-on-white. -rv or gnuplot*reverseVideo: on requests white-on-black. #### color_resources For color displays, gnuplot honors the following resources (shown here with their default values) or the greyscale resources. The values may be color names as listed in the X11 rgb.txt file on your system, hexadecimal RGB color specifications (see X11 documentation), or a color name followed by a comma and an intensity value from 0 to 1. For example, blue, 0.5 means a half intensity blue. gnuplot*background: white gnuplot*textColor: black gnuplot*borderColor: black gnuplot*axisColor: black gnuplot*line1Color: red gnuplot*line2Color: green gnuplot*line3Color: blue gnuplot*line4Color: magenta gnuplot*line5Color: cyan gnuplot*line6Color: sienna gnuplot*line7Color: orange gnuplot*line8Color: coral The command-line syntax for these is, for example, Example: gnuplot -background coral #### grayscale_resources When -gray is selected, gnuplot honors the following resources for grayscale or color displays (shown here with their default values). Note that the default background is black. gnuplot*background: black gnuplot*textGray: white gnuplot*borderGray: gray50 gnuplot*axisGray: gray50 gnuplot*line1Gray: gray100 gnuplot*line2Gray: gray60 gnuplot*line3Gray: gray80 gnuplot*line4Gray: gray40 gnuplot*line5Gray: gray90 gnuplot*line6Gray: gray50 gnuplot*line7Gray: gray70 gnuplot*line8Gray: gray30 #### line_resources gnuplot honors the following resources for setting the width (in pixels) of plot lines (shown here with their default values.) 0 or 1 means a minimal width line of 1 pixel width. A value of 2 or 3 may improve the appearance of some plots. gnuplot*borderWidth: 2 gnuplot*axisWidth: 0 gnuplot*line1Width: 0 gnuplot*line2Width: 0 gnuplot*line3Width: 0 gnuplot*line4Width: 0 gnuplot*line5Width: 0 gnuplot*line6Width: 0 gnuplot*line7Width: 0 gnuplot*line8Width: 0 gnuplot honors the following resources for setting the dash style used for plotting lines. 0 means a solid line. A two-digit number jk (j and k are >= 1 and <= 9) means a dashed line with a repeated pattern of j pixels on followed by k pixels off. For example, '16' is a "dotted" line with one pixel on followed by six pixels off. More elaborate on/off patterns can be specified with a four-digit value. For example, '4441' is four on, four off, four on, one off. The default values shown below are for monochrome displays or monochrome rendering on color or grayscale displays. For color displays, the default for each is 0 (solid line) except for axisDashes which defaults to a '16' dotted line. gnuplot*borderDashes: 0 gnuplot*axisDashes: 16 gnuplot*line1Dashes: 0 gnuplot*line2Dashes: 42 gnuplot*line3Dashes: 13 gnuplot*line4Dashes: 44 gnuplot*line5Dashes: 15 gnuplot*line6Dashes: 4441 gnuplot*line7Dashes: 42 gnuplot*line8Dashes: 13 ### xlib The xlib terminal driver supports the X11 Windows System. It generates gnulib_x11 commands. set term x11 behaves similarly to set terminal xlib; set output "|gnuplot_x11". xlib has no options, but see x11. ## tics The set tics command can be used to change the tics to be drawn outwards. Syntax: set tics {<direction>} show tics where <direction> may be in (the default) or out. See also set xtics for more control of major (labelled) tic marks and set mxtics for control of minor tic marks. ## ticslevel Using splot, one can adjust the relative height of the vertical (Z) axis using set ticslevel. The numeric argument provided specifies the location of the bottom of the scale (as a fraction of the z-range) above the xy-plane. The default value is 0.5. Negative values are permitted, but tic labels on the three axes may overlap. To place the xy-plane at a position 'pos' on the z-axis, ticslevel should be set equal to (pos - zmin) / (zmin - zmax). Syntax: set ticslevel {<level>} show tics See also set view. ## ticscale The size of the tic marks can be adjusted with set ticscale. Syntax: set ticscale {<major> {<minor>}} show tics If <minor> is not specified, it is 0.5*<major>. The default size is 1.0 for major tics and 0.5 for minor tics. Note that it is possible to have the tic marks pointing outward by specifying a negative size. ## timestamp The command set timestamp places the time and date of the plot in the left margin. Syntax: set timestamp {"<format>"} {top|bottom} {{no}rotate} {<xoff>}{,<yoff>} {"<font>"} set notimestamp show timestamp The format string allows you to choose the format used to write the date and time. Its default value is what asctime() uses: "%a %b %d %H:%M:%S %Y" (weekday, month name, day of the month, hours, minutes, seconds, four-digit year). With top or bottom you can place the timestamp at the top or bottom of the left margin (default: bottom). rotate lets you write the timestamp vertically, if your terminal supports vertical text. The constants <xoff> and <off> are offsets from the default position given in character screen coordinates. <font> is used to specify the font with which the time is to be written. The abbreviation time may be used in place of timestamp. Example: set timestamp "%d/%m/%y %H:%M" 80,-2 "Helvetica" See set timefmt for more information about time format strings. ## timefmt This command applies to timeseries where data are composed of dates/times. It has no meaning unless the command set xdata time is given also. Syntax: set timefmt "<format string>" show timefmt The string argument tells gnuplot how to read timedata from the datafile. The valid formats are: Format Explanation %d day of the month, 1--31 %m month of the year, 1--12 %y year, 0--99 %Y year, 4-digit %j day of the year, 1--365 %H hour, 0--24 %M minute, 0--60 %S second, 0--60 %b three-character abbreviation of the name of the month %B name of the month Any character is allowed in the string, but must match exactly. \t (tab) is recognized. Backslash-octals (\nnn) are converted to char. If there is no separating character between the time/date elements, then %d, %m, %y, %H, %M and %S read two digits each, %Y reads four digits and %j reads three digits. %b requires three characters, and %B requires as many as it needs. Spaces are treated slightly differently. A space in the string stands for zero or more whitespace characters in the file. That is, "%H %M" can be used to read "1220" and "12 20" as well as "12 20". Each set of non-blank characters in the timedata counts as one column in the using n:n specification. Thus 11:11 25/12/76 21.0 consists of three columns. To avoid confusion, gnuplot requires that you provide a complete using specification if your file contains timedata. Since gnuplot cannot read non-numerical text, if the date format includes the day or month in words, the format string must exclude this text. But it can still be printed with the "%a", "%A", "%b", or "%B" specifier: see set format for more details about these and other options for printing timedata. (gnuplot will determine the proper month and weekday from the numerical values.) See also set xdata and Time/date for more information. Example: set timefmt "%d/%m/%Y\t%H:%M" tells gnuplot to read date and time separated by tab. (But look closely at your data---what began as a tab may have been converted to spaces somewhere along the line; the format string must match what is actually in the file.) Time Data Demo ## title Syntax: set title {"<title-text>"} {<xoff>}{,<yoff>} {"<font>,{<size>}"} show title Specifying constants <xoff> or <yoff> as optional offsets for the title will move the title <xoff> or <yoff> character screen coordinates (not graph coordinates). For example, "set title ,-1" will change only the y offset of the title, moving the title down by roughly the height of one character. <font> is used to specify the font with which the title is to be written; the units of the font <size> depend upon which terminal is used. set title with no parameters clears the title. See syntax for details about the processing of backslash sequences and the distinction between single- and double-quotes. ## tmargin ## trange ## urange The set urange and set vrange commands set the parametric ranges used to compute x, y, and z values when in splot parametric mode. Please see set xrange for details. ## variables The show variables command lists all user-defined variables and their values. Syntax: show variables ## version The show version command lists the version of gnuplot being run, its last modification date, the copyright holders, and email addresses for the FAQ, the info-gnuplot mailing list, and reporting bugs--in short, the information listed on the screen when the program is invoked interactively. Syntax: show version {long} When the long option is given, it also lists the operating system, the compilation options used when gnuplot was installed, the location of the help file, and (again) the useful email addresses. ## view The set view command sets the viewing angle for splots. It controls how the 3-d coordinates of the plot are mapped into the 2-d screen space. It provides controls for both rotation and scaling of the plotted data, but supports orthographic projections only. Syntax: set view <rot_x> {,{<rot_z>}{,{<scale>}{,<scale_z>}}} show view where <rot_x> and <rot_z> control the rotation angles (in degrees) in a virtual 3-d coordinate system aligned with the screen such that initially (that is, before the rotations are performed) the screen horizontal axis is x, screen vertical axis is y, and the axis perpendicular to the screen is z. The first rotation applied is <rot_x> around the x axis. The second rotation applied is <rot_z> around the new z axis. <rot_x> is bounded to the [0:180] range with a default of 60 degrees, while <rot_z> is bounded to the [0:360] range with a default of 30 degrees. <scale> controls the scaling of the entire splot, while <scale_z> scales the z axis only. Both scales default to 1.0. Examples: set view 60, 30, 1, 1 set view ,,0.5 The first sets all the four default values. The second changes only scale, to 0.5. See also set ticslevel. ## vrange The set urange and set vrange commands set the parametric ranges used to compute x, y, and z values when in splot parametric mode. Please see set xrange for details. ## x2data ## x2dtics ## x2label ## x2mtics ## x2range ## x2tics ## x2zeroaxis ## xdata This command sets the datatype on the x axis to time/date. A similar command does the same thing for each of the other axes. Syntax: set xdata {time} show xdata The time option signals that the datatype is indeed time/date. If the option is not specified, the datatype reverts to normal. See set timefmt to tell gnuplot how to read date or time data. The time/date is converted to seconds from start of the century. There is currently only one timefmt, which implies that all the time/date columns must confirm to this format. Specification of ranges should be supplied as quoted strings according to this format to avoid interpretation of the time/date as an expression. The function 'strftime' (type "man strftime" on unix to look it up) is used to print tic-mark labels. gnuplot tries to figure out a reasonable format for this unless the set format x "string" has supplied something that does not look like a decimal format (more than one '%' or neither %f nor %g). See also Time/date for more information. ## xdtics The set xdtics commands converts the x-axis tic marks to days of the week where 0=Sun and 6=Sat. Overflows are converted modulo 7 to dates. set noxdtics returns the labels to their default values. Similar commands do the same things for the other axes. Syntax: set xdtics set noxdtics show xdtics See also the set format command. ## xlabel The set xlabel command sets the x axis label. Similar commands set labels on the other axes. Syntax: set xlabel {"<label>"} {<xoff>}{,<yoff>} {"<font>{,<size>}"} show xlabel Specifying the constants <xoff> or <yoff> as optional offsets for a label will move it <xoff> or <yoff> character widths or heights. For example, " set xlabel -1" will change only the x offset of the xlabel, moving the label roughly one character width to the left. The size of a character depends on both the font and the terminal. <font> is used to specify the font in which the label is written; the units of the font <size> depend upon which terminal is used. To clear a label, put no options on the command line, e.g., "set y2label". The default positions of the axis labels are as follows: xlabel: The x-axis label is centered below the bottom axis. ylabel: The position of the y-axis label depends on the terminal, and can be one of the following three positions: 1. Horizontal text flushed left at the top left of the plot. Terminals that cannot rotate text will probably use this method. If set x2tics is also in use, the ylabel may overwrite the left-most x2tic label. This may be remedied by adjusting the ylabel position or the left margin. 2. Vertical text centered vertically at the left of the plot. Terminals that can rotate text will probably use this method. 3. Horizontal text centered vertically at the left of the plot. The EEPIC, LaTeX and TPIC drivers use this method. The user must insert line breaks using \\ to prevent the ylabel from overwriting the plot. To produce a vertical row of characters, add \\ between every printing character (but this is ugly). zlabel: The z-axis label is centered along the z axis and placed in the space above the grid level. y2label: The y2-axis label is placed to the right of the y2 axis. The position is terminal-dependent in the same manner as is the y-axis label. x2label: The x2-axis label is placed above the top axis but below the plot title. It is also possible to create an x2-axis label by using new-line characters to make a multi-line plot title, e.g., set title "This is the title\n\nThis is the x2label" Note that double quotes must be used. The same font will be used for both lines, of course. If you are not satisfied with the default position of an axis label, use set label instead--that command gives you much more control over where text is placed. Please see set syntax for further information about backslash processing and the difference between single- and double-quoted strings. ## xmtics The set xmtics commands converts the x-axis tic marks to months of the year where 1=Jan and 12=Dec. Overflows are converted modulo 12 to months. The tics are returned to their default labels by set noxmtics. Similar commands perform the same duties for the other axes. Syntax: set xmtics set noxmtics show xmtics See also the set format command. ## xrange The set xrange command sets the horizontal range that will be displayed. A similar command exists for each of the other axes, as well as for the polar radius r and the parametric variables t, u, and v. Syntax: set xrange [{{<min>}:{<max>}}] {{no}reverse} {{no}writeback} show xrange where <min> and <max> terms are constants, expressions or an asterisk to set autoscaling. If the data are time/date, you must give the range as a quoted string according to the set timefmt format. Any value omitted will not be changed. The same syntax applies to yrange, zrange, x2range, y2range, rrange, trange, urange and vrange. The reverse option reverses the direction of the axis, e.g., set xrange [0:1] reverse will produce an axis with 1 on the left and 0 on the right. This is identical to the axis produced by set xrange [1:0], of course. reverse is intended primarily for use with autoscale. The writeback option essentially saves the range found by autoscale in the buffers that would be filled by set xrange. This is useful if you wish to plot several functions together but have the range determined by only some of them. The writeback operation is performed during the plot execution, so it must be specified before that command. For example, set xrange [-10:10] set yrange [] writeback plot sin(x) set noautoscale y replot x/2 results in a yrange of [-1:1] as found only from the range of sin(x); the [-5:5] range of x/2 is ignored. Executing show yrange after each command in the above example should help you understand what is going on. In 2-d, xrange and yrange determine the extent of the axes, trange determines the range of the parametric variable in parametric mode or the range of the angle in polar mode. Similarly in parametric 3-d, xrange, yrange, and zrange govern the axes and urange and vrange govern the parametric variables. In polar mode, rrange determines the radial range plotted. <rmin> acts as an additive constant to the radius, whereas <rmax> acts as a clip to the radius---no point with radius greater than <rmax> will be plotted. xrange and yrange are affected---the ranges can be set as if the graph was of r(t)-rmin, with rmin added to all the labels. Any range may be partially or totally autoscaled, although it may not make sense to autoscale a parametric variable unless it is plotted with data. Ranges may also be specified on the plot command line. A range given on the plot line will be used for that single plot command; a range given by a set command will be used for all subsequent plots that do not specify their own ranges. The same holds true for splot. Examples: To set the xrange to the default: set xrange [-10:10] To set the yrange to increase downwards: set yrange [10:-10] To change zmax to 10 without affecting zmin (which may still be autoscaled): set zrange [:10] To autoscale xmin while leaving xmax unchanged: set xrange [*:] ## xtics Fine control of the major (labelled) tics on the x axis is possible with the set xtics command. The tics may be turned off with the set noxtics command, and may be turned on (the default state) with set xtics. Similar commands control the major tics on the y, z, x2 and y2 axes. Syntax: set xtics {axis | border} {{no}mirror} {{no}rotate} { autofreq | <incr> | <start>, <incr> {,<end>} | ({"<label>"} <pos> {,{"<label>"} <pos>}...) } set noxtics show xtics axis or border tells gnuplot to put the tics (both the tics themselves and the accompanying labels) along the axis or the border, respectively. If the axis is very close to the border, the axis option can result in tic labels overwriting other text written in the margin. mirror tells gnuplot to put unlabelled tics at the same positions on the opposite border. nomirror does what you think it does. rotate asks gnuplot to rotate the text through 90 degrees, which will be done if the terminal driver in use supports text rotation. norotate cancels this. The defaults are border mirror norotate for tics on the x and y axes, and border nomirror norotate for tics on the x2 and y2 axes. For the z axis, the the {axis | border} option is not available and the default is nomirror. If you do want to mirror the z-axis tics, you might want to create a bit more room for them with set border. set xtics with no options restores the default border or axis if xtics are being displayed; otherwise it has no effect. Any previously specified tic frequency or position {and labels} are retained. Positions of the tics are calculated automatically by default or if the autofreq option is given; otherwise they may be specified in either of two forms: The implicit <start>, <incr>, <end> form specifies that a series of tics will be plotted on the axis between the values <start> and <end> with an increment of <incr>. If <end> is not given, it is assumed to be infinity. The increment may be negative. If neither <start> nor <end> is given, <start> is assumed to be negative infinity, <end> is assumed to be positive infinity, and the tics will be drawn at integral multiples of <step>. If the axis is logarithmic, the increment will be used as a multiplicative factor. Examples: Make tics at 0, 0.5, 1, 1.5, ..., 9.5, 10. set xtics 0,.5,10 Make tics at ..., -10, -5, 0, 5, 10, ... set xtics 5 Make tics at 1, 100, 1e4, 1e6, 1e8. set logscale x; set xtics 1,100,10e8 The explicit ("<label>" <pos>, ...) form allows arbitrary tic positions or non-numeric tic labels. A set of tics is a set of positions, each with its own optional label. Note that the label is a string enclosed by quotes. It may be a constant string, such as "hello", may contain formatting information for converting the position into its label, such as "%3f clients", or may be empty, "". See set format for more information. If no string is given, the default label (numerical) is used. In this form, the tics do not need to be listed in numerical order. Examples: set xtics ("low" 0, "medium" 50, "high" 100) set xtics (1,2,4,8,16,32,64,128,256,512,1024) set ytics ("bottom" 0, "" 10, "top" 20) In the second example, all tics are labelled. In the third, only the end tics are labelled. However they are specified, tics will only be plotted when in range. Format (or omission) of the tic labels is controlled by set format, unless the explicit text of a labels is included in the set xtic (<label>) form. Minor (unlabelled) tics can be added by the set mxtics command. In case of timeseries data, position values must be given as quoted dates or times according to the format timefmt. If the <start>, <incr>, <end> form is used, <start> and <end> must be given according to timefmt, but <incr> must be in seconds. Times will be written out according to the format given on set format, however. Examples: set xdata time set timefmt "%d/%m" set format x "%b %d" set xrange ["01/12":"06/12"] set xtics "01/12", 172800, "05/12" set xdata time set timefmt "%d/%m" set format x "%b %d" set xrange ["01/12":"06/12"] set xtics ("01/12", "" "03/12", "05/12") Both of these will produce tics "Dec 1", "Dec 3", and "Dec 5", but in the second example the tic at "Dec 3" will be unlabelled. ## xzeroaxis ## y2data ## y2dtics ## y2label The set y2dtics command sets the label for the y2 (right-hand) axis. Please see set xlabel. ## y2mtics ## y2range ## y2tics ## y2zeroaxis ## ydata ## ydtics ## ylabel ## ymtics ## yrange ## ytics ## yzeroaxis ## zdata ## zdtics ## zero The zero value is the default threshold for values approaching 0.0. Syntax: set zero <expression> show zero gnuplot will not plot a point if its imaginary part is greater in magnitude than the zero threshold. This threshold is also used in various other parts of gnuplot as a (crude) numerical-error threshold. The default zero value is 1e-8. zero values larger than 1e-3 (the reciprocal of the number of pixels in a typical bitmap display) should probably be avoided, but it is not unreasonable to set zero to 0.0. ## zeroaxis The x axis may be drawn by set xzeroaxis and removed by set noxzeroaxis. Similar commands behave similarly for the y, x2, and y2 axes. Syntax: set {x|x2|y|y2|}zeroaxis { {linestyle | ls <line_style>} | { linetype | lt <line_type>} { linewidth | lw <line_width>}} set no{x|x2|y|y2|}zeroaxis show {x|y|}zeroaxis By default, these options are off. The selected zero axis is drawn with a line of type <line_type> and width <line_width> (if supported by the terminal driver currently in use), or a user-defined style <line_style>. If no linetype is specified, any zero axes selected will be drawn using the axis linetype (linetype 0). set zeroaxis l is equivalent to set xzeroaxis l; set yzeroaxis l. set nozeroaxis is equivalent to set noxzeroaxis; set noyzeroaxis. ## zlabel ## zmtics ## zrange The set zrange command sets the range that will be displayed on the z axis. The zrange is used only by splot and is ignored by plot. Please see set xrange for details. ## ztics # shell The shell command spawns an interactive shell. To return to gnuplot, type logout if using VMS, exit or the END-OF-FILE character if using Unix, endcli if using AmigaOS, or exit if using MS-DOS or OS/2. A single shell command may be spawned by preceding it with the ! character ( if using VMS) at the beginning of a command line. Control will return immediately to gnuplot after this command is executed. For example, in Unix, AmigaOS, MS-DOS or OS/2,
! dir
prints a directory listing and then returns to gnuplot.
On an Atari, the ! command first checks whether a shell is already loaded and uses it, if available. This is practical if gnuplot is run from gulam, for example.
# splot
See plot for features common to the plot command; only differences are discussed in detail here. Note specifically that the binary and matrix options (discussed under "datafile-modifiers") are not available for plot.
Syntax:
splot {<ranges>}
<function> | "<datafile>" {datafile-modifiers}}
{<title-spec>} {with <style>}
{, {definitions,} <function> ...}
where either a <function> or the name of a data file enclosed in quotes is supplied. The function can be a mathematical expression, or a triple of mathematical expressions in parametric mode.
By default splot draws the xy plane completely below the plotted data. The offset between the lowest ztic and the xy plane can be changed by set ticslevel. The orientation of a splot projection is controlled by set view. See set view and set ticslevel for more information.
The syntax for setting ranges on the splot command is the same as for plot. In non-parametric mode, the order in which ranges must be given is xrange, yrange, and zrange. In parametric mode, the order is urange, vrange, xrange, yrange, and zrange.
The title option is the same as in plot. The operation of with is also the same as in plot, except that the plotting styles available to splot are limited to lines, points, linespoints, dots, and impulses; the error-bar capabilities of plot are not available for splot.
The datafile options have more differences.
## data-file
As for plot, discrete data contained in a file can be displayed by specifying the name of the data file, enclosed in quotes, on the splot command line.
Syntax:
splot '<file_name>' {binary | matrix}
{index <index list>}
{every <every list>}
{using <using list>}
The special filenames "" and "-" are permitted, as in plot.
In brief, binary and matrix indicate that the the data are in a special form, index selects which data sets in a multi-data-set file are to be plotted, every specifies which datalines (subsets) within a single data set are to be plotted, and using determines how the columns within a single record are to be interpreted.
The options index and every behave the same way as with plot; using does so also, except that the using list must provide three entries instead of two.
The plot options thru and smooth are not available for splot, but cntrparams and dgrid3d provide limited smoothing cabilities.
Data file organization is essentially the same as for plot, except that each point is an (x,y,z) triple. If only a single value is provided, it will be used for z, the datablock number will be used for y, and the index of the data point in the datablock will be used for x. If two values are provided, gnuplot gives you an error message. Three values are interpreted as an (x,y,z) triple. Additional values are generally used as errors, which can be used by fit.
Single blank records separate datablocks in a splot datafile; splot treats datablocks as the equivalent of function y-isolines. No line will join points separated by a blank record. If all datablocks contain the same number of points, gnuplot will draw cross-isolines between datablocks, connecting corresponding points. This is termed "grid data", and is required for drawing a surface, for contouring (set contour) and hidden-line removal (set hidden3d). See also splot grid data
It is no longer necessary to specify parametric mode for three-column splots.
### binary
splot can read binary files written with a specific format (and on a system with a compatible binary file representation.)
In previous versions, gnuplot dynamically detected binary data files. It is now necessary to specify the keyword binary directly after the filename.
Single precision floats are stored in a binary file as follows:
<N+1> <y0> <y1> <y2> ... <yN>
<x0> <z0,0> <z0,1> <z0,2> ... <z0,N>
<x1> <z1,0> <z1,1> <z1,2> ... <z1,N>
: : : : ... :
which are converted into triplets:
<x0> <y0> <z0,0>
<x0> <y1> <z0,1>
<x0> <y2> <z0,2>
: : :
<x0> <yN> <z0,N>
<x1> <y0> <z1,0>
<x1> <y1> <z1,1>
: : :
These triplets are then converted into gnuplot iso-curves and then gnuplot proceeds in the usual manner to do the rest of the plotting.
A collection of matrix and vector manipulation routines (in C) is provided in binary.c. The routine to write binary data is
int fwrite_matrix(file,m,nrl,nrl,ncl,nch,row_title,column_title)
An example of using these routines is provided in the file bf_test.c, which generates binary files for the demo file demo/binary.dem.
The index keyword is not supported, since the file format allows only one surface per file. The every and using filters are supported. using operates as if the data were read in the above triplet form. Binary File Splot Demo.
### example datafile
A simple example of plotting a 3-d data file is
splot 'datafile.dat'
where the file "datafile.dat" might contain:
# The valley of the Gnu.
0 0 10
0 1 10
0 2 10
1 0 10
1 1 5
1 2 10
2 0 10
2 1 1
2 2 10
3 0 10
3 1 0
3 2 10
Note that "datafile.dat" defines a 4 by 3 grid ( 4 rows of 3 points each ). Rows (datablocks) are separated by blank records.
Note also that the x value is held constant within each dataline. If you instead keep y constant, and plot with hidden-line removal enabled, you will find that the surface is drawn 'inside-out'.
Actually for grid data it is not necessary to keep the x values constant within a datablock, nor is it necessary to keep the same sequence of y values. gnuplot requires only that the number of points be the same for each datablock. However since the surface mesh, from which contours are derived, connects sequentially corresponding points, the effect of an irregular grid on a surface plot is unpredictable and should be examined on a case-by-case basis.
### matrix
The matrix flag indicates that the ASCII data are stored in matrix format. The z-values are read in a row at a time, i. e.,
z11 z12 z13 z14 ...
z21 z22 z23 z24 ...
z31 z32 z33 z34 ...
and so forth. The row and column indices are used for the x- and y-values.
## grid_data
The 3D routines are designed for points in a grid format, with one sample, datapoint, at each mesh intersection; the datapoints may originate from either evaluating a function, see set isosamples, or reading a datafile, see splot datafile. The term "isoline" is applied to the mesh lines for both functions and data. Note that the mesh need not be rectangular in x and y, as it may be parameterized in u and v, see set isosamples.
However, gnuplot does not require that format. In the case of functions, 'samples' need not be equal to 'isosamples', i.e., not every x-isoline sample need intersect a y-isoline. In the case of data files, if there are an equal number of scattered data points in each datablock, then "isolines" will connect the points in a datablock, and "cross-isolines" will connect the corresponding points in each datablock to generate a "surface". In either case, contour and hidden3d modes may give different plots than if the points were in the intended format. Scattered data can be converted to a {different} grid format with set dgrid3d.
The contour code tests for z intensity along a line between a point on a y-isoline and the corresponding point in the next y-isoline. Thus a splot contour of a surface with samples on the x-isolines that do not coincide with a y-isoline intersection will ignore such samples. Try:
set xrange [-pi/2:pi/2]; set yrange [-pi/2:pi/2]
set function style lp
set contour
set isosamples 10,10; set samples 10,10;
splot cos(x)*cos(y)
set samples 4,10; replot
set samples 10,4; replot
## splot_overview
splot can display a surface as a collection of points, or by connecting those points. As with plot, the points may be read from a data file or result from evaluation of a function at specified intervals, see set isosamples. The surface may be approximated by connecting the points with straight line segments, see set surface, in which case the surface can be made opaque with set hidden3d. The orientation from which the 3d surface is viewed can be changed with set view.
Additionally, for points in a grid format, splot can interpolate points having a common amplitude (see set contour) and can then connect those new points to display contour lines, either directly with straight-line segments or smoothed lines (see set cntrparams). Functions are already evaluated in a grid format, determined by set isosamples and set samples, while file data must either be in a grid format, as described in data-file, or be used to generate a grid (see set dgrid3d).
Contour lines may be displayed either on the surface or projected onto the base. The base projections of the contour lines may be written to a file, and then read with plot, to take advantage of plot's additional formatting capabilities.
# test
test creates a display of line and point styles and other useful things appropriate for the terminal you are using.
Syntax:
test
# update
This command writes the current values of the fit parameters into the given file, formatted as an initial-value file (as described in the fitsection). This is useful for saving the current values for later use or for restarting a converged or stopped fit.
Syntax:
update <filename> {<filename>}
If a second filename is supplied, the updated values are written to this file, and the original parameter file is left unmodified.
Otherwise, if the file already exists, gnuplot first renames it by appending .old and then opens a new file. That is, "update 'fred'" behaves the same as "!rename fred fred.old; update 'fred.old' 'fred'". [On DOS and other systems that use the twelve-character "filename.ext" naming convention, "ext" will be "old" and "filename" will be related (hopefully recognizably) to the initial name. Renaming is not done at all on VMS systems, since they use file-versioning.]
# Graphical User Interfaces
Several graphical user interfaces have been written for gnuplot and one for win32 is included in this distribution. In addition, there is a Macintosh interface at
ftp://ftp.ee.gatech.edu/pub/mac/gnuplot
and several X11 interfaces include three Tcl/Tk located at the usual Tcl/Tk repositories.
# Bugs
Floating point exceptions (floating point number too large/small, divide by zero, etc.) may occasionally be generated by user defined functions. Some of the demos in particular may cause numbers to exceed the floating point range. Whether the system ignores such exceptions (in which case gnuplot labels the corresponding point as undefined) or aborts gnuplot depends on the compiler/runtime environment.
The bessel functions do not work for complex arguments.
The gamma function does not work for complex arguments.
As of gnuplot version 3.7, all development has been done using ANSI C. With current operating system, compiler, and library releases, the OS specific bugs documented in release 3.5, now relegated to old_bugs, may no longer be relevant.
Bugs reported since the current release may be located via the official distribution site:
ftp://ftp.dartmouth.edu/pub/gnuplot
http://www.cs.dartmouth.edu/gnuplot_info.html
Please e-mail any bugs to bug-gnuplot@dartmouth.edu.
# Old_bugs
There is a bug in the stdio library for old Sun operating systems (SunOS Sys4-3.2). The "%g" format for 'printf' sometimes incorrectly prints numbers (e.g., 200000.0 as "2"). Thus, tic mark labels may be incorrect on a Sun4 version of gnuplot. A work-around is to rescale the data or use the set format command to change the tic mark format to "%7.0f" or some other appropriate format. This appears to have been fixed in SunOS 4.0.
Another bug: On a Sun3 under SunOS 4.0, and on Sun4's under Sys4-3.2 and SunOS 4.0, the 'sscanf' routine incorrectly parses "00 12" with the format "%f %f" and reads 0 and 0 instead of 0 and 12. This affects data input. If the data file contains x coordinates that are zero but are specified like '00', '000', etc, then you will read the wrong y values. Check any data files or upgrade the SunOS. It appears to have been fixed in SunOS 4.1.1.
Suns appear to overflow when calculating exp(-x) for large x, so gnuplot gets an undefined result. One work-around is to make a user-defined function like e(x) = x<-500 ? 0 : exp(x). This affects plots of Gaussians (exp(-x*x)) in particular, since x*x grows quite rapidly.
Microsoft C 5.1 has a nasty bug associated with the %g format for 'printf'. When any of the formats "%.2g", "%.1g", "%.0g", "%.g" are used, 'printf' will incorrectly print numbers in the range 1e-4 to 1e-1. Numbers that should be printed in the %e format are incorrectly printed in the %f format, with the wrong number of zeros after the decimal point. To work around this problem, use the %e or %f formats explicitly.
gnuplot, when compiled with Microsoft C, did not work correctly on two VGA displays that were tested. The CGA, EGA and VGA drivers should probably be rewritten to use the Microsoft C graphics library. gnuplot compiled with Borland C++ uses the Turbo C graphics drivers and does work correctly with VGA displays.
VAX/VMS 4.7 C compiler release 2.4 also has a poorly implemented %g format for 'printf'. The numbers are printed numerically correct, but may not be in the requested format. The K&R second edition says that for the %g format, %e is used if the exponent is less than -4 or greater than or equal to the precision. The VAX uses %e format if the exponent is less than -1. The VAX appears to take no notice of the precision when deciding whether to use %e or %f for numbers less than 1. To work around this problem, use the %e or %f formats explicitly. From the VAX C 2.4 release notes: e,E,f,F,g,G Result will always contain a decimal point. For g and G, trailing zeros will not be removed from the result.
VAX/VMS 5.2 C compiler release 3.0 has a slightly better implemented %g format than release 2.4, but not much. Trailing decimal points are now removed, but trailing zeros are still not removed from %g numbers in exponential format.
The two preceding problems are actually in the libraries rather than in the compilers. Thus the problems will occur whether gnuplot is built using either the DEC compiler or some other one (e.g. the latest gcc).
ULTRIX X11R3 has a bug that causes the X11 driver to display "every other" graph. The bug seems to be fixed in DEC's release of X11R4 so newer releases of ULTRIX don't seem to have the problem. Solutions for older sites include upgrading the X11 libraries (from DEC or direct from MIT) or defining ULTRIX_KLUDGE when compiling the x11.trm file. Note that the kludge is not an ideal fix, however.
The constant HUGE was incorrectly defined in the NeXT OS 2.0 operating system. HUGE should be set to 1e38 in plot.h. This error has been corrected in the 2.1 version of NeXT OS.
Some older models of HP plotters do not have a page eject command 'PG'. The current HPGL driver uses this command in HPGL_reset. This may need to be removed for these plotters. The current PCL5 driver uses HPGL/2 for text as well as graphics. This should be modified to use scalable PCL fonts.
On the Atari version, it is not possible to send output directly to the printer (using /dev/lp as output file), since CRs are added to LFs in binary output. As a work-around, write the output to a file and copy it to the printer afterwards using a shell command.
On AIX 4, the literal 'NaNq' in a datafile causes the special internal value 'not-a-number' to be stored, rather than setting an internal 'undefined' flag. A workaround is to use set missing 'NaNq'.
There may be an up-to-date list of bugs since the release on the WWW page:
http://www.cs.dartmouth.edu/gnuplot_info.html
Please report any bugs to bug-gnuplot@dartmouth.edu.
Created automatically by doc2html
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2015-09-05 07:45:31
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http://www.cmstatistics.org/RegistrationsV2/CMStatistics2017/viewSubmission.php?in=822&token=0s4510nr7175npn4s7n557q3nqrp619s
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CMStatistics 2017: Start Registration
View Submission - CMStatistics
B0822
Title: Hierarchical functional clustering using equivalence test with application to perfusion imaging Authors: Yves Rozenholc - University Paris Descartes (France) [presenting]
Fuchen Liu - University Paris Descartes (China)
Charles A Cuenod - University Paris Descartes (France)
Abstract: Perfusion imaging allows non invasive access to tissue micro-vascularization. Promising tool to build imaging biomarkers, it suffers from low SNR, improved by averaging homogeneous functional information in large regions of interest. We propose a new automatic segmentation of such image sequence into functionally homogeneous regions. At its core, HiSET (Hierarchical Segmentation using Equivalence Test) aims to cluster functional signals discretely observed with noise on a finite metric space. Assuming independent fixed Gaussian noise, HiSET uses p-values of a multiple equivalence test as dissimilarity measure. It consists of two steps only varying through the neighborhood structure. The first benefit from local regularities on the metric space to control the complexity, the second recovers (spatially) disconnected homogeneous structures at a larger scale. Given a maximal expected homogeneity discrepancy $\delta$, both steps stop automatically through a control of the type I error, providing an adaptive segmentation. Tuning parameter $\delta$ can be interpreted as a multi-resolution diameter around functional patterns recover by the segmentation. When the landscape is functionally piecewise constant with well separated functional features, HiSET is proven to retrieve the exact partition with high probability when the number of observation times is large enough. HiSET outperforms state-of-the-art clustering methods for perfusion imaging sequences.
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2021-01-15 23:54:38
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https://plainmath.net/8226/geologist-collected-specimens-specimens-geologist-instructs-laboratory
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# A geologist has collected 10 specimens of basaltic rock and 10 specimens of granite. The geologist instructs a laboratory assistant to randomly select
A geologist has collected 10 specimens of basaltic rock and 10 specimens of granite. The geologist instructs a laboratory assistant to randomly select 15 of the speciems for analysis
1) What the pmf of the number of granite specimens selected for analysis?
2) What is the probability that the number of granite specimens selected for analysis is greater than 7?
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Velsenw
Total number of specimen is 20 (10+10). So, the probability that a randomly selected specimen is granite is $\frac{10}{20}=\frac{1}{2}=0.5$.
Consider a random variable X which represents the number of granite specimen in the sample.
X will follow binomial distribution with parameters n = 15 and p = 0.5
The p.m.f of X can be defined as:
$P\left(x=x\right)=\left(\begin{array}{c}15\\ x\end{array}\right){0.5}^{x}{\left(1-0.5\right)}^{15-x}$
x=0,1,2,...,15
The probability that number of granite selected for the analysis is greater than 7 can be calculated as:
$P\left(X>7\right)=1-P\left(x\le 7\right)$
$=1-\sum _{x=0}^{7}\left(\begin{array}{c}15\\ x\end{array}\right){0.5}^{x}{\left(1-0.5\right)}^{15-x}$
=1-0.5
=0.5
So, the required probability is 0.5
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2022-06-27 23:51:39
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http://meetings.aps.org/Meeting/MAR09/Event/93338
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### Session A18: Bulk Block Copolymers I
8:00 AM–11:00 AM, Monday, March 16, 2009
Room: 319
Chair: Thomas Epps, University of Delaware
Abstract ID: BAPS.2009.MAR.A18.14
### Abstract: A18.00014 : Dynamics of Disordered PI-PtBS Diblock Copolymer
10:36 AM–10:48 AM
Preview Abstract MathJax On | Off Abstract
#### Author:
Hiroshi Watanabe
(Kyoto University)
Viscoelastic ($G^*$) and dielectric ($\varepsilon''$) data were examined for a LCST-type diblock copolymer composed of polyisoprene (PI; M = 53K) and poly(\textit{p}-\textit{tert}- butyl styrene) (PtBS; M = 42K) blocks disordered at $T \quad \le 120 \textrm{C}^{\circ}$. Only PI had the type-A dipole parallel along the chain backbone. Thus, the $\varepsilon''$ data reflected the global motion of the PI block, while the $G^*$ data detected the motion of the copolymer chain as a whole. Comparison of these data indicated that the PI block relaxed much faster than the PtBS block at low $T$ and the dynamic heterogeneity due to PtBS was effectively quenched to give a frictional nonuniformity for the PI block relaxation. The $\varepsilon''$ data were thermo-rheologically complex at low $T$, partly due to this nonuniformity. However, the block connectivity could have also led to the complexity. For testing this effect, the $\varepsilon''$ data were reduced at the iso- frictional state defined with respect to bulk PI. In this state, the $\varepsilon''$ data of the copolymer at low and high $T$, respectively, were close to the data for the star-branched and linear bulk PI. Thus, the PI block appeared to be effectively tethered in space at low $T$ thereby behaving similarly to the star arm while the PI block tended to move cooperatively with the PtBS block at high $T$ to behave similarly to the linear PI, which led to the complexity of the $\varepsilon''$ data. The PtBS block also exhibited the complexity (noted from the $G^*$ data), which was well correlated with the complexity of the PI block.
