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6.1 Sky Models<a id='deconv:sec:skymodels'></a>
Before we dive into deconvolution methods we need to introduce the concept of a sky model. Since we are making an incomplete sampling of the visibilities with limited resolution we do not recover the 'true' sky from an observation. The dirty image is the 'true' sky convol... | fig = plt.figure(figsize=(16, 7))
gc1 = aplpy.FITSFigure('../data/fits/deconv/KAT-7_6h60s_dec-30_10MHz_10chans_uniform_n100-model.fits', \
figure=fig, subplot=[0.0,0.1,0.35,0.8])
gc1.show_colorscale(vmin=-0.1, vmax=1.0, cmap='viridis')
gc1.hide_axis_labels()
gc1.hide_tick_labels()
plt.title('Sky... | 6_Deconvolution/6_1_sky_models.ipynb | landmanbester/fundamentals_of_interferometry | gpl-2.0 |
Left: a point-source sky model of a field of sources with various intensities. Right: PSF response of KAT-7 for a 6 hour observation at a declination of $-30^{\circ}$.
By convolving the ideal sky with the array PSF we effectively are recreating the dirty image. The figure on the left below shows the sky model convolved... | fig = plt.figure(figsize=(16, 5))
fh = fits.open('../data/fits/deconv/KAT-7_6h60s_dec-30_10MHz_10chans_uniform_n100-model.fits')
skyModel = fh[0].data
fh = fits.open('../data/fits/deconv/KAT-7_6h60s_dec-30_10MHz_10chans_uniform_n100-psf.fits')
psf = fh[0].data
fh = fits.open('../data/fits/deconv/KAT-7_6h60s_dec-30_10M... | 6_Deconvolution/6_1_sky_models.ipynb | landmanbester/fundamentals_of_interferometry | gpl-2.0 |
Left: the point-source sky model convolved with the KAT-7 PSF with the residual image added. Centre: the original dirty image. Right: the difference between the PSF-convoled sky model and the dirty image.
Now that we see we can recreate the dirty image from a sky model and the array PSF, we just need to learn how to do... | fig = plt.figure(figsize=(16, 7))
gc1 = aplpy.FITSFigure('../data/fits/deconv/KAT-7_6h60s_dec-30_10MHz_10chans_uniform_n100-residual.fits', \
figure=fig, subplot=[0.1,0.1,0.35,0.8])
gc1.show_colorscale(vmin=-0.8, vmax=3., cmap='viridis')
gc1.hide_axis_labels()
gc1.hide_tick_labels()
plt.title('R... | 6_Deconvolution/6_1_sky_models.ipynb | landmanbester/fundamentals_of_interferometry | gpl-2.0 |
Left: residual image after running a CLEAN deconvolution. Right: restored image constructed from convolving the point-source sky model with an 'ideal' PSF and adding the residual image.
Deconvolution, as can be seen in the figure on the left, builds a sky model by subtracts sources from the dirty image and adding them ... | def gauss2d(sigma):
"""Return a normalized 2d Gaussian function, sigma: size in pixels"""
return lambda x,y: (1./(2.*np.pi*(sigma**2.))) * np.exp(-1. * ((xpos**2. + ypos**2.) / (2. * sigma**2.)))
imgSize = 512
xpos, ypos = np.mgrid[0:imgSize, 0:imgSize].astype(float)
xpos -= imgSize/2.
ypos -= imgSize/2.
sigma... | 6_Deconvolution/6_1_sky_models.ipynb | landmanbester/fundamentals_of_interferometry | gpl-2.0 |
All of the lower case models accept formula and data arguments, whereas upper case ones take endog and exog design matrices. formula accepts a string which describes the model in terms of a patsy formula. data takes a pandas data frame or any other data structure that defines a __getitem__ for variable names like a str... | dta = sm.datasets.get_rdataset("Guerry", "HistData", cache=True)
df = dta.data[["Lottery", "Literacy", "Wealth", "Region"]].dropna()
df.head() | v0.13.1/examples/notebooks/generated/formulas.ipynb | statsmodels/statsmodels.github.io | bsd-3-clause |
Fit the model: | mod = ols(formula="Lottery ~ Literacy + Wealth + Region", data=df)
res = mod.fit()
print(res.summary()) | v0.13.1/examples/notebooks/generated/formulas.ipynb | statsmodels/statsmodels.github.io | bsd-3-clause |
Categorical variables
Looking at the summary printed above, notice that patsy determined that elements of Region were text strings, so it treated Region as a categorical variable. patsy's default is also to include an intercept, so we automatically dropped one of the Region categories.
If Region had been an integer var... | res = ols(formula="Lottery ~ Literacy + Wealth + C(Region)", data=df).fit()
print(res.params) | v0.13.1/examples/notebooks/generated/formulas.ipynb | statsmodels/statsmodels.github.io | bsd-3-clause |
Patsy's mode advanced features for categorical variables are discussed in: Patsy: Contrast Coding Systems for categorical variables
Operators
We have already seen that "~" separates the left-hand side of the model from the right-hand side, and that "+" adds new columns to the design matrix.
Removing variables
The "-" ... | res = ols(formula="Lottery ~ Literacy + Wealth + C(Region) -1 ", data=df).fit()
print(res.params) | v0.13.1/examples/notebooks/generated/formulas.ipynb | statsmodels/statsmodels.github.io | bsd-3-clause |
Multiplicative interactions
":" adds a new column to the design matrix with the interaction of the other two columns. "*" will also include the individual columns that were multiplied together: | res1 = ols(formula="Lottery ~ Literacy : Wealth - 1", data=df).fit()
res2 = ols(formula="Lottery ~ Literacy * Wealth - 1", data=df).fit()
print(res1.params, "\n")
print(res2.params) | v0.13.1/examples/notebooks/generated/formulas.ipynb | statsmodels/statsmodels.github.io | bsd-3-clause |
Many other things are possible with operators. Please consult the patsy docs to learn more.
Functions
You can apply vectorized functions to the variables in your model: | res = smf.ols(formula="Lottery ~ np.log(Literacy)", data=df).fit()
print(res.params) | v0.13.1/examples/notebooks/generated/formulas.ipynb | statsmodels/statsmodels.github.io | bsd-3-clause |
Define a custom function: | def log_plus_1(x):
return np.log(x) + 1.0
res = smf.ols(formula="Lottery ~ log_plus_1(Literacy)", data=df).fit()
print(res.params) | v0.13.1/examples/notebooks/generated/formulas.ipynb | statsmodels/statsmodels.github.io | bsd-3-clause |
Any function that is in the calling namespace is available to the formula.
Using formulas with models that do not (yet) support them
Even if a given statsmodels function does not support formulas