To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2009.MAR.A18.14
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2013-05-22 04:46:33
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https://www.gradesaver.com/textbooks/math/algebra/elementary-algebra/chapter-5-exponents-and-polynomials-chapters-1-5-cumulative-review-problem-set-page-233/39
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# Chapter 5 - Exponents and Polynomials - Chapters 1-5 Cumulative Review Problem Set - Page 233: 39
.12
#### Work Step by Step
First, we put the numbers in scientific notation, and then we use the rules of exponents to obtain: $$3 \times 10^{-5} \times 4 \times 10^{3} \\ 12 \times 10^{-5+3} \\ 12 \times 10^{-2} \\ .12$$
After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.
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2019-01-23 21:54:56
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https://republicofsouthossetia.org/question/all-members-of-our-painting-team-paint-at-the-same-rate-if-20-members-can-paint-a-6000-square-fo-15812496-31/
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## All members of our painting team paint at the same rate. If $20$ members can paint a $6000$ square foot wall in $24$ minutes, then how long
Question
All members of our painting team paint at the same rate. If $20$ members can paint a $6000$ square foot wall in $24$ minutes, then how long would it take the $20$ members to paint a $9000$ square foot wall, in minutes?
in progress 0
3 months 2022-02-14T03:04:12+00:00 2 Answers 0 views 0
36 minutes
Step-by-step explanation:
The amount of time needed and the amount of wall to paint are directly proportional. So, when we multiply the amount of wall to paint by 4/3 (going from 6000 square feet to 9000 square feet), we multiply the time needed by 9000/6000 = 3/2. Therefore, the 20 members need 24 * 3/2 = 36 minutes to paint the 9000 square foot wall.
2. Let x represent time taken by 20 members to paint 9000 square foot wall.
We have been given that all members of our painting team paint at the same rate. 20 members can paint a 6000 square foot wall in 24 minutes. We are asked to find the time taken by 20 members to paint 9000 square foot wall.
We will use proportions to solve our given problem.
$$\frac{\text{Time taken}}{\text{Area of wall painted}}=\frac{24\text{ min}}{6000\text{ ft}^2}$$
$$\frac{x}{9000\text{ ft}^2}=\frac{24\text{ min}}{6000\text{ ft}^2}$$
$$\frac{x}{9000\text{ ft}^2}\times 9000\text{ ft}^2=\frac{24\text{ min}}{6000\text{ ft}^2}\times 9000\text{ ft}^2$$
$$x=\frac{24\text{ min}}{6}\times 9$$
$$x=4\text{ min}\times 9$$
$$x=36\text{ min}$$
Therefore, it will take 36 minutes for 20 members to paint 9000 square foot wall.
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2022-05-16 05:52:41
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https://preprint.impa.br/visualizar?id=1907
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Preprint A11/2001
The dynamics of the Jouanolou foliation on the complex projective 2-space
Luiz Henrique de Figueiredo | Camacho, César
Keywords:
We prove that the Jouanolou foliation of degree k<=5 admits no nontrivial minimal sets. The proof uses reliable computations based on interval arithmetic.
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2021-09-21 19:56:09
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http://clay6.com/qa/38373/name-the-octant-in-which-the-point-2-4-7-lies-
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Browse Questions
# Name the octant in which the point $(2,-4,-7)$ lies.
$\begin{array}{1 1}\text{2nd octant} \\ \text{4th octant } \\ \text{6th octant} \\ \text{8th octant }\end{array}$
If the $y$ and $z$ coordinates are $-ve$ and $x$ coordinate is $+ve$,
then the point is in $8^{th}$ octant.
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2016-10-23 14:19:43
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https://www.gradesaver.com/textbooks/math/precalculus/precalculus-6th-edition-blitzer/chapter-10-section-10-3-geoetric-sequences-and-series-exercise-set-page-1076/89
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## Precalculus (6th Edition) Blitzer
The amount by which we multiply each time is called the common ratio of the sequence. The general form of the geometric sequence is $a,ar,a{{r}^{2}},a{{r}^{3}},\cdots$. And $r$ is the common ratio.
The geometric sequence is the sequence in which each term after the first is obtained by multiplying the preceding term by a fixed nonzero constant ($r$). $a,ar,a{{r}^{2}},a{{r}^{3}},\cdots$. Consider the sequence, $1,2,4,8,16\ldots$ In the sequence given above, the common ratio between two consecutive term is constant. For example, \begin{align} & \frac{2}{1}=\frac{4}{2} \\ & =\frac{8}{4} \\ & =\frac{16}{8} \\ & =2 \end{align} So, 2 is the fixed nonzero common ratio.
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2021-06-18 02:38:23
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https://www.physicsforums.com/threads/adding-primitive-roots-of-unity.704548/
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# Adding primitive roots of unity
1. Aug 6, 2013
### Artusartos
1. The problem statement, all variables and given/known data
I was trying to figure out whether or not $\zeta_5 + \zeta_5^2$ and $\zeta_5^2 + \zeta_5^3$ were complex (where $\zeta_5$ is the fifth primitive root of unity).
2. Relevant equations
3. The attempt at a solution
$\zeta_5 + \zeta_5^2 = \cos(2\pi/5) + i\sin(2\pi/5) + (\cos(2\pi/5) + i\sin(2\pi/5))^2 = \cos(2\pi/5) + i\sin(2\pi/5) + \cos(4\pi/5) + i\sin(4\pi/5)$.
Since $i\sin(2\pi/5)$ and $i\sin(4\pi/5)$ do not cancel out each other, $\zeta_5 + \zeta_5^2$ must be complex, right?
$\zeta_5^2 + \zeta_5^3 = (\cos(2\pi/5) + i\sin(2\pi/5))^2 + (\cos(2\pi/5) + i\sin(2\pi/5))^3 = \cos(4\pi/5) + i\sin(4\pi/5) + \cos(6\pi/5) + i\sin(6\pi/5)$
But again, the complex numbers don't cancel out each other, right?
2. Aug 6, 2013
### tiny-tim
draw an argand diagram!!
(ie mark them out as vectors on a unit circle)
3. Aug 6, 2013
### haruspex
$\bar{\zeta_n}\zeta_n = 1$, so $\bar{\zeta_n} = 1/\zeta_n$. Suppose $\zeta_n^r+\zeta_n^s$ is real. What can you deduce about r+s?
4. Aug 7, 2013
### Artusartos
When I draw a diagram, I need to go three times the angle of $\zeta_5$ for $\zeta_5+\zeta_5^2$, and so I end up in quadrant three, right? So it is not real.
But for $\zeta_5^2 + \zeta_5^3$ or $\zeta_5+\zeta_5^4$ we need to go 2+3=1+4=5 times the angle of $\zeta_5$, and so we will be going all the way and end up back in 1, right? So it must be real.
Do you think that's correct?
Last edited: Aug 7, 2013
5. Aug 7, 2013
### tiny-tim
Hi Artusartos!
I'm not sure what you're doing there (looks more like multiplication than addition ).
Draw the vectors OB and OC (for $\zeta_5^2$ and $\zeta_5^3$), and then use the parallelogram law to add them …
what do you see?
6. Aug 7, 2013
### Artusartos
Well, that looks like it's in the second quaderant, right?
7. Aug 7, 2013
### tiny-tim
do you know the parallelogram law?
you should be seeing two vectors OB and OC, and a parallelogram with BOC on three sides
8. Aug 7, 2013
### Artusartos
Oh I'm sorry. I was looking at $\zeta_5$ instead of $\zeta_5^2$ and $\zeta_5^2$ instead of $\zeta_5^3$...
So if I look at $\zeta_5^2 + \zeta_5^3$, then it lies on the x-axis and so the sine is zero and it must be real, right?
9. Aug 7, 2013
### tiny-tim
yup!
(though it worries me that you add "the sine is zero" …
i see what you mean, but it really has nothing to do with the problem, does it? )
10. Aug 7, 2013
### Artusartos
Thanks a lot.
But I'm not sure why it doesn't have to do with this problem. We want sine to be zero, because it is the complex term in $\cos(2\pi/n) + i\sin(2\pi/n)$, right?
11. Aug 7, 2013
### tiny-tim
First, you need an "r" there: $r[\cos(2\pi/n) + i\sin(2\pi/n)]$.
Second, it's much simpler to say that a real number is a complex number x + iy with y = 0 …
and the x + iy form is perfect for addition (of two complex numbers), while the re (polar) form is pretty much useless!
12. Aug 7, 2013
### haruspex
Seems you didn't like my hint, so I'll take it a bit further:
If $\zeta_n^r+\zeta_n^s$ is real then $\zeta_n^r+\zeta_n^s = \bar{\zeta_n^r}+\bar{\zeta_n^s} = 1/\zeta_n^r+1/\zeta_n^s$. Multiplying out, $\zeta_n^{2r+s}+\zeta_n^{r+2s} = \zeta_n^r+\zeta_n^s = \zeta_n^{r+s}(\zeta_n^r+\zeta_n^s)$. Can you take it from there?
13. Aug 7, 2013
### Artusartos
Thanks. So if $\zeta_n^r+\zeta_n^s$ is real, then $r+s$ must be a multiple of $n$.
So now I should prove that $\zeta_n^r+\zeta_n^s = \bar{\zeta_n^r}+\bar{\zeta_n^s}$, right?
But shouldn't we be proving the converse instead? That if $r+s$ is a multiple of $n$, then $\zeta_n^r+\zeta_n^s$ must be real?
14. Aug 7, 2013
### haruspex
There is another solution to the equation.
Not sure what you mean. If the sum is real then $\zeta_n^r+\zeta_n^s = \overline{\zeta_n^r+\zeta_n^s}$, from which the above follows quickly.
It depends. You asked whether a particular sum of powers is real. We've shown that if it is then a certain relationship holds. If the powers do not satisfy that relationship then the sum is not real. If the powers do satisfy it then, yes, there's a bit more work to do, but it's basically running the same argument backwards.
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2018-01-17 20:34:43
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https://sk.sagepub.com/reference/behavioralsciences/n993.xml
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• Entry
• Entries A-Z
### False Negative
In inferential statistics, this term is also known as the “Type II error,” “â error,” or “error of the second kind” and describes the error of failing to reject a null hypothesis (groups do not differ significantly in the variable x) when the alternative hypothesis would be more adequate (groups differ significantly in the variable x). The probability of committing this error is formulated as “â,” and the power of the statistical test is “1 - â.” False negatives may occur due to random error in measurement. They may also occur due to low effect sizes of the investigated relationship between variables, which determines the power of the statistical test. The â cannot be set like á, the significance level of a test, which influences ...
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2020-07-09 13:35:31
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https://typeset.io/institutions/goddard-space-flight-center-1eh4mi8z
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Institution
# Goddard Space Flight Center
FacilityGreenbelt, Maryland, United States
About: Goddard Space Flight Center is a(n) facility organization based out in Greenbelt, Maryland, United States. It is known for research contribution in the topic(s): Galaxy & Solar wind. The organization has 19058 authors who have published 63344 publication(s) receiving 2786037 citation(s). The organization is also known as: GSFC & Space Flight Center.
Topics: Galaxy
##### Papers
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Journal ArticleDOI
Abstract: A new method for analysing nonlinear and non-stationary data has been developed. The key part of the method is the empirical mode decomposition method with which any complicated data set can be dec...
16,171 citations
Journal ArticleDOI
Abstract: The combination of seven-year data from WMAP and improved astrophysical data rigorously tests the standard cosmological model and places new constraints on its basic parameters and extensions. By combining the WMAP data with the latest distance measurements from the baryon acoustic oscillations (BAO) in the distribution of galaxies and the Hubble constant (H0) measurement, we determine the parameters of the simplest six-parameter ΛCDM model. The power-law index of the primordial power spectrum is ns = 0.968 ± 0.012 (68% CL) for this data combination, a measurement that excludes the Harrison–Zel’dovich–Peebles spectrum by 99.5% CL. The other parameters, including those beyond the minimal set, are also consistent with, and improved from, the five-year results. We find no convincing deviations from the minimal model. The seven-year temperature power spectrum gives a better determination of the third acoustic peak, which results in a better determination of the redshift of the matter-radiation equality epoch. Notable examples of improved parameters are the total mass of neutrinos, � mν < 0.58 eV (95% CL), and the effective number of neutrino species, Neff = 4.34 +0.86 −0.88 (68% CL), which benefit from better determinations of the third peak and H0. The limit on a constant dark energy equation of state parameter from WMAP+BAO+H0, without high-redshift Type Ia supernovae, is w =− 1.10 ± 0.14 (68% CL). We detect the effect of primordial helium on the temperature power spectrum and provide a new test of big bang nucleosynthesis by measuring Yp = 0.326 ± 0.075 (68% CL). We detect, and show on the map for the first time, the tangential and radial polarization patterns around hot and cold spots of temperature fluctuations, an important test of physical processes at z = 1090 and the dominance of adiabatic scalar fluctuations. The seven-year polarization data have significantly improved: we now detect the temperature–E-mode polarization cross power spectrum at 21σ , compared with 13σ from the five-year data. With the seven-year temperature–B-mode cross power spectrum, the limit on a rotation of the polarization plane due to potential parity-violating effects has improved by 38% to Δα =− 1. 1 ± 1. 4(statistical) ± 1. 5(systematic) (68% CL). We report significant detections of the Sunyaev–Zel’dovich (SZ) effect at the locations of known clusters of galaxies. The measured SZ signal agrees well with the expected signal from the X-ray data on a cluster-by-cluster basis. However, it is a factor of 0.5–0.7 times the predictions from “universal profile” of Arnaud et al., analytical models, and hydrodynamical simulations. We find, for the first time in the SZ effect, a significant difference between the cooling-flow and non-cooling-flow clusters (or relaxed and non-relaxed clusters), which can explain some of the discrepancy. This lower amplitude is consistent with the lower-than-theoretically expected SZ power spectrum recently measured by the South Pole Telescope Collaboration.
10,928 citations
Journal ArticleDOI
Abstract: WMAP precision data enable accurate testing of cosmological models. We find that the emerging standard model of cosmology, a flat � -dominated universe seeded by a nearly scale-invariant adiabatic Gaussian fluctuations, fits the WMAP data. For the WMAP data only, the best-fit parameters are h ¼ 0:72 � 0:05, � bh 2 ¼ 0:024 � 0:001, � mh 2 ¼ 0:14 � 0:02, � ¼ 0:166 þ0:076 � 0:071 , ns ¼ 0:99 � 0:04, and � 8 ¼ 0:9 � 0:1. With parameters fixed only by WMAP data, we can fit finer scale cosmic microwave background (CMB) measure- ments and measurements of large-scale structure (galaxy surveys and the Lyforest). This simple model is also consistent with a host of other astronomical measurements: its inferred age of the universe is consistent with stellar ages, the baryon/photon ratio is consistent with measurements of the (D/H) ratio, and the inferred Hubble constant is consistent with local observations of the expansion rate. We then fit the model parameters to a combination of WMAP data with other finer scale CMB experiments (ACBAR and CBI), 2dFGRS measurements, and Lyforest data to find the model's best-fit cosmological parameters: h ¼ 0:71 þ0:04 � 0:03 , � bh 2 ¼ 0:0224 � 0:0009, � mh 2 ¼ 0:135 þ0:008 � 0:009 , � ¼ 0:17 � 0:06, ns(0.05 Mpc � 1 )=0 :93 � 0:03, and � 8 ¼ 0:84 � 0:04. WMAP's best determination of � ¼ 0:17 � 0:04 arises directly from the temperature- polarization (TE) data and not from this model fit, but they are consistent. These parameters imply that the age of the universe is 13:7 � 0:2 Gyr. With the Lyforest data, the model favors but does not require a slowly varying spectral index. The significance of this running index is sensitive to the uncertainties in the Ly� forest. By combining WMAP data with other astronomical data, we constrain the geometry of the universe, � tot ¼ 1:02 � 0:02, and the equation of state of the dark energy, w < � 0:78 (95% confidence limit assuming w �� 1). The combination of WMAP and 2dFGRS data constrains the energy density in stable neutrinos: � � h 2 < 0:0072 (95% confidence limit). For three degenerate neutrino species, this limit implies that their mass is less than 0.23 eV (95% confidence limit). The WMAP detection of early reionization rules out warm dark matter. Subject headings: cosmic microwave background — cosmological parameters — cosmology: observations — early universe On-line material: color figure
10,236 citations
Journal ArticleDOI
B. P. Abbott1, Richard J. Abbott1, T. D. Abbott2, Matthew Abernathy1 +1008 moreInstitutions (96)
TL;DR: This is the first direct detection of gravitational waves and the first observation of a binary black hole merger, and these observations demonstrate the existence of binary stellar-mass black hole systems.
Abstract: On September 14, 2015 at 09:50:45 UTC the two detectors of the Laser Interferometer Gravitational-Wave Observatory simultaneously observed a transient gravitational-wave signal. The signal sweeps upwards in frequency from 35 to 250 Hz with a peak gravitational-wave strain of $1.0 \times 10^{-21}$. It matches the waveform predicted by general relativity for the inspiral and merger of a pair of black holes and the ringdown of the resulting single black hole. The signal was observed with a matched-filter signal-to-noise ratio of 24 and a false alarm rate estimated to be less than 1 event per 203 000 years, equivalent to a significance greater than 5.1 {\sigma}. The source lies at a luminosity distance of $410^{+160}_{-180}$ Mpc corresponding to a redshift $z = 0.09^{+0.03}_{-0.04}$. In the source frame, the initial black hole masses are $36^{+5}_{-4} M_\odot$ and $29^{+4}_{-4} M_\odot$, and the final black hole mass is $62^{+4}_{-4} M_\odot$, with $3.0^{+0.5}_{-0.5} M_\odot c^2$ radiated in gravitational waves. All uncertainties define 90% credible intervals.These observations demonstrate the existence of binary stellar-mass black hole systems. This is the first direct detection of gravitational waves and the first observation of a binary black hole merger.
8,011 citations
Journal ArticleDOI
Abstract: The relationships between various linear combinations of red and photographic infrared radiances and vegetation parameters are investigated. In situ spectrometers are used to measure the relationships between linear combinations of red and IR radiances, their ratios and square roots, and biomass, leaf water content and chlorophyll content of a grass canopy in June, September and October. Regression analysis shows red-IR combinations to be more significant than green-red combinations. The IR/red ratio, the square root of the IR/red ratio, the vegetation index (IR-red difference divided by their sum) and the transformed vegetation index (the square root of the vegetation index + 0.5) are found to be sensitive to the amount of photosynthetically active vegetation. The accumulation of dead vegetation over the year is found to have a linearizing effect on the various vegetation measures.
7,225 citations
##### Authors
Showing all 19058 results
NameH-indexPapersCitations
Anton M. Koekemoer1681127106796
Alexander S. Szalay166936145745
David W. Johnson1602714140778
Donald G. York160681156579
Gillian R. Knapp145460121477
Olaf Reimer14471674359
R. A. Sunyaev141848107966
Christopher T. Russell137237897268
Hui Li1352982105903
Neil Gehrels13472780804
Christopher B. Field13340888930
Igor V. Moskalenko13254258182
William T. Reach13153590496
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2023-01-29 00:19:50
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https://asmedigitalcollection.asme.org/fluidsengineering/article/139/1/011201/373003/Effect-of-Microstructure-Geometric-Form-on-Surface
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Low Reynolds number flow of liquids over micron-sized structures and the control of subsequently induced shear stress are critical for the performance and functionality of many different microfluidic platforms that are extensively used in present day lab-on-a-chip (LOC) domains. However, the role of geometric form in systematically altering surface shear on these microstructures remains poorly understood. In this study, 36 microstructures of diverse geometry were chosen, and the resultant overall and facet shear stresses were systematically characterized as a function of Reynolds number to provide a theoretical basis to design microstructures for a wide array of applications. Through a set of detailed numerical calculations over a broad parametric space, it was found that the top facet (with respect to incident flow) of the noncylindrical microstructures experiences the largest surface shear stress. By systematically studying the variation of the physical dimensions of the microstructures and the angle of incident flow, a comprehensive regime map was developed for low to high surface shear structures and compared against the widely studied right circular cylinder in cross flow.
Introduction
Low Reynolds number flow of viscous fluids over solid surfaces in either a confined or an open environment is a ubiquitous phenomenon that can be commonly observed. In this flow regime with Reynolds number, Re < 100, and in many LOC practical applications with Re < 1, the fluid motion at all the physical solid–fluid interfaces is usually considered to follow the no-slip boundary condition [1]. Therefore, the resulting transverse, nonzero velocity gradients contribute toward fluid shear which has been successfully exploited in numerous practical applications over the years, including biosensors, advanced health care diagnostics, materials processes, and energy-related technology advancements [27].
The operational efficiency for these diverse applications is critically impacted by the ability to maintain specific regimes of shear stress on the functional surfaces within the underlying devices. For example, lower surface shear was beneficial in improving the functionality of microfluidic chips with enhanced capture yield of circulating tumor cells [3], while in the case of artificial heart valves, reducing high-shear-induced coagulation of blood on the valve surface minimized the risk of thrombogenesis and thromboembolism [4]. For energy-related applications, lower surface shear increased microbial fuel cell sensitivity toward detecting Cu(II) toxicity [2].
On the other hand, flows with higher shear rate were beneficial in inducing microbial enrichment of microbial fuel cell anodes, resulting in a threefold increase in power output [5]. Furthermore, customized microfluidic cell culture chips were shown to exhibit superior gene expression under increased fluid shear [8]. However, in most low Re number (Re < 100) flow applications, shear stress is manipulated solely by modulating the flow rate due to the ease in controlling external pressure or potential gradients that act as common driving forces for these flows, especially in LOC environments. In contrast, an open question remains: What is the extent to which shear stress can be controlled by engineering passive structures that can systematically manipulate the shear without the need to actively adjust flow rate?
Studies on the effect of surface geometries on surface shear stress have mainly focused on considerations of surface roughness. This includes studies on developing a correlation between the effect of actual roughness to that of closely packed sand grains [9], an evaluation of the skin friction coefficient and equivalent sand roughness data on various rough surfaces [10], and an analysis on randomly placed, nonuniform, three-dimensional roughness with irregular geometry and arrangement [11]. Canonical flows over solid surfaces have predominantly focused on cylinders, which have been extensively studied for shear, both numerically and experimentally, for many years, and comprehensive reviews exist [1215]. However, studies that investigate low Reynolds number flows (Re < 100) for surface shear on noncylindrical, three-dimensional structures are scarce—many studies that consider noncylindrical forms are in two-dimensional flows or focus on the fluid flow and do not mention surface shear effects. Indeed, the study of surface shear is limited to specific ad hoc applications or targeted operating conditions [16,17]. Some simple radial geometries such as cylindrical disks and spheroids have been investigated and have shown that high-pressure stagnation zones correspond to areas of low surface shear stress, but no conclusions were formed regarding the relationship between geometric form and surface shear stress [18]. Similarly, in a computational fluid dynamics study that used images to align a competitive swimmer with the flow field, it was found that larger surface shear stresses were observed on areas of the body that presented a complex surface geometry, such as the head, shoulders, and heels [19].
Due to the scarcity of studies that investigate surface shear on distinguishable three-dimensional structural forms in low Reynolds number flows, no generalizations exist on how the surface structure actually manipulates or modulates shear stress under these conditions. Therefore, no generalizations exist on how the surface structure actually manipulates or modulates shear stress. However, in many applications, the geometry and layout of the physical structure in the flow path are critical for the device or system operation [20,21]. For example, many bioprocessing devices and bioreactors rely on the integrity of a biofilm adhered to their functional surfaces, and past works [22,23] have shown the dependence of biofilm morphology on surface shear stress. Surface structure geometry in several practical applications is typically chosen based on considerations such as ease of fabrication [24] or on what materials are commercially available [25] without much design focus on the flow–structure interaction, which actually governs the operation of these devices. Therefore, the resulting systems are inherently unoptimized for intended, shear-dependent functions because specific effects of geometry on surface shear stress were not explicitly considered.
Therefore, the purpose of this work is to provide a systematic analysis for low Reynolds number flow of water (a common working fluid in many LOC flows) over various microstructures on a flat, solid surface and subsequently characterize the induced fluid shear stress on the microstructure surface. Specifically, a regime map that directly correlates various microstructure shapes to regimes of surface shear stress has been developed. The regime map comprises a wide array of microstructures, such as cones, pyramids, rectilinear prisms, and other forms commonly found in engineering applications to provide a direct correlation between structure geometry, inlet flow conditions, and surface shear stress. Such regime maps can potentially provide starting point data to engineer higher operational efficiencies for applications due to the ability to now explicitly incorporate the geometric dependence of shear stress. In addition, the contribution of various microstructure facets (front, rear, side, and top of a structure) with respect to incoming flow toward overall fluid shear was also quantified as the structure was exposed to fully developed low Reynolds number flows. It is important to recognize that the focus of this work is on the study of external flows over microstructures where the wall constraints can be considered negligible.
Methodology
In this paper, 36 geometric forms, each with the same height of 100 μm, were heuristically chosen based on common geometries found in a variety of engineering applications (as discussed in Sec. 1) and compared for relative shear stress, based on their detailed facet geometries with respect to incident or incoming flow (Fig. 1). The total wetted surface area for all the geometric shapes is plotted in Fig. S1, which is available under the “Supplemental Materials” tab on the ASME Digital Collection. Velocity gradients on individual facets are discussed for a cube, a common geometric form as a representative case. Using a cube of edge length of 100 μm as a base structure, the surface areas, edge lengths, and facet angles were systematically altered in incremental steps to study the effect of gradual changes in geometrical form over the base structure. In order to observe trends in surface shear stress based on the physical orientation of a structure with respect to the incident flow, a right pyramid and a cube were altered in systematic steps through one full rotation as observed with respect to the incident flow.
Fig. 1
Fig. 1
Close modal
All the structures were modeled in a three-dimensional computational domain to simulate external flows over the structures' surfaces (see Fig. S2, which is available under the “Supplemental Materials” tab on the ASME Digital Collection). Initial coarse meshes were successively refined until mesh-independent solutions were achieved [26]. To test against the presence of numerical artifacts in the computed solutions [27], each simulation was performed with two iterative numerical methods (GMRES [28] and Bi-CGSTAB [29]) along with two methods of mesh generation Delaunay [30] and advancing front [31]. The results from the methods were compared to confirm agreement of their solutions to within 1% [27]. To eliminate the effect of singularities in the models [32], geometrically sharp features (e.g., edges and corners) were modified to fillets (radius of 5 μm) [32], and the surface shear rate was evaluated at least 3–5 grid elements [32], corresponding to a length of 5 μm away from such features. It is worth noting that the critical dimension is 100 μm for all the features of interest (FOI) (as discussed later), and therefore, the presence of a 5 μm fillet at the edges and corners of structures did not yield any significant changes in the reported results. All the governing equations were solved under steady-state, isothermal, and laminar flow conditions with Reynolds numbers of 0.001, 0.1, and 100 and with water modeled as an incompressible, Newtonian working fluid [33]. Calculation of Re was based on a microstructure critical dimension of 100 μm. The steady-state continuity and Navier–Stokes equations for these conditions reduce to
$∇ ⋅ V=0$
(1)
$ρ V⋅∇ V=−∇ p+μ ∇ 2V$
(2)
$Re=ρ uin hμ$
(3)
where $∇$ denotes the gradient operator, $V$ is the fluid velocity vector, $uin$ is the inlet velocity, $ρ$ is the fluid density, $p$ is the fluid pressure, h is the microstructure height (100 μm for all the structures), and $μ$ is the fluid viscosity of water at room temperature. All the numerical calculations were performed with comsol multiphysics v4.4 [34]. Average surface shear stress, $τ¯s$, was obtained from Newton's law of viscosity [33] by determining local shear rate magnitude, $γ˙$ from each grid point and averaging over the domain. The shear rate magnitude is calculated as
$γ˙=12Γ.:Γ. Γ˙=∇V+(∇V)T$
(4)
where: is the tensor contraction operator, and the superscript $T$ denotes the matrix transpose. Throughout this paper, “front facet” refers to the structural component facing the incident flow. Additionally, the overall and facet shear stress of all the microstructures discussed in this paper were nondimensionalized with respect to a reference case explicitly listed in Sec. 3. All the models were solved using the supercomputing cluster at the Ohio Supercomputer Center that employs 8328 HP Intel Xeon x5650 central processing units with 12 cores and 48 GB of memory per HP SL390 G7 node. The numerical model was validated with the past work [3], and good agreement was found on the spatial variation of velocity around the cylinders and the x-component of shear stress on the periphery of cylinder, as shown in Fig. S3, which is available under the “Supplemental Materials” tab on the ASME Digital Collection.
Results and Discussion
Regime Map.
The 36 distinct geometric shapes considered in this study are divided into four categories based on traditional geometric definitions, namely: (1) rectilinear prisms (eight shapes with noncircular top), (2) radial prisms (11 shapes with top facet having a radial profile), (3) nonvertical prisms (ten shapes with top facet having varying heights), and (4) apex structures (seven shapes with no-top facet) as summarized in Fig. 1.
For a given Re, the overall shear stress of a microstructure, $(τs)all$, was divided by the overall shear stress of a cylinder and reported as $(τ¯s)all$, thus nondimensionalizing the stress and providing a direct comparison to the cylinder, which has been one of the most common structures used in a variety of flow configurations as discussed in Sec. 1. Moreover, comparing the shear stress of the 36 cases chosen here with respect to the cylinder also facilitates ready comparison with the published data [35] and provides easy visualization to existing engineering applications that employ cylinders. Due to the nondimensionalization, $(τ¯s)all$ =1 for a cylinder as shown in the regime map (Fig. 2). $(τs)all$ for a 100 μm diameter (and height) cylinder was calculated to be 7.5 × 10−5 N/m2 (Re = 0.001), 7.5 × 10−3 N/m2 (Re = 0.1), and 16.1 N/m2 (Re = 100). As the nondimensionalized shear stress for all the microstructures reported in this study was similar for Re = 0.001 and 0.1, results for Re = 0.1 will be discussed as a representative condition. The nondimensionalized overall shear stress, $(τ¯s)all$, for each structure (Fig. 2) as well as differences in front, top, side, and rear facets were examined (Figs. 3 and 4). The three-dimensional orientation of all the microstructures with respect to a global Cartesian coordinate frame and also the direction of incident flow are explicitly shown in Fig. 2.
Fig. 2
Fig. 2
Close modal
Fig. 3
Fig. 3
Close modal
Fig. 4
Fig. 4
Close modal
In Fig. 2, a shear stress regime map for the overall shear stress, $(τ¯s)all$, as a function of geometry is presented for Re = 0.1 (with Re = 0.001 being similar to Re = 0.1) and 100. Rectilinear prisms have $(τ¯s)all$ varying in the range of 0.73–0.88 for Re = 0.1, suggesting that the overall shear on a cubic prism is only 73% of the shear stress seen by a cylinder under similar flow conditions and critical dimensions. In rectilinear prisms, when the fluid contacts the front facet, the velocity gradient is larger but limited only to the edges and small everywhere else, in contrast to curvilinear prisms, where the velocity drop is extended out over nearly the entire surface area of the structure, resulting in higher surface shear stress. This is the first of many results that suggest a fluid flow over sharply angled features (such as rectilinear prisms) will, in general, result in lower surface shear stress when compared to curvilinear surfaces. At Re = 100, rectilinear prisms have $(τ¯s)all$ varying over a broader range of 0.62–0.97. Nonvertical prisms exhibited an even wider spread in the magnitude of $(τ¯s)all$ (0.38–0.80 compared to a cylinder) for Re = 0.1, but was confined between 0.37 and 0.72 at Re = 100. Radial prisms exhibited larger regimes of $(τ¯s)all$ in magnitude (0.82–1.1 at Re = 0.1 and 0.74–1.2 at Re = 100); however, apex forms exhibited lower regimes of $(τ¯s)all$ with respect to the rectilinear and radial prisms with the exception of the cone at Re = 0.1, where $(τ¯s)all$ was estimated to be 0.92 or nearly the same as the cylinder, despite not having a top facet. Apex structures due to minimal cross-sectional area (normal to the flow field) would allow for increased momentum of the fluid flow over the entire structure reducing the velocity gradients over their surface. If true, then structures 19, 23, 25, and 26 (all forms with cross-sectional area less than 1 μm2) should also experience less surface shear stress in the Re = 100 case, which is demonstrated by the results.
It is important to note that $(τ¯s)all$ is an area-averaged value of shear stress over all the exposed facets as shown in Eq. (5). Therefore, though individual facets exhibit varied magnitudes of shear stress, given by $(τ¯s)i$ which is independent of the facet area $Ai$, the overall shear stress, $(τ¯s)all$, is influenced by both $(τ¯s)i$ and $Ai$
$(τ¯s)all=∑i(τ¯s)iAi∑iAi$
(5)
The regime map study thus clearly indicates that although the overall shear stress experienced by a microstructure is similar at Re = 0.001 and 0.1, further extrapolation of shear stress at higher Re (100) is not obvious and therefore was explicitly evaluated (Fig. 2). In short, the regime map provides data trends for low Reynolds number flow that can be used for selection of geometric categories for a variety of applications as discussed in Sec. 1.
Velocity Gradients and Impact on Shear Stress.
Nondimensionalized shear stress experienced by individual facets (front, rear, side, and top facets) for all the 36 microstructures is plotted at Re = 0.1, 100 in Figs. 3, and 4, respectively. Shear stress experienced at each facet was nondimensionalized with $(τs)all$ of a cylinder at the respective Re, as discussed in Sec. 3.1.
In Fig. 3, critical facet stress $(τ¯s)i$ of 0.5 (after nondimensionalization, i.e., 50% of the overall shear on a cylinder) was benchmarked for front and rear facets, as the transition between high $((τ¯s)i>0.5)$ and low $((τ¯s)i≤0.5)$ shear stress structures. Similarly, as the top facet was found to experience higher shear stress in comparison to all other facets, a critical facet stress $(τ¯s)i$ of 1.5 was chosen to differentiate between high shear and low shear structures. The $(τ¯s)i$ of side facets, though greater than 0.5, varied over a narrow range for all the microstructures (average $(τ¯s)i≈$ 0.79 ± 0.13). Similarly, critical shear stresses of 1 for the front facet, 0.3 for the rear facet, 1 for the side facet, and 1.5 for the top facet were chosen to differentiate high shear and low shear structures at Re = 100, as shown in Fig. 4. This classification between “high shear” and “low shear” structures in Figs. 3 and 4 was implemented to aid in the selection of microstructures for shear-dependent applications. Nondimensionalized facet shear stress as a function of Re is plotted for all the microstructures in Fig. S4, which is available under the “Supplemental Materials” tab on the ASME Digital Collection.
Next, the role of velocity gradients in contributing to the overall shear was evaluated by considering a cube of side 100 μm as a representative structure. The velocity gradients were nondimensionalized with respect to the overall shear rate of a cylinder at Re = 0.1 (7.89 s−1). The nondimensionalized velocity gradients that contribute to shear in the X, Y, and Z directions across the top facet were calculated and are shown in Fig. 5 for a cube of side 100 μm at Re = 0.1 as a representative case. As discussed in Sec. 2, data were plotted beginning at 5 μm from each edge in order to eliminate the effects of singularities. Therefore, each cross section of the cube reported in Fig. 5 has an area of 90 μm × 90 μm instead of 100 μm × 100 μm. The effect of this strategy is discussed and shown to be valid in the supporting information section (Fig. S5, which is available under the “Supplemental Materials” tab on the ASME Digital Collection).
Fig. 5
Fig. 5
Close modal
The velocity vector is given by $V=u x̂+vŷ+w ẑ$, where $x̂$, $ŷ$, and $ẑ$ are the unit vectors along the coordinate axes (shown in Fig. 5). Since the top facet is located in the X–Y plane, and due to the symmetric structure of the cube, the nondimensionalized velocity gradient is expected to dominate along Z (velocity gradient∼O(10 deg)) and was found to be negligible across the X,Y direction (velocity gradient ∼ O(10−15)) as shown in Fig. 5. The gradient of the velocity along Z is attributed to the no-slip boundary condition at the top facet, which leads to the development of a transverse boundary layer. This transverse boundary layer and the resulting velocity gradient are the primary causes of the surface shear stress calculated on the facet. Since the incident flow is in the X direction, $|u|$ (magnitude of $u$) is greater than $|v|$, and therefore, the magnitude of $∂v/∂z$ is smaller by an order of magnitude compared to $∂u/∂z$, as also shown in Fig. 5. In addition, contribution of $∂v/∂z$ toward $(τ¯s)top$ can be ignored when averaged, given the symmetry involved in the structure. Similarly, the average of $∂w/∂z$ across the top facet was estimated to be zero (not shown) and therefore does not contribute toward the shear stress experienced by the top facet. From Fig. 5, $∂u/∂z$ exhibits the maximum magnitude compared to all other velocity gradients that contribute toward shear stress. The negligible magnitude of all other velocity gradients, $(∂v/∂x), (∂w/∂x), (∂u/∂y),(∂w/∂y)$ ∼ O(10−15) as observed in Fig. 5 suggests that the variation of velocity $V$ in a direction normal to a particular facet predominantly influences the magnitude of shear stress at that facet. Therefore, the surface shear stress is largest along the edges of the facet (∼1.5 times larger than the average over the facet) and peaks near the corners of the facet (∼2.5 times larger than the average over the facet). Thus, one would hypothesize that structures having multiple edges and corners should experience higher overall shear stress, but as can be seen from Figs. 3 and 4, this is not the case. This discrepancy arises as the actual surface area of edges and corners is negligible compared to the overall facet area and therefore contributes minimally (<2%) to the overall average shear stress.
Figure 6 shows the nondimensionalized velocity gradients that primarily influence $(τ¯s)i$ plotted across the front ($−x̂$ being the normal unit vector), side ($−ŷ$ being the normal unit vector), and rear ($x̂$ being the normal unit vector) facets for a cube with edge length 100 μm at Re = 0.1. Orientation of the cube with respect to the three-dimensional axis and incoming flow is as shown in Fig. 5. Since $|u|$ > $| v,w |$, the gradient of $v, w$ (experienced only at the front and rear facets) is expected to be less than the gradient of $u$ (experienced only at the side facet). Therefore, as shown in Fig. 6, the shear rate experienced by the side facet is about 2.5 times greater than the front and rear facet shear stresses $((τ¯s)side >(τ¯s)front,(τ¯s)rear)$ for a cube. This trend is in agreement with the results reported for Re = 0.1 for a cube and suggests that, in any structure with facets of similar orientation and shape to those of a cube, the side facets will strongly contribute to the overall shear stress for the structure (and referring to Figs. 2 and 3, this appears to be the case: structures with overall form similar to that of the cube experience comparable magnitudes of surface shear stress). However, for noncubic geometries, it is clear from the regime map (Fig. 2) that the overall geometric form affects the shear stress on individual facets differently (Figs. 3 and 4) and therefore justifies the need for such a regime map in designing next-generation LOC devices with embedded microstructures [3,3639].
Fig. 6
Fig. 6
Close modal
Parametric Manipulation of Physical Dimensions.
As shown in Fig. 7, four physical dimensions of a cube were incremented to progressively alter its shape, to achieve the final structures shown by the third image in each sequence at the top of each figure panel. The shear stress on each individual facet in this discussion is now nondimensionalized with respect to $(τs)front$ or the shear stress on the front facet of a cube, i.e., the facet of the geometry facing the incoming flow experienced by an unaltered cube at Re = 100, and reported as $(τ¯s)i$ in Figs. 7(a)7(d), to facilitate easy comparison to the unaltered case. For Re = 100, $(τ¯s)front$ of the unaltered cube was calculated to be 12.5 N/m2.
Fig. 7
Fig. 7
Close modal
In Fig. 7(a), the results of incrementing 0 deg ≤ $θp$ ≤ 26.6 deg are shown ($θp$ is the angle of tilt for each side of the cube), which transforms a cube into a right pyramid as it increases. It was found that the shear stress at the top facet, $(τ¯s)top$, increased with a quadratic dependence on $θp$ ($R2$ = 0.98, where $R2$ is the coefficient of determination) for the systematic translation of a cube to a pyramid. This scaling is expected because as the flat faces of the cube were systematically altered to approach triangular cross sections, the surface area of the top facet continued to decrease.
Moreover, the front facet exhibits a strong linear correlation ($r$ =−0.91, where $r$ is the linear correlation coefficient) between decreasing $(τ¯s)front$ and increasing $θp$. Though the front and rear facets have the same area, the shear stress experienced by the rear facet is an order of magnitude lower than that of the front facet. Additionally, $(τ¯s)rear$ was found to be invariant with a change in surface area, unlike $(τ¯s)front$, which implies that the shear stress experienced by each facet is strongly influenced by the overall geometric form and Re. At $θp$ = 0, all the facets of a cube have equal surface area and from Eq. (4), the overall stress is dominated by $(τ¯s)top$, which has the maximum magnitude, which is in agreement with the discussion in Sec. 3.2. However, at $θp$ = 26.6 deg, the top surface vanishes (or collapses to a point as the pyramid tip) and therefore does not contribute to overall stress. Unlike the side and rear facets whose shear stress is invariant to $θp$, $(τ¯s)front$ decreases linearly and therefore from Eq. (4), $(τ¯s)all$ decreases linearly as observed in Fig. 7(a), suggesting that the front facet is instrumental in dictating $(τ¯s)all$ with an increase in $θp$.
In Fig. 7(b), results are shown for incrementing 0 ≤ $Rv$ ≤ 50 μm, i.e., increasing cube edge curvature ($Rv$) to round-out the cube and eventually reach a cylinder. The results for the shear stress on the front curves suggest that the “sharper” a geometric feature is (in this case, smaller values of $Rv$), the more surface shear stress it will exhibit, as expected in Ref. [40] and from previous discussions, above. Also, with increase in $Rv$, the surface area of the top facet decreases by 21.5% from a square ($Rv$ = 0 μm) to a circle ($Rv$ = 50 μm), compared to a 100% decrease in the case discussed in Fig. 7(a). In addition, the top facet experiences the highest transverse velocity gradients when $Rv$ > 25 μm, as indicated by a higher value of $(τ¯s)top$ in comparison to other facets in Fig. 7(b). Therefore, coupled with a significant contributed area and shear stress toward the estimation of $(τ¯s)all$ ($(τ¯s)top$ contributes 36.0–41.5% to overall shear with increase in $Rv$), the top facet dictates the variation of $(τ¯s)all$ with $Rv$.
In Fig. 7(c), the results of incrementing the angle of tilt, $θw$, of the front face of a cube are shown. Therefore, the area of the front and side facets varies with $θw$, and the area of the rear facet remains fixed as shown in Fig. 7(c). Again, $(τ¯s)top$ shows a quadratic increase (R2 = 0.97) for the evaluated values of $θw$. Despite an overall increase in $θw$ from 0 deg to 45 deg, thereby increasing the front facet area by 41%, $(τ¯s)front$ only increases by 0.86%. In comparison, the percent contribution of $(τ¯s)sides$ to $(τ¯s)all$ is 16.9 ± 0.25% for all the values of $θw$, suggesting $(τ¯s)sides$ is independent of $θw$. Together, these results suggest that the top and front facets dictate $(τ¯s)all$ for all the values of $θw$.
In Fig. 7(d), results are shown for incrementing 0 ≤ $Rt$ ≤ 50 μm, i.e., increasing the curvature ($Rt$) of the cube's top facet. As $Rt$ is increased, the height (and therefore area) of the front facet was systematically reduced to maintain the total height of the structure at 100 μm. The results for the front curve and the top facets confirmed previous results that sharper geometric features result in larger values of $(τ¯s)i$ along expected trends [40]. $(τ¯s)all$ exhibits only a 3.4% overall decrease, while $(τ¯s)front$ shows a strong linear correlation (r=−0.99) with $Rt$, decreasing 41.5% overall, and remaining within 21.5% of $(τ¯s)all$. It is important to note that the area of the newly formed front curve increases as $Rt$ increases.
A common trend observed in all the cases was that the magnitude of shear stress on the rear facet, $(τ¯s)rear$, remains small (∼3%) and is mostly unaltered by the changes to structure morphology, in agreement with the regime map (Re = 100, Fig. 2(b)). Similarly, minimal changes in the value of $(τ¯s)all$ suggest that in most low Reynolds number based flows, the surfaces exposed to the incoming fluid (typically the front and top facets) dictates the performance characteristics. Also, a decrease in the area of the front facet when transformed from a cube (Figs. 7(a), 7(b), and 7(d)) results in a decrease in $(τ¯s)front$. However, decreasing the surface area of the top facet (Figs. 7(a)7(d)) leads to a quadratic increase in the magnitude of $(τ¯s)top$ most likely due to the increase in the amount of area exposed to a large velocity gradient near the edges of the facet. Overall, the results suggest that to produce a structure with larger overall surface shear stress, smaller top facets, rounder top facets, and flatter front facets normal to the incident flow are preferred, but of most importance is the form of the top facet. Thus, the trends previously observed and discussed in relation to Fig. 2 are further illuminated. In conclusion, the overall results in Fig. 7 suggest that the shear stress experienced by various facets is strongly influenced by the overall geometric form of microstructures.
Effect of Altering Angle of Rotation.
The effect of changing the angle of orientation with respect to the incident flow for a pyramid, $ϕp$, and cube, $ϕc$, was investigated (Fig. 8). The axis of rotation for both the pyramid and cube is shown in Fig. 8. To facilitate comparison between the rotated structures and their nonrotated forms, the reported values of shear stress were nondimensionalized with $(τs)front$ at $ϕp$ = 0 deg and $ϕc$ = 0 deg.
Fig. 8
Fig. 8
Close modal
In Fig. 8(a), the pyramid's feature of interest (FOI = front facet at $ϕp$ = 0 deg) exhibits a global minimum at $ϕp$ = 180 deg. The maximum values of $(τ¯s)FOI$ occur at $ϕp$ = 60 deg and 300 deg. Therefore, the magnitude of shear stress at the front is maximum when angled at ± 60 deg from the incident flow. From Fig. 2, we see that, in general, structures 5 and 8 (which have angled, square front facets) experience larger surface shear stress than the cube, whose front facet is normal to the flow. This result indicates that the surface shear stress on a structural form can be manipulated and achieved purely by changing its orientation with respect to the incoming flow. The shear stress exhibits a smooth, sinusoidal distribution of both $(τ¯s)all$ and $(τ¯s)FOI$ as $ϕp$ is varied, i.e., the overall and facet shear stress is symmetric as the orientation of the structure with respect to incoming flow is varied. Figure 8(b) shows the effect of changing $ϕc$ for a cube. The maximum values of $(τ¯s)FOI$ occur at $(τ¯s)FOI$ = 50 deg and 310 deg (i.e., ±50 deg with respect to the incident flow, which agrees closely with the results for the pyramid). For the top facet, the maximum values of $(τ¯s)top$ occur at $ϕc$ = 45 deg, 135 deg, 225 deg, and 315 deg, corresponding to orientations that exhibit a maximum gradient in velocity for the same top facet surface area.
Summary and Conclusions
A systematic numerical analysis for the 36 diverse geometries was analyzed to estimate overall and individual facet shear stress at Reynolds numbers (Re) of 0.001, 0.1, and 100, which spans five orders of magnitude for relatively low Re flows typically seen in many viscous flow and LOC applications. The structures were divided into four categories based on the geometry of the top facet, namely: rectilinear prisms, radial prisms, nonvertical prisms, and apex structures.
Overall shear stress of a microstructure was nondimensionalized with the overall shear stress of a cylinder at a given Re and reported in a regime map. The results indicate that the nondimensionalized facet and overall shear stress for all the 36 structures were found to be the same at Re = 0.001 and 0.1. However, as Re was increased to 100, facet and overall shear stress was found to vary in comparison to Re = 0.1. Since the low Reynolds number flow is incident in one-direction, the magnitude of the transverse velocity components is lower compared to the axial component (which is along the direction of flow). Therefore, facets that include the gradient of axial velocity toward the estimation of shear rate experience a higher magnitude of shear stress compared to facets that take into account the transverse component of velocity. In addition, by changing the angle of rotation, critical angles were found for a cube and pyramid for which the surface shear stress was maximum in magnitude. The results of this work are expected to provide a broad basis for choosing microstructures that are essential for shear-dependent applications.
Acknowledgment
The computational facilities at the Ohio Supercomputing Center (OSC) are acknowledged for the support. The U.S. Department of Energy (DOE) is acknowledged for the partial funding support for the personnel through ARPA-E under Grant No. DE-AR0000282. The discussions with Tong Lin are also acknowledged.
Nomenclature
• $Ai$ =
area of facet of interest
•
• $p$ =
fluid pressure (components vary spatially)
•
• $r$ =
linear correlation coefficient
•
• $Rt$ =
radius of curvature of top facet
•
• $Rv$ =
•
• $R2$ =
coefficient of determination
•
• Re =
Reynolds number
•
• $u$ =
X component of $V$
•
• $uin$ =
inlet velocity
•
• $v$ =
Y component of $V$
•
• $V$ =
Eulerian fluid velocity (components vary spatially)
•
• $w$ =
Z component of $V$
•
• X =
global Cartesian coordinate in the direction of inlet flow (see Fig. 2)
•
• $x̂$ =
unit vector along X
•
• Y =
global Cartesian coordinate perpendicular to the flow
•
• $ŷ$ =
unit vector along Y
•
• Z =
global Cartesian coordinate perpendicular to the flow
•
• $ẑ$ =
unit vector along Z
•
• $γ.$ =
average shear rate
•
• $θp$ =
angle of inclination of each facet of cube
•
• $θw$ =
angle of incidence of front facet normal to the incident flow
•
• $μ$ =
fluid viscosity (water in this study)
•
• $ρ$ =
fluid density (water in this study)
•
• $(τs)i$ =
average shear stress of facet i (N/m2)
•
• $(τs)i$ =
shear stress of facet i (N/m2)
•
• $(τ¯s)i$ =
nondimensionalized average shear stress of facet i
•
• $(τ¯s)all$ =
nondimensionalized overall shear stress of microstructure
•
• $(τ¯s)front$ =
nondimensionalized average shear stress of front facet
•
• $(τ¯s)rear$ =
nondimensionalized average shear stress of rear facet
•
• $(τ¯s)side$ =
nondimensionalized average shear stress of side facet
•
• $(τ¯s)top$ =
nondimensionalized average shear stress of top facet
•
• $ϕc$ =
angle of rotation of cube
•
• $ϕp$ =
angle of rotation of pyramid
References
1.
Prakash
,
S.
, and
Yeom
,
J.
,
2014
,
Nanofluidics and Microfluidics: Systems and Applications
,
Elsevier
,
New York
.
2.
Shen
,
Y.
,
Wang
,
M.
,
Chang
,
I. S.
, and
Ng
,
H. Y.
,
2013
, “
Effect of Shear Rate on the Response of Microbial Fuel Cell Toxicity Sensor to Cu(II)
,”
Bioresour. Technol.
,
136
, pp.
707
710
.
3.
Nagrath
,
S.
,
Sequist
,
L. V.
,
Maheswaran
,
S.
,
Bell
,
D. W.
,
Irimia
,
D.
,
Ulkus
,
L.
,
Smith
,
M. R.
,
Kwak
,
E. L.
,
Digumarthy
,
S.
,
Muzikansky
,
A.
,
Ryan
,
P.
,
Balis
,
U. J.
,
Tompkins
,
R. G.
,
Haber
,
D. A.
, and
Toner
,
M.
,
2007
, “
Isolation of Rare Circulating Tumour Cells in Cancer Patients by Microchip Technology
,”
Nature
,
450
(
7173
), pp.
1235
1239
.
4.
Dasi
,
L. P.
,
Murphy
,
D. W.
,
Glezer
,
A.
, and
Yoganathan
,
A. P.
,
2008
, “
Passive Flow Control of Bileaflet Mechanical Heart Valve Leakage Flow
,”
J. Biomech.
,
41
(
6
), pp.
1166
1173
.
5.
Pham
,
H. T.
,
Boon
,
N.
,
Aelterman
,
P.
,
Clauwaert
,
P.
,
De Schamphelaire
,
L.
,
Van Oostveldt
,
P.
,
Verbeken
,
K.
,
Rabaey
,
K.
, and
Verstraete
,
W.
,
2008
, “
High Shear Enrichment Improves the Performance of the Anodophilic Microbial Consortium in a Microbial Fuel Cell
,”
Microbiol. Biotechnol.
,
1
(
6
), pp.
487
496
.
6.
Prakash
,
S.
,
Pinti
,
M.
, and
Bhushan
,
B.
,
2012
, “
Theory, Fabrication and Applications of Microfluidic and Nanofluidic Biosensors
,”
Philos. Trans. R. Soc. London, Ser. A
,
370
(
1967
), pp.
2269
2303
.
7.
Kellie
,
B. M.
,
Silleck
,
A. C.
,
Bellman
,
K.
,
Snodgrass
,
R.
, and
Prakash
,
S.
,
2013
, “
Deposition of Few-Layered Graphene in a Microcombustor on Copper and Nickel Substrates
,”
,
3
(
19
), pp.
7100
7105
.
8.
Hattori
,
K.
,
Munehira
,
Y.
,
Kobayashi
,
H.
,
Satoh
,
T.
,
Sugiura
,
S.
, and
Kanamori
,
T.
,
2014
, “
Microfluidic Perfusion Culture Chip Providing Different Strengths of Shear Stress for Analysis of Vascular Endothelial Function
,”
J. Biosci. Bioeng.
,
118
(
3
), pp.
327
332
.
9.
Sigal
,
A.
, and
Danberg
,
J. E.
,
1990
, “
New Correlation of Roughness Density Effect on the Turbulent Boundary Layer
,”
AIAA J.
,
28
(
3
), pp.
554
556
.
10.
Coleman
,
H. W.
,
Hodge
,
B. K.
, and
Taylor
,
R. P.
,
1984
, “
A Re-Evaluation of Schlichting's Surface Roughness Experiment
,”
ASME J. Fluids Eng.
,
106
(
1
), pp.
60
65
.
11.
van Rij
,
J. A.
,
Belnap
,
B. J.
, and
Ligrani
,
P. M.
,
2002
, “
Analysis and Experiments on Three-Dimensional, Irregular Surface Roughness
,”
ASME J. Fluids Eng.
,
124
(
3
), pp.
671
677
.
12.
Zdravkovich
,
M. M.
,
1997
,
Flow Around Circular Cylinders
, Vol.
1
: Fundamentals,
Oxford University Press
, Oxford, UK.
13.
Beaudan
,
B.
, and
Moin
,
P.
,
1994
, “
Numerical Experiments on the Flow Past a Circular Cylinder at Sub-Critical Reynolds-Number
,” Report No. TF-62, Center for Turbulence Research, Stanford University, Stanford, CA.
14.
Williamson
,
C. H. K.
,
1996
, “
Vortex Dynamics in the Cylinder Wake
,”
Annu. Rev. Fluid Mech.
,
28
(
1
), pp.
477
539
.
15.
Rosetti
,
G. F.
,
Vaz
,
G.
, and
Fujarra
,
A. L. C.
,
2012
, “
URANS Calculations for Smooth Circular Cylinder Flow in a Wide Range of Reynolds Numbers: Solution Verification and Validation
,”
ASME J. Fluids Eng.
,
134
(
12
), p.
121103
.
16.
Agimelen
,
O. S.
, and
Olmsted
,
P. D.
,
2013
, “
Apparent Fracture in Polymeric Fluids Under Step Shear
,”
Phys. Rev. Lett.
,
110
(
20
), p.
204503
.
17.
Gao
,
T.
,
Hu
,
H. H.
, and
Castañeda
,
P. P.
,
2012
, “
Shape Dynamics and Rheology of Soft Elastic Particles in a Shear Flow
,”
Phys. Rev. Lett.
,
108
(
5
), p.
058302
.
18.
Gutierrez
,
R. A.
, and
Crumpler
,
E. T.
,
2007
, “
Potential Effect of Geometry on Wall Shear Stress Distribution Across Scaffold Surfaces
,”
Ann. Biomed. Eng.
,
36
(
1
), pp.
77
85
.
19.
Popa
,
C. V.
,
Zaidi
,
H.
,
Arfaoui
,
A.
,
Polidori
,
G.
,
Taiar
,
R.
, and
Fohanno
,
S.
,
2011
, “
Analysis of Wall Shear Stress Around a Competitive Swimmer Using 3D Navier–Stokes Equations in CFD
,”
Acta Bioeng. Biomech.
,
13
(
1
), pp.
3
11
.
20.
Choi
,
S.
,
Karp
,
J. M.
, and
Karnik
,
R.
,
2012
, “
Cell Sorting by Deterministic Cell Rolling
,”
Lab Chip
,
12
(
8
), pp.
1427
1430
.
21.
Loutherback
,
K.
,
Chou
,
K.
,
Newman
,
J.
,
Puchalla
,
J.
,
Austin
,
R.
, and
Sturm
,
J.
,
2010
, “
Improved Performance of Deterministic Lateral Displacement Arrays With Triangular Posts
,”
Microfluid. Nanofluid.
,
9
(
6
), pp.
1143
1149
.
22.
Huang
,
Z.
,
McLamore
,
E. S.
,
Chuang
,
H. S.
,
Zhang
,
W.
,
Wereley
,
S.
,
Leon
,
J. L. C.
, and
Banks
,
M. K.
,
2013
, “
Shear-Induced Detachment of Biofilms From Hollow Fiber Silicone Membranes
,”
Biotechnol. Bioeng.
,
110
(
2
), pp.
525
534
.
23.
Kim
,
J.
,
Kim
,
H.-S.
,
Han
,
S.
,
Lee
,
J.-Y.
,
Oh
,
J.-E.
,
Chung
,
S.
, and
Park
,
H.-D.
,
2013
, “
Hydrodynamic Effects on Bacterial Biofilm Development in a Microfluidic Environment
,”
Lab Chip
,
13
(
10
), pp.
1846
1849
.
24.
Langhamer
,
O.
,
Wilhelmsson
,
D.
, and
Engström
,
J.
,
2009
, “
Artificial Reef Effect and Fouling Impacts on Offshore Wave Power Foundations and Buoys—A Pilot Study
,”
Estuarine Coastal Shelf Sci.
,
82
(
3
), pp.
426
432
.
25.
Logan
,
B.
,
Cheng
,
S.
,
Watson
,
V.
, and
,
G.
,
2007
, “
Graphite Fiber Brush Anodes for Increased Power Production in Air-Cathode Microbial Fuel Cells
,”
Environ. Sci. Technol.
,
41
(
9
), pp.
3341
3346
.
26.
Patanakar
,
S. V.
,
1980
,
Numerical Heat Transfer and Fluid Flow
,
McGraw-Hill
,
New York
.
27.
Sprittles
,
J. E.
, and
Shikhmurzaev
,
Y. D.
,
2011
, “
Viscous Flow in Domains With Corners: Numerical Artifacts, Their Origin and Removal
,”
Comput. Methods Appl. Mech. Eng.
,
200
(
9–12
), pp.
1087
1099
.
28.
,
Y.
, and
Schultz
,
M.
,
1986
, “
GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
,”
SIAM J. Sci. Stat. Comput.
,
7
(
3
), pp.
856
869
.
29.
Van der Vorst
,
H. A.
,
1992
, “
Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems
,”
SIAM J. Sci. Stat. Comput.
,
13
(
2
), pp.
631
644
.
30.
Meng
,
Q.
,
Thanh-Tung
,
C.
, and
Tiow-Seng
,
T.
,
2013
, “
Computing 2D Constrained Delaunay Triangulation Using the GPU
,”
IEEE Trans. Visual. Comput. Graphics
,
19
(
5
), pp.
736
748
.
31.
Löhner
,
R.
,
2014
, “
,”
Arch. Comput. Methods Eng.
,
21
(
2
), pp.
127
140
.
32.
Sprittles
,
J. E.
, and
Shikhmurzaev
,
Y. D.
,
2011
, “
Viscous Flows in Corner Regions: Singularities and Hidden Eigensolutions
,”
Int. J. Numer. Methods Fluids
,
65
(
4
), pp.
372
382
.
33.
Kundu
,
P. K.
,
Cohen
,
I. M.
, and
Dowling
,
D. R.
,
2012
,
Fluid Mechanics
, 5th ed.,
,
Boston, MA
, p.
iii
.
34.
COMSOL
,
2013
, “
comsol Multiphysics Release Notes
35.
Tamayol
,
A.
,
Yeom
,
J.
,
Akbari
,
M.
, and
Bahrami
,
M.
,
2013
, “
Low Reynolds Number Flows Across Ordered Arrays of Micro-Cylinders Embedded in a Rectangular Micro/Minichannel
,”
Int. J. Heat Mass Transfer
,
58
(
1–2
), pp.
420
426
.
36.
Chien-Yu
,
F.
,
Sheng-Yang
,
T.
,
Shih-Mo
,
Y.
,
Long
,
H.
,
Cheng-Hsien
,
L.
, and
Hwan-You
,
C.
,
2014
, “
A Microfluidic Chip With a U-Shaped Microstructure Array for Multicellular Spheroid Formation, Culturing and Analysis
,”
Biofabrication
,
6
(
1
), p.
015009
.
37.
Stone
,
H. A.
,
Stroock
,
A. D.
, and
Ajdari
,
A.
,
2004
, “
Engineering Flows in Small Devices
,”
Annu. Rev. Fluid Mech.
,
36
(
1
), pp.
381
411
.
38.
Gogolides
,
E.
,
Ellinas
,
K.
, and
Tserepi
,
A.
,
2015
, “
Hierarchical Micro and Nano Structured, Hydrophilic, Superhydrophobic and Superoleophobic Surfaces Incorporated in Microfluidics, Microarrays and Lab on Chip Microsystems
,”
Microelectron. Eng.
,
132
, pp.
135
155
.
39.
Sugioka
,
K.
,
Masuda
,
M.
,
Hongo
,
T.
,
Cheng
,
Y.
,
Shihoyama
,
K.
, and
Midorikawa
,
K.
,
2004
, “
Three-Dimensional Microfluidic Structure Embedded in Photostructurable Glass by Femtosecond Laser for Lab-on-Chip Applications
,”
Appl. Phys. A
,
79
(
4–6
), pp.
815
817
.
40.
Park
,
H.
,
Park
,
H.
, and
Kim
,
J.
,
2013
, “
A Numerical Study of the Effects of Superhydrophobic Surface on Skin-Friction Drag in Turbulent Channel Flow
,”
Phys. Fluids
,
25
(
11
), p.
110815
.
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https://commons.apache.org/proper/commons-math/javadocs/api-3.5/org/apache/commons/math3/exception/class-use/NotPositiveException.html
|
## Uses of Classorg.apache.commons.math3.exception.NotPositiveException
• Packages that use NotPositiveException
Package Description
org.apache.commons.math3.analysis.differentiation
This package holds the main interfaces and basic building block classes dealing with differentiation.
org.apache.commons.math3.analysis.interpolation
Univariate real functions interpolation algorithms.
org.apache.commons.math3.complex
Complex number type and implementations of complex transcendental functions.
org.apache.commons.math3.distribution
Implementations of common discrete and continuous distributions.
org.apache.commons.math3.genetics
This package provides Genetic Algorithms components and implementations.
org.apache.commons.math3.linear
Linear algebra support.
org.apache.commons.math3.ml.clustering
Clustering algorithms.
org.apache.commons.math3.optim.nonlinear.scalar.noderiv
This package provides optimization algorithms that do not require derivatives.
org.apache.commons.math3.optimization.direct
This package provides optimization algorithms that don't require derivatives.
org.apache.commons.math3.random
Random number and random data generators.
org.apache.commons.math3.stat.clustering
All classes and sub-packages of this package are deprecated.
org.apache.commons.math3.stat.inference
Classes providing hypothesis testing.
org.apache.commons.math3.stat.interval
Classes providing binomial proportion confidence interval construction.
org.apache.commons.math3.util
Convenience routines and common data structures used throughout the commons-math library.
• ### Uses of NotPositiveException in org.apache.commons.math3.analysis.differentiation
Constructors in org.apache.commons.math3.analysis.differentiation that throw NotPositiveException
Constructor and Description
FiniteDifferencesDifferentiator(int nbPoints, double stepSize)
Build a differentiator with number of points and step size when independent variable is unbounded.
FiniteDifferencesDifferentiator(int nbPoints, double stepSize, double tLower, double tUpper)
Build a differentiator with number of points and step size when independent variable is bounded.
• ### Uses of NotPositiveException in org.apache.commons.math3.analysis.interpolation
Constructors in org.apache.commons.math3.analysis.interpolation that throw NotPositiveException
Constructor and Description
LoessInterpolator(double bandwidth, int robustnessIters, double accuracy)
Construct a new LoessInterpolator with given bandwidth, number of robustness iterations and accuracy.
MicrosphereInterpolator(int elements, int exponent)
Create a microsphere interpolator.
SmoothingPolynomialBicubicSplineInterpolator(int degree)
Deprecated.
SmoothingPolynomialBicubicSplineInterpolator(int xDegree, int yDegree)
Deprecated.
• ### Uses of NotPositiveException in org.apache.commons.math3.complex
Methods in org.apache.commons.math3.complex that throw NotPositiveException
Modifier and Type Method and Description
List<Complex> Complex.nthRoot(int n)
Computes the n-th roots of this complex number.
• ### Uses of NotPositiveException in org.apache.commons.math3.distribution
Constructors in org.apache.commons.math3.distribution that throw NotPositiveException
Constructor and Description
EnumeratedDistribution(List<Pair<T,Double>> pmf)
Create an enumerated distribution using the given probability mass function enumeration.
EnumeratedDistribution(RandomGenerator rng, List<Pair<T,Double>> pmf)
Create an enumerated distribution using the given random number generator and probability mass function enumeration.
EnumeratedIntegerDistribution(int[] singletons, double[] probabilities)
Create a discrete distribution using the given probability mass function definition.
EnumeratedIntegerDistribution(RandomGenerator rng, int[] singletons, double[] probabilities)
Create a discrete distribution using the given random number generator and probability mass function definition.
EnumeratedRealDistribution(double[] singletons, double[] probabilities)
Create a discrete distribution using the given probability mass function enumeration.
EnumeratedRealDistribution(RandomGenerator rng, double[] singletons, double[] probabilities)
Create a discrete distribution using the given random number generator and probability mass function enumeration.
HypergeometricDistribution(int populationSize, int numberOfSuccesses, int sampleSize)
Construct a new hypergeometric distribution with the specified population size, number of successes in the population, and sample size.
HypergeometricDistribution(RandomGenerator rng, int populationSize, int numberOfSuccesses, int sampleSize)
Creates a new hypergeometric distribution.
MixtureMultivariateNormalDistribution(RandomGenerator rng, List<Pair<Double,MultivariateNormalDistribution>> components)
Creates a mixture model from a list of distributions and their associated weights.
• ### Uses of NotPositiveException in org.apache.commons.math3.genetics
Methods in org.apache.commons.math3.genetics that throw NotPositiveException
Modifier and Type Method and Description
void ListPopulation.setPopulationLimit(int populationLimit)
Sets the maximal population size.
Constructors in org.apache.commons.math3.genetics that throw NotPositiveException
Constructor and Description
ElitisticListPopulation(int populationLimit, double elitismRate)
Creates a new ElitisticListPopulation instance and initializes its inner chromosome list.
ElitisticListPopulation(List<Chromosome> chromosomes, int populationLimit, double elitismRate)
ListPopulation(int populationLimit)
Creates a new ListPopulation instance and initializes its inner chromosome list.
ListPopulation(List<Chromosome> chromosomes, int populationLimit)
Creates a new ListPopulation instance.
• ### Uses of NotPositiveException in org.apache.commons.math3.linear
Methods in org.apache.commons.math3.linear that throw NotPositiveException
Modifier and Type Method and Description
abstract RealVector RealVector.getSubVector(int index, int n)
Get a subvector from consecutive elements.
FieldVector<T> FieldVector.getSubVector(int index, int n)
Get a subvector from consecutive elements.
RealVector ArrayRealVector.getSubVector(int index, int n)
Get a subvector from consecutive elements.
OpenMapRealVector OpenMapRealVector.getSubVector(int index, int n)
Get a subvector from consecutive elements.
FieldVector<T> ArrayFieldVector.getSubVector(int index, int n)
Get a subvector from consecutive elements.
FieldVector<T> SparseFieldVector.getSubVector(int index, int n)
Get a subvector from consecutive elements.
RealMatrix RealMatrix.power(int p)
Returns the result of multiplying this with itself p times.
FieldMatrix<T> FieldMatrix.power(int p)
Returns the result multiplying this with itself p times.
RealMatrix AbstractRealMatrix.power(int p)
Returns the result of multiplying this with itself p times.
FieldMatrix<T> AbstractFieldMatrix.power(int p)
Returns the result multiplying this with itself p times.
• ### Uses of NotPositiveException in org.apache.commons.math3.ml.clustering
Constructors in org.apache.commons.math3.ml.clustering that throw NotPositiveException
Constructor and Description
DBSCANClusterer(double eps, int minPts)
Creates a new instance of a DBSCANClusterer.
DBSCANClusterer(double eps, int minPts, DistanceMeasure measure)
Creates a new instance of a DBSCANClusterer.
• ### Uses of NotPositiveException in org.apache.commons.math3.optim.nonlinear.scalar.noderiv
Constructors in org.apache.commons.math3.optim.nonlinear.scalar.noderiv that throw NotPositiveException
Constructor and Description
CMAESOptimizer.Sigma(double[] s)
• ### Uses of NotPositiveException in org.apache.commons.math3.optimization.direct
Constructors in org.apache.commons.math3.optimization.direct that throw NotPositiveException
Constructor and Description
CMAESOptimizer.Sigma(double[] s)
• ### Uses of NotPositiveException in org.apache.commons.math3.random
Methods in org.apache.commons.math3.random that throw NotPositiveException
Modifier and Type Method and Description
int RandomDataImpl.nextHypergeometric(int populationSize, int numberOfSuccesses, int sampleSize)
Deprecated.
Generates a random value from the Hypergeometric Distribution.
int RandomDataGenerator.nextHypergeometric(int populationSize, int numberOfSuccesses, int sampleSize)
Generates a random value from the Hypergeometric Distribution.
double[] HaltonSequenceGenerator.skipTo(int index)
double[] SobolSequenceGenerator.skipTo(int index)
• ### Uses of NotPositiveException in org.apache.commons.math3.stat.clustering
Constructors in org.apache.commons.math3.stat.clustering that throw NotPositiveException
Constructor and Description
DBSCANClusterer(double eps, int minPts)
Deprecated.
Creates a new instance of a DBSCANClusterer.
• ### Uses of NotPositiveException in org.apache.commons.math3.stat.inference
Methods in org.apache.commons.math3.stat.inference that throw NotPositiveException
Modifier and Type Method and Description
static double TestUtils.chiSquare(double[] expected, long[] observed)
double ChiSquareTest.chiSquare(double[] expected, long[] observed)
Computes the Chi-Square statistic comparing observed and expected frequency counts.
static double TestUtils.chiSquare(long[][] counts)
double ChiSquareTest.chiSquare(long[][] counts)
Computes the Chi-Square statistic associated with a chi-square test of independence based on the input counts array, viewed as a two-way table.
static double TestUtils.chiSquareDataSetsComparison(long[] observed1, long[] observed2)
double ChiSquareTest.chiSquareDataSetsComparison(long[] observed1, long[] observed2)
Computes a Chi-Square two sample test statistic comparing bin frequency counts in observed1 and observed2.
static double TestUtils.chiSquareTest(double[] expected, long[] observed)
double ChiSquareTest.chiSquareTest(double[] expected, long[] observed)
Returns the observed significance level, or p-value, associated with a Chi-square goodness of fit test comparing the observed frequency counts to those in the expected array.
static boolean TestUtils.chiSquareTest(double[] expected, long[] observed, double alpha)
boolean ChiSquareTest.chiSquareTest(double[] expected, long[] observed, double alpha)
Performs a Chi-square goodness of fit test evaluating the null hypothesis that the observed counts conform to the frequency distribution described by the expected counts, with significance level alpha.
static double TestUtils.chiSquareTest(long[][] counts)
double ChiSquareTest.chiSquareTest(long[][] counts)
Returns the observed significance level, or p-value, associated with a chi-square test of independence based on the input counts array, viewed as a two-way table.
static boolean TestUtils.chiSquareTest(long[][] counts, double alpha)
boolean ChiSquareTest.chiSquareTest(long[][] counts, double alpha)
Performs a chi-square test of independence evaluating the null hypothesis that the classifications represented by the counts in the columns of the input 2-way table are independent of the rows, with significance level alpha.
static double TestUtils.chiSquareTestDataSetsComparison(long[] observed1, long[] observed2)
double ChiSquareTest.chiSquareTestDataSetsComparison(long[] observed1, long[] observed2)
Returns the observed significance level, or p-value, associated with a Chi-Square two sample test comparing bin frequency counts in observed1 and observed2.
static boolean TestUtils.chiSquareTestDataSetsComparison(long[] observed1, long[] observed2, double alpha)
boolean ChiSquareTest.chiSquareTestDataSetsComparison(long[] observed1, long[] observed2, double alpha)
Performs a Chi-Square two sample test comparing two binned data sets.
static double TestUtils.g(double[] expected, long[] observed)
double GTest.g(double[] expected, long[] observed)
Computes the G statistic for Goodness of Fit comparing observed and expected frequency counts.
static double TestUtils.gDataSetsComparison(long[] observed1, long[] observed2)
double GTest.gDataSetsComparison(long[] observed1, long[] observed2)
Computes a G (Log-Likelihood Ratio) two sample test statistic for independence comparing frequency counts in observed1 and observed2.
static double TestUtils.gTest(double[] expected, long[] observed)
double GTest.gTest(double[] expected, long[] observed)
Returns the observed significance level, or p-value, associated with a G-Test for goodness of fit comparing the observed frequency counts to those in the expected array.
static boolean TestUtils.gTest(double[] expected, long[] observed, double alpha)
boolean GTest.gTest(double[] expected, long[] observed, double alpha)
Performs a G-Test (Log-Likelihood Ratio Test) for goodness of fit evaluating the null hypothesis that the observed counts conform to the frequency distribution described by the expected counts, with significance level alpha.
static double TestUtils.gTestDataSetsComparison(long[] observed1, long[] observed2)
double GTest.gTestDataSetsComparison(long[] observed1, long[] observed2)
Returns the observed significance level, or p-value, associated with a G-Value (Log-Likelihood Ratio) for two sample test comparing bin frequency counts in observed1 and observed2.
static boolean TestUtils.gTestDataSetsComparison(long[] observed1, long[] observed2, double alpha)
boolean GTest.gTestDataSetsComparison(long[] observed1, long[] observed2, double alpha)
Performs a G-Test (Log-Likelihood Ratio Test) comparing two binned data sets.
static double TestUtils.gTestIntrinsic(double[] expected, long[] observed)
double GTest.gTestIntrinsic(double[] expected, long[] observed)
Returns the intrinsic (Hardy-Weinberg proportions) p-Value, as described in p64-69 of McDonald, J.H.
static double TestUtils.rootLogLikelihoodRatio(long k11, long k12, long k21, long k22)
• ### Uses of NotPositiveException in org.apache.commons.math3.stat.interval
Methods in org.apache.commons.math3.stat.interval that throw NotPositiveException
Modifier and Type Method and Description
ConfidenceInterval BinomialConfidenceInterval.createInterval(int numberOfTrials, int numberOfSuccesses, double confidenceLevel)
Create a confidence interval for the true probability of success of an unknown binomial distribution with the given observed number of trials, successes and confidence level.
• ### Uses of NotPositiveException in org.apache.commons.math3.util
Methods in org.apache.commons.math3.util that throw NotPositiveException
Modifier and Type Method and Description
static long ArithmeticUtils.binomialCoefficient(int n, int k)
static long CombinatoricsUtils.binomialCoefficient(int n, int k)
Returns an exact representation of the Binomial Coefficient, "n choose k", the number of k-element subsets that can be selected from an n-element set.
static double ArithmeticUtils.binomialCoefficientDouble(int n, int k)
static double CombinatoricsUtils.binomialCoefficientDouble(int n, int k)
Returns a double representation of the Binomial Coefficient, "n choose k", the number of k-element subsets that can be selected from an n-element set.
static double ArithmeticUtils.binomialCoefficientLog(int n, int k)
static double CombinatoricsUtils.binomialCoefficientLog(int n, int k)
Returns the natural log of the Binomial Coefficient, "n choose k", the number of k-element subsets that can be selected from an n-element set.
static void CombinatoricsUtils.checkBinomial(int n, int k)
Check binomial preconditions.
static void MathArrays.checkNonNegative(long[] in)
Check that all entries of the input array are >= 0.
static void MathArrays.checkNonNegative(long[][] in)
Check all entries of the input array are >= 0.
static long ArithmeticUtils.factorial(int n)
static long CombinatoricsUtils.factorial(int n)
Returns n!.
static double ArithmeticUtils.factorialDouble(int n)
static double CombinatoricsUtils.factorialDouble(int n)
Compute n!, the factorial of n (the product of the numbers 1 to n), as a double.
static double ArithmeticUtils.factorialLog(int n)
static double CombinatoricsUtils.factorialLog(int n)
Compute the natural logarithm of the factorial of n.
static BigInteger ArithmeticUtils.pow(BigInteger k, BigInteger e)
Raise a BigInteger to a BigInteger power.
static BigInteger ArithmeticUtils.pow(BigInteger k, int e)
Raise a BigInteger to an int power.
static BigInteger ArithmeticUtils.pow(BigInteger k, long e)
Raise a BigInteger to a long power.
static int ArithmeticUtils.pow(int k, int e)
Raise an int to an int power.
static int ArithmeticUtils.pow(int k, long e)
Deprecated.
As of 3.3. Please use ArithmeticUtils.pow(int,int) instead.
static long ArithmeticUtils.pow(long k, int e)
Raise a long to an int power.
static long ArithmeticUtils.pow(long k, long e)
Deprecated.
As of 3.3. Please use ArithmeticUtils.pow(long,int) instead.
static long ArithmeticUtils.stirlingS2(int n, int k)
static long CombinatoricsUtils.stirlingS2(int n, int k)
Returns the Stirling number of the second kind, "S(n,k)", the number of ways of partitioning an n-element set into k non-empty subsets.
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2021-11-29 02:10:46
|
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|
https://physics.stackexchange.com/questions/474561/why-there-are-3-significant-figures-in-86400-but-5-in-86400-s-because-of-unit
|
# Why there are 3 significant figures in 86400 but 5 in 86400 s ( because of Unit)
My book states one rule for determining the number of significant figures as under:
All zeroes to the right of a non zero digit but to the left of an understood decimal point are not significant . Eg. 86400 has 3 significant figures.
But such zeroes are significant if they come from a measurement. So 86400 has 3 significant figures but 86400 s has 5 significant figures. Also 5100kg has 4 significant figures.
Please explain me whether this rule is correct. Thank you
• I'd write $8.64\times 10^4$ or $86.4\times 10^3$ or some variant of that if I wanted to be clear that the trailing zeros didn't count towards significant figures: I'd find $86400$ ambiguous. But likely there are rules which I'm unaware of.
– user107153
Apr 23, 2019 at 15:20
• Alternately, you could write 86.4 ks. Admittedly this usage is rare enough with seconds that you would probably rather use exponential notation as suggested by @tfb. Apr 23, 2019 at 15:37
• Sig figs are a fairly crude way to express uncertainty. AFAIK (but I am an engineer not a physicist), you won't use them (except to understand why you don't write "$1.23456\pm0.1$") after you're done with undergrad lab courses. So if you book says this is a rule, then it's a rule, at least for this class. Apr 23, 2019 at 15:58
• I have never seen a rule about units making the zeroes significant, my knowledge was that trailing zeroes like that can be significant or not depending on context i.e. other numbers in the problem. So to me both those numbers can have either 3,4, or 5 significant figures but will be important based on previous numbers used and/or any present uncertainties Apr 23, 2019 at 17:08
• The rules are to some extent arbitrary and depend on the person. These rules are "correct" in the sense that your book would accept it as correct, but they could easily be "incorrect" according to the next book you use. Apr 23, 2019 at 19:02
I have seen this usage before, but it is not a common convention, so if you use it, you should explicitly say so. The argument behind it is that giving 86400 as a number of seconds implies that the number is precise up to that given unit: if you wanted to express three digits of precision only, you would write $$864\times10^2s$$, so that you are always reporting your results as an integer number of some units (in this second case, the "units" are $$10^2s$$). The much more common convention is to just use scientific notation in the usual way.
Your first example is a little unusual, because $$86\,400 = 24\times60\times60$$ is exactly the number of seconds in a twenty-four hour day. So in many contexts you might find yourself using $$86\,400\,\text{seconds}/\text{day}$$ as an infinite-precision unit-conversion factor. (Although, since leap seconds are inserted into Coordinated Universal Time at intervals possibly as frequent as every six months, there is a sub-$$10^{-7}$$ uncertainty in using this conversion blindly for very long intervals in the modern era.) You might compare to using the speed of light as a conversion factor between lengths and distances, where the value $$c = 299\,792\,458\,\rm m / s$$ has nine nonzero leading digits but is defined to have infinite precision.
For your second example: if I think about my experience with five-ton objects and the kinds of apparatus that would be typically used to determine their masses (lorries and cranes would be involved), I would be very shocked to measure a mass of $$5100\rm\, kg$$ with a precision of $$\pm1\,\rm kg$$. Heck, it takes several kilograms of lifting hardware to safely attach a five-ton object to a crane. Without a description of the measurement technique and its calibration chain, I would trust at measurement of "$$5100\,\rm kg$$" to $$\pm100\,\rm kg$$, using the regular rules for significant figures.
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2022-06-29 20:25:48
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https://www.ms.u-tokyo.ac.jp/seminar/2018/sem18-197.html
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複素解析幾何セミナー
開催情報 月曜日 10:30～12:00 数理科学研究科棟(駒場) 128号室 平地 健吾, 高山 茂晴, 野村 亮介
2018年11月05日(月)
10:30-12:00 数理科学研究科棟(駒場) 128号室
On the quasiconformal equivalence of Dynamical Cantor sets (JAPANESE)
[ 講演概要 ]
Let $E$ be a Cantor set in the Riemann sphere $\widehat{\mathbb C}$, that is, a totally disconnected perfect set in $\widehat{\mathbb C}$.
The standard middle one-thirds Cantor set $\mathcal{C}$ is a typical example.
We consider the complement $X_{E}:=\widehat{\mathbb C}\setminus E$ of the Cantor set $E$.
It is an open Riemann surface with uncountable many boundary components.
We are interested in the quasiconformal equivalence of such surfaces.
In this talk, we discuss the quasiconformal equivalence for the complements of Cantor sets given by dynamical systems.
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2023-03-23 02:19:35
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https://www.ideals.illinois.edu/handle/2142/79479
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## Files in this item
FilesDescriptionFormat
application/vnd.openxmlformats-officedocument.presentationml.presentation
293600.pptx (2MB)
PresentationMicrosoft PowerPoint 2007
application/pdf
800.pdf (22kB)
AbstractPDF
## Description
Title: OBSERVATION AND ANALYSIS OF THE A1-A2 SPLITTING OF CH3D Author(s): Abe, Masashi Contributor(s): Sasada, Hiroyuki; Sera, Hideyuki Subject(s): Mini-symposium: High-Precision Spectroscopy Abstract: Sub-Doppler resolution spectroscopy of CH$_{3}$D has been carried out for the $nu _1$ and $nu _4$ fundamental bands using a comb-referenced difference-frequency generation spectrometer. Thirty transitions from the low-$J''$ and $K'' = 3$ levels are observed with a resolution of 60 to 100 kHz, and the $A_1$-$A_2$ splitting is resolved for twenty-three of the thirty transitions. Most of them are overlapped in Doppler broadening and resolved for the first time, as far as we know. The absolute transition frequencies are determined with a typical uncertainty of 4 kHz. The $A_1$-$A_2$ splitting constant of the $K'' = 3$ levels is yielded as $2h_{3,v=0} = (1.5641 pm 0.0026)$ Hz for the ground vibrational state. Those of the $K' = 3$ levels for the $v_1 = 1$ states and of the ($K' = 2$, $l = -1$) and ($K' = 4$, $l = 1$) levels for the $v_4 = 1$ state are also determined including the $J'$-dependent terms. Issue Date: 23-Jun-15 Publisher: International Symposium on Molecular Spectroscopy Citation Info: ACS Genre: CONFERENCE PAPER/PRESENTATION Type: Text Language: English URI: http://hdl.handle.net/2142/79479 Date Available in IDEALS: 2016-01-05
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2017-07-26 01:02:21
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http://rpg.stackexchange.com/questions/5990/other-than-its-class-feature-what-powers-allow-the-battlemind-to-place-encounte
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# Other than its class feature, what powers allow the battlemind to place encounter-long marks?
I'm trying to find out which powers allow the Battlemind to place encounter-long marks. I know that the class feature Battlemind's Demand lets you do this to two targets, but most of the other powers only let a Battlemind mark until the end of your next turn.
Are there any other powers that let the Battlemind mark until the end of the encounter?
-
## 1 Answer
• Precognitive Eye - Daily 15 - Pg 43 Psionic Power
• Focus Bind - Daily 19 - Pg 45 Psionic Power
• Iron Presence - At Will 23 (w/Augment 6 in Close Burst 2) - Pg 46 Psionic Power
Note: Luring Steel - Daily 13 - 51 PHB3 - lets you use Battlemind's demand against different numbers of targets depending on augmentation. Also Iron Presence without augmentation functions the same as Battlemind's Demand with augmentation.
-
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2016-07-26 10:22:58
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https://wizedu.com/questions/411/the-assumptions-of-the-production-order-quantity
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##### Question
In: Operations Management
# The assumptions of the production order quantity model are met in a situation where annual demand is 3650 units
The assumptions of the production order quantity model are met in a situation where annual demand is 3650 units, the setup cost is $50, holding cost is$12 per unit per year, the daily demand rate is 10 and the daily production rate is 100. The production order quantity for this problem is approximate.
## Solutions
##### Expert Solution
For above data, production order quantity can be calculated by,
$$\sqrt{2 * K * D / h *(1-x)}$$
where,
$$\mathrm{K}=$$ Setup cost
$$\mathrm{D}=$$ Annual demand
$$\mathrm{h}=$$ Holding cost
$$\mathrm{x}=\mathrm{d} / \mathrm{p}$$ (daily demand rate/ daily production rate)
Hence, in this case,
production order quanity $$=\sqrt{2 * 50 * 3650 / 12 *(1-10 / 100)}=184$$ (rounding off)
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2021-02-27 16:47:40
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https://mathvault.ca/hub/higher-math/math-symbols/algebra-symbols/
|
# Algebra Symbols
A comprehensive collection of 225+ symbols used in algebra, categorized by subject and type into tables along with each symbol's name, usage and example.
Algebra is a subfield of mathematics pertaining to the manipulation of symbols and their governing rules. The following is a compilation of symbols from the different branches of algebra, which include basic algebra, number theory, linear algebra and abstract algebra.
For readability purpose, these symbols are categorized by their function and topic into charts and tables. Other comprehensive lists of symbols — as categorized by subject and type — can be also found in the relevant pages below (or in the navigational panel).
Get the master summary of mathematical symbols in eBook form — along with each symbol’s usage and LaTeX code.
## Constants
In algebra, constants are symbols used to denote key mathematical elements and sets. The following tables document the most common of these — along with each symbol’s name, usage and example.
(For common constants in general, see common math constants.)
### Key Mathematical Sets
In algebra, certain sets of numbers (or other more elaborated objects) tend to occur more frequently than others. These sets are often denoted by some variants of alphabetical letters — many of which are of the blackboard bold typeface.
## Variables
Since algebra is concerned with the manipulation of mathematical symbols, it often draws upon a wide range of variables as placeholders for varying objects and quantities. The following table documents the most common of these — along with their respective usage and example.
## Delimiters
In mathematics, delimiters are symbols used to denote the separation between independent mathematical entities. The following table features some of the most common delimiters in algebra. For common delimiters in general, see common delimiters.
## Function-related Symbols
As a foundational component of algebra, function plays a key role in establishing the rules pertaining to the manipulation of symbols. The following table documents some of the most common function-related operators and notational symbols — along with their meaning and example.
## Operators
In algebra, operators can be thought of as a special type of function mapping one or multiple mathematical entities to another, and are often given special names or notations due to their repeated occurrences.
In particular, these operators are often related to numbers, key functions, linear algebra and abstract algebra — the vast majority of which are found in the tables below. For common operators in general, see common operators.
## Relational Symbols
In algebra, relational symbols are used to express the relationship between two mathematical entities, and are often related to concepts such as equality, comparison, divisibility and other higher-order relationships. The following tables document the most common of these — along with their usage and meaning.
### Relational Symbols in Abstract Algebra
For the master list of symbols, see mathematical symbols. For lists of symbols categorized by type and subject, refer to the relevant pages below for more.
Get the master summary of mathematical symbols in eBook form — along with each symbol’s usage and LaTeX code.
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2021-09-22 01:37:49
|
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http://languagelog.ldc.upenn.edu/nll/?cat=27
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Joining a crowd of other recent fraudsters, Paul Roberts and Deborah Briton returned from their Spanish vacation and subsequently turned in a completely fake claim against the Thomas Cook package-vacation company, alleging that their time in Spain had been ruined by stomach complaints for which the hotel and the company should be held liable. They sought more than $25,000 in damages for the fictional malady. The judge sentenced them to jail. And in this report of the case my colleague Bob Ladd noticed that Sam Brown, the prosecuting attorney, showed himself to be so terrified of blundering into a singular they that he would not even risk using they with plural reference, preferring to utter a totally ungrammatical sentence: *Sam Brown, prosecuting, said: "Both defendants knew that in issuing this claim he or she would be lying in order to support it." Beware of struggling to obey prescriptive injunctions that don't come naturally to you; they can warp your ability to use your native language sensibly. Read the rest of this entry » Comments off ## Or the arbitrary cat, horse, or pig I think Mark Liberman may have been concerned that perhaps my post "Pronominal reference to the arbitrary dog" hinted at being tempted toward the Recency Illusion. Not true, of course: even when surprised by some point of usage that I notice, I never conclude I must therefore be the first to have encountered it. On encountering the use of singular they for a dog, I didn't say "This has never happened before"; I said "we should expect this sort of use to increase in frequency." But anyway, just in case, Mark sent me some other cases of animals being referred to with singular they. They presumably indicate that where sex is irrelevant, the use of it should nonetheless be avoided, because it might offend the animal. https://www.bengalcats.co/why-do-cats-knead/ You see, the repetitive movement is not only serving as a way to promote milk flow, it also encourages maternal instinct and establishes a bond between a cat and their kittens. http://www.ancientegyptonline.co.uk/cat.html When a cat died, their human family would go into a deep mourning and shave their eyebrows. [By the way, notice that the foregoing example is ambiguous (cat's eyebrows vs. family members' eyebrows), and the ambiguity is caused solely by the refusal to use it for the arbitrary cat. People will risk being incomprehensible rather than change their mind about whether they could compromise on a pronoun gender choice. Or maybe the point is just that people do not avoid, and do not know to avoid, or even notice, dangers of ambiguity for the hearer or reader.] Read the rest of this entry » Comments off ## Pronominal reference to the arbitrary dog Following Bean's guest post about being scorned by an 8-year-old child for not using singular they when it was appropriate, Language Log now presents the first evidence (to my knowledge) of a newspaper abandoning the usual use of it to refer to animals, and instead using singular they for an unknown arbitrary animal. This is from an article in the Metro (a free UK daily) on what to do if you find someone's dog close to death because it has been locked in a car on a hot day; I boldface the pronouns of interest: Get the dog out of the car and move them to a shaded, or cooler area. Then, douse the dog with cool water and let them drink small amounts of it. Make sure the water is cool but not cold, to avoid shock. If the dog is not displaying signs of heatstroke, let them rest while you establish how long they were in the car, and make a note of the vehicle's registration. Read the rest of this entry » Comments off ## Schooled on singular "they" [This is a guest post by Bean] My eight-year-old daughter in conversation with me last night: Scene: I am giving her a sock, which she had brought home, only to find she already had both of her socks. So it logically must belong to some other girl (it's obviously a girl's sock). Me: So, bring this lost sock back to school, and put it in the lost and found. Do you remember who was wearing it? Well, anyway if the other girl is looking for it she can find it. I'm assuming it was a girl so I'm going with "she". Daughter [scornfully]: You mean "they". Read the rest of this entry » ## What a woman can't do with their body Mark Meckes noticed a tweet about an interview with Emma Watson, who was being discussed in this Language Log post, and mentioned it in a comment thereto. It was completely off topic (and thus violated the Language Log comments policy), but I felt it was too interesting to be left languishing down there in a comment on a post about preposition doubling, so I'm repeating it here, where it can have its own post: If you think @EmmaWatson is a hypocrite, maybe consider you shouldn't be telling a woman what they can and can't do with their own body. Two occurrences of singular they (they and their), with the phrase a woman as antecedent! Read the rest of this entry » Comments off ## The Daily Mail deluding themselves An amusing slip in the Daily Mail (online here), in an opinion piece by Dan Hodges on the decline of the Labour Party and its singularly unsuccessful leader Jeremy Corbyn. Hodges says that "anyone who thinks Labour's problems began on September 12, 2015, when Corbyn was elected, are deluding themselves." It's unquestionably a grammatical mistake, of course. Not about pronoun choice, but about verb agreement. Read the rest of this entry » Comments off ## The craven feminine pronoun The Times Literary Supplement diarist who hides behind the initials "J.C." makes this catty remark (issue of January 6, 2017, page 36) about Sidney E. Berger's The Dictionary of the Book: A Glossary of Book Collectors: "Predictions were that the Internet would do away with dealers' catalogs and it is true that many a dealer has gone from issuing catalogs to listing her whole stock online." Bookselling and book collecting are among the world's stubbornly male pastimes — deplorable, no doubt, but less so than the use of the craven pronoun throughout The Dictionary of the Book (Rowman & Littlefield,$125).
J.C. (who, Jonathan Ginzburg informs me, is widely known to be an author, book dealer, and bibliophile named James Campbell) is objecting to the use of she as a gender-neutral pronoun. And you can just guess that a snooty writer in TLS who quibbles about other people's grammar choices would hate singular they. J.C. would probably regard it as "abominable", the way Simon Heffer does. Which can only mean that he advocates use of the traditional practice of he as the gender-neutral 3rd-person singular pronoun, the one that The Cambridge Grammar of the English Language (CGEL) calls "purportedly sex-neutral he (see pp. 491–493).
Read the rest of this entry »
## Choosing their pronouns for oneself
The following sentence can be found (as of 15 September 2016) in this Wikipedia article about the effects of rape on the victim:
Sometimes in an effort to shield oneself from believing such a thing could happen to their loved one, a supporter will make excuses for why the event occurred.
The clash in pronoun choice (the switch from one to their) makes this clearly anomalous. What exactly could have led to its being written? I think at least two unease-promoting factors are involved.
Read the rest of this entry »
## Annals of singular 'they': another case with known sex
Karen Thomson, a Sanskritist and antiquarian bookseller living in Oxford, wrote to me to point out the following very significant example of singular they in a Financial Times interview with TV writer and director Jill Soloway:
People will recognise that just because somebody is masculine, it doesn't mean they have a penis. Just because somebody's feminine, it doesn't mean they have a vagina. That's going to be the evolution over the next five years.
You see what makes this not just a dramatic claim in terms of sexual politics but a linguistically very revealing example?
Read the rest of this entry »
## Typical options like “he� and “she�
Collin Binkley, "He? She? Ze? Colleges add gender-free pronouns, alter policy", AP 9/18/2015
Welcome to Harvard. Feel free to pick a pronoun on this form: __ He. __ She. __ Ze. __ E. __ They.
During the registration process at Harvard University, students are now allowed to indicate which pronouns they use, with suggested gender-neutral options like "ze" or "they." Harvard isn't the first college to embrace gender-neutral pronouns, but it's among a wave of major institutions that are widening their policies and pronouns to acknowledge transgender students, as well as "genderqueer" students, who don't identify as male or female.
Read the rest of this entry »
## The manuscript they would have written
Here's a very nice case of modern sex-neutral pronoun-choice style, with the unusual feature that the antecedent for the two occurrences of singular they (which prescriptivsts hate so much) is not only a definite noun phrase, but a definite noun phrase denoting a unique individual. The sentence comes from a Buzzfeed listicle drawn from "Shit Academics Say" (@AcademicsSay) on Twitter. I underline the antecedent and the two pronouns:
We wish to thank Reviewer 2 for their critical feedback & sincerely apologize for not having written the manuscript they would have written.
Read the rest of this entry »
## I met someone and they make me happy
When the delightfully cute UK Olympic diving star Tom Daley decided to come out as bisexual, he made a statement (see this news report) with a charmingly clever use of singular they:
"In spring this year my life changed massively when I met someone, and they make me feel so happy, so safe and everything just feels great," Daley said. "That someone is a guy."
His use of "they" for the first reference to his new romantic interest has "someone" as its antecedent, and rather than being a bound variable semantically (as in Everyone should look after their own gear), it's just a free pronoun meaning "he or she, as the context may dictate". He could have used he, as typical conservative usage advice books would have insisted. Except that it would have utterly ruined his rhetorical design.
Read the rest of this entry »
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2017-11-23 03:42:54
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https://homework.zookal.com/questions-and-answers/please-answer-asapppp-pleaseeee-a-firm-has-issued-15-million-923118311
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2. Finance
###### Question details
A firm has issued $15 million bonds that pay a 4.5% annual coupon and the yield to maturity is 5%. The market price of the bonds is$12.5 million.
There are 3 million preference shares outstanding, which have a book value of $2.5 per share and which are trading for$3.00$per share. The preference shares pay an annual dividend of$0.42 per share.
There are 5 million ordinary shares outstanding, which have a book value of $1.95 per share and which are currently priced at$2.40 per share. The firm’s ordinary shares have a beta of 0.80. The yield on long‐term government bonds is 2.5% p.a. The expected market return is 8% p.a.
The corporate tax rate is 35%.
a) What is the market value of preference shares? (2 marks)
b) What is the cost of preference shares? (2 marks)
c) What is the market value of ordinary shares? (2 marks)
d) What is the cost of ordinary shares? (2 marks)
e) What is the firm’s weighted average cost of capital (WACC)? (4 marks)
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2021-03-02 18:09:18
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http://learnche.mcmaster.ca/3P4/Assignment_4_-_2014
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# Assignment 4 - 2014
Due date(s): 28 February 2014, in class (PDF) Assignment questions (PDF) Assignment solutions
Assignment objectives: using MATLAB to simulate and test control systems; self-learning new concepts from the simulation.
Question 1 [15]
1. What is the following MATLAB/Simulink simulation a representation of?
2. Attach a copy of the Scope output for a step input of unit magnitude, occurring at a time of 2 units into the simulation. Your simulation should run until the process reaches steady state.
3. What is the final value of the Scope output variable when simulated until it reaches steady state?
Demonstrate/show/prove theoretically (i.e. without using Simulink) that this value is correct.
4. Add a time delay to the process of 2 units (as shown below) and resimulate the response to a point in time so that it reaches steady state.
Show the Scope output and describe what you notice.
Explain why it takes longer to reach steady state as compared to your answer in part 1.
5. Next, simulate the process with a time delay
1. of 5 units and
2. of 10 units.
Attach the Scope output for these simulations, and explain why you observe the behaviour noticed.
6. In general, what do you conclude about time delays in a process?
Solution
1. The MATLAB/Simulink simulation is a representation of a closed-loop feedback control system with proportional control only of a first-order process. It consists of a set-point, controller, a transfer function representing the first-order process, and the output (controlled variable).
3. The final value of the output variable when simulated until it reaches steady state is 0.6 units. The overall transfer function for the system is:
$\begin{split}G(s) &= \dfrac{CV(s)}{SP(s)} \\ G(s) &= \dfrac{G_c G_p}{1 + G_c G_p} \\ G(s) &= \dfrac{(0.5) \dfrac{3}{2.5s+1}}{1 + (0.5) \dfrac{3}{2.5s+1}} \\ CV(s) &= \dfrac{(0.5) \dfrac{3}{2.5s+1}}{1 + (0.5) \dfrac{3}{2.5s+1}} \cdot {SP(s)} \\ CV(s) &= \dfrac{(0.5) \dfrac{3}{2.5s+1}}{1 + (0.5) \dfrac{3}{2.5s+1}} \cdot \dfrac{e^{-2s}}{s}\end{split}$
The above uses that the step input of unit magnitude occurs at a time of 2 units into the simulation (however you can use any time for the step to occur). Then, applying the Final Value Theorem (FVT):
$\begin{split}\lim_{t \to \infty} CV(t) &= \lim_{s \to 0} s CV(s) \\ &= \lim_{s \to 0} s \dfrac{(0.5) \dfrac{3}{2.5s+1}}{1 + (0.5) \dfrac{3}{2.5s+1}} \cdot \dfrac{e^{-2s}}{s} \\ &= \lim_{s \to 0} \dfrac{(0.5)(3)}{2.5s+1 + (0.5)(3)} \cdot e^{-2s} \\ &= 0.6\end{split}$
Note that the delay in the step input does not affect the final value.
4. The time delay simply reduces the ability of the system to react. See the graph below: at time $$t=2$$ we make the set point change of 1 unit. So immediately the error is 1 unit (blue curve). The controller takes action (yellow curve is half the values of the blue curve), but because of the time delay in the process the controller sees the error is still 1 unit. So the controller keeps supplying this 1 unit increase to the process (which was more input than was required).
After an additional 2 units of time (now we are $$t=4$$), the system starts to react (purple curve). As CV approaches the set point, the error starts to get smaller, and so the MV also decreases (around $$t=7$$). This reduction is later reflected in the purple CV, so it decreases. There is a bit of oscillation while it settles down.
5. If the time delay is increased to 5 units of time we observe stronger oscillations, because now there is a longer delay of 5 units (it oscillates for the reason described in the prior part). Unfortunately now the controller has to counteract that oscillation, so it starts to close the valve. Again the 2 units of delay take a while to take an effect on the process, so the controller repeats the same issue, just in the opposite direction. This leads to the oscillation you observed in the output here.
The above is with 5 units of delay.
Once the delay exceeds some critical value we actually have made the system unstable. The controller input to the process is so strong (as it waits and waits for the system to react), that it is has changed the valve position too much. When it tries to undo the previous input, it overcompensates yet again. The amount of overcompensation is so great it destabilizes the entire system, as shown below.
6. In general, time delays in process can reduce the stability of a closed-loop system and make it more challenging for the controller to bring the output to the steady state. Therefore, the controller may take longer to stabilize the process or system may even become unstable. When designing control systems for processes, time delays should be taken into account to achieve desired controller performance.
In fact, any control engineering will focus on how to reduce the delay by as much as possible. Delays always prevent us from taking good control action; we say "time delays are a limitation for good process performance". There is no controller that can counteract a delay (because you cannot counteract something you don't know about).
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2017-10-24 01:53:23
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http://en.wikipedia.org/wiki/Gaussian_isoperimetric_inequality
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# Gaussian isoperimetric inequality
In mathematics, the Gaussian isoperimetric inequality, proved by Boris Tsirelson and Vladimir Sudakov and independently by Christer Borell, states that among all sets of given Gaussian measure in the n-dimensional Euclidean space, half-spaces have the minimal Gaussian boundary measure.
## Mathematical formulation
Let $\scriptstyle A$ be a measurable subset of $\scriptstyle\mathbf{R}^n$ endowed with the Gaussian measure γ n. Denote by
$A_\varepsilon = \left\{ x \in \mathbf{R}^n \, | \, \text{dist}(x, A) \leq \varepsilon \right\}$
the ε-extension of A. Then the Gaussian isoperimetric inequality states that
$\liminf_{\varepsilon \to +0} \varepsilon^{-1} \left\{ \gamma^n (A_\varepsilon) - \gamma^n(A) \right\} \geq \varphi(\Phi^{-1}(\gamma^n(A))),$
where
$\varphi(t) = \frac{\exp(-t^2/2)}{\sqrt{2\pi}}\quad{\rm and}\quad\Phi(t) = \int_{-\infty}^t \varphi(s)\, ds.$
## Remarks on the proofs
The original proofs by Sudakov, Tsirelson and Borell were based on Paul Lévy's spherical isoperimetric inequality. Another approach is due to Bobkov, who introduced a functional inequality generalizing the Gaussian isoperimetric inequality and derived it from a certain two-point inequality. Bakry and Ledoux gave another proof of Bobkov's functional inequality based on the semigroup techniques which works in a much more abstract setting. Later Barthe and Maurey gave yet another proof using the Brownian motion.
The Gaussian isoperimetric inequality also follows from Ehrhard's inequality (cf. Latała, Borell).
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2015-01-30 06:37:32
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https://www.physicsforums.com/threads/uncertainty-principle-cause-infinite-wavefunction-solutions.800880/
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# Uncertainty Principle cause infinite wavefunction solutions?
1. Mar 2, 2015
### a dull boy
Dear Physics Forum,
Is the Uncertainty Principle the cause of the infinite solutions to Schrodinger's equation? I get the sense it is not. Could you elaborate a little?
Thanks, Mark
2. Mar 2, 2015
### Staff: Mentor
No, completely unrelated.
But maybe first you should think about why you would expect anything other than multiple solutions to Schrodinger's equation. Does it surprise you that classical mechanics says that more than one pattern of waves on the surface of the ocean is possible, and that this pattern can change over time as the waves move, hit land, are disturbed by passing ships? Every one of these patterns, at any moment and over the surface of the entire earth, is a different solution to the classical equation that describes the movement of water.
The movement of a particle is described by Schrodinger's equation. Particles can move in different directions at different speeds, so you'd expect to find multiple solutions to Schrodinger's equation.
Last edited: Mar 2, 2015
3. Mar 2, 2015
### a dull boy
...I think part of my confusion has to do with Einstein's comment that God does not play dice. I can see two source of this comment, the Uncertainty Principle and the infinite wavefunction solutions. For the latter, I thought there was only a single wavefunction solution for each principle quantum number n. But I am pretty sure I am wrong, and psi squared gives you the probability of the particle being at the Bohr radius for a particular energy level. For a given energy level, why is it only probable the electron is at the Bohr radius? I thought perhaps the Uncertainty Principle, but I'm wrong.
Thanks for your help Nugatory
4. Mar 2, 2015
### a dull boy
One more followup, I was speaking about stationary states, and my sense was that you got infinite solutions for a single particle speed/momentum...
5. Mar 2, 2015
### Staff: Mentor
(Actually there are multiple solutions for each principal quantum number, with different values of angular momentum and spin (represented by the m, l, and s numbers); this is just a property of the particular forces acting on the electron in this particular situation. However, that's beside the point here; the multiple solutions for the same n aren't the source of the randomness to which Einstein objected.)
The probabilistic nature of quantum mechanics comes from the fact that if $\psi_1$ and $\psi_2$ are solutions to the Schrodinger equation, so is any linear combination of them. For example, if $\psi_1$ is a the solution corresponding to a 100% chance of finding the electron spin up and $\psi_2$ is the solution for a 100% of chance of finding the electron spin down, then $\frac{\sqrt{2}}{2}(\psi_1+\psi_2)$ is also a perfect good solution of Schrodinger's equation; in fact it's the solution in which we have a 50/50 chance of finding the spin up or down. (Don't be misled by the way that the third solution looks more complicated and less "fundamental" then the first too. That's just an accident of the way that I wrote them - all three look like some flavor of $\psi_3\pm\psi_4$ where $\psi_3$ and $\psi_4$ are solutions with 100% probability of finding the spin aligned oin one direction or the other along something other than the vertical or horizontal axes).
It's that probabilistic answer from a single clearly defined and unambiguous wave function that disturbed Einstein (and many other physicists of the era - Einstein was just especially good at articulating the problem). The uncertainty principle comes from a related different source: Those solutions for which the momentum is definite can only be written as a sum of solutions in which the position is definite, and vice versa. Thus, if we set the system up so that there is no uncertainty in the momentum more than one position value has to be possible. The uncertainty principle tells us what the spread in possible position values must be.
It's the same thing as above. The states in which the energy is definite are sums of states in which the position has different values, so there some randomness in what number will actually come out of a position measurement. You could say that this is caused by the uncertainty principle, but it's better to think of it and the uncertainty principle as both being caused by the way that solutions to the Schrodinger equation are always sums of other solutions.
6. Mar 2, 2015
### a dull boy
Yes! Thanks so much, I get it!
Best, Mark
7. Mar 4, 2015
### a dull boy
Please allow me one more follow-up - trying to discern superposition from the uncertainty principle. I understand I can't measure position and momentum simultaneously because they are conjugate variables. But what about spin and position, or spin and momentum? I bet you can't simultaneously measure those on a single particle with accuracy, yet I'm not sure why - they should be unrelated.
Best, Mark
8. Mar 4, 2015
### bhobba
The uncertainty relations are actually a theorem about non-commuting observables:
http://physics.stackexchange.com/questions/10362/how-does-non-commutativity-lead-to-uncertainty
If they commute then there is no uncertainty issue. Spin and position in the direction of the spin commute - momentum and position in the direction of the momentum do not.
As an aside why that is, is quite interesting:
http://physicspages.com/2013/01/15/angular-momentum-commutators-with-position-and-momentum/
Thanks
Bill
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2017-08-24 01:57:53
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http://codeforces.com/problemset/problem/592/A
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Please subscribe to the official Codeforces channel in Telegram via the link https://t.me/codeforces_official. ×
A. PawnChess
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output
Galois is one of the strongest chess players of Byteforces. He has even invented a new variant of chess, which he named «PawnChess».
This new game is played on a board consisting of 8 rows and 8 columns. At the beginning of every game some black and white pawns are placed on the board. The number of black pawns placed is not necessarily equal to the number of white pawns placed.
Lets enumerate rows and columns with integers from 1 to 8. Rows are numbered from top to bottom, while columns are numbered from left to right. Now we denote as (r, c) the cell located at the row r and at the column c.
There are always two players A and B playing the game. Player A plays with white pawns, while player B plays with black ones. The goal of player A is to put any of his pawns to the row 1, while player B tries to put any of his pawns to the row 8. As soon as any of the players completes his goal the game finishes immediately and the succeeded player is declared a winner.
Player A moves first and then they alternate turns. On his move player A must choose exactly one white pawn and move it one step upward and player B (at his turn) must choose exactly one black pawn and move it one step down. Any move is possible only if the targeted cell is empty. It's guaranteed that for any scenario of the game there will always be at least one move available for any of the players.
Moving upward means that the pawn located in (r, c) will go to the cell (r - 1, c), while moving down means the pawn located in (r, c) will go to the cell (r + 1, c). Again, the corresponding cell must be empty, i.e. not occupied by any other pawn of any color.
Given the initial disposition of the board, determine who wins the game if both players play optimally. Note that there will always be a winner due to the restriction that for any game scenario both players will have some moves available.
Input
The input consists of the board description given in eight lines, each line contains eight characters. Character 'B' is used to denote a black pawn, and character 'W' represents a white pawn. Empty cell is marked with '.'.
It's guaranteed that there will not be white pawns on the first row neither black pawns on the last row.
Output
Print 'A' if player A wins the game on the given board, and 'B' if player B will claim the victory. Again, it's guaranteed that there will always be a winner on the given board.
Examples
Input
.................B....B.....W.............W.....................
Output
A
Input
..B.......W...........B..............W........B.................
Output
B
Note
In the first sample player A is able to complete his goal in 3 steps by always moving a pawn initially located at (4, 5). Player B needs at least 5 steps for any of his pawns to reach the row 8. Hence, player A will be the winner.
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2021-09-21 00:31:06
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https://chemistry.stackexchange.com/questions/19900/find-the-valences-of-z-26
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# Find the valences of Z=26
I've tried this:
But its hows that the valence of Fe in normal state is 4, when in the periodic table it isn't. Why does this happen? Can you show me the answer with configuration formula in the states with energy?
• You have the electron configuration of iron in your post. Just writing that out is only the first step. What have you done with it to attempt to figure out valences? – Ben Norris Nov 23 '14 at 11:54
## 1 Answer
Hint: $$_{26}Fe\equiv1s^22s^22p^63s^23p^64s^23d^6\equiv [Ar]\ce{\underbrace{ ^ v }_{4s^2} \underbrace{ ^ v ,\;^ ,\;^ ,\;^ ,\;^ }_{3d^6} }$$ Think now what will be the configuration after losing electrons:
Spoiler:
! $$Fe^{2+}\to[Ar]\ce{\underbrace{ - }_{4s^2} \underbrace{ ^ v ,\;^ ,\;^ ,\;^ ,\;^ }_{3d^6}=[Ar]\underbrace{ ^ }_{4s^2} \underbrace{ ^ ,\;^ ,\;^ ,\;^ ,\;^ }_{3d^6} }$$
! $$Fe^{3+}\to[Ar]\ce{\underbrace{ - }_{4s^2} \underbrace{ ^ ,\;^ ,\;^ ,\;^ ,\;^ }_{3d^6} }$$
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2021-01-16 22:08:50
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http://hiro.readthedocs.io/en/latest/
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Hiro - time manipulation utilities for python¶
Often testing code that can be time dependent can become either fragile or slow. Hiro provides context managers and utilities to either freeze, accelerate or decelerate and jump between different points in time. Functions exposed by the standard library’s time, datetime and date modules are patched within the the contexts exposed.
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2017-12-17 11:34:25
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https://www.usgs.gov/center-news/volcano-watch-whats-happening-mauna-loa
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# Volcano Watch — What's happening at Mauna Loa?
Release Date:
Mauna Loa has gone 18.5 years without eruption--the second longest dry spell since detailed records begin in 1843. The longest period without eruption lasted 25 years, between 1950 and 1975. Clearly the past 52 years have been much less active than the previous 107.
Following its latest eruption, in March-April 1984, the volcano continued to inflate, quickly at first but then more slowly. By the early 1990s, the level of inflation had nearly reached that before 1984. This alone is an unreliable measure of the readiness for any volcano to erupt, because volcanoes change internally over time so that the basis of comparison also changes. The continued inflation, however, did make people wonder if the next eruption was to be sooner rather than later.
By 1994, however, the inflation had ceased, and the summit actually began to deflate. The rate of deflation was small but steady, continuing right up to May of this year. The pattern of slow deflation changed rather abruptly in mid-May. In fact, our best estimate is that the pattern changed on Mother's Day, the same day that Kilauea's currently active lava flow started.
Since then, the summit area of Mauna Loa has been slowly swelling and stretching. Distances across the summit caldera are lengthening at a rate of 5-6 cm (2-2.5 inches) per year. That means that, as of today, the caldera has widened about 2 cm (0.8 inches) since May 12. This is small stuff, indeed, but it does mark a noticeable, perhaps notable, change from the pattern of the preceding 9 years. The GPS measurements also show that the summit area is getting slightly higher, consistent with swelling.
These measurements are made with sophisticated GPS equipment that uses satellite orbits and signals to locate receivers on earth. This is acknowledged as the best means to track small changes in shape of the earth's surface. Could there be some error in this complicated method that we are overlooking, something that happened with the satellite orbits, for example?
To test that possibility, we have used a completely independent means to measure ground deformation-an old-fashioned, unsophisticated, non-electronic way to measure ground tilt. This method--called dry tilt in Hawaii and tilt-leveling, spirit-level tilt, or single-setup leveling elsewhere-uses standard surveying techniques to measure elevations of bench marks in a small area. If the elevations change from one survey to the next, the ground has tilted.
To make a long story short, the dry tilt measurements at the summit of Mauna Loa confirm the GPS results, though with less precision. The summit area is indeed swelling, slowly but measurably.
We then extended the measurement of existing GPS stations farther out on the flanks of the volcano to see if those parts of the volcano are also moving. The measurements show that the swelling is affecting more of the volcano than just the summit. In particular, the upper part of the southeast flank is showing outward movement.
You might think that this slow, slight swelling would be accompanied by increased seismicity. Well, that is not the case. Rocks bend before they break. That is an oversimplified way to say that slow swelling will likely not be accompanied by an increase in number or size of earthquakes.
Before the latest two eruptions, there were large increases in both numbers of earthquakes and the amount of energy released by these earthquakes. Though we must be cautious in saying that such an increase will definitely precede the next eruption, that is a reasonable expectation. On that basis alone, we see no reason to say that an eruption will take place any time soon-that is, in the next few weeks.
The small changes indicated by GPS measurements could have gone unseen in the past, when the instrumentation was less precise and the data were acquired infrequently rather than daily. There could have been several such spurts of swelling that we were unable to measure long before the 1975 and 1984 eruptions. And, such spurts may even be routine.
The overall story is a bit muddy because of what has happened since the 1984 eruption. The changed pattern--from swelling for the first 9 years to slight deflation for the next 9 years to very slight inflation now--is more difficult to interpret than one steady inflation.
With the help of Stanford University, HVO has already added one new GPS station on Mauna Loa and plans to install more GPS and electronic borehole tilt stations in the next few months. The seismic coverage is good and able to detect any increase in seismicity that might take place. We will report any significant changes as they take place via both the media and our web site (hvo.wr.usgs.gov); updates will be on the web site by the time you read this article.
### Volcano Activity Update
Eruptive activity of Kilauea Volcano continued unabated at the Puu Oo vent during the past week. Molten lava is flowing near the end of the Chain of Craters road, and the National Park Service is allowing visitors to get up close to the action where it is safe. The new ocean entry at Middle Highcastle between the older West Highcastle and Highcastle entries has developed a delta that measures 570 m (1,870 ft) along the coastline and extends 50 m (165 ft) beyond the old shoreline. We have received a disturbing report from a late night viewer of stupid people going beyond the boundary of the safe viewing area and on to the unstable bench of the active Wilipe`a ocean entry. Shortly after leaving the bench, the area collapsed into the sea!
No earthquakes were reported felt during the week ending on September 26.
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2020-07-12 03:11:57
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https://www.vedantu.com/formula/dimesional-formula-of-kinematics-viscosity
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# Dimesional Formula of Kinematics Viscosity
View Notes
## Dimensions
Dimensions of the physical quantity are the power to which the base quantities are raised to represent that quantity. Dimensions of any given quantity tell us about how and which way different physical quantities are related. Finding dimensions of different physical quantities has many real-life applications and is helpful in finding units and measurements. Imagine a physical quantity X which depends mainly on base mass(m), length(L), and time(T) with their respective powers, then we can represent dimensional formula as [MaLbTc]
### Dimensional Formula
The dimensional formula of any physical quantity is that expression which represents how and which of the base quantities are included in that quantity.
It is written by enclosing the symbols for base quantities with appropriate power in square brackets i.e ( ).
E.g: Dimension formula of mass is: (M)
### Dimensional Equation
The equation obtained by equating a physical quantity with its dimensional formula is called a dimensional equation.
### Application of Dimensional Analysis
1. To convert a physical quantity from one system of the unit to the other:
It is based on a fact that magnitude of a physical quantity remain same whatever system is used for measurement i.e magnitude = numeric value(n) multiplied by unit (u) = constant
n1u1= n1u2
2. To check dimensional correctness of a given physical relation:
If in a given relation, the terms of both sides have the same dimensions, then the equation is dimensionally correct. This concept is best known as the principle of homogeneity of dimensions.
3. To derive a relationship between different physical quantities:
Using the principle of homogeneity of dimension, the new relation among physical quantities can be derived if the dependent quantities are known.
### Limitation of this Method
• This method can be used only if dependency is of multiplication type. The formula containing exponential, trigonometric, and logarithmic functions can not be derived using this method. The formula containing more than one term, which is added or subtracted likes s = ut+ ½ at2 also cannot be derived.
• The relation derived from this method gives no information about the dimensionless constants.
### Kinematic Viscosity
Viscosity: Viscosity is the property of the fluid ( liquid or gas ) by virtue of which it opposes the relative motion between its adjacent layers. It is the fluid friction or internal friction. The internal tangential force which tries to retard the relative motion between the layers is called viscous force.
Properties of Viscosity:
• It opposes motion.
• It acts tangentially in a direction opposite to that of motion.
• It comes into play when the two layers of a liquid are in relative motion.
### Dependence of Viscosity Fluids
On the temperature of fluid:
• Since cohesive force decreases with an increase in temperature. Therefore with the rise in temperature the viscosity of liquid decreases.
• The viscosity of gases results from the diffusion of gas molecules from one moving layer to another moving layer. Now with an increase in temperature the rate of diffusion increases. So, the viscosity also increases. Thus the viscosity of gases increases with the rise of temperature.
On the pressure of fluid:
• The viscosity of liquids increases with an increase in pressure.
• The viscosity of gas increases is practically independent of pressure.
### Dimensional Formula of Kinematic Viscosity
The dimensional formula of Kinematic Viscosity is written as M0 L2 T-1
Where M represents mass, L represents length and T represents time.
### Derivation of the Dimensional Formula of Chemical Kinematic
The chemical formula can be formulaically written as:
Kinematic viscosity (ν) = Dynamic viscosity × [Density]-1. . . . (1)
As, Density = Mass × [Volume]-1
⇒ ρ(density) = [M1 L0 T0] × [M0 L3 T0]-1
∴ The dimensional formula of density = [M1 L-3 T0] . . . . (2)
As, Dynamic viscosity (η) = Tangential Force × distance between layers × [Area × velocity]-1. . . .(3)
Now, Tangential Force = M × a = M × [L T-2]
∴ The dimension of force = M1 L1 T-2 . . . . (4)
And, the dimensional formula of the area and velocity = L2 and L1 T-1 . . . . (5)
On substituting equation (4) and (5) in equation (3) we get,
Dynamic viscosity (η) = [M L T-2] × [L] × [L2]-1 × [L1 T-1]-1 = [M1 L-1 T-1].
Therefore, the dimensions of dynamic viscosity = [M1 L-1 T-1] . . . .(6)
On putting equation (2) and (6) in equation (1) we get,
Kinematic viscosity (ν) = Dynamic viscosity × [Density]-1
Or, ν = [M1 L-1 T-1] × [M1 L-3 T0]-1 = [M0 L2 T-1].
Therefore, the Kinematic viscosity is dimensionally represented as [M0 L2 T-1].
1. Explain the Properties on Which Viscosity Depends?
On the temperature of fluid:
• Since cohesive force decreases with an increase in temperature. Therefore with the rise in temperature the viscosity of liquid decreases.
• The viscosity of gases is the result of the diffusion of gas molecules from one moving layer to another moving layer. Now with an increase in temperature the rate of diffusion increases. So, the viscosity also increases. Thus the viscosity of gases increases with the rise of temperature.
On the pressure of fluid:
• The viscosity of liquids increases with an increase in pressure.
• The viscosity of gas increases is practically independent of pressure.
2. Write a Few Limitations of Dimensional Formula?
• This method can be used only if dependency is of multiplication type. The formula containing exponential, trigonometric, and logarithmic functions can not be derived using this method. The formula containing more than one term which is added or subtracted likes s = ut+ ½ at2 also cannot be derived.
• The relation derived from this method gives no information about the dimensionless constants.
3. Write a Few Properties of Viscosity?
Few properties of viscosity are discussed below:
1. It opposes motion.
2. It acts tangentially in a direction opposite to that of motion.
3. It comes into play when the two layers of a liquid are in relative motion.
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2021-01-15 14:55:29
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https://www.additudemag.com/forums/reply/197088/
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# Reply To: I have symptoms, but I was a high achiever
Home Welcome to the ADDitude Forums For Adults Symptoms, Diagnosis & Beyond I have symptoms, but I was a high achiever Reply To: I have symptoms, but I was a high achiever
#197088
lanusp
Participant
Thank you so much for your answers! Whatever the root of my difficulties is, you made me feel less alone.
I really needed some clarification about the high achieving thing. I will not try to force an undue diagnosis in myself, if that is the case; but I’ll make sure that, in case ADHD gets excluded, it is for a solid reason.
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2021-05-05 22:06:56
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http://derekogle.com/NCGraphing/modules/Student_Projects/Wittmann_FinalProject.html
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# Packages and Data
setwd("C:/Users/Taylo/Desktop/GraphClassRScripts")
library(tidyverse)
gb <- read.csv("GreenBay.csv",stringsAsFactors=FALSE) %>%
select(STATION,DATE,DailyAverageDewPointTemperature,DailyAverageDryBulbTemperature,DailyAverageRelativeHumidity,DailyAverageSeaLevelPressure,DailyAverageWetBulbTemperature,DailyAverageWindSpeed,DailyDepartureFromNormalAverageTemperature,DailyMaximumDryBulbTemperature,DailyMinimumDryBulbTemperature,DailyPeakWindDirection,DailyPeakWindSpeed,DailyPrecipitation,DailySnowfall) %>%
rename(DewPoint=DailyAverageDewPointTemperature,AvgTemp=DailyAverageDryBulbTemperature,RH=DailyAverageRelativeHumidity,Pressure=DailyAverageSeaLevelPressure,WBTemp=DailyAverageWetBulbTemperature,WindSpeed=DailyAverageWindSpeed,TempAnom=DailyDepartureFromNormalAverageTemperature,MaxTemp=DailyMaximumDryBulbTemperature,MinTemp=DailyMinimumDryBulbTemperature,WindDirection=DailyPeakWindDirection,PeakWind=DailyPeakWindSpeed,Precip=DailyPrecipitation,Snowfall=DailySnowfall) %>%
filter(!is.na(DewPoint)) %>%
mutate(DATE=stringr::str_remove(DATE,"T.*\$"),
DATE=as.Date(DATE,format="%Y-%m-%d"),
year=lubridate::year(DATE),
mon=lubridate::month(DATE,label=TRUE),
mon2=forcats::fct_rev(mon),season=case_when(
mon %in% c("Dec","Jan","Feb") ~ "Winter",mon %in% c("Mar","Apr","May") ~ "Spring", mon %in% c("Jun","Jul","Aug") ~ "Summer",mon %in% c("Sep","Oct","Nov") ~ "Fall"),season=factor(season,levels=c("Spring","Summer","Fall","Winter")))
gb2 <- gb %>%
group_by(mon2) %>%
mutate(med.avg.temp=median(AvgTemp))
str(gb)
head(gb)
# Daily Max Temperatures by Month
The following graph comes from a set of weather data for Green Bay, Wisconsin from the year 2010 through the end of 2019 (A ten year data set). It was obtained from the National Oceanic and Atmospheric Administration (NOAA). The data includes daily recordings of variables such as temperature, precipitation, etc. The goal of this graph was to illustrate not only expected monthly temperature trends, but also the spread of the data each month.
p <- ggplot(data=gb2,mapping=aes(x=MaxTemp,y=mon2)) +
geom_boxplot(aes(fill=med.avg.temp),alpha=.8) +
stat_summary(fun=mean,geom="point",color="#F0E442",fill="#F0E442",size=1,shape=21) +
scale_x_continuous(breaks=seq(-10,120,10),name="Temperature (°F)") +
theme_bw() +
theme(panel.grid.minor=element_blank(),legend.position="none") +
labs(title="Daily High Temperatures for Green Bay, Wisconsin",
subtitle="2010-2019, grouped by month",
caption="Source: https://www.ncdc.noaa.gov/",
y=element_blank()) +
theme(panel.grid.major=element_line(linetype="dashed"),
plot.title=element_text(face="bold",size=14),
axis.title=element_text(face="bold",size=12),
axis.text=element_text(size=11))
p
The graph above clearly shows the relationship between month and daily high temperature for Green Bay, Wisconsin over the last ten years. July has the higher temperatures, whle January has the lowest. Furthermore, one can see that a month like March has a great amount of spread, most likely resulting from the fact that spring in Wisconsin can vary quite a bit weather-wise from year to year. The spread decreases as summer occurs and then spreads again in the fall for similar reasons to that of spring. March also has the most outliers, again a probable result of it varying a lot from year to year. December also has a few outliers on its lower end. This could be a result of some cold snaps that can occur in the winter where temperatures fall way below average. It should be noted that these temperatures are dry bulb temperatures, meaning there is no influence for a heat index or wind chill.
The graph is constructed using boxplots. I felt that boxplots were a good choice, because they are easy to read and compare in large numbers; there are 12 months to view at once. I personally like the boxplots to go from top to bottom as a visual, compared to the months going along the x-axis. I also colored the boxplots according to the temperature they represent. This made it easy to see at a glance that July had the warmest temperatures while Janurary had the coldest.
# Wind Speeds by Season
The following graph comes from a set of weather data for Green Bay, Wisconsin from the year 2010 through the end of 2019 (A ten year data set). It was obtained from the National Oceanic and Atmospheric Administration (NOAA). The data includes daily recordings of variables such as temperature, precipitation, etc. When constructing this graphic, I was interested in knowing if it tended to be windier in the winter season compared to that of summer. Meteorologically, winter should be windier than summer.
library(plyr)
library(dplyr)
cdat <- ddply(gb2, "season", summarise, rating.mean=mean(WindSpeed,na.rm=TRUE))
clrs<-c("#009E73","#F0E442","#D55E00","#0072B2")
p2 <- ggplot(data=gb2,mapping=aes(x=WindSpeed)) +
geom_histogram(mapping=aes(fill=season),binwidth=1,color="black",alpha=.7) +
geom_vline(data=cdat,
aes(xintercept=rating.mean),
linetype="dashed",
size=1,
colour="black") +
scale_x_continuous(name="Wind Speed (mph)",
limits=c(0,25),
breaks=seq(0,25,5),
expand=expansion(mult=c(0,NA))) +
scale_y_continuous(name="Number of Days",
expand=expansion(mult=c(0,.05)),
breaks=seq(0,120,30)) +
facet_grid(row=vars(season)) +
theme_bw() +
scale_fill_manual(values=clrs)+
theme(legend.position="none") +
theme(strip.background=element_rect(fill="gray70"),
panel.spacing=unit(0,unit="mm"),
panel.grid.major=element_line(linetype="dashed"),
panel.grid.minor=element_blank(),
plot.title=element_text(face="bold",size=14),
axis.title=element_text(face="bold",size=12),
axis.text.x=element_text(size=11)) +
labs(title="Average Daily Wind Speed for Green Bay, Wisconsin",
subtitle="2010-2019",
caption="*Seasons follow the meterological definition by month.
Source: https://www.ncdc.noaa.gov/")
p2
The graph above illistates the relationship between the wind speed according to season. It is a histogram, meaning the y-axis depicts frequency. In this case, it is the number of days that experienced certain wind speeds. For an easier time of analysis, I included a line showing the place of the mean for each season. Using this mean line, one can see that winter tends to be windier than summer. However, you can also see that winter has a mean very close to that of spring. One can also see that summer tends to have less variability in wind while winter has the greatest variation.
I chose a histogram for a couple reasons. The first is that I think it was a good way to display my data as the main focus was to see which season had the windiest days. The other reason was to avoid year being a factor. Because winter is December, January, and February, it includes multiple years. Using a histrogram avoids this issue. I colored each graph with respect to the season and used colors off of the color blind friendly color palette. I also divided the histogram by every one mph. This created a nice, representitive spread for analysis compared to other binwidths tried. I also added a mean line because it made a nice visual for quick analysis.
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2022-10-03 11:53:11
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https://code.tutsplus.com/courses/kotlin-fundamentals/lessons/string-templates-and-interpolation
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FREELessons: 20Length: 1.7 hours
• Overview
• Transcript
# 3.2 String Templates and Interpolation
In this lesson, I describe how to use string interpolation. I'll show you some examples to explain the concept.
## 5.Conclusion1 lesson, 01:17
### 3.2 String Templates and Interpolation
Hello, all. In this lesson, we will be learning about string templates and interpolation. This is one of the very beautiful features that Kotlin has provided us with. Here, I have already written a few codes. Let me explain, what is it? In the main function I have defined a variable element and assigned a value of square to it and it is of string type. Because we have initialized element here itself it gives us a warning. It says explicitly given type is redundant here, so we can remove this data type and assign the value directly to element variable. We have the class Geometry here, for which I have instantiated an object objGeometry. In the last lesson, we had studied about constructor. So here we have the constructor of the Geometry class, which accepts a parameter figure, which is again of the string type. So here, while instantiating the object of Geometry class, I have passed a variable of string type, I have passed element. And then with the help of the object of Geometry class, I have called the display function of Geometry class. Now let us run our code so as to ensure that everything is fine as of now. So here we have successfully run our code, it says element is square. Now let us jump into the main topic. How do we use the string template in Kotlin? So we have displayed element as figure. There I have used the traditional way of using the plus operator to contact and aid the strings. But here with Kotlin, we are to use the string interpolation. For string interpolation, what we need to do is prepend the dollar sign with the variable name, and here we have element is dollar figure. This is the variable and here the dollar operator. Let me change it to equal to and now let us run our code and see if all goes well. Shift F10, So here we have element is square. So we have successfully used string interpolation. What if we want to print the length of the element variable which has the string square? We will first see the register method of doing it, and then we will jump to string interpolation. I will comment this out. Now running it, We get length of the string is six. Since it has six characters we get the length of the string is six. Now let us use string interpolation to print this. Let's see what we get. Here we get length of the string is square.length. Why do we get this? We should get six, right? Yes, we need six. But what happens here is the variable element is taken for interpolation, but .length is treated as string. So to impose interpolation in the entire element.length, we need to put it inside the curly braces. And then prepend the $operator with this expression. Now let us run our code and see if we get the correct output. And yes, we have length of the string is six. Samely, if we want to perform some mathematical operations, let's say we need to find out the area of the square whose side is four. And now we need to find out the area of the square. So we write, We will write it this way. Side into side will be in the curly braces, so this entire thing is interpolated. Now let's run our code and see what happens. So here we have area of the square is 16. Now let us try something else. Let us find out the area of the square using the function in the geometry class. Let us change our class name to Square, so that it becomes a little more meaningful, since we need to find out the area of the square. Since the element is square, we will take its side as the parameter, which will be of integer type. We will remove the display function. I remove these two print statements. And here we have the element as squared, the side as four, and we have the object instantiated as the square class and passing the side variable as parameter to it. Let us create a function area which will written as the area of the square. Here in the area function we have a variable a, which is assigned to the area of the square, which is side into side. And then it returns the area of the square, which is of integer type. Therefore, we have the written type for area function as integer here. Now let us call this method from our main method. Here I have called the area function using the object of the class square, and I have assigned this value which is returned from the area function to area square. And then I'll have printed the area of the square. Now let us see what happens. We have successfully printed the area of the square as 16. How can we optimize it a little more? Instead of assigning the value of area to a variable, we can directly call this from our print statement itself. So instead of area square, we write this, and we will remove this line of code. So here we have area of the square is$objSquare.area. Let us see what happens now. This is what happens, objSquare is the object of the square class, hence we have Square here. This is some garbage value which Kotlin returns, and here .area is treated as a string. We have already seen this example with the length function. So what do we do here? We put this inside the curly braces. So let us now run our code and see what happens. Now we get the desired output. The area of the square is 16. This way we have called the area function in the print statement itself and carried out interpolation in it and printed the output. So these are the few examples how we can use the string template. If we have an expression or if we are using some function with the variable, we need to enclose it within the curly braces so that the interpolation takes place with the entire string. It makes our code look cleaner and more concise. That is all for this lesson. In the next lesson we will be learning about the ranges and the double dot operators in Kotlin. Till then, stay tuned, happy coding, and keep smiling.
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2022-08-14 21:55:46
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https://mariohellmich.de/projects/trl-cal/trl-cal.html
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# TRL Calibration
Besides the well known SOLT calibration method (or TOSM in Rohde & Schwarz terms) there are a number of other ways to achieve a full two-port calibration of a vector network analyzer (VNA). One of them is the thru-reflect-line calibration (TRL). As its name implies, TRL uses a through standard, a reflect standard, and one or more transmission lines of appropriate length for the intended frequency range to determine the error terms of the underlying error model, which is somewhat different than the model commonly used for TOSM (but can be mapped to the traditional and more comprehensive error model if some additional quantities, the switch terms, are known).
In TOSM, the match standard is instrumental for calibrating to system impedance. This role is played by the impedance of the line(s) in TRL. A salient feature of TRL is that neither the reflect and the thru, nor the loss of the line(s), need to be accurately known. Since highly precise coaxial airlines or waveguides with very well controlled impedance can be manufactured, TRL can achieve an enormous accuracy.
TRL has the drawback that since the phase shift of the line standard must be within certain limits, it only works over a limited frequency band, and it cannot be sensibly used with very low frequencies (but can be extended to low frequencies by other means). A further issue is that it needs a more complex VNA architecture than TOSM to fully determine the error parameters of the usual 12-term error model. To this end, some measurements must be performed in which both the incident and the scattered wave at a port are measured simultaneously while the other port is configured as a source. Obviously this requires a VNA with four receivers (a so-called dual reflectometer configuration). Therefore true TRL is not available on three receiver VNAs such as the venerable Hewlett-Packard HP 8753, and even less so on transmission-reflection VNAs such as HP 8752, and on virtually all ham radio or hobbyist kit.
Another advantage of TRL is that it lends itself very well to in-fixture calibrations. This is exactly what we shall explore here.
## The TRL board
The most simple way to manufacture a test fixture for components like SMD capacitors, inductors, ferrite beads, etc., is to realize it on an ordinary PCB that can be produced with one of the many inexpensive PCB pool services. This allows putting the necessary TRL calibration standards on the board as well. Certainly this does not yield the most accurate test fixture, in particular if the board is ordinary FR4 and one saves on an impedance controlled service, but it has the advantage that the components are tested in their natural environment.
The TRL board that I have designed can be seen in the above picture. It contains the following features for calibration, verification, and testing:
• A thru standard for TRL
• A 50 Ohms match standard
• A 25 Ohms mismatch standard for verification
• An open standard for verification
• A short standard, used as a reflect standard for TRL
• A line of 45 mm length, used as a line standard for TRL
• A series fixture for 0805 components
• A shunt fixture for 0805 components
The board is designed to be usable up to about 2 GHz (it fails to achieve that, see below). The transmission lines and calibration elements on the board are realized as grounded and fenced coplanar waveguides. I have not run a sophisticated 3D EM simulation of the board but instead designed it according to the usual approximation formulas for coplanar waveguides, which should be acceptable at the frequencies involved. The board is designed assuming the following parameters:
• Board thickness: 1.55 mm
• Permittivity: 4.5
• Loss tangent: 0.02
• Trace surface: Cu
The SMA launchers are Cinch model 142-0771-831. There are 12 of them, and at a price of about € 7.35 they essentially determine the cost of this amusement. Repeatability of the connectors is vital for precision, but for the limited accuracy requirements here these medium quality ones should be sufficient. The board has been manufactured by JLCPCB from Shenzhen with their standard prototype service. The design files, including Gerber files and Excellon drill files, which have been done with KiCad, can be downloaded here. The schematic for the board is available here as a pdf file.
The length of the thru is assumed zero by standard TRL calibration algorithms (unless no offset length is entered into the cal kit definition in the analyzer). This puts the two reference planes of the resulting calibration at the center of the thru line, thus reference planes are 15.5 mm inwards from each board edge. The reflect (i.e., short), open, match and mismatch standards, correspondingly, are also located 15.5 mm inwards from the board edge, and therefore have zero offset length with respect to the reference planes (notice that this not necessary for the reflect standard in TRL). The line is exactly 45 mm between the reference planes, i.e., its length is 76 mm in total. The test fixtures are placed such that the reference planes lie exactly at the outer edges of their SMD pads.
## Some TRL background
In the following I will briefly recall some background information on TRL calibration. I will not, however, give an exhaustive mathematical exposition on how the error terms are determined from measurements of the standards. For this refer to the literature, in particular Dunsmore's book [1] for a leisurely treatment, and the original paper by Engen and Hoer [2] (which is a bit outdated since it assumes a VNA with a dual six-port reflectometer design, which only uses power level measurements to determine the amplitudes and phases of the incident and scattered waves at its two test ports).
The natural error model that goes along with TRL is the 8-term error model. In this error model, a virtual transformation network is placed between the reference plane of the measurement and the physical port of the VNA; it accounts for the errors associated with each port. This virtual network is commonly known as an error box, and is described by its four S-parameters. For two ports one thus obtains eight error terms, of which in fact only seven are independent. The mathematics of this setup is most easily described by considering the transfer matrices $T_{\rm DUT}$, $T_1$ and $T_2$ of the DUT and of the the two error boxes instead of the corresponding S-matrices. The transfer matrix that is actually measured by the reflectometers is then found as the product $T_{\rm meas}=T_1T_{\rm DUT}T_2$, from which $T_{\rm DUT}=T_1^{-1}T_{\rm meas}T_2^{-1}$ and finally the corresponding S-matrix $S_{\rm DUT}$ can be obtained.
As in the case of TOSM, a system of equations for the error terms is obtained when the different TRL calibration standards are connected to the VNA ports. This system of equations can be solved for the error terms, and the solutions can be evaluated numerically after the calibration standards have been measured. See, e.g., Dunsmore's book [1] for explicit solutions, and also Pozar's book [3] for an easy derivation under the simplifying assumption that both error boxes are identical, which is, however easily generalized.
The thru standard is usually assumed to be flush, i.e., its S-matrix is assumed to be the unit matrix (so there is no loss and no reflection). This is appropriate for coaxial flush connections, and in case of TRL it will place the reference planes at the center of the coplanar waveguide. If the thru is assumed to have a certain length, i.e., consists of a piece of transmission line, the corresponding calibration scheme is often called line-reflect-line (LRL). The reflect standard only needs to have a nonzero reflection coefficient, which does not need to be known exactly (but its magnitude should be close to 1); it can be obtained as a by-product of the solutions of the TRL calibration equations along with the error terms. However, the reflection coefficient has to be exactly the same for both ports.
The line standard needs to have an impedance equal to the system impedance, but can have losses. Its propagation constant can be obtained as a by-product from the TRL equations. The line must have a phase shift different from 0° and 180° over the frequency range in which a calibration is to be achieved, because otherwise it would not be distinguishable from the thru, and the system of equations for the error terms would be underdetermined. To avoid degradation of accuracy due to noise, the phase shift should in practice be not too close to 0° or 180° (this is checked by common VNA algorithms). A rule of the thumb is to require it to be more than 20° and less than 160°. If a large frequency band is to be covered, it can be split and several lines of different lengths can be used. There is also a variant which simultaneously uses all lines at any frequency with appropriate weighting, known as NIST multiline calibration, see the paper by Marks [4]. This calibration is implemented in the firmware of many modern professional VNAs.
At low frequencies the required line lengths become impractical. Then the line standard can be replaced with a match, which looks like a line with infinite length. Since at low frequencies good match standards are easily available, this is a satisfactory way to extend TRL to low frequencies while maintaining its accuracy at high frequencies. This degenerate case of TRL with a “line of infinite length” in the form of a match is known as thru-reflect-match (TRM) calibration.
The 8-term error model with its two error boxes assumes that the port match is independent of whether the port is configured as a source or as a receiver. For a real VNA this is not exactly true since the source is routed through a switch to the individual ports. Of course the error due to the switch should also be addressed for precise results. This is routinely done in the traditional 12-term error model, which implicitly accounts for the differences in source and receive port match in that it uses two completely separate 6-term error models in the forward and reverse direction. In order to map the 8-term error model to the 12-term model, the additional errors in the 12-term model must be accounted for by measuring additional quantities. These are the so-called switch terms, which are defined as follows. Let $a_1$, $b_1$ and $a_2$, $b_2$ be the incident and scattered waves of port 1 and 2, respectively. The two switch terms are defined as $\Gamma_{\rm f}=\frac{a_2}{b_2}\Bigg|_{\text{source at port 1}},$ and $\Gamma_{\rm r}=\frac{a_1}{b_1}\Bigg|_{\text{source at port 2}}.$ As was remarked above, a VNA with four receiver channels is needed to measure these quantities. They are usually measured along with the thru. When the error terms of the 8-term model and the switch terms are known, they can be converted to the standard 12-term error model. (More precisely, the 8-term error model parameters and the switch terms yield 10 error parameters; for the 12-term model, the forward and reverse crosstalk errors also need to be included, which can, however, be neglected in most situations unless there is a non-negligible amount of crosstalk in the test setup). The explicit transformation equations are easily derived or can be found in the literature (see, e.g., Dunsmore's book [1]).
## Board design considerations
As already mentioned, all features on the board are realized with grounded and fenced coplanar waveguides. With the usual approximation formulas for coplanar waveguides, which were used to obtain an impedance of 50 Ohms, the design is very straightforward. The launchers are not exactly compatible with the coplanar waveguide structure; the necessary center conductor width is a little bit larger than the line width in the footprint recommended by the manufacturer. See the detail of a screen-shot from the CAD here. However, at frequencies below 2 GHz not much error is to be expected as there is no discontinuity in the center conductor width.
The solder mask should not be removed from the component side or from the center conductors of the coplanar waveguides. Even though solder mask may have a poorly defined geometry and permittivity, it will ensure that the trace surfaces are copper when the board is manufactured in a standard pool process. The available surface finishes from most manufacturers are, in general, not very well suited for the present purpose. For example, HAL has a poorly defined surface geometry, and ENIG only yields a very thin gold layer (about 50 to 100 nm) on a much thicker nickel layer (about 5 µm), which is needed as a diffusion barrier. Due to the skin effect a large fraction of the current will flow in the nickel layer, which has a smaller conductivity than copper. Moreover, the nickel layer is deposited in an electroless way with an auto-catalytic reaction using a phosphor compound as reducing agent. Therefore, phosphor will be deposited along with nickel, and depending on the phosphor concentration the nickel layer will have unpredictable and frequency dependent magnetic properties.
## Coplanar waveguide impedance
Since in TRL the characteristic impedance of the line is used to calibrate to the reference impedance, it is interesting to determine it by a measurement. We bypass all questions of how to define impedance of a planar circuit, which, strictly speaking, is not well defined as the quotient of voltage and current at a point on the line (even though a grounded coplanar waveguide can be considered to support a TEM mode to a good approximation). Obviously, such a measurement needs an independent calibration which does not use the line as an impedance standard. It is easiest to use a TOSM calibration, which will put the reference planes in the SMA connectors. The drawback is, of course, that then the coplanar waveguide to connector transitions are within the reference planes. Nevertheless, since the line length is large in relation to the transition and no extreme accuracy is required, we shall follow this approach.
There are several ways to measure the characteristic impedance of a transmission line. The first method starts out from the following idea. Suppose that a line of length $\ell$ and with transmission constant $\gamma=\alpha+\mathord{\rm i}\beta$ and impedance $Z$ is shorted at one end. Then, looking into its other end, one sees the impedance $Z_{\rm in}=Z\cdot\tanh(\gamma\ell).$ Using $\beta=2\pi f/(c_0v_{\rm p})$, where $f$ is the frequency, $c_0$ the speed of light in vacuum, and $v_{\rm p}$ the phase velocity factor, we can measure $Z_{\rm in}$ as a function of frequency and curve fit the above expression to the results in order to obtain the unknowns, among them $Z$. We use the line standard on the board, i.e., the 76 mm coplanar waveguide, and short one of its ends with a SMA short. Then we measure S11 at its opposite end and obtain the impedance from this measurement. The result is plotted below, directly by the analyzer.
After exporting the impedance data from the analyzer, curve fitting to the above expression can be done; the result is plotted here. Curve fitting was done by a GNU Octave script (using the Octave Forge optim package); the script can be downloaded here. Fitting this function is a bit finnicky, and due to the poles the regression algorithm needs good start values. It is seen that the peak height in the model is, unlike the measurement, not frequency dependent. The reason is that the attenuation constant $\alpha$ was assumed to be frequency independent. However, since we are only interested in the coplanar waveguide impedance, this model is adequate. The parameters obtained from the curve fitting are as follows:
• Impedance $Z$: $46.60\;\Omega$
• Attenuation constant $\alpha$: $0.43\;{\rm m^{-1}}$
• Phase velocity factor $v_{\rm p}$: $0.43$
We see that $Z$ deviates from the nominal value of 50 Ohms by about −7%. This is within the limits that are to be expected from a non-impedance controlled board manufacturing process. Recall that this result was measured with respect to reference planes in the SMA connectors, and therefore includes errors from the connector to waveguide transition, as well as imprecisions of the short.
There is a more direct way to measure the impedance of a shorted transmission line with a VNA. When a lossless transmission line with impedance $Z$ is shorted at one end, the impedance looking into its other end is $Z_{\rm in}=\mathord{\rm i}Z\cdot\tan(\beta\ell).$ Thus at the frequencies where $\tan(\beta\ell)=\pm1$, i.e., when $\beta\ell=(2n+1)\pi/4$, $n=0,1,2,\ldots$, we have $Z_{\rm in}=\mathord{\rm i}Z$. These frequencies are easily found by identifying the frequencies $f_{\infty, n}$ of the $n$-th pole, i.e., where $\lvert Z_{\rm in}(f_{\infty, n})\rvert=\infty$. Then at the frequencies $f_{0,n}=f_{\infty, n}\Bigl(1\pm\frac{1}{4n-2}\Bigr)$ we have $Z_{\rm in}=\mathord{\rm i}Z$, and consequently $\lvert Z_{\rm in}\rvert=\lvert Z\rvert$. This has been demonstrated in the above plot, where the markers M1 and M3 are placed at the first two such frequencies. We obtain 47.787 Ohms and 46.041 Ohms for the magnitude of the transmission line impedance, in good agreement with the result from the curve fit (notice that the curve fitting method has neglected the frequency dependence of $Z$ and thus gives an average result).
A second and very well known method to measure the impedance $Z$ of a lossy transmission line works as follows. The line is terminated on one end first with an open, and then with a short, and in both cases the impedance at the other end is measured. The impedance looking into the shorted line is $Z_{\rm in}^{\rm s}=Z\cdot\tanh(\gamma\ell)$, as already said above, and $Z_{\rm in}^{\rm o}=Z\cdot\coth(\gamma\ell)$ for the open line. This directly yields $Z=\sqrt{Z_{\rm in}^{\rm o}Z_{\rm in}^{\rm s}}.$ Hence it is possible to obtain $Z$ as a function of frequency—at least in theory. I have put this method to work, using opens and shorts from a calibration kit. The result can be seen in the following plot.
The result is rather disappointing; the impedance as a function of frequency shows a number of unphysical discontinuities and variations. The reason is the unwieldy progression of $Z_{\rm in}^{\rm o}$ and $Z_{\rm in}^{\rm s}$ with frequency: when one of it has a pole and tends to infinity, the other approaches zero, and vice versa, so that their product remains smooth (in theory the poles of the product are removable). If the open and short used to terminate the transmission line have slightly different offset lengths (an open will always show fringing), the poles and zeros of both functions will not exactly coincide. Moreover, the reflection coefficients of the open and short will be different from ±1. This leads to a progression as shown in the plot, which seriously limits the practicality of this method, even though it is included in may textbooks. One approach to improve this situation could be to fit a mathematical model of the line to the spiky curve obtained from $\sqrt{Z_{\rm in}^{\rm o}Z_{\rm in}^{\rm s}}$.
A third method to measure the impedance of a lossless transmission line, which is somewhat related to the second one, is by terminating one end of the line with an arbitrary but frequency independent impedance $Z_{\rm L}$. Then, looking into the other end, one sees an impedance $Z_{\rm in }=Z\frac{1+\Gamma\mathord{\rm e}^{-2\mathord{\rm i}\beta\ell}}{1-\Gamma\mathord{\rm e}^{-2\mathord{\rm i}\beta\ell}}=Z\frac{1+\lvert\Gamma\rvert\mathord{\rm e}^{\mathord{\rm i}\arg(\Gamma)}\mathord{\rm e}^{-2\mathord{\rm i}\beta\ell}}{1-\lvert\Gamma\rvert\mathord{\rm e}^{\mathord{\rm i}\arg(\Gamma)}\mathord{\rm e}^{-2\mathord{\rm i}\beta\ell}},$ where $\Gamma=\frac{Z_{\rm L}-Z}{Z_{\rm L}+Z}.$ With varying frequency or line length, $Z_{\rm in}$ moves on a circle in the Smith chart, and will assume its largest and smallest magnitude when $Z_{\rm in}$ is real. At these frequencies $Z_{\rm in}$ is given by $Z_{\rm max}=Z(1+\lvert\Gamma\rvert)/(1-\lvert\Gamma\rvert)$ and $Z_{\rm min}=Z(1-\lvert\Gamma\rvert)/(1+\lvert\Gamma\rvert)$. This immediately yields $Z=\sqrt{Z_{\rm max}Z_{\rm min}}.$ This method also has been put to work: the line has been terminated by a SMA termination on one end, and its impedance at the other end has been measured. The result is plotted below. From the formula above and using the first minimum and maximum one finds a line impedance of 47.44 Ohms, in reasonably good agreement with the previous result.
There are yet more methods to measure transmission line impedance. One example is the calibration comparison technique which was introduced by Williams, Arz and Grabinski [5]. It employs a two-tier TRL calibration using known impedance standards in the medium one wants to measure (coplanar waveguide on FR4 in this case). First one calibrates by TRL using these standards, and then one performs a second-tier TRL calibration with the unknown line. This will create error boxes at the ends of the unknown line with respect to the first calibration. These characterize the impedance differences, and from them the line impedance can be found. This requires, of course, the availability of known impedance standards, but eliminates the influence of connectors. A method by Marks ans Williams [6] derives the characteristic impedance from a measurement of the propagation constant (which can be obtained as a by-product by solving the TRL calibration equations), the line capacitance, and suitable modeling.
## Measuring a capacitor
It is time to put the board to use. As an example I have soldered two standard 100 nF ceramic capacitors with Y5V dielectric in a 0805 SMD package, rated at 50 V DC, into the series and shunt test fixtures. The capacitors are Samsung model CL21F104ZBCNNNC.
Before any data can be taken, the VNA has to be calibrated. To this end a TRL calibration using the TRL standards on the board is performed, in which the short plays the role of the reflect standard. The calibration is extended by TRM to lower frequencies, for which the match standard is used. Originally the board was designed to be usable up to about 2 GHz, but with that upper frequency limit the analyzer firmware issues a warning since the phase shift of the line exceeds 180°. The reason is some deviations of the board parameters from theory; for the same reason the line impedance deviates a little from 50 Ohms, as has been shown above. By an independent measurement I have verified that the line section between both TRL reference planes has 180° phase shift at 1.865 GHz, i.e., at this frequency the line looks looks the tru. For this reason I limit the frequency range to 1.8 GHz for the following measurements.
For comparison I will take all measurements also with a UOSM calibration, which places the reference planes in the SMA connectors of the board.
Measurement results of the capacitor in the series fixture are plotted below. It is seen that its impedance increases linearly with frequency because of the parasitic series inductance; at 1 GHz a series impedance of 12.9 Ohms is measured. The series resonance is well below the lower measurement limit of 50 MHz in the plot (typically the series resonance is at 10 to 20 MHz for a 100 nF capacitor in a 0805 package).
Let us compare this result to the same measurement but with the reference planes in the SMA connectors. Observe that the magnitude of S21 does not look much different except for some additional fractions of a dB loss, but the phase shift is much larger. As a consequence the measured series impedance is much larger: we obtain 196.2 Ohms at 1 GHz. This is of course comes about because the lines between capacitor and reference plane are transforming. This shows nicely that at the frequencies involved even a few mm of trace matter a lot. And it is a good reminder to keep traces as short as possible when using 100 nF as a decoupling capacitor on an IC.
Now let's measure the same capacitor in the shunt fixture. The results with reference planes right at the capacitor are shown below. The plot shows nothing unexpected. In the forward (i.e., S21) measurement we find that the measured impedance is decreasing with frequency. This is due to the increasing impedance of the capacitor due to its parasitic series inductance. The impedance looking into one end of the capacitor (the yellow trace on the plot below, calculated from S11) shows a corresponding increase. At 1 GHz we find an impedance of about 5.2 Ohms (compare this to the measured 12 Ohms in series configuration—in this case there are another 50 Ohms in parallel). These results also indicate the limits of a 100 nF ceramic capacitor for supply voltage decoupling at these frequencies, its impedance is already quite large.
When the reference planes are within the SMA connectors, the results in the forward S21 direction do not look much different. However, the reflection measurement is markedly different due to the transformation done by the trace between capacitor and SMA jack. The impedance looking into the SMA connector shows a maximum at 1.72 GHz. What might be mistaken for a resonance is due to the trace, which transforms the approximate short (more precisely approximately 9 Ohms to ground, as can be seen from the TRL measurement) at the capacitor to an open at the connector. This can be nicely confirmed by a look at the S11 Smith chart. Again, a few mm of trace do matter a lot at these frequencies.
An alternative use of the shunt fixture would be to disconnect one trace to its SMA connector right at the SMD pad (this avoids creating a stub). Then one could use the fixture for pure S11-measurements of a component.
## Conclusion
A TRL board with test fixtures is a useful tool to have in the lab for quickly testing various components. A good idea for improvement would be to add more line standards to increase the upper frequency limit of the board by multi-line TRL. However, at larger frequencies FR4 tends to become more uncontrollable. For precise measurements one should preferably use an impedance controlled board manufacturing process.
To be continued by some more details on impedance measurement and applications of TRL...
## Bibliography
1. Dunsmore, J.P.: Handbook of Microwave Component Measurements. Chichester: Wiley (2012).
2. Engen, G.F, Hoer, C.A.: "Thru-reflect-line": An improved technique for calibrating the dual six-port automatic network analyzer. IEEE Trans. Microwave Theory Tech. 27, 987–993 (1979).
3. Pozar, D.M.: Microwave Engineering. 4th Ed. New York: Wiley (2012).
4. Marks, R.B.: A multiline method of network analyzer calibration. IEEE Trans. Microwave Theory Tech. 39, 1205–1215 (1991).
5. Williams, D.F., Arz, U., Grabinski, H.: Characteristic-impedance measurement error on lossy substrates. IEEE Microwave Wireless Comp. Lett. 11, 299–301 (2001).
6. Marks, R.B., Williams, D.F: Characteristic impedance determination using propagation constant measurement. IEEE Microwave Guided Wave Lett. 1, 141–143 (1991).
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2020-04-01 05:21:57
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https://practicepaper.in/gate-me/gear-and-gear-train
|
# Gear and Gear Train
Question 1
A schematic of an epicyclic gear train is shown in the figure. The sun (gear 1) and planet (gear 2) are external, and the ring gear (gear 3) is internal. Gear 1, gear 3 and arm OP are pivoted to the ground at O. Gear 2 is carried on the arm OP via the pivot joint at P, and is in mesh with the other two gears. Gear 2 has 20 teeth and gear 3 has 80 teeth. If gear 1 is kept fixed at 0 rpm and gear 3 rotates at 900 rpm counter clockwise (ccw), the magnitude of angular velocity of arm OP is __________rpm (in integer).
A 300 B 600 C 900 D 1200
GATE ME 2022 SET-1 Theory of Machine
Question 1 Explanation:
Speed of gear 1 $N_1 =0$,
Speed of gear 3 $N_3 =900rpm$,
Speed of Arm $N_{arm} =?$,
Teeth of gear 1 $z_1=?$
Teeth of gear 2 $z_2=20$
Teeth of gear 3 $z_3=80$
Teeth of gear 2
\begin{aligned} z_3&=z_1+2z_2\\ 80&=z_1+2(20)\\ z_1&=40 \end{aligned}
$\begin{array}{|c|c|c|c|c|c|} \hline \text{S.No}&\text{Condition of mtotion} &\text{Speed of arm} &\text{Speed of gear 1} &\text{Speed of gear 2} &\text{Speed of gear 3}\\ \hline 1&\text{Arm is fixed and gear 1 with +x rev}&0&+1&\frac{-z_1}{z_2}(1)&\frac{-z_1}{z_3}(1)\\ \hline 2&\text{Arm is fixed and gear 1 with +x rev}&0&+x&\frac{-z_1}{z_2}(x)&\frac{-z_1}{z_3}(x)\\ \hline 3&\text{Arm with +y rev}&+y&y&+y&+y\\ \hline 4&\text{Total }&y&x+y &y-x\frac{z_1}{z_2}&y-\frac{z_1}{z_3}(x)\\ \hline \end{array}$
\begin{aligned} N_1&=x+y=0\\ \Rightarrow x&=-y \\ N_3&=y-\frac{z_1}{z_3}(x)=900\\ &=y-\frac{40}{80}(x)=900\\ \Rightarrow y-\frac{40}{80}(-y)=900\\ 1.5y&=900\\ y&=600 rpm \end{aligned}
Question 2
A power transmission mechanism consists of a belt drive and a gear train as shown in the figure.
Diameters of pulleys of belt drive and number of teeth (T) on the gears 2 to 7 are indicated in the figure. The speed and direction of rotation of gear 7, respectively, are
A 255.68 rpm; clockwise B 255.68 rpm; anticlockwise C 575.28 rpm; clockwise D 575.28 rpm; anticlockwise
GATE ME 2021 SET-2 Theory of Machine
Question 2 Explanation:
\begin{aligned} T_{3} &=44 \\ T_{6} &=36 \\ T_{2} &=18 \\ T_{4} &=15 \\ \frac{N_{1}}{N_{0}} &=\frac{d_{0}}{d_{1}} \\ \Rightarrow\qquad N_{1} &=\frac{150}{250} \times 2500\\ N_{1}&=15,00=N_{2} \\ N_{3}&=\frac{N_{2} \times T_{2}}{T_{3}}=\frac{1500 \times 18}{44}=613.63636=N_{4} \\ N_{6}&=\frac{N_{4} \times T_{4}}{T_{6}}=\frac{613.63636 \times 15}{36} \\ &=255.6818=N_{7}(\text { Clockwise }) \end{aligned}
Gear 5 is idler.
Question 3
The sun (S) and the planet (P) of an epicyclic gear train shown in the figure have identical number of teeth
If the sun (S) and the outer ring (R) gears are rotated in the same direction with angular speed $\omega _S \; and \; \omega _R$, respectively, then the angular speed of the arm AB is
A $\frac{3}{4}\omega _R + \frac{1}{4}\omega _S$ B $\frac{1}{4}\omega _R + \frac{3}{4}\omega _S$ C $\frac{1}{2}\omega _R - \frac{1}{2}\omega _S$ D $\frac{3}{4}\omega _R - \frac{1}{4}\omega _S$
GATE ME 2020 SET-2 Theory of Machine
Question 3 Explanation:
\begin{aligned} r_{s}+2 r_{p}&=r_{R} \\ \Rightarrow \quad T_{s}+2 T_{p}&=T_{R} \quad (T_{P}=T_{S})\\ 3 T_{P}&=T_{R} \\ \Rightarrow \quad 3 T_{p}&=T_{R} \end{aligned}
\begin{aligned} y+x&=\omega_{S} \\ y-\frac{x}{3}&=\omega_{R}\\ & \text{Substract by,}\\ \frac{4 x}{3} &=\left(\omega_{S}-\omega_{R}\right) \\ x &=\frac{3}{4}\left(\omega_{S}-\omega_{R}\right) \\ y &=\omega_{S}-x=\omega_{S}-\frac{3}{4}\left(\omega_{S}-\omega_{R}\right) \\ &=\omega_{S}-\frac{3 \omega_{S}}{4}+\frac{3 \omega_{R}}{4}=\frac{\omega_{S}}{4}+\frac{3 \omega_{R}}{4} \end{aligned}
Question 4
A balanced rigid disc mounted on a rigid rotor has four identical point masses, each of 10 grams, attached to four points on the 100 mm radius circle shown in the figure.
The rotor is driven by a motor at uniform angular speed of 10 rad/s. If one of the masses gets detached then the magnitude of the resultant unbalance force on the rotor is ______ N. (round off to 2 decimal places).
A 0.1 B 1 C 10 D 0.001
GATE ME 2020 SET-1 Theory of Machine
Question 4 Explanation:
$\omega=10 \mathrm{rad} / \mathrm{s}, r=100 \mathrm{mm}=0.1 \mathrm{m}$
If one mass is detached then
Now, unbalance tone, F=$m r \omega^{2}$
$\begin{array}{l} =\frac{10}{1000} \times 0.1 \times(10)^{2}=\frac{10 \times 0.1 \times 100}{1000} \\ =0.1 \mathrm{N} \end{array}$
Question 5
A spur gear has pitch circle diameter D and number of teeth T. The circular pitch of the gear is
A $\frac{\pi D}{T}$ B $\frac{T}{D}$ C $\frac{D}{T}$ D $\frac{2 \pi D}{T}$
GATE ME 2019 SET-2 Theory of Machine
Question 5 Explanation:
Circular pitch : It is the distance between two similar points on adjacent teeth measured along pitch
circle circumference circular pitch
$\left(P_{c}\right)=\frac{\text { Pitch circlecircum }}{\text { Number of teeth }}=\frac{\pi D}{T}$
Question 6
A spur gear with 20$^{\circ}$ full depth teeth is transmitting 20 kW at 200 rad/s. The pitch circle diameter of the gear is 100 mm. The magnitude of the force applied on the gear in the radial direction is
A 0.36 kN B 0.73 kN C 1.39 kN D 2.78kN
GATE ME 2019 SET-1 Theory of Machine
Question 6 Explanation:
$\begin{array}{l} \phi=20^{\circ}, P=20 k W, \omega=200 \mathrm{rad} / \mathrm{s}, d=100 \mathrm{mm}=0.1 \mathrm{m} \\ \text { Torque }=\text { Power } / \omega \\ \mathrm{T}=\frac{20000}{200}=100 \mathrm{Nm} \\ \text { Now, } \mathrm{T}=\mathrm{F}_{\mathrm{T}} \times \frac{\mathrm{d}}{2} \\ \Rightarrow 100=\mathrm{F}_{\mathrm{T}} \times \frac{0.1}{2} \\ \Rightarrow \mathrm{F}_{\mathrm{T}}=2000 \mathrm{N}\\ \frac{F_{R}}{F_{T}}=\tan \phi \\ \Rightarrow \mathrm{F}_{\mathrm{R}}=2000 \times \tan 20^{\circ} \\ \Rightarrow \mathrm{F}_{\mathrm{R}}=727.94 \mathrm{N}=0.73 \mathrm{kN} \end{array}$
Question 7
A frictionless gear train is shown in the figure. The leftmost 12-teeth gear is given a torque of 100 N-m. The output torque from the 60-teeth gear on the right in N-m is
A 5 B 20 C 500 D 2000
GATE ME 2018 SET-2 Theory of Machine
Question 7 Explanation:
\begin{aligned} \tau_{1}&=100 \mathrm{Nm}\\ \text{Let speed of 1 is }N_{1} \\ (1,2):\qquad N_{2}&=N_{1} \times \frac{T_{1}}{T_{2}}=N_{1} \times \frac{12}{48}=\frac{N_{1}}{4} \\ N_{3}=N_{2}&=\frac{N_{1}}{4}\\ (3,4) \qquad N_{4}&=N_{3} \times \frac{T_{3}}{T_{4}}=\frac{N_{1}}{4} \times \frac{12}{60} \\ N_{4}&=\frac{N_{1}}{20} \end{aligned}
By Power conservation
(Assume $\eta$ (efficiency) =1)
\begin{aligned} \tau_{1} \times N_{1} &=\tau_{4} \times N_{4} \\ 100 \times N_{1} &=\tau_{4} \times \frac{N_{1}}{20} \\ \tau_{4} &=2000 \mathrm{N}-\mathrm{m} \end{aligned}
Question 8
An epicyclic gear train is shown in the figure below. The number of teeth on the gears A, B and D are 20, 30 and 20, respectively. Gear C has 80 teeth on the inner surface and 100 teeth on the outer surface. If the carrier arm AB is fixed and the sun gear A rotates at 300 rpm in the clockwise direction, then the rpm of D in the clockwise direction is
A 240 B -240 C 375 D -375
GATE ME 2018 SET-1 Theory of Machine
Question 8 Explanation:
$T_{A}=20, T_{B}=30, T_{D}=20, T_{C}=80(\text { Inner }), T_{C}=100 \text { (Outer) }$
Arm is fixed, no epicyclic nature. Taking clockwise direction as positive.
\begin{aligned} N_{A}&=+300 \\ (A, B) \qquad N_{B}&=-\frac{300 \times 20}{30}=-200\\ (B, C)\qquad N_{C}&=-200 \times \frac{30}{80}=-75\\ (C, D)\qquad N_{D}&=+75 \times \frac{100}{20}=+375 \end{aligned}
Question 9
A gear train shown in the figure consists of gear P, Q, R and S. Gear Q and gear R are mounted on the same shaft. All the gears are mounted on parallel shafts and the number of teeth of P, Q, R and S are 24, 45, 30 and 80, respectively. Gear P is rotating at 400 rpm. The speed (in rpm) of the gear S is _____
A 90 B 120 C 245 D 150
GATE ME 2017 SET-2 Theory of Machine
Question 9 Explanation:
$\begin{array}{ll} T_{P}=24 \\ T_{Q}=45 & N_{P}=400 \mathrm{rpm} \\ T_{R}=30 & N_{S}=? \\ T_{S}=80 \end{array}$
$Here gear R is not meshing at all.
[latex] \begin{array}{l} \frac{N_{P}}{N_{Q}}=\frac{T_{O}}{T_{P}}=\frac{45}{24} \qquad \cdots(1)\\ \frac{N_{Q}}{N_{S}}=\frac{T_{S}}{T_{Q}}=\frac{80}{45}\qquad \cdots(2)\\ \text{By }(1) \times(2) \\ \frac{N_{P}}{N_{S}}=\frac{45}{24} \times \frac{80}{45} \\ N_{S}=N_{P} \times \frac{24}{80}=\frac{400 \times 24}{80} \\ N_{S}=120 \text { r.p.m } \end{array}$
Question 10
In an epicyclic gear train, shown in the figure, the outer ring gear is fixed, while the sun gear rotates counterclockwise at 100rpm. Let the number of teeth on the sun, planet and outer gears to be 50, 25, and 100, respectively. The ratio of magnitudes of angular velocity of the planet gear to the angular velocity of the carrier arm is _________.
A 3 B 4 C 5 D 6
GATE ME 2017 SET-1 Theory of Machine
Question 10 Explanation:
We take convention clockwise (+ve)
\begin{aligned} N_{D} &=0 \\ N_{S} &=-100 \\ T_{S} &=50, \quad T_{P}=25, T_{D}=100 \\ \frac{N_{P}}{N_{\mathrm{ARM}}}&=? \end{aligned}
$y+x=-100 \qquad \cdots(i)$
$y-\frac{x}{2}=0 \qquad \cdots(ii)$
By equation (i) - (ii)
\begin{aligned} \frac{3 x}{2} &=-100=x=\frac{-200}{3} \\ y &=-100-x=-100+\frac{200}{3}=\frac{-100}{3} \\ N_{p} &=y-2 x=\frac{-100}{3}+\frac{400}{3}=\frac{300}{3}=100 \\ N_{\mathrm{ARM}} &=y=\frac{-100}{3} \\ \frac{N_{P}}{N_{\mathrm{ARM}}} &=\frac{100}{\frac{-100}{3}}=-3 \\ \left| \frac{N_{\mathrm{P}}}{N_{\mathrm{ARM}}}\right | &=3 \end{aligned}
There are 10 questions to complete.
### 2 thoughts on “Gear and Gear Train”
1. Sir,I think 19ans wrong ans:10rpm anticlockwise direction
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2022-10-03 07:34:15
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https://search.r-project.org/CRAN/refmans/Clustering/html/weather.html
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weather {Clustering} R Documentation
## One of the most known testing data sets in machine learning. This data sets describes several situations where the weather is suitable or not to play sports, depending on the current outlook, temperature, humidity and wind.
### Description
One of the most known testing data sets in machine learning. This data sets describes several situations where the weather is suitable or not to play sports, depending on the current outlook, temperature, humidity and wind.
### Usage
data(weather)
### Format
A data frame with 14 observations on 5 variables:
One of the most known testing data sets in machine learning. This data sets describes several situations where the weather is suitable or not to play sports, depending on the current outlook, temperature, humidity and wind.
Outlook
sunny, overcast, rainy
Temperature
hot, mild, cool
Humidity
high, normal
Windy
true, false
Play
yes, no
### Source
KEEL, <http://www.keel.es/>
[Package Clustering version 1.7.7 Index]
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2022-11-30 04:01:53
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https://acooke.org/cute/HangmanTac0.html
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## Hangman Tactics
From: andrew cooke <andrew@...>
Date: Sat, 5 Jan 2013 23:05:30 -0300
This is hilarous. Or at least mildly amusing. A huge amount of (readable,
carefully explained, correct) analysis takes you from "calling out the vowels"
(oh how naive) through - well, I won't list everything - to the optimal
statistical approach: calling out the vowels (in a slightly different order)!
http://www.datagenetics.com/blog/april12012/index.html
Andrew
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2021-09-16 12:04:09
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https://nylogic.github.io/logic-workshop/2023/03/03/the-complexity-of-radical-constructions-in-rings-and-modules.html
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March 3
Chris Conidis, CUNY
The complexity of radical constructions in rings and modules
We present two different elementary algebraic constructions that are as complicated as possible and whose complexity vastly exceeds those typically found in the elementary algebra literature. The first is the prime radical of a noncommutative ring, while the second is the radical of a module. These constructions contrast similar constructions in more familiar contexts that we will also mention along the way.
Video
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2023-04-01 17:45:11
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https://zbmath.org/?q=an:0905.35043
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# zbMATH — the first resource for mathematics
The complex Ginzburg-Landau equation on large and unbounded domains: Sharper bounds and attractors. (English) Zbl 0905.35043
Let $$\Omega\subset{\mathbb R}^d$$ be a smooth (possibly unbounded) domain. The paper deals with the study of the complex Ginzburg-Landau equation $u_t=(1+i\alpha)\Delta u+Ru-(1+i\beta)| u| ^{2}u\qquad\text{in $$\Omega \times (0,\infty)$$}.$ Using an appropriate weighted $$L^p$$-space the author obtains new bounds on the long-time behaviour of solutions. These a priori estimates are essentially independent of the underlying domain, and they improve previous bounds related to a polynomial growth with respect to the instability parameter. The author’s analysis includes the standard case where $$u$$ is periodic of period 1 with respect to each coordinate. There are also established sharp estimates on the maximal influence of the boundaries on the dynamics in the interior. This enables the author to prove the existence of global attractors and to compare two attractors associated to two semigroups on different domains in the case of a large joint domain. Moreover, every orbit in one of the attractors can be approximated by a pseudo-orbit inside the other attractor.
The paper is of significant relevance in the study of dynamics of parabolic equations on large or unbounded domains.
##### MSC:
35K55 Nonlinear parabolic equations 35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs 35B45 A priori estimates in context of PDEs 37C70 Attractors and repellers of smooth dynamical systems and their topological structure
Full Text:
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2021-09-18 07:58:54
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https://physics.stackexchange.com/questions/450722/angular-momentum-in-different-points
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# Angular momentum in different points
I have a question about angular momentum: Is it possible to have a system where angular momentum is conserved relative to 1 point,but not conserved relative to another?
Consider central-force motion, such as a planet moving around a (very massive) star. The angular momentum of such a planet is constant if we take the origin as the center of the star. It is not constant if we take the origin to be any other point.
• But "constant" is different from "conserved." In the new system, there is a torque on the planet about any other point, so the torque is providing the change of the angular momentum. That torque-time integral is part of the conservation law. – Bill N Dec 27 '18 at 23:10
• @BillN: If you're defining angular momentum to be conserved whenever $\Delta \mathbf{L} = \int \pmb{\tau} \, dt$, then I'm pretty sure that the statement "angular momentum is conserved" is tautological. – Michael Seifert Dec 27 '18 at 23:39
• @BillN How do you define "conserved"? – FGSUZ Dec 28 '18 at 0:07
• @BillN Okay, I see your point, but I'm sorry to disagree, or not disagree, but just not joining your view. For me, they'll keep being the same, but I'll be very careful to clarify this point from now on. Let me explain my view: I only say "conserved" when talking about "total" amounts. So total momentum is conserved because it is constant. I never use "conserved" with partial systems, because saying "momentum 1 is conserved but not constant" is like "okay, it's not a random number, but it's still unspecified", so it's not useful for me. Hope you understand. – FGSUZ Dec 28 '18 at 21:29
• @BillN We are just using different definitions of what it means for something to be conserved within a system, but we agree on a deeper level. I agree with you within your definition, which I don't think is necessarily wrong. Thanks for the discussion. – Aaron Stevens Dec 29 '18 at 2:20
Is it possible to have a system where angular momentum is conserved relative to 1 point,but not conserved relative to another?
Total angular momentum will be conserved but the angular momentum of any part of the system will have a value dependent on where you take your base point.
Angular momentum relative to an origin $${\mathcal O_1}$$
$$\mathbf{L_{\mathcal O_1}} = \mathbf{r_{\mathcal O_1} \times p_{\mathcal O_1}}$$
where $$\mathbf r_{\mathcal O_1}$$ is the position vector to the particle relative to some origin $${\mathcal O_1}$$. Now suppose that angular momentum is conserved in $${\mathcal O_1}$$. Then
$$\frac{d \mathbf L_1}{dt} = \mathbf{\dot{r_1} \times p_1} + \mathbf{r_1 \times \dot{p_1}} = \frac{1}{m} \mathbf{p_1 \times p_1} + \mathbf{r_1 \times \dot{p_1}} =0$$
but since the direction of momentum is frame-independent, the first term vanishes (that is, $$\mathbf{p_1} = \mathbf{p}$$). It then follows that
$$\mathbf{r_1 \times F_1} =0 .$$
Now, let's look at some other origin $$\mathcal{O}_2$$, given that $$L$$ is conserved in $$\mathcal O_1$$. Well the first term much vanish again, that's fine but what about the second term? Does
$$\mathbf{r_2 \times F_2} \stackrel{?}{=}0.$$
Well, no not necessarily. Namely, just choose an origin in which the force is perpendicular to your position vector.
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2020-02-26 03:30:20
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http://www.hep.ph.ic.ac.uk/seminars/abstracts/2017/20171116.html
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## Latest neutrino oscillation results from the T2K experiment
Patrick Dunne
T2K is a long baseline neutrino experiment situated in Japan. We fire beams of muon neutrinos and antineutrinos 295km across the country then observe them using the 50 kTon Super Kamiokande detector. By studying how many of these neutrinos have oscillated into different flavours and whether the oscillations occur differently for antineutrinos we have sensitivity to CP violation in the neutrino sector, the neutrino mass hierarchy and the mixing angles between the neutrino flavours. I will present the latest results from the T2K collaboration, using data collected up to May this year, including new limits on the CP violating parameter \delta_{CP}.
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2019-02-21 15:30:16
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https://thwack.solarwinds.com/free-tools-trials/f/ftp-voyager/15990/ftp-voyager-scheduler/119616
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# FTP Voyager Scheduler
Question.
In FTP voyager scheduler, under setting up actions. Can you use a network Drive or folder as the local folder. It currently on lists the local drives on the machine that voyager is installed on. Even when you type in a network path at the bottom of the action setup it disregards the network path that you enter. Have even tried mapping a drive to the network path but can not see it in the action setup.
Any help would be appreciated.
Dave
Parents
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2021-05-08 23:24:58
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https://desvl.xyz/2021/07/08/Cesaro-operator-in-L2/
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## An example in elementary calculus
Consider a sequence of real or complex numbers $(s_n)$. If $s_n \to s$, then
Here, $\pi_n$ is called the Cesàro sum of $(s_n)$. The proof is rather simple. Given $\varepsilon>0$, there exists some $N>0$ such that $|s_n-s|<\varepsilon$ for all $n > N$. Therefore we can write
For fixed $N$, we can pick $n$ big enough such that $N/n<1/2$ (i.e. $n>2N$) and
Hence $\pi_n$ converges to $s$. But the converse is not true in general. For example, if we put $s_n=(-1)^n$, then it diverges but $\pi_n \to 0$. If $\pi_n$ converges, we say $(s_n)$ is Cesàro summable.
If we treat $\pi_n$ as an integration with respect to the counting measure, things become interesting. Why don’t we investigate the operator defined to be
In this blog post we investigate this operator in Hilbert space $L^2(0,\infty)$.
## The Cesàro operator
Put $L^2=L^2(0,\infty)$ relative to Lebesgue measure, and the Cèsaro operator $C$ is defined as follows:
### Compactness and boundedness of $C$
From the example above, we shouldn’t expect $C$ to be too normal or well-behaved. But fortunately it is at the very least continuous: due to Hardy’s inequality, we have $\lVert C \rVert = 2$. I organised several proofs of this. But $C$ is not compact.
Consider a family of functions $(\varphi_A)_{A>0}$ where
(I owe Oliver Diaz for this family of functions.) It’s not hard to show that $\lVert \varphi_A \rVert = 1$. If we apply $C$ on it we see
Hence $\lVert C\varphi_A \rVert = \frac{\sqrt{1+A^2}}{A}$. Meanwhile for $B>A$, we have
It follows that
If we compute the norm on the right hand side we get
As a result, if we pick $f_n=\varphi_{2^n}$, then for any $m>n$ we get
Therefore, we find a sequence $(f_n)$ on the unit ball such that $(Cf_n)$ has no convergent subsequence.
Also we can find its adjoint operator:
Hence the adjoint is given by
$C^\ast$ is not compact as well. Further, another application of Fubini’s theorem shows that
Hence $I-C$ is an isometry, $C$ is normal.
### Bilateral shift, spectrum
In this section we study the spectrum of $C$ and $C^\ast$, which will be derived from properties of bilateral shift, which comes from $\ell^2$ space. For convenience we write $\mathbb{N}=\mathbb{Z}_{\geq 0}$. This section can also help you understand the connection between $L^2(0,1)$ and $L^2(0,\infty)$.
An operator $U$ on a Hilbert space $H$ is called a simple unilateral shift if $H$ has a orthonormal basis $(e_n)_{n \in \mathbb{N}}$ such that $U(e_n)=e_{n+1}$ for all $n \in \mathbb{N}$. This is nothing but right-shift operator in the sense of basis. Besides, we call $U$ a unilateral shift of multiplicity $m$ if $U$ is a direct sum of $m$ simple unilateral shifts (note: $m$ can be any cardinal number, finite or infinite).
If we consider the difference between $\mathbb{N}$ and $\mathbb{Z}$, we have the definition of bilateral shift. An operator $W$ on $K$ is called a simple bilateral shift if $K$ has a orthonormal basis $(e_n)_{n \in \mathbb{Z}}$ such that $We_{n}=e_{n+1}$ for all $n \in \mathbb{Z}$. Besides, if we consider the subspace $H$ which is spanned by $(e_n)_{n \in \mathbb{N}}$, we see $W|_H$ is simply a unilateral shift. Before we begin, we investigate some elementary properties of uni/bilateral shifts.
(Proposition 1) A simple unilateral shift $U$ is an isometry.
Proof. Note $(Ue_m,Ue_n)=(e_{m+1},e_{n+1})=\delta_{m+1,n+1}=\delta_{mn}=(e_m,e_n)$. $\square$
(Proposition 2) A simple bilateral shift $W$ is unitary, hence is also an isometry.
Proof. Note $(We_m,e_n)=(e_{m+1},e_n)=\delta_{m+1,n}=\delta_{m,n-1}=(e_m,W^{-1}e_n)$, which follows that $W^\ast=W^{-1}$. $\square$
Now let the Hilbert space $K$ and its subspace $H$ (invariant under $W$) be given. Consider the ‘orthonormal’ operator given by $Re_n=e_{-(n+1)}$. It follows that $R$ is a unitary involution and
With these tools, we are ready for the most important theorems.
$W=I-C^\ast$ is a simple bilateral shift on $K=L^2$.
Step 1 - Obtaining missing subspace, operator and basis
Here we put $H=L^2(0,1)$, which can be canonically embedded into $L^2(0,\infty)$ in the obvious way (consider all $L^2$ functions vanish outside $(0,1)$). It is natural to put this, as there are many similarities between $L^2(0,1)$ and $L^2(0,\infty)$.
Explicitly,
Also we claim the basis to be generated by $e_0= \chi_{(0,1)}$. First of all we show that $(We_n)_{n \geq 0}$ is orthonormal. Note as we have proved, $W^\ast W = (I-C)(I-C^\ast)=I$. Without loss of generality we assume that $m \geq n$ and therefore
If $m=n$, then $(e_m,e_n)=(e_0,e_0)=1$. Hence it is reduced to prove that $(W^ke_0,e_0)=0$ for all $k>0$. First of all we have
meanwhile
Hence $We_0 \perp e_0$. Suppose now we have $(W^ke_0,e_0)=0$, then
Note $W^ke_0$ always vanishes when $x \geq 1$: when we are doing inner product, $[1,\infty)$ is automatically excluded. With these being said, $(W^ne_0)_{n \geq 0}$ forms a orthonormal set. By The Hausdorff Maximality Theorem, it is contained in a maximal orthonormal set. But since $H=L^2(0,1)$ is separable (if and only if it admits a countable basis) (proof), $(W^ke_0)$ forms a basis of $H$. From now on we write $(e_n)_{n \geq 0}$.
To find the involution $R$, note first $W=I-C^\ast$ is already unitary (also, if it is not unitary, then it cannot be a bilateral shift, we have nothing to prove), whose inverse or adjoint is $W^\ast=I-C$ as we have proved earlier. Hence we have
But we have no idea what $R$ is exactly. We need to find it manually (or we have to guess). First of all it shall be guaranteed that $RH=H^\perp$. Since $H$ contains all $L^2$ functions vanish on $[1,\infty)$, functions in $RH$ should vanish on $(0,1)$. It is natural to put $R(f)(x)=g(x)f\left( \frac{1}{x}\right)$ for the time being. $g$ should be determined by $e_{-1}$. Note $e_0\left(\frac{1}{x}\right)=\chi_{[1,\infty)}$ almost everywhere, we shall put $g(x)=-\frac{1}{x}$. It is then clear that $Re_0=W^{-1}e_0$ and $RH=H^\perp$. For the third condition, we need to show that
Note
Step 2 - With these, $W$ in step 1 has to be a simple bilateral shift
This is independent to the spaces chosen. To finish the proof, we need a lemma:
Suppose $K$ is a Hilbert space, $H$ is a subspace and $e_0 \in H$. $W$ is a unitary operator such that $W^ne_0 \in H$ for all $n \geq 0$ and $(e_n=W^ne_0)_{n \geq 0}$ forms a orthonormal basis of $H$. $R$ is a unitary involution on $K$ such that
then $W$ is a simple bilateral shift.
Indeed, objects mentioned in step 1 fit in this lemma. To begin with, we write $e_n=W^ne_0$ for all $n \in \mathbb{Z}$. Then $(e_n)_{n \in \mathbb{Z}}$ is an orthonormal set because for arbitrary $m,n \in \mathbb{Z}$, there is a $j \in \mathbb{Z}$ such that $m+j,n+j \geq 0$. Therefore
Since $(e_0,e_1,\cdots)$ spans $H$, $RH=H^{\perp}$, we see $(Re_0,Re_1,\cdots)$ spans $H^{\perp}$. But
hence $(e_{-1},e_{-2},\cdots)$ spans $H^\perp$. By definition of $W$, it is indeed a bilateral shift. And our proof is done $\square$
## References
• Walter Rudin, Functional Analysis.
• Arlen Brown, P. R. Halmos, A. L. Shields, Cesàro operators.
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2021-07-26 22:55:23
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http://math.stackexchange.com/questions/236873/variance-and-standard-deviation-of-multiple-dice-rolls
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# Variance and Standard Deviation of multiple dice rolls
I'm trying to determine what the variance of rolling $5$ pairs of two dice are when the sums of all $5$ pairs are added up (i.e. ranging from $10$ to $60$).
My first question is, when I calculate the variance using $E[X^2]-E[X]^2$ I get $2.91$, but my Excel spreadsheet and other sites I've googled give $3.5$ with no explanation of what me taking place. Which one is correct?
Second, to calculate the variance of a random variable representing the sum of the $5$ pairs (i.e. between $10$ and $60$), is it simply $5 \times Var(X)$? What about the standard deviation, is it $\sigma \sqrt{n}$?
Last, is there any difference between calculating the dice sums as "$5$ pairs of $2$ dice" and "$10$ dice"? Will it make a practical difference? (I find it easier to calculate it as $10$ dice).
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It is not the variance, but the expected value of a dice roll, $E(X)$ that is 3.5. – wnvl Nov 14 '12 at 1:53
The assumptions in the second and third part of the question are all correct. – wnvl Nov 14 '12 at 1:55
So, in other words the standard deviation of 5 pairs of 2 dice and the standard deviation of 10 dice is 5.3759? Can you confirm? – CodyBugstein Nov 14 '12 at 2:02
In your problem, there are five independent experiments, each of which is the sum of two die rolls. This is different from ten dice rolls. For example, you would expect a mean of 7 from your experiment, and 3.5 from the single dice rolls.
In excel, create two columns of five rows of random die rolls (=INT(RAND()*6)+1 in cells A1..B5), and then add the first two columns in the third column to make the random variable you want statistics on (=A1+B1, etc. in cells C1..C5).
After this, the excel built-in functions AVERAGE(C1:C5), VAR(C1:C5), and STDEV(C1:C5) can be used to compute the average ${\tt AVERAGE}=\frac{1}{N} \sum X_i$, sample variance ${\tt VAR}=\frac{1}{N-1} \sum (X_i-\bar{X})^2$, and sample standard deviation ${\tt STDEV} = \sqrt{{\tt VAR}}$.
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So we are tossing $10$ dice. Let $X_i$ be the result of the $i$-th toss. Let $Y=X_1+X_2+\cdots +X_{10}$. It seems that you want the variance of $Y$.
The variance of a sum of independent random variables is the sum of the variances. Now calculate the variance of $X_i$. This as usual is $E(X_i^2)-(E(X_i))^2$.
We know that $E(X_i)=3.5$. For $E(X_i^2)$, note that this is $$\frac{1}{6}(1^2+2^2+3^2+4^2+5^2+6^2).$$
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2016-07-24 09:04:17
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https://plainmath.net/94714/rewrite-the-expression-in-terms-of-the-g
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# Rewrite the expression in terms of the given function. 1/(1+cos x)+cos x/(1-cos x);cot x
Kymani Hatfield 2022-10-22 Answered
Rewrite the expression in terms of the given function.
$\frac{1}{1+\mathrm{cos}x}+\frac{\mathrm{cos}x}{1-\mathrm{cos}x};\mathrm{cot}x$
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honejata1
$\frac{1}{1+\mathrm{cos}x}+\frac{\mathrm{cos}x}{1-\mathrm{cos}x};\mathrm{cot}x\phantom{\rule{0ex}{0ex}}=\frac{1-\mathrm{cos}x+\left(1+\mathrm{cos}x\right)\left(\mathrm{cos}x\right)}{1-{\mathrm{cos}}^{2}x}\phantom{\rule{0ex}{0ex}}=\frac{1+{\mathrm{cos}}^{2}x}{1-{\mathrm{cos}}^{2}x}\phantom{\rule{0ex}{0ex}}=\frac{1+{\mathrm{cos}}^{2}x}{{\mathrm{sin}}^{2}x}\phantom{\rule{0ex}{0ex}}=\frac{1}{{\mathrm{sin}}^{2}x}+\frac{{\mathrm{cos}}^{2}x}{{\mathrm{sin}}^{2}x}\phantom{\rule{0ex}{0ex}}={\mathrm{csc}}^{2}x+{\mathrm{cot}}^{2}x\phantom{\rule{0ex}{0ex}}=\left(1+{\mathrm{cot}}^{2}x\right)+\mathrm{cot}x\phantom{\rule{0ex}{0ex}}=1+2{\mathrm{cot}}^{2}x$
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2022-12-04 04:09:54
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http://mathhelpforum.com/algebra/169857-electronic-bank-teller-question.html
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# Math Help - Electronic bank teller question
1. ## Electronic bank teller question
An electronic bank teller registered $775 after it had counted 120 notes and$975 after it had counted 160 notes.
Find a formula for the sum registered, in terms of the number of notes counted.
Was there a sum already on the register when counting began?
If so, how much?
2. Let Y = sum registered
N = Number of notes counted
a = value of notes
S= sum in the register when counting began...
$775 = 120a+s$
$975=160a+s$
then.....
3. Thanks so much.
I had this question in my worksheet as well.
I ended up getting it right.
4. Thanks for all of your help.
|
2015-04-25 12:19:53
|
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|
https://codereview.stackexchange.com/questions/240219/jquery-form-find-radio-class
|
In my application we have four inputs radio controls and on the load the value is checked to true. When the user select another radio and then save the form I want to get the new value. I am using the find class but then I need to use checked[0] is there a better way to do this?
JS
$("#form").submit(function (event) { event.preventDefault(); console.log('free-text-form'); var sortOrder =$(this).data('sortorder');
console.log(sortOrder);
var form = $(this); console.log('Processing Current Check'); var checked = form.find(".radio-Class:checked"); var currentChecked = checked[0]; console.log(currentChecked); console.log(currentChecked.value); if (checkedRegRef.length == 1) { var NewId = currentChecked.value; console.log(NewId); } }); Working Example https://jsfiddle.net/tjmcdevitt/vh9n5srL/87/ • Error in console: Uncaught ReferenceError: checkedRegRef is not defined – Sᴀᴍ Onᴇᴌᴀ Apr 9 at 19:05 • Sorry I corrected it – Jefferson Apr 10 at 12:48 ## 2 Answers With checked[0] you are getting a reference to the actual DOM element (instead of the jQuery object) but that is unnecessary in your case since jQuery provides a val() method, which returns the current value of the first element in the set of matched elements. So in your case, you could simply do: var checkedVal = form.find(".radio-Class:checked").val(); A better way to get the selected value as pointed out here by @Peter J is to use the input[name=radioName]:checked selector. Selecting through name attributes ensures that you select the desired radio group since these are meant to be unique. For better performance, you can pass in the form id as the second argument inside the selector method, which is used as a context here (this is same as if you would use $("#form").find("input[name=radioName]:checked")), here is the refactored code:
$("#form").submit(function(event) { var$formEl = $(this); var$labelEl = $formEl.find('#label1'); var radioVal =$('input[name=RegimenReferences]:checked', $formEl).val(); event.preventDefault();$labelEl.text(radioVal);
});
body {
background: #20262E;
font-family: Helvetica;
}
#form {
background: #fff;
font-size: 25px;
text-align: center;
transition: all 0.2s;
margin: 0 auto;
width: 300px;
}
button {
background: #0084ff;
border: none;
font-size: 15px;
color: #fff;
}
#banner-message.alt {
background: #0084ff;
color: #fff;
margin-top: 40px;
width: 200px;
}
#banner-message.alt button {
background: #fff;
color: #000;
}
<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.3.1/jquery.min.js"></script>
<form id="form" class="form-horizontal" data-sortorder="1">
<p>Update Values</p>
<label id="label1" type="text">1</label>
<div>
(a) aaaaaa
</label>
</div>
<div>
(b) bbbbbb
</label>
</div>
<div>
(c) cccccc
</label>
</div>
<div>
(c) cccccc
</label>
</div>
<div class="text-center">
<button type="submit" class="btn btn-primary modal-submit-btn">Save</button>
<button type="button" class="btn btn-default modal-close-btn" data-dismiss="modal">Close</button>
</div>
</form>
Edit 1: Since you already got the form selected you can pass that as the context therefore you don't need the form id.
I am using the find class but then I need to use checked[0] is there a better way to do this?
As was already answered, the val() method can be used to get the value of the first element matched in the collection. Additionally .eq() could be used to get a reference to the first element if necessary.
The accepted answer to In jQuery, how do I get the value of a radio button when they all have the same name? mentions both the jQuery .val() method, as well as a vanilla Javascript technique.
Because this answer keeps getting a lot of attention, I'll also include a vanilla JavaScript snippet.
It is wise to consider whether you really need jQuery on your page. Take a look at youmightnotneedjquery.com/ (and also this article). If you decide to eliminate it, you could just access the form elements via HtmlFormElement.elements and the forms property.
const label = document.getElementById('label1');
event.preventDefault();
label.innerHTML = document.forms[0].elements.RegimenReferences.value;
});
With the approach above there are no function calls to query the DOM for the elements in the form submission callback handler. This may not be much faster but would require fewer function calls.
## Other review points
• Indentation is inconsistent - the first line in the callback function is indented with three spaces, then the next line is indented with a tab and a space and then subsequent lines appear to be indented with twelve spaces. It is best to use consistent indentation for the sake of readability.
• DOM lookups aren't cheap so it is wise to store those in variables - e.g. const label as defined in the snippet above.
• There is an Unused Variable: sortOrder (other than being logged to the console)
• It is wise to use strict equality comparisons unless there is a chance one operand might not have the same type. For example - instead of:
if (checkedRegRef.length == 1) {
if (checkedRegRef.length === 1) {
• Just out of curiosity and this might not be the best example, but when you say "DOM lookups aren't cheap so it is wise to store those in variables", isn't this debatable in this case if the label is intended to only change after the form is submitted? I always assumed that you don't want to store the DOM lookup by default and only if it's worth it. So my thinking here was: "I have a label which only changes after the user clicks the button, I don't want to bloat the memory until then". Even this is a very insignificant case, do I raise a valid point ? – htmn Apr 15 at 15:46
• Yes it is debatable, and depends on various factors like how often the user would likely submit the form. In the "best case" scenario the user might only submit the form once or twice, leading to the callback function getting called and consequently the call to .find() to lookup the label element. In the "worst case" scenario the form might get submitted multiple times, leading to that lookup each time the callback is executed. – Sᴀᴍ Onᴇᴌᴀ Apr 15 at 15:52
|
2020-08-14 17:46:31
|
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|
https://math.stackexchange.com/questions/3923944/find-volume-using-triple-integration-with-cylindrical-coordinates
|
# Find volume using triple integration with cylindrical coordinates
Find volume of $$E$$ using triple integration and cylindrical coordinates, when $$E$$ is bounded by $$x^2+y^2=x,\quad y=0,\quad y=x,\quad z=0,\quad z=\sqrt{x^2+y^2}$$ I know that in cylindrical coordinates $$x=r\cos\varphi,\quad y=r\sin\varphi,\quad z=h,\quad \text{ where } r\geq0 \text{ and } 0\leq\varphi\leq2\pi$$ but I'm very confused how to set up this integral. Cylindrical coordinates are quite new for me and it's hard to understand, how to make this conversion. So I would be grateful if anyone can help me with this.
$$x^2+y^2=x$$ in polar form is just $$r=\cos\varphi$$. The lines $$y=0$$ and $$y=x$$ intersect this curve at $$\varphi=0$$ and $$\varphi=\frac\pi4$$ respectively. So our outer integrals are $$\int_{\varphi=0}^{\pi/4}\int_{r=0}^{\cos\varphi}r\,dr\,d\varphi$$ The bounds of $$z$$ are just $$z=0$$ to $$z=r$$ in cylindrical coordinates, so our final answer is $$\int_{\varphi=0}^{\pi/4}\int_{r=0}^{\cos\varphi}\int_{z=0}^rr\,dz\,dr\,d\varphi$$
I imagine the projection of your figure on $$Oxy$$ as upper segment cropped from circle by line $$y=x$$. So, firstly let's consider volume in Cartesian coordinates $$\int\limits_{0}^{\frac{1}{2}}\int\limits_{x}^{\sqrt{\frac{1}{4}-\left(x-\frac{1}{2}\right)^2}}\int\limits_{0}^{\sqrt{x^2+y^2}}dzdydx$$ So to find borders for cylindrical coordinates we need to solve inequalities
$$\begin{array}{} 0 \leqslant r \cos \phi \leqslant \frac{1}{2} & \\ r \cos \phi \leqslant r \sin \phi \leqslant \sqrt{\frac{1}{4} -\left(r \cos \phi-\frac{1}{2}\right)^2 } & \\ 0 \leqslant z \leqslant r \end{array}$$ From 1-st and 2nd line inequalities we have $$0 \leqslant \cos \phi \leqslant \sin \phi$$, so we obtain $$\phi \in \left[\frac{\pi}{4},\frac{\pi}{2} \right]$$ and $$0 \leqslant r \leqslant \cos \phi$$
$$\int\limits_{\frac{\pi}{4}}^{\frac{\pi}{2}}\int\limits_{0}^{\cos \phi}\int\limits_{0}^{r}rdzdrd\phi$$
Addition: In case where we consider "sector" of circle i.e. part of circle between lines $$y=x$$ and $$y=0$$, then volume in Cartesian coordinates will be
$$\int\limits_{0}^{\frac{1}{2}}\int\limits_{0}^{x}\int\limits_{0}^{\sqrt{x^2+y^2}}dzdydx+\int\limits_{\frac{1}{2}}^{1}\int\limits_{0}^{\sqrt{\frac{1}{4}-\left(x-\frac{1}{2}\right)^2}}\int\limits_{0}^{\sqrt{x^2+y^2}}dzdydx$$
Good news in this case is, that we can calculate this volume again using the founded volume in previous , circle segment, case subtracting it from the volume over the entire semicircle, which is
$$\int\limits_{0}^{1}\int\limits_{0}^{\sqrt{\frac{1}{4}-\left(x-\frac{1}{2}\right)^2}}\int\limits_{0}^{\sqrt{x^2+y^2}}dzdydx=\int\limits_{0}^{\frac{\pi}{2}}\int\limits_{0}^{\cos \phi}\int\limits_{0}^{r}rdzdrd\phi$$ so we obtain $$\int\limits_{0}^{\frac{\pi}{2}}\int\limits_{0}^{\cos \phi}\int\limits_{0}^{r}rdzdrd\phi-\int\limits_{\frac{\pi}{4}}^{\frac{\pi}{2}}\int\limits_{0}^{\cos \phi}\int\limits_{0}^{r}rdzdrd\phi = \int\limits_{0}^{\frac{\pi}{4}}\int\limits_{0}^{\cos \phi}\int\limits_{0}^{r}rdzdrd\phi$$
• @Math Lover. I am familiar with this point of view, as Parcly Taxel's answer is 1h before your comment, and I decided to suggest OP possible alternative. My solution is not "between $y$ -axis and the circle", it is up of $y=x$ and down of circle and, as I wrote in first sentence of my answer, is upper segment cropped from circle. Formally $y=0$ also participates (although at one point) in upper segment bounds, so we have 2 possible answers: one Parcly Taxel's, one mine. Can you suggest a formal arguments in your favor? – zkutch Nov 26 '20 at 23:27
• I think we should all be grateful for your comment(s), as it makes picture more clear. Meanwhile, I wrote addition, where I linked both approaches. – zkutch Nov 27 '20 at 4:31
• That is good addition! – Math Lover Nov 27 '20 at 4:37
|
2021-05-06 00:21:41
|
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|
https://brilliant.org/problems/its-hip-to-be-square/
|
# It's hip to be a square!
Number Theory Level 4
$$M$$ and $$N$$ are integers such that
$M^2 = N^2 + 8N -3 .$
What is the sum of all possible (distinct) values of $$N^2$$?
×
|
2016-10-24 07:00:31
|
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|
https://mathalino.com/tag/reviewer/circular-beam
|
# circular beam
## Hollow Circular Beam with Known Cracking Moment
Situation
A concrete beam with cross section in Figure CO4-2B is simply supported over a span of 4 m. The cracking moment of the beam is 75 kN·m.
1. Find the maximum uniform load that the beam can carry without causing the concrete to crack, in kN/m.
A. 35.2 C. 33.3 B. 37.5 D. 41.8
2. Find the modulus of rapture of the concrete used in the beam.
A. 4.12 MPa C. 3.77 MPa B. 3.25 MPa D. 3.54 MPa
3. If the hallow portion is replaced with a square section of side 300 mm, what is the cracking moment of the new section in kN·m?
A. 71.51 C. 78.69 B. 76.58 D. 81.11
## Bending Stress and Shearing Stress in Timber Beam
Bending Stress $f_b = \dfrac{M}{S} = \dfrac{Mc}{I}$ Horizontal Shear Stress $f_v = \dfrac{VQ}{Ib}$ For Rectangular Sections $f_b = \dfrac{6M}{bd^2}$ $f_v = \dfrac{3V}{2bd}$
|
2020-09-26 14:56:59
|
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|
https://ecrypt-eu.blogspot.co.uk/2017/
|
## Friday, June 16, 2017
### Boomerang Attacks
In cryptography, a boomerang attack is a method of cryptanalysis that is based on differential cryptanalysis.
Boomerang attacks were first introduced by Wagner and allow an adversary to concatenate two high probability differential trails to attack a cipher. This is especially useful if there is a lack of long differentials with sufficient probabilities. The adversary can therefore decompose the encryption function $F$ in two subciphers $f$ and $g$ such that $F = f \circ g$. Then the adversary can search for high probability trails $\Delta \rightarrow \Delta^*$ with probability $p$ for $f$ and $\nabla \rightarrow \nabla^*$ with probability $q$ for $g$. The differential trails can then be combined in a chosen plaintext/adaptive chosen ciphertext attack to mount a boomerang distinguisher and then a key recovery attack based on this distinguisher to recover the secret key.
A boomerang distinguisher
The basic attack works as follows:
1. The adversary chooses a random plaintext $X_1$ and calculates $X_2 = X_1 \oplus \Delta$.
2. The adversary requests the ciphertexts for $X_1$ and $X_2$ from an encryption oracle which are $Y_1 = F(X_1)$ and $Y_2 = F(X_2)$
3. Calculate ciphertexts $Y_3 = Y_1 \oplus \nabla$ and $Y_4 = Y_2 \oplus \nabla$.
4. Request the decryptions of $Y_3$ and $Y_4$ to obtain $X_3 = F^{-1}(Y_3)$ and $X_4 = F^{-1}(Y_4)$.
5. If the difference between $X_3$ and $X_4$ is the same as between $X_1$ and $X_2$, namely $\Delta$ we obtain a correct quartett $(X_1, X_2, X_3, X_4)$.
Calculating a correct quartet requires an attacker to consider both plaintext pairs $(X_1, X_2)$ and $(X_3, X_4)$ and results in a total probability of (pq)^2.
For an attack to succeed, for the probability of the boomerang distinguisher it must hold that $(pq) > 2^{n/2}$. For N plaintext pairs, an adversary expects about $N\cdot(pq)^2$ correct quartets in an attack, while there are only $N\cdot2^{-n}$ (where n is the blocksize) correct quartets for an ideal primitive.
## Thursday, April 27, 2017
### Yet Another "Ni Hao (Hello)"
Hello, everyone. I am Junwei Wang from China. It’s pleasant to be an ECRYPT-NET fellow and to receive funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie actions (MSCA).
I received my bachelor degree and master degree from Shandong University in 2012 and the University of Luxembourg in 2015, respectively. My master thesis is about the practical implementation of countermeasures resistant again high-order differential power analysis (DPA). Presently, I am doing my Ph.D. student at CryptoExperts under the supervisor of Jean-Sébastien CORON, Sihem MESNAGER, Pascal PAILLIER, and Matthieu RIVAIN. My research interest is white-box cryptography.
The advent of content-protected applications and mobile payment systems in recent years motivates the exploration of a solution to protect sensitive information from being extracted under the white-box context in which the attacker has the power of control the whole process of the execution of software. Though some theoretical evidence reveals the fact that no generic obfuscator can be constructed to shield algorithms to be attacked, and all existed practical schemes has been broken, it is still interesting to investigate new schemes which can withstand all the existing attacks, and to propose and analyse a new attacking method which is more generic than the existing ones. I hope somebody has similar interest with me, then we can deeply explore this area together.
By the way, I am looking forward to meeting with you in Paris during EUROCRYPT.
## Monday, April 17, 2017
### What does privacy mean to you? A 5-day challenge
I recently came across The Privacy Paradox project, a call by WNYC Studios to take part in a five-day-long challenge on defining what does privacy mean to yourself.
Amongst its best features, the process can be started anytime, by anyone, just by registering with an e-mail account. From that moment and during the five following days, you will receive a daily e-mail explaining you the topic addressed by that day's podcast, most of them finishing with an easy demand to the listener to reflect on the matter.
With the audio's length ranging from 11 to 15 minutes, and the topics from cryptography --with Bruce Schneier starring on the first episode-- to psychology, there is something on it for everyone, and at a very accessible level. I personally found the format very nice and entertaining, and it is maybe something to learn about when we talk about privacy with people not so interested in the topic.
Finally, the people behind the project also gathered a nice list with things you can do to face the current privacy situation.
## Tuesday, April 11, 2017
### Robust encryption for symmetric primitives
Robustness for encryption schemes has been introduced in the context of public-key encryption in the work of Abdalla, Bellare and Neven. In a nutshell, it states that a ciphertext cannot be decrypted under two different keys. Later, their work has been extended, by taking into account the cases where the keys are adversarially generated.
The work of Farshim, Orlandi and Roşie studies the robustness in the context of symmetric primitives under the incorrect usage of keys. Roughly speaking, a key-robust scheme does not output ciphertexts/tags that are valid with respect to distinct keys. Key-robustness is a notion that is often tacitly expected/assumed in protocol design --- as is the case with anonymous auction, oblivious transfer, or public-key encryption.
To motivate the new notion, "consider the following protocol, for constructing a ${3 \choose 2}$-OT protocol using only ${3 \choose 1}$-OTs: the sender picks $3$ random keys $k_1,k_2,k_3$ and inputs the message $x_1=(k_2,k_3),x_2=(k_1,k_3)$ and $x_3=(k_1,k_2)$ to the OT. At the same time, the sender sends encryptions of his messages under these keys, i.e., sends $c_i=E(k_i,m_i)$ for $i=1..3$. Now the receiver inputs the index of the message he does not want to learn to the ${3 \choose 1}$-OT and learns all keys except $k_i$. Intuitively the fact that the messages are sent only once (encrypted) should guarantee that the sender's choice of messages is uniquely defined. However, consider the following attack: the corrupt sender inputs $x^*_1=(k_2, k^*)$ (instead of $x_1$) such that $D(k^*,c_3)=m^*_3$ with $m^*_3\neq m_3$ and $m^*_3\neq \bot$. This means that the receiver will see two different versions of $m_3$ depending on whether the receiver asked for the pair $(2,3)$ or $(1,3)$. (This attack is an example of input-dependence and is a clear breach of security since it cannot be simulated in the ideal world)."
In terms of the results, the new work considers "both notions where the adversary has control over the keys and notions where the keys are generated honestly. The strongest notion that is formulated is called complete robustness and allows an adversary to generate the keys used in the system. The work shows that whether the adversary is in control of the keys or not makes a significant difference, by giving separations between the notions. While previous work in the public-key setting also had to deal with adversarially generated keys that were also invalid, this is not an issue in the setting, since in the symmetric world keys are often bit-strings of some pre-specified length and can be easily checked for validity. By focusing on correctly formed keys it can can shown equivalence between complete robustness and a syntactically simpler notion, which we call full robustness." Then, it is shown that full robustness composes well: any fully robust symmetric encryption when combined with a fully robust MAC results in a fully robust AE scheme. Analogous composition results also hold for MAC-then-Encrypt and Encrypt-and-MAC.
One of the most interesting question is if "feasibility results for robustness in the public-key setting can be translated to the symmetric setting. This turns out not to be the case. The main reason for this is that in the asymmetric setting the public key can be used as a mechanism to commit to its associated secret key. In the symmetric case, on the other hand, there is no such public information. It might be tempting to think that one can just commit to the secret key and append it to the ciphertext. Unfortunately this approach cannot be proven secure due to a circular key-dependency between the encryption and the commitment components. To give a provably secure construction, with the authors constructing appropriate commitments that can be used in this setting. This requires a right-injective PRG, that can be in turn based on one-way permutations. This result relies on the one-time security of the MAC and its collision-resistance, which once again is based on right-injective PRGs."
## Monday, April 3, 2017
### Three everyday git scenarios
You may remember Ralph's post on git basics from a little over a year ago. In this post, I'll share three things I've learned are possible (and practically painless) to do with git that go beyond the basic add, merge, push, and pull. Everything in this post is done from the command line.
## Scenario 1
You're working on a project with others. These hardworking colleagues of yours just pushed a bunch of commits and you want to see exactly what they changed since your last commit.
### What to do
Use git diff. Besides using it to show unstaged changes, you can also use git diff to show changes between any two commits. Suppose that after your last commit, your colleagues made 4 commits. To see the changes, use git diff HEAD~4 HEAD or git diff HEAD^^^^ HEAD. If you don't want to count how many commits there were, you can look up the abbreviated commit IDs (SHA-1 hashes in hex) using git log --oneline. Then, you could use something like git diff 54180a8 129ec44.
There's a lot more to git diff: you can use it to compare specific files, you can show differences at the word level rather than at the line level, etc. If you want to learn more about it, see its page on the git website. If you're working on LaTeX files, git-latexdiff is convenient: given any two commits, it will produce a PDF file showing the changes, with removed text striked through and in red, and added text underlined and in blue.
## Scenario 2
You were in the zone, hacking away at multiple issues and successfully completing all of them. Well done, you! Wait—each issue should have its own commit...
### What to do
Use interactive staging: use git add -p or git add --patch to add the file or files. Git will look at each file you want to add and split the changes into hunks. For each hunk, it will show you the diff and ask you what to do with it:
Stage this hunk [y,n,q,a,d,/,s,e,?]?
Here is the full list of options. They're pretty easy to remember, especially if you're a vi user who is used to navigating with HJKL.
y - stage this hunk
n - do not stage this hunk
q - do not stage this hunk or any of the remaining ones
a - stage this hunk and all later hunks in the file
d - do not stage this hunk or any of the later hunks in the file
g - select a hunk to go to
/ - search for a hunk matching the given regex
j - leave this hunk undecided, see next undecided hunk
J - leave this hunk undecided, see next hunk
k - leave this hunk undecided, see previous undecided hunk
K - leave this hunk undecided, see previous hunk
s - split the current hunk into smaller hunks
e - manually edit the current hunk
? - print help
git add -p is a powerful command that helps you keep your commits reasonably sized. It does require some care, though, since each individual commit should be consistent.
## Scenario 3
You have to stop working, but you haven't finished fixing the issue you're working on.
### What to do
You should do something because you don't want to have a dirty working directory.
Option 1: commit now, then use git commit --amend (introduced in Ralph's post) once you've finished what you were working on. git commit --amend is useful for a bunch of other things, like adding files you forgot to stage to a commit and fixing typos in a commit message.
Commits are local, so what should you do if you're worried about hardware failure? If you're working on a personal project, it may be acceptable to push this commit and later push the amended commit. You'll need the -f (--force) flag for the latter push. If you're working on a project with others, however, it would be bad practice to amend a commit that you've already pushed. Instead, you could create a temporary personal branch, commit your changes to this branch, and push it to the remote repository. Then, you could push the amended commit to this branch without worrying about rewriting anyone else's history and merge it with the main branch when you've finished fixing the issue.
Option 2: shelve your changes with git stash, which will sweep away both staged and unstaged changes, leaving you with a clean working directory. You can stash changes more than once. To see all stashes, use git stash list. To re-apply the most recent stash you made, use git stash pop. By default, git stash excludes new files (that haven't yet been staged) and ignored files. git stash is also useful when you want to see upstream changes made by someone else, but aren't ready to commit your work.
There's much more you can do with stashes: apply one stash to multiple branches, delete stashes you no longer need, stash parts of a file, etc. Stashes are always local; they can never be pushed to a remote repository. Atlassian has a good, detailed tutorial on git stash.
Some books you may (or may not) find useful.
## Tuesday, March 21, 2017
### Learn You a GPU For Great Good! (Part 1?)
Side note: I stole the title from the most famous, most awesome Haskell book I know.
If you are reading this blog you are most likely interested in cryptography. Today I want to convince you that GPUs are also, well, pretty awesome. I have personally done a few crypto-related projects using GPUs and this post is my attempt at crystallizing the knowledge and experience I built up during that time.
The purpose of this post is to provide a simple, meaningful introduction to developing GPU-accelerated programs. We will discuss setup, the two primary frameworks, basic code examples and development workflow as well as some optimization tips. In the end, I want to show that developing this type of application is not hard at all. If the post is successful I may do a follow-up with a few more detailed and tricky examples. Throughout this post I will assume you are familiar with basic C and/or C++, as the code examples will be in that language. I will not focus too much on develop complicated kernels or how to exploit multi-dimensional parallelism, I will leave that for a later post. Instead, I will focus on a few things that may help you in making the firsts steps towards GPU programming easier, as well as a few things that may help it scale a bit better.
## The Why & When
GPU programming was originally designed for, and should be used for, large-scale parallel computation problems. The more parallelism you can utilize, the better GPUs will fit your problem. The most simple example is probably when you loop over a very large collection of elements, performing on each a simple operation independently.
For large-scale parallel computation problems I tend to think of three different architectural setups that you can use (they also mix). The simplest is utilizing multi-core CPUs (possibly over many machines). This has the shortest development time due to its familiarity and easy-of-use and is suitable to many applications. CPUs are of course trivially available. On the other end of the spectrum is the development of custom hardware clusters, utilizing many FPGAs or even ASICs. Development time is fairly long, even for experienced hardware designers; the upside is that this very likely gives you optimal performance.
GPUs fall somewhere in the middle. Development time is very close to that for CPUs; the primary constraint is availability. It is simply easier to get access to CPU clusters. However, these days you can also rent all the GPU power you need from Amazon EC2 instances, as was done for the recent SHA1 collision. If you solve the availability issue, you can get a lot of bang out of your buck performance-wise.
## The How
First, you need to get your hands on a machine with a GPU, preferably a remote machine or otherwise a machine with more than one GPU. The reason is that if your GPU is also driving your desktop environment, programming errors may cause your computer to hang or crash. It also allows you to more easily run long-lasting kernels as well as giving you more reliable performance.
### CUDA vs OpenCL
Assuming you have a GPU in your system, your next choice is between CUDA and OpenCL, two programming environments for GPU programming. If you do not plan to use an NVIDIA GPU you are stuck with OpenCL, whereas you otherwise have the choice of using CUDA.
Having used both for different projects at different times, I can say that both are perfectly usable and that the differences are mostly superficial. OpenCL is more portable and integrates easier into existing projects; CUDA has the superior tool-chain.
The examples in this post will be for CUDA, as it typically involves less boilerplate. Also, we will use the more basic CUDA C++ implementation, as it provides a better basis for understanding than special-purpose libraries. This is particularly relevant if you want to computations that are not a native part of these libraries, which is definitely true if you want to, for instance, compute CPA-like correlations in parallel.
### Hello World
I am not one to break tradition and thus we start the "Hello world" of classic parallel programming, namely SAXPY. Or, more formally, given input vectors $\textbf{x}, \textbf{y}$ of length $n$ and a scalar $a$, compute the output vector $\textbf{z}$ where $\textbf{z} = a\textbf{x} + \textbf{y}$.
First let us consider the basic C implementation of this function, where $z = y$, i.e., we update $y$ using the scalar $a$ and a vector $x$.
1: void saxpy(int n, float a, float * __restrict__ x, float * __restrict__ y) {
2: for (int i = 0; i < n; ++i) {
3: y[i] = a*x[i] + y[i];
4: }
5: }
6:
7: // ...
8: int n = 1 << 20;
9: // allocate vectors x,y of n elements each.
10: // ...
11:
12: saxpy(n, 3.14, x, y);
Nothing too special going on here. We simply iterate over every element and perform our update with the scalar $a=3.14$. Note the use of the __restrict__ keyword to indicate that x and y point to different objects in memory. Just giving the compiler a helping hand, which is generally a useful thing to do. Anything that makes it behave less like a random function, I say.
Conversion to CUDA is straightforward. In GPU programming you are always defining what a single parallel unit of computation is doing, this is called a kernel. When programming such a kernel, you are computing from the point of view of the thread. Before delving in too deep, let us see what the CUDA-equivalent code looks like.
1: __global__
2: void saxpy(int n, float a, float * __restrict__ x, float * __restrict__ y) {
3: int i = blockIdx.x*blockDim.x + threadIdx.x;
4: if (i < n) {
5: y[i] = a*x[i] + y[i];
6: }
7: }
8:
9: // ...
10: const int n = 1<<20;
11:
12: // allocate and initialize host-side buffers x,y
13: // ...
14:
15: // allocate device-side buffers x,y
16: cudaMalloc((void **)&d_x, sizeof(float) * n);
17: cudaMalloc((void **)&d_y, sizeof(float) * n);
18:
19: // copy host-side buffers to the device
20: cudaMemcpy(d_x, x, sizeof(float) * n, cudaMemcpyHostToDevice);
21: cudaMemcpy(d_y, y, sizeof(float) * n, cudaMemcpyHostToDevice);
22:
23: // compute the saxpy
24: const int threads_per_block = 256;
25: const int number_of_blocks = n / threads_per_block;
26: saxpy<<<number_of_blocks, threads_per_block>>>(n, 3.14, d_x, d_y);
27:
28: // copy the output buffer from the device to the host
29: cudaMemcpy(y, d_y, sizeof(float) * n, cudaMemcpyDeviceToHost);
30:
31: // free the device buffers
32: cudaFree(d_x);
33: cudaFree(d_y);
34:
35: // clean up the x, y host buffers
36: // ...
Let us consider the kernel first, denoted by the simple fact of the function definition starting with __global__. The parameters to the function are the same as before, nothing special there. Line 3 is a key first step in any kernel: we need to figure out the correct offset into our buffers x and y. To understand this, we need to understand CUDA's notion of threads and blocks (or work groups and work items in OpenCL).
The Grid
The CUDA threading model is fairly straightforward to imagine. A thread essentially computes a single instance of a kernel. These threads form groups called blocks that have somewhat-more-efficient inter-thread communication primitives. The blocks together form what is known as the grid. The grid can have up to three dimensions, i.e., the blocks can be ordered into $(x,y, z)$ coordinates. The same goes for threads inside a block, they can be addressed with $(x, y, z)$ coordinates as well.
Mostly though, I have tended to stick to 1-dimensional grids. This is simply dividing a vector of $n$ elements into $n/m$-sized sequential blocks (even better if $n$ is a multiple of $m$).
A quick note about warps (or wavefronts in OpenCL), which is a related concept. A warp is a unit of scheduling, it determines the amount of threads that actually execute in lockstep. It is good practice to have your block size as a multiple of the warp size but other than that you should not worry overly much about warps.
In this case we find our thread by multiplying the block id with the size of block and then adding the offset of the thread within the block. The rest of the kernel is straightforward, we simply perform the same computation as in the original code but we omit the for-loop. The conditional at line 4 makes sure we do not write outside the bounds of our vector, though that should not happen if we choose our grid carefully.
The rest of the code is the standard boilerplate that you will find in most CUDA programs. A key notion is that there is a distinction between buffers allocated on the device (the GPU) and buffers allocated on the host. Note that on line 26 we schedule the kernel for execution. The first two weird-looking parameters (within angle brackets) are the number of blocks and the block size respectively.
### Improving & Testing "Hello World"
To showcase a few things that I found helpful we are going to improve this simple code example. And because this is my blog post and I decide what is in it, I get to talk to you about how to test your code. GPU code tends to be a bit flaky: it breaks easily. Thus, I argue that creating simple tests for your code is essential. These do not have to be very complicated but I recommend that you use a proper framework for writing unit tests. For C++ I have had success with Catch and doctest, both single-headers that you include into your project.
Before we include these tests however, I propose that we make two more changes to the program. First of all, we are going to add better error checking. Most of the cudaFoo functions return a value indicating whether the operation was successful. Otherwise, we get something which we can use to determine the error.
1: #define check(e) { _check((e), __FILE__, __LINE__); }
2:
3: inline cudaError_t _check(cudaError_t result, const char *file, int line) {
4: if (result != cudaSuccess) {
5: fprintf(stderr, "CUDA Runtime Error: %s (%s:%d)\n", cudaGetErrorString(result), file, line);
6: assert(result == cudaSuccess);
7: }
8: return result;
9: }
And then simply wrap the cudaFoo functions with this check macro. Alternatively, you may want to rewrite this to use exceptions instead of asserts. Pick your poison.
Another thing I would recommend adding if you are doing CUDA in C++ is wrapping most of the allocation and de-allocation logic in a class. I generally take a more utilitarian view of classes for simple pieces of code and thus the following is not necessarily idiomatic or good C++ code.
1: class Saxpy {
2: public:
3: const int n;
4: float *d_x;
5: float *d_y;
6: float *x;
7: float *y;
8:
9: Saxpy(const int n) : n(n) {
10: x = new float[n];
11: y = new float[n];
12:
13: check(cudaMalloc((void **)&d_x, sizeof(float) * n));
14: check(cudaMalloc((void **)&d_y, sizeof(float) * n));
15: }
16:
17: ~Saxpy() {
18: check(cudaFree(d_x));
19: check(cudaFree(d_y));
20:
21: delete[] x;
22: delete[] y;
23: }
24:
25: Saxpy& fill() {
26: for (int i = 0; i < n; ++i) {
27: x[i] = i / 12.34;
28: y[i] = i / 56.78;
29: }
30:
31: check(cudaMemcpy(d_x, x, sizeof(float) * n, cudaMemcpyHostToDevice));
32: check(cudaMemcpy(d_y, y, sizeof(float) * n, cudaMemcpyHostToDevice));
33:
34: return *this;
35: }
36:
37: Saxpy& run(float a) {
38: const int threads_per_block = 256;
39: const int number_of_blocks = n / threads_per_block;
40: saxpy<<<number_of_blocks, threads_per_block>>>(n, a, d_x, d_y);
41:
42: return *this;
43: }
44:
47: check(cudaMemcpy(y, d_y, sizeof(float) * n, cudaMemcpyDeviceToHost));
48: return *this;
49: }
50: };
Why we went through all this trouble becomes clear if we put this in a test (I am using doctest syntax as an example).
1: TEST_CASE("testing saxpy") {
2: float a = 3.14;
3: const int n = 1024;
4: Saxpy s(n);
5:
7:
8: for (int i = 0; i < n; ++i) {
9: // we didn't keep the old y values so we recompute them here
10: float y_i = i / 56.78;
11: // the approx is because floating point comparison is wacky
12: CHECK(s.y[i] == doctest::Approx(a * s.x[i] + y_i));
13: }
14: }
That is a, for C++ standards, pretty concise test. And indeed, our tests succeed. Yay.
===============================================================================
[doctest] test cases: 1 | 1 passed | 0 failed | 0 skipped
[doctest] assertions: 1024 | 1024 passed | 0 failed |
### A Final Improvement
Because this post is already too long I will conclude with one last really nice tip that I absolutely did not steal from here. Actually, the NVIDIA developer blogs contain a lot of really good CUDA tips.
Our current kernel is perfectly capable of adapting to a situation where we give it less data than the grid can support. However, if we give it more data, things will break. This is where gride-stride loops come in. It works by looping over the data one grid at a time while maintaining coalesced memory access (which is something I will write about next time).
Here's our new kernel using these kinds of loops.
1: __global__
2: void saxpy(int n, float a, float *x, float *y) {
3: for (int i = blockIdx.x * blockDim.x + threadIdx.x; i < n; i += blockDim.x * gridDim.x) {
4: y[i] = a * x[i] + y[i];
5: }
6: }
## Conclusion
I hope this convinces you that GPU programming is actually pretty simple. The kernel here is pretty trivial, but as long as you understand that within the kernel you can basically write C/C++, you are going to do just fine.
If there is a next post I will write more about memory in GPUs, a very important topic if you want your code to actually run fast. If you want to skip ahead you should read about the different types of memory (global, local, shared, texture, etc.) and what memory coalescing entails.
Until next time.
## Tuesday, March 14, 2017
### What are lattices?
Do all the cool post-quantum cryptographers around you talk about lattices and all you can think about is a good salad?
Don't worry! You can be part of the hip crowd at the next cocktail party in just three easy steps!
First, I will tell you what a lattice is. It is actually really easy.
Second, we will prove a tiny fact about lattices so that those poor neurons that did all the work in the first step have some friends.
Third, nothing. There isn't even a third step. That's how easy it is!
So, let's tackle the first step. What, actually, is a lattice?
The answer could not be easier. It is simply a grid of points. Like this:
Easy, right?
The formal definition is just as simple:
Given $n$ linearly independent vectors $b_1, b_2, \ldots, b_n \in \mathbb{R}^m$, the lattice generated by them is defined as
$\mathcal{L}(b_1, b_2, \ldots, b_n) = \left\{ \sum x_i b_i \middle| x_i \in \mathbb{Z} \right\}.$
We can add those so called basis vectors $b_i$ to our diagram and will readily see how each point is constructed.
And now you already know what a lattice is! In the next step we will talk about some more definitions and show the proof of a theorem.
We will be discussing something related to the question of what the length of the shortest non-zero vector in a given lattice $\mathcal{L}$ is.
Definition:
$\lambda_1(\mathcal{L})$ is the length of the shortest non-zero vector in $\mathcal{L}$. We use the euclidean norm for the definition of length.
And we also need the volume of a lattice which we are not going to define formally we will just take it to be the volume of that $n$ dimensional parallelogram in the picture:
Now we can already prove Blichfeld's Theorem! It makes a statement about where we can find a lattice point and roughly goes as follows:
For a lattice $\mathcal{L}\subseteq \mathbb{R}^n$ and a set $S \subseteq \mathbb{R}^n$ where the volume of $S$ is bigger than the volume of the lattice there exist two nonequal points $z_1, z_2 \in S$ such that $z_1 - z_2 \in \mathcal{L}$.
And here is the idea of the proof in a graphical way! First we simply draw an example for the set $S$ in blue:
Now we cut up our set and move all the parts into our first parallelogram!
As you can see there is quite a bit of overlap and the fact that the full volume of the set is bigger than the volume of the lattice aka the parallelogram guarantees there will be at least some overlap somewhere. But if there is overlap then we have two points, that have been moved by multiples of the base vectors and which are now at the same position!
And therefore their difference must be a multiple of base vectors as well and we have found a difference which is a lattice point! Hooray!
Now we will use a little trick to expand this result and make a statement about an actual point from the set being on the lattice not just the difference of two points!
What we will show is called Minkowski's Convex Body Theorem and it states roughly
Let $\mathcal{L}$ be a lattice. Then any centrally-symmetric convex set $S$, with volume bigger than $2^n$ times the volume of the lattice contains a nonzero lattice point.
So after this we will know such a set it will contain a lattice point and using a simple sphere as the set allows us to put a bound on $\lambda_1(\mathcal{L})$.
Let's get to it then!
First we blow up our lattice to twice its size along every dimension!
Now we add our centrally-symmetric convex set $S$. Again in blue.
And because we picked the volume of $S$ to be bigger than $2^n$ times the volume of the lattice we still get the colliding points from the last theorem EVEN in the double size lattice!
But since our set $S$ is symmetric about the origin if $z_2 \in S$ it follows that $-z_2 \in S$ and because it is convex $z_1, -z_2 \in S$ implies $\frac{z_1 - z_2}{2} \in S$. And because we've double the size of the lattice and $z_1 - z_2$ is on the bigger lattice it follows that $\frac{z_1 - z_2}{2} \in \mathcal{L}$ and we have shown that a point in our set is also in the lattice.
You can see it quite clearly in the next picture.
As already stated above if we use a simple sphere for this set we can give a bound on $\lambda_1(\mathcal{L})$ based on the volume of $\mathcal{L}$. It is known as Minkowski's First Theorem and states:
$\lambda_1(\mathcal{L}) \leq \sqrt{n}(vol(\mathcal{L})^{1/n}.$
Isn't that great?!
If you have now completely fallen in love with lattices but would appreciate real math instead of pictures, worry not!
You will find steps 3 - 14 on Oded Regev's course website! Enjoy!
And in case you accidentally run into him at a conference here is the picture from his website so you don't miss the opportunity to say hello.
## Saturday, March 4, 2017
### GMP - Arithmetic without limitations
Theoretical research in cryptography can be extremely exciting but, on the other hand, a lot of effort should be devoted to correctly and securely implementing cryptosystems that help protect people's privacy. The presence of a bug in a software can be very annoying but if this software deals with crypto and security, then the consequences can be catastrophic.
For many cryptosystems based on number theoretic problems, one of the first issues that a developer faces is the size of the numbers involved in the computations. These numbers are composed of thousands of bits (or hundreds of digits) and they need to be added, multiplied, raised to some powers, etc. Performing these operations is complicated, and doing it efficiently is even more complicated. But thankfully there are tools (libraries) that come to the rescue.
In this post, I will talk about GMP, The GNU Multiple Precision Arithmetic Library. Quoting from the library's homepage, "GMP is a free library for arbitrary precision arithmetic, operating on signed integers, rational numbers, and floating-point numbers. There is no practical limit to the precision except the ones implied by the available memory in the machine GMP runs on. GMP has a rich set of functions, and the functions have a regular interface." This library is written in C but also offers an interface for C++ code, and we are going to focus on this particular one. The final goal of this post will be to implement a simple but complete example of an RSA cryptosystem, from key generation to encryption and decryption of messages.
But, before moving on, a little disclaimer: implementing cryptographic solutions is not an easy task and using homemade solutions is generally considered as not a good idea because of bugs and lack of scrutiny by other members of the community. The sole goal of this post is to show some of the potential of the GMP library.
• Data type -- the basic data type that we will deal with is mpz_class. We can think of it as an arbitrary-sized integer. Some of the functions we will talk about only accepts parameters of type mpz_t, which is the corresponding C type. Luckily, we can always call the function get_mpz_t on a mpz_class object to obtain the corresponding mpz_t object;
• Generating random numbers -- first of all, we consider the problem of generating random numbers with a specific size (measured in bits). GMP offers a function called get_z_bits, that takes in input a number of bits and returns a number with that many bits. But be careful! It means that the returned number takes up to that number of bits. So calling it with argument '3' means that the returned value will be a number between 0 and 7. Instead, what we want is a number that is represented exactly by 3 bits, so 4, 5, 6, or 7. Doing that is quite straightforward: given a number of bits k, we want a random number in the range $\left[2^{k-1}, 2^k\right)$. In order to handle this exponentiation (since $k$ can be very big), we are going to use the function mpz_ui_pow_ui, that raises an unsigned int basis to an unsigned int power and writes the result to a mpz_t object. In order to draw a random number, we are going to initialize a random number generator with this code:
gmp_randclass rng(gmp_randinit_mt)
.
Note: this example uses the Mersenne Twister PRNG, which is known to be insecure for cryptographic applications. After this is done, our function for generating a random number with a specific number of bits can look like the following
mpz_class generate_rand_exact_bits (const unsigned int size)
{
// 2^(size-1)
mpz_class out;
mpz_ui_pow_ui(out.get_mpz_t(), 2, size-1);
// 2^(size)
mpz_class bound;
mpz_ui_pow_ui(bound.get_mpz_t(), 2, size);
// random offset
mpz_class rand = rng.get_z_range(bound-out);
return (out + rand);
}
• Generating prime numbers -- generating random numbers is nice but often not sufficient; we need to generate random-looking prime numbers. This task is obviously harder because there are more constraints that have to be satisfied. Thankfully, GMP comes to the rescue once again: we can in fact take advantage of the function mpz_probab_prime_p that takes as input a mpz_t object that represents the candidate prime and a number that specifies how many times the Miller-Rabin primality test has to be executed, and returns 0 if the candidate is not prime, 1 if it is probably prime and 2 if it is surely prime. Repeating the test 50 times gives a very high degree of confidence on the primality of the candidate, so we are going to generate a random number and test it until we find a candidate that passes all the tests. The code for a function that performs this task can be the following
mpz_class generate_prime_exact_bits (const unsigned int size)
{
mpz_class candidate;
do {
candidate = generate_rand_exact_bits(size);
} while (mpz_probab_prime_p(candidate.get_mpz_t(), REPEAT_MILLER_RABIN) == 0);
return candidate;
}
• Modular exponentiation -- the goal of this step is to take a basis $b$, an exponent $e$ and a modulus $m$ and compute $b^e \mod m$. GMP already offers a function called mpz_powm that does what we need, but we can "beautify" it a little bit by wrapping it in another function like the following:
mpz_class mod_exp (const mpz_class base, const mpz_class exp, const mpz_class mod)
{
mpz_class out;
mpz_powm (out.get_mpz_t(), base.get_mpz_t(), exp.get_mpz_t(), mod.get_mpz_t());
return out;
}
• Encryption and decryption -- once we have the function mod_exp for modular exponentiation, RSA encryption and decryption are trivial:
mpz_class rsa_encrypt (const mpz_class pk, const mpz_class m, const mpz_class mod)
{
return mod_exp (m, pk, mod);
}
mpz_class rsa_decrypt (const mpz_class sk, const mpz_class c, const mpz_class mod)
{
return mod_exp (c, sk, mod);
}
Now, we will put everything together and in the main function we will do the following:
1. generate two numbers rsa_p and rsa_q which are prime and composed of an arbitrary (here 2048) number of bits;
2. multiply together rsa_p and rsa_q to obtain the modulus rsa_mod;
3. calculate the Euler's totient function of the modulus by multiplying (rsa_p -1) and (rsa_q - 1);
4. choose a public exponent rsa_pk: here we are going to use 65537;
5. compute the secret exponent rsa_sk by calculating the multiplicative inverse of rsa_pk modulo rsa_totient. For this task, we can use the function mpz_invert offered by GMP;
6. generate a random 32-bits message;
7. encrypt it and decrypt it to show that the message is recovered correctly
The full code is available here. Assuming that it is saved in a file called main.cpp, it can be compiled with the following command:
g++ -Wall -o main main.cpp -lgmp -lgmpxx
Finally, here is a possible output of the program:
p: 23792449500522212951496314702038682121347194317959904876008718825662914075875899470581320800653437713536069408253411676817620646430212407540403369694134781759107125478056393908946127803961090931948553568336876469309822272887045095561051090700123699901361196085633529272849875353866567000752182158071024473204684307004694765510326847369963753315267894351158697231078788807690227802109570252088084877486698404206015111529669790467025281249212356222609928349702116676081721161733842190421613247070310376995600752548098115546539048072846637620536666595226297844398938704443953343779702008604938853732596401295126782941987
q: 29112805945439121371217246384724375309040486330485414315973357532238818896560861590487525988011993439077520550311524035984480970497774071062272700839286098068182559422588276697743896386738257138746524032717815962171954684796109782069096410172414189261142167684350607916360394902788649692558546060677368837462937413290555419196322614840219369972120722061013641236619226520826654042088554099043918184746705620357166310881550460726728460067235575345180739677700783783242815237362918214982959525838694224404066952951953880663045068810920848575666730532567285210572753317549500155052830379131918899635413209365556429526661
Modulus: 692664965275363134868164310308043386530889977137116066460956916982191344093600913377382983586757778122293014614580541617686926517513948142377215870615527742653194700493457784251321237254925462486660424748287684799960005285232140262663908204076330275297015032277805385557802277182249107190208144962072627103333702166712562912412455374055377823609059561406201023023953754548932692770545184532804691011451566435370564027281954154745605054059335653411252856827668944053539165109486066934327992280592181117681540307774187890207024741310917968286855939570200842820225004987124097822236170460663883584621535528990367892742357001025439624939219952367312627679661863266398010079250545044069312072321631423895274591504669908947731669841676290437961150479342566664751624244101084250756141019398564481030304316812644414619975245318775213481846709606949913834082310037698177108248900032520946078124914227912956069612730720184002438971635446900598624230868985779777067182408067527262398836477646176180149265564531633256045959807480886640631812690951578507074608608075924577570127277599939833799849839997452314926854023853061044555560190656563707831534988797823714162801693363417381512465247240619960211197273430707134124687895683306648515432815407
Totient: 692664965275363134868164310308043386530889977137116066460956916982191344093600913377382983586757778122293014614580541617686926517513948142377215870615527742653194700493457784251321237254925462486660424748287684799960005285232140262663908204076330275297015032277805385557802277182249107190208144962072627103333702166712562912412455374055377823609059561406201023023953754548932692770545184532804691011451566435370564027281954154745605054059335653411252856827668944053539165109486066934327992280592181117681540307774187890207024741310917968286855939570200842820225004987124097822236170460663883584621535528990367892742304095769993663604897238806225864622231475585749564760058562967711410339349194662834205744716004477795118079883111354725159048862414580186148948173567663370928851334497919810423614292621945066549280167717720521050364932649266758956452162536825639219086396668750961940935703957656300852919419991965254045660967825180303374046162336317566884059120678910850226498009948160851632383720333508904913956745247482616068631268540358255880854866759476646002336609572536933340525303598355554521449451080152039954160522951063655835325404680939946676605489966289587929410275548597966757698440898319397266934527673695987832220346760
Message: 2699077189
Ciphertext: 681377152725050864187889498396285584066530595533108416812276566730393956984527765118715661493472361295191987186484833223806930407591255557303290975217436524165953995313143542640632193731686512007342253568013661854913604989704338096439627987512846172004801196181232822308088685943243400345975426883909096147339045273787325984512823244957423398055174828695879849942493712502158108081782163024167101957978799078692054106581518638832961868215165854308314877242675212188837955873975174727647247990393606326403876490500815929414980002030276198625866328310973421532151059071628038306926281825502507926893439321472535762059281448571817796845306517579637703981694846774635322811199431875663174162751403156127612351378340405058549628085390124779083962094777489309709766752481986327599769351343828713992159924065615106068412838813886565270542810886921193120790895042994364186375596015716254331672407180666306582326345460867181975252903332881845979999145141098787286539117576791635044116865176716309063466576180971588107298159543491564320012605624880056428982408094160945322909734375254637560779872935691072801422766106105016077161030768880774211449289008906840655161792691129673110760644874000744631018536155622276779954270891913007605935768473
Decrypted: 2699077189
## Monday, February 27, 2017
### Side-channel analysis
For many years cryptographers and industry implemented crypto algorithms on microcontrollers and ASICs simply by translating the algorithms into assembly or rtl language. Only thing that mattered was correct functionality of the design. However, in mid to late nineties some interesting attacks of cryptographic implementations were shown, that were able to completely break the security of it, reveal secret keys, while the underlying cryptographic algorithm remained mathematically unbroken. First, the timing attack was introduced. Namely the attacker was able discover information based on the time server took to respond to a query since this time depended on the secret key that was used. Most simple application of this is square and multiply algorithm used for RSA exponentiation. Namely, for every bit of the exponent square, or square and multiply operation is used. This will result in different execution times for different exponents.
Kocher et al. introduced new type of side-channel attack by revealing that information obtained from the power measurements can be also used to extract secret values from devices such as smart cards. We start from assuming that the power signal consist of random noise and deterministic one dependent on the processed value $x$
$P = L(x) + R$
Random noise is modeled as a Gaussian distribution with zero mean, and deterministic key dependant value $L(x)$ is usually hamming weight or hamming distance of the value . Following on, we choose intermediate value to be targeted. Good target of the attack for symmetric designs is S-box output, since small hamming weight difference in the input of the sbox leads to not so small hamming weight difference in the output. In the original work it was simply a one bit value, that could be either one or zero. The simplest example is thus by using one output bit of the S-box, with the assumption that power consumption is different for one and zero value. For example, take one S-box operation of the first round of AES. It is calculated using equation below
$SO_i = S(pt_i \oplus key_i)$
Since we are unaware of what is the correct key value, we construct key guesses and calculate the targeted value, e.g. first bit of the S-box output. Now, for every key guess, we separate power traces into two groups, one that contains power traces for which the key guess produces target value one and other where target value is zero. Lastly, we compute the average of two groups, reducing the influence of the noise, and then we subtract these averages. If our key guess is wrong, difference of means will be negligible, since the power traces in two groups don’t correspond to correct values, and are thus uncorrelated. However, the correct key guess will have a noticeable spike in the point in time where first bit of S-box output is computed.
This very simple, yet very effective attack opened a new area of research. Soon, more elaborate attacks were devised, attacking bytes instead of bits using correlation. More advanced attacks include correlation with variance instead of the mean, or even higher statistical moments. These attacks are usually unpractical for orders higher than two, since the noise influence hardens the attacker’s possibility to retrieve the secret value. Profiling of the devices is sometimes performed in order to devise a more accurate model of the deterministic leakage functions. These attacks are known as template attacks. Designers also came up with various ways of trying to thwart these attacks, such as increasing the noise level by adding redundant circuitry or operations, and shuffling the execution operation. Other methods include secure logic design styles such as WDDL, where logical cells are designed to consume amount of power regardless of their output. Methods on the algorithmic level, e.g. Threshold Implementations, try to ensure no information leakage happens during the execution of the algorithm, regardless of the underlying leakage model of the design technology.
Since classical DPA and correlation analysis involve constructing guesses for all possible key bytes/nibbles, it can be very time consuming. This is where leakage tests became prominent. They tell if a set of randomly chosen traces can be distinguished for set of traces with fixed input value. It works in a very similar way to one bit DPA. 2 Sets of traces are obtained, one with random inputs and one with fixed inputs. Welsh t-test is used to measure if two sets can be distinguished from one another. If $\mu, \ s$, and $n$ are mean, variance and cardinality of a set, t values are calculated as follows
$t = \frac{\mu_0 - \mu_1}{\sqrt{\frac{s_0^2}{n_0} + \frac{s_1^2}{n_1}}}$
Approximating statistical degree of freedom with $n=n_0 + n_1$ we can with confidence 0.99999 claim that two sets are distinguishable for $t > 4.5$. This type of leakage tests allows the designers to be more efficient since it reduces the testing time of the design. Downside of the approach is that leakage tests do not reveal how can the secret values be extracted, only that there is a possibility for an attacker to do so.
In best paper of CHES 2016: Differential Computation Analysis: Hiding Your White-Box Designs is Not Enough, side-channel analysis has been successfully used to break many white-box implementations. This time analysis has been performed on stack layout, instead of power traces, but the principle remained the same. Taking into account that white-box cryptography is currently being widely considered to be added to many software based designs, together with plethora of IoT devices that require protection, side-channel analysis importance will continue to be an important aspect of design process of cryptographic implementation. Thus, researchers will continue to work on improvement of leakage detection and key recovery methods to further reduce cost and time to market of new devices.
## Sunday, February 19, 2017
### Differential privacy
These days one reads a lot about the right to privacy. But what is it and how does it differ between the real and the digital description of the world? Briefly, it is a person's right to have and more importantly maintain control over information about oneself, which is fundamental to human's freedom of self-determination. In the digital context one seemingly lost this right in favor of using free services, handy tools that satisfy people's urge to communicate with each other and stay in touch and up-to-date at all times. Since more and more people realize that behind such apps and web pages naturally there are business models, society increasingly demands to reclaim control over collected personal data, which has been provided, unsolicited or involuntarily, to online merchants or telephony service providers at the time of use, for example. On the other hand collecting user information in databases is crucial as corporations offering named services see it. In order to make good products, tailored recommendations, and especially in the age of big data and machine learning, precise predictions by evaluating various functions on the data.
Statistical database queries have been studied quite some time now, and in fact it turns out that often it is sufficient to allow query access only to a population's aggregate data, not individual records, to derive useful statistics and achieve desired functionality! A common approach is to merely allow aggregate queries (i.e. range, histogram, average, standard deviation, ...) and rather than returning exact answers about sensitive data fields to specify intervals or give imprecise, statistically noisy counts.
You might have asked yourself, don't cryptographic techniques that have been omnipresent in this blog such as FHE (Fully Homomorphic Encryption) or secure MPC (Multi-Party Computation) solve this problem? Wouldn't it be possible to encrypt the user data yet for the service provider to compute useful statistics on it?
Indeed, it could be realized with the general FHE, MPC toolkit, but currently it is inefficient to operate them at that scale in practice, such that statistics over huge quantities of data are useful to infer statements about a given database. Hence specific, more slender tools have been designed to overcome this gap. Whereas FHE avoids a trusted 3rd party to compute (i.e. arbitrary functions or sophisticated statistics) on users sensitive data, here typically one explicitly allows a trusted 3rd party to collect and aggregate data in a privacy-preserving fashion. Users might do so i.e. when installing an app and argue to have an advantage for themselves like good default settings, an overall performance gain; or it might be a requirement to share information in order to use the service for free in the first place.
Differential privacy (often abbreviated DP) is a framework for formalizing privacy in statistical databases. It can protect against so called de-anonymization techniques that try identifying an individual record by linking two separately released databases that have been stripped off (quasi-)identifiers and look innocuous. Especially apriori knowledge or known partial history can be leveraged to derive more information from a released "anonymized dataset" other than the purpose it was originally intended to serve.
Let's look at a mathematical definition that captures and formalizes the notion of privacy and which has been studied in cryptography in the past 10 years. Let $d,n$ be a positive integers and $f: X^n \rightarrow \mathbb {R} ^{d}$ some statistics on a database comprised of $n$ records.
An algorithm $\mathcal {A}: X^n \rightarrow \mathbb {R} ^{d}$ that computes $f$ is said to have the $(\epsilon, 0)$-differential private attribute or ($\mathcal {A}$ is $\epsilon$-DP, for short) if for all neighboring subsets of a given database $x_{1} \neq x_{2}$ and $x_{1} \sim x_{2} := x_{1} \sim_1 x_{2}$ (they differ in just 1 element), and all subsets $S \subseteq \mathbb {R} ^{d}:$
\begin{align}
\mathbb{P}[\mathcal{A}(x_{1})\in S]\leq e^{\epsilon } \cdot \mathbb{P}[\mathcal{A}(x_{2})\in S]
\end{align}
holds. Looking more closely at this definition $\forall x_{1}, x_{2} \in X^n, x_{1} \sim x_{2}:$
$$\mathbb{P}[{\mathcal{A}}(x_{1})\in S] \leq e^{\epsilon } \mathbb{P}[{\mathcal{A}}(x_{2})\in S] \Leftrightarrow \frac{\mathbb{P}[{\mathcal{A}}(x_{1})\in S]}{\mathbb{P}[\mathcal{A}(x_{2})\in S]} \leq e^{\epsilon }\\ \Leftrightarrow \log \left(\frac{\mathbb P[\mathcal{A}(x_{1})\in S]}{\mathbb{P}[{\mathcal{A}}(x_{2})\in S]}\right) \leq {\epsilon}$$
we can identify the so called "privay loss" of an algorithm (or in this context often called mechanism) $\mathcal {A}$. In this setting $\epsilon$ can be called the privacy budget. In less exact terms it captures the following: By specifying the privacy budget, it is possible to control the level of privacy and make an algorithm respect this additional constraint by techniques introduced below.
For those familiar with the concept of max-divergence, the definition of privacy loss is in fact the definition of $$D_\infty( A(x_1) || A(x_2)) := \max_{S\subseteq {\textbf supp}(A(x_1))} \log \left(\frac{\mathbb P[\mathcal{A}(x_{1})\in S]}{\mathbb{P}[{\mathcal{A}}(x_{2})\in S]} \right).$$
Furthermore, the multiplicative factor $e^\epsilon$ can be -- using a common approximation for small $\epsilon<1$ -- viewed as $1+\epsilon$:
$$e^\epsilon = exp(\epsilon) = 1 + \epsilon + \epsilon^2 + \dots \approx 1 + \epsilon.$$
In less formal terms this definition says that a given result is approximately the same whether it is computed using the first or the second, neighboring database.
A more general definition, that adds flexibility -- but also makes the proofs less elegant and more technical -- is $(\epsilon, \delta)$ -differentially privacy, when
$$\mathbb P[{\mathcal {A}}(x_{1})\in S]\leq e^{\epsilon } \cdot \mathbb P[{\mathcal {A}}(x_{2})\in S] + \delta.$$
Interpreting the definition, the goal of DP is that the risk of violating one's privacy should not substantially increase as a result of either appearing in a statistical database or not. Thus an analyst should not be able to learn any information about a record (i.e. participating an online questionnaire) that couldn't have been learned if one had opted not to participate or answered the questions randomly by rolling a die or flipping a coin rather than answering truthfully.
To overcome the fundamental challenge -- the trade-off between utility of data or accuracy of returned answers and privacy of records -- the set goal is to learn as much as possible about a group's data while revealing as little as possible about any individual within the group. Transforming an algorithm into a DP-algorithm requires probabilistic tools. The sensitivity of a function of $f$ is a good measure of how much statistical noise is needed to mask an answer:$$\Delta f=\max_{x_1 \sim x_2} ||f(x_{1})-f(x_{2})||_{1} = \max_{x_1 \sim x_2} \sum_{i=1}^d |f(x_{1})_i-f(x_{2})_i|.$$Low sensitivity of a function, i.e. small change of output given two neighboring inputs, allows to add statistical noise to achieve privacy yet don't use utility. The Laplace mechanism, adds noise from the Laplace distribution $\mathcal L(\lambda)$, i.e. noise $\eta(x)\propto \exp(-|x|/\lambda)$ which has 0 mean and $\lambda$ standard deviation. Substituting Laplace noise with other probability distributions, such with a 0 mean Gaussian and $\lambda$ standard deviation would be possible, but influences proof details.
A typical construction now is, instead of computing $f(x)$ directly, to compute $\mathcal A(x) = f(x) + \eta(x)$ and obtain a $\epsilon = \frac{\Delta f}{\lambda}$-DP algorithm, since the noise of two neighboring databases doesn't exceed this $\epsilon$ even in the worst-case. In terms of composability, sequential respectively parallel composition leads to a sum of all occurring $\epsilon_i$ resp. maximum of all occurring $\epsilon_i$ differentially private steps within the composed mechanism. This allows to efficiently turn algorithms into DP-algorithm.
These basic construction, including detailed proofs, and much more were covered during the 7th BIU Winter School on Cryptography named "Differential Privacy: From Theory to Practice" featuring speakers, who defined and contributed already roughly 10 years ago to the field. Slides are already online and video recordings about to appear on the webpage.
Furthermore, relationships of DP to various, related scientific fields ranging from statistics to machine learning and finally game theory were explored.
Concluding, in wake of the growing awareness of privacy issues in the digital domain, together with stricter interpretation of legislation and finally the possibility to satisfy most interests by anonymized data anyways; several big players strive to provide differentially private collection of data. Some companies market themselves as quasi-pioneers in privacy topics for some reasons: It pays off to be perceived as the first one; they would be facing various problems in the near future anyways, if they don't respect these issues; and most importantly, they can continue their business model: creating value of user's data. The more information is queried from the database, the more statistical noise has to mask the correct answer in order to meet a predefined privacy budget bound. This total allowed, justifiable privacy leakage can be specified in the number of admissible queries or the answer accuracy.
Provable cryptography avoids the situation of mere obfuscation that can be undone by a clever enough attacker / strategy -- given the security assumption holds -- and provides bounds and thus a guideline on how to choose parameters to guarantee a desired level of privacy. Algorithms invest a given privacy budget at privacy-critical steps. With this in mind, differential privacy is an additional design paradigm for cryptographic algorithms and protocols to keep in mind.
I'd like to end this cryptologic point of view on achieving privacy goals on the internet, as I started; with a fundamental sociological question. One thought that remains standing out is: Shall we collect as much data in the first place? Is it really necessary to predict individuals as online merchants? Do we want this ubiquitous tracking? As with advanced technologies, who's long-term effects cannot be predicted, maybe also in aggregating big data and tracking the only winning move seems to be not to collect data in the first place.
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2017-06-23 06:53:35
|
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https://flashman.neocities.org/MD/section-10.1.CIS.html
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## Calculus II (Differential equations, Integration and Series) *Work in Progress! (5/2018)
Introduction: The concept of a function developed after the relation between variables used for coordinates in geometry was connected in the work on the calculus by G. Leibniz . As the function concept evolved, its connection to geometry lessened until in the 20th century the theory of functions and visualization with mapping diagrams was considered a part of the theory of sets while the calculus continued to be visualized primarily with graphs. In the mid and later half of the 20th century some calculus texts (see for example M. Spivak and S. Stein) used mapping diagrams to visualize important differential calculus concepts (limits) and tools (the chain rule). These treated some material that was not easy or convenient to visualize with graphs.
The methods for studying functions with calculus can become quite abstract sometimes when visualization is restricted to the cartesian graph. This is due in part to the limitations of visualizing the relationship between two distinct variables with a single point. These subtle concepts can sometimes be better understood by visually separating the information in a mapping diagram.
Mapping diagrams provide tools for visualizing functions beyond the constraints of cartesian geometry to investigate the calculus concepts of continuity, differentiability, and integrability as well as some of the computations related to the calculus. In the previous chapter, Calculus I (Continuity and Differentiability), the emphasis was on using mapping diagrams to visualize many of the key concepts and results of continuity and differential calculus. In this chapter the emphasis is on calculus concepts and results related to differential equations, integration and series. Chapter 11 remains to discuss multi-variable functions and their calculus.
Much of the work here appears in other formats as part of The Sensible Calculus
Since the study of differential equations, integration and series calculus relies heavily on continuity and differentiable functions reviewing the visualization of Calculus I (Continuity and Differentiability) is most useful at this time.
10 Calculus II Differential equations, Integration and Series
10.1 Euler’s method
10.2 Definite Integration
10.3 The Fundamental Theorem of Calculus
10.4 Taylor and MacLaurin Theory and Practice
10.5 Sequences and Series Tests
10.6 Power Series
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2021-03-09 00:28:24
|
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https://axiomsofchoice.org/set_of_divisors_function
|
Set of divisors function
Function
definiendum $\mathrm{divisors}:\mathbb N^+\to\mathcal{P}(\mathbb N)$ definiendum $\mathrm{divisors}(n):=\{a\ |\ \exists (b\in\mathbb N).\ a\cdot b=n\}$
make this into a set
Code
A related Boolean function is
divides :: Integral a => a -> a -> Bool
divides d n = rem n d == 0
|
2021-04-21 23:11:14
|
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https://cran.wustl.edu/web/packages/mcunit/vignettes/introduction.html
|
# Introduction to mcunit
Increasingly sophisticated MCMC and Monte Carlo algorithms raise the scope for errors, either in derivations of mathematical quantities needed for sampling, or implementation errors. Testing for such errors should be an integral and routine part of the workflow of any Bayesian analysis.
mcunit makes it easy to do this, by allowing for unit testing MCMC and other Monte Carlo implementations within the framework of the testthat package (Wickham 2011). The methods correspond to those proposed in Gandy and Scott (2020). They are based on statistical hypothesis testing, and are designed to achieve an arbitrarily low false rejection probability, so that the user can be confident that a correctly implemented algorithm will almost certainly not be rejected. By default, this false rejection rate is set to $$10^{-5}$$.
MCMC samplers can be testes using expect_mcmc or expect_mcmc_reversible. These functions use different statistical hypothesis tests described in Section 2.1 and 2.2 of (Gandy and Scott 2020) respectively. expect_mcmc_reversible requires that the sampler to be tested is (or at least, is expected to be) reversible.
This vignette demonstrates how to use these tests, using the following simple example. Consider the model $y \sim \theta_1 + \theta_2 + \epsilon,$ where $$\theta := (\theta_1,\theta_2)$$ is apriori independent, zero mean normal with standard deviation $$\sigma=10$$. The white noise term $$\epsilon$$ is independent from $$\theta$$ and also zero mean normal but with variance $$\sigma_{\epsilon}^2$$ = 0.1. While inference is easy here, we consider drawing samples from the posterior $$\pi(\theta \mid y)$$ using a Gibbs sampler. The posterior conditional distributions for $$\theta_1$$ and $$\theta_2$$ are normal with expectations $\mathbb{E}(\theta_i | y, \theta_j) = \frac{\sigma^2}{\sigma^2_{\epsilon} + \sigma^2}(y - \theta_j),$ and variances $\mathbb{V}(\theta_i | y, \theta_j) = \frac{1}{\frac{1}{\sigma^2_{\epsilon}} + \frac{1}{\sigma^2}}.$
## Correct Sampler
Start with a correctly implemented random scan Gibbs sampler. First load the package and set the seed.
require(mcunit)
## Loading required package: mcunit
set.seed(10)
The following function updates one element of $$\theta$$ given the other and given the observed data $$y$$.
gibbsUpdate <- function(y, theta_j) {
# Samples theta_i given y and theta_j
mean <- 100 * (y - theta_j) / (100 + 0.1)
var <- 1. / (1. / 100 + 1. / 0.1)
rnorm(1, mean=mean, sd=sqrt(var))
}
The argument y is the observed data, and theta_j is the component to condition on. From this, we define a correctly implemented random scan sampler.
randomScan <- function(theta, y, thinning) {
# Random Scan Gibbs
for(i in 1:thinning) {
# select index to update
i <- sample.int(2,1)
theta[i] <- gibbsUpdate(y, theta[i %% 2 + 1])
}
theta
}
This function takes the current state of the chain theta, the data y and a thinning parameter which determines the number of individual updates to make before returning the new state.
Our task is to test the correctness of randomScan. We will do this using both expect_mcmc and expect_mcmc_reversible. This latter method can be used because the sampler should, if correct, be reversible.
Both methods require a list object which describes the MCMC sampler to be tested. The list must contain the following elements:
• object$genprior: A function with no arguments that generates a sample from the prior distribution. No default value. • object$gendata: A function that takes as input the parameter value (of the type generated by genprior) and returns the observed data as an arbitrary R object. No default value.
• object$stepMCMC: A function that takes three arguments: • theta: the current position of the chain (of the same type as produced by the prior), • dat: the observed data (of the same type as produced by gendat) • thinning: the number of steps the chain should take. 1 corresponds to one step. • object$test: Function that takes either one or two arguments, and returns a vector with components which will be used for checking the MCMC sampler. The first argument is interpreted as a parameter value, and if a second argument exists, it is interpreted as a data value. An example is the identity function: $$f(\theta) = \theta$$. Alternatively, if you have access to the model’s likelihood function, you could use $$p(y \mid \theta)$$.
Please see the documentation for expect_mcmc and expect_mcmc_reversible for further details on this.
We begin constructing this list by defining the prior sampler and the data sampler.
obj <- list()
obj$genprior <- function() rnorm(n=2, mean=0, sd=10) obj$gendata <- function(theta) sum(theta) + rnorm(n=1, mean=0, sd=sqrt(0.1))
As test functions, we use the components $$\theta_1$$, $$theta_2$$, the prior density $$\pi(\theta)$$ and likelihood function $$p(y \mid \theta)$$. The density and likelihood appear to be a good default choice because they are one-dimensional regardless of the dimension of the parameter vector and data.
priorDensity <- function(theta) prod(dnorm(theta, mean=0, sd=10))
likelihood <- function(theta, y) dnorm(y, mean=sum(theta), sd=sqrt(0.1))
testVec <- function(theta, y) c(theta[1], theta[2], priorDensity(theta), likelihood(theta, y))
obj$test <- testVec Finally, we are left to define a single MCMC step. obj$stepMCMC <- function(theta, dat, thinning) randomScan(theta, dat, thinning)
print(obj)
## $genprior ## function() rnorm(n=2, mean=0, sd=10) ## ##$gendata
## function(theta) sum(theta) + rnorm(n=1, mean=0, sd=sqrt(0.1))
##
## $test ## function(theta, y) c(theta[1], theta[2], priorDensity(theta), likelihood(theta, y)) ## ##$stepMCMC
## function(theta, dat, thinning) randomScan(theta, dat, thinning)
First consider expect_mcmc. We use $$100$$ thinning steps between samples to give the test some power to detect errors.
expect_mcmc(obj, thinning = 100)
No errors were detected, because there are none. Recall that the false rejection rate is set to $$10^{-5}$$ by default, and so repeated application of this test should very rarely flag randomScan.
This sampler is also reversible, and so we try expect_mcmc_reversible.
expect_mcmc_reversible(obj, thinning = 10, nsteps = 10)
Again, no error is detected (as expected).
## A Correct Non-Reversible Sampler
Consider systematic scan of the vector $$\theta$$ rather than random scan.
systematicScan <- function(theta, y, thinning) {
# Systematic Scan Gibbs
for(i in 1:thinning) {
theta[1] <- gibbsUpdate(y, theta[2])
theta[2] <- gibbsUpdate(y, theta[1])
}
theta
}
This sampler is correct and expect_mcmc is unlikely to falsely detect errors.
obj$stepMCMC <- function(theta, dat, thinning) systematicScan(theta, dat, thinning) expect_mcmc(obj, thinning = 100) Good. What happens using expect_mcmc_reversible with thinning of $$1$$? expect_mcmc_reversible(obj, thinning = 1, nsteps = 10) The test failed. This illustrates why expect_mcmc_reversible should not be used for a non-reversible sampler - we have no guarantee over the false rejection rate. Even though this sampler is correctly implemented, we are erroneously detecting an error. ## An Incorrect Sampler Now we make a genuine mistake in the sampler, and investigate whether the methods detect it. We replace the variance terms $$\sigma^2$$ and $$\sigma^2_{\epsilon}$$ in $$\mathbb{V}(\theta_i | y, \theta_j)$$ with their corresponding standard deviations (i.e. $$\sigma$$ and $$\sigma_{\epsilon}$$). gibbsUpdate <- function(y, theta_j) { # Samples theta_i given y and theta_j mean <- 100 * (y - theta_j) / (100 + 0.1) var <- 1. / (1. / 10 + 1. / sqrt(0.1)) rnorm(1, mean=mean, sd=sqrt(var)) } Also make sure to switch back to random scan… obj$stepMCMC <- function(theta, dat, thinning) randomScan(theta, dat, thinning)
Rerunning the tests…
expect_mcmc(obj, thinning = 100)
## Error: Test failed for components with p-values=NULL in iteration 1
expect_mcmc_reversible(obj, thinning = 10, nsteps = 10)
## Error: Test failed for components with p-values=NULL in iteration 1
Great! Both tests detect a problem. Even better, you can be pretty much sure there is a problem because the chance of a false rejection is upper bounded by $$10^{-5}$$!
## References
Gandy, A., and Scott, J. (2020), “Unit testing for MCMC and other Monte Carlo methods.”
Wickham, H. (2011), “Testthat: Get started with testing,” The R Journal, 3, 5–10.
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2023-02-06 03:15:26
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http://doc.rero.ch/record/211335
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Faculté des sciences
## Defining the Impact of Non-Native Species
### In: Conservation Biology, 2014, p. -
Non-native species cause changes in the ecosystems to which they are introduced. These changes, or some of them, are usually termed impacts; they can be manifold and potentially damaging to ecosystems and biodiversity. However, the impacts of most non-native species are poorly understood, and a synthesis of available information is being hindered because authors often do not clearly define... More
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2021-10-16 00:48:45
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https://www.satyenkale.com/pubs/hardness-of-online-sleeping-combinatorial-optimization-problems/
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Satyen Kale, Chansoo Lee and Dávid Pál
Proceedings of 30th Annual Conference on Neural Information Processing Systems (NeurIPS), 2016
We show that several online combinatorial optimization problems that admit efficient no-regret algorithms become computationally hard in the sleeping setting where a subset of actions becomes unavailable in each round. Specifically, we show that the sleeping versions of these problems are at least as hard as PAC learning DNF expressions, a long standing open problem. We show hardness for the sleeping versions of Online Shortest Paths, Online Minimum Spanning Tree, Online $$k$$-Subsets, Online $$k$$-Truncated Permutations, Online Minimum Cut, and Online Bipartite Matching. The hardness result for the sleeping version of the Online Shortest Paths problem resolves an open problem presented at COLT 2015 [Koolen, Warmuth, Adamskiy-2015].
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2019-06-18 05:05:49
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http://physics.stackexchange.com/questions/65957/from-position-space-to-momentum-space/65960
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# From position space to momentum space
Lets say I have a state vector $\left|\Psi(t)\right\rangle$ in a position space with an orthonormal position basis. If I now use an operator $\hat{p}$ on this basis I will get basis which corresponds to a momentum space and projections of a $\left|\Psi(t)\right\rangle$ on these base vectors will now be $\left|\Psi(p,t)\right\rangle$?
In other words. Do operators transform basis or a state vector or both?
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– Qmechanic May 26 '13 at 10:12
Having a basis is extremely useful, but a vector in a vector space exists, independent of the basis. So, $|\Psi(t)\rangle$ is an element of a Hilbert space and that's that. It's just a function of time. The existence of a basis of a vector space is given by the axiom of choice, and we can decompose a vector in terms of basis vectors, but I reiterate that that does not define a vector. Btw, $|x\rangle$ is not strictly a basis set of the Hilbert space, not being normalizable... – nervxxx May 26 '13 at 14:57
The wavefunction vector $|\Psi (t) \rangle$ is supposed to be a function of time only. When you write $| \Psi (t) \rangle$ you are not considering the projection of the wavefunction nor on the position neither on the momentum space, but just the state of the system at time $t$, which is nothing but a postulate of Quantum Mechanics. You will have the wavefunction in coordinate (or momentum or any other observable) once you project your state vector on a basis of the observable you have chosen. For instance, in coordinate space: $$\langle \mathbf{x} | \Psi (t) \rangle := \Psi (\mathbf{x},t)$$. which is the probability amplitude of finding my system (here we have just one coordinate, so we suppose we are dealing with a single particle system) at position $\mathbf{x}$ at time $t$. If you want to switch from coordinate space to momentum space, i.e. you want to have the following probability amplitude: $$\langle \mathbf{p} | \Psi (t) \rangle = \tilde{\Psi}(\mathbf{p} ,t)$$ (where we have used $\tilde{\Psi}$ to mean that is not the same function of $\mathbf{p}$ as $\Psi$ was for $\mathbf{x}$), we can write like this: $$\tilde{\Psi}(\mathbf{p},t)=\int\,d\mathbf{x} \langle\mathbf{p}|\mathbf{x}\rangle\langle\mathbf{x}|\Psi(t)\rangle$$ for each $t$, having inserted the completeness relation of the space coordinate observable. Now, knowing that $\langle \mathbf{p} | \mathbf{x} \rangle = \frac{1}{\sqrt{2\pi \hbar}}\exp(\frac{i}{\hbar}\mathbf{p}\cdot\mathbf{x}),$ you find that that projection of wavefunction in momentum space is the fourier transform of the coordinate-space wave function.
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But how do i get base vectors for momentum if i know base vectors of position space? – 71GA May 26 '13 at 11:17
It's the same thing, you have to make a fourier transform of the coordinate-space eigenstates, i.e.: $$|\mathbf{p}\rangle=\int \,d\mathbf{x} |\mathbf{x} \rangle \langle \mathbf{x} | \mathbf{p} \rangle$$ – user24959 May 26 '13 at 12:01
When you express a state vector in terms of a basis, you're expressing it as a sum of other state vectors:
$$\sum_i c_i | \Psi_i \rangle$$
If you have some linear operator that acts on a state to transform it into some other state or into some other basis, acting on the individual basis vectors and then doing the sum is the same as applying the operator to the total state.
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2016-05-28 22:07:54
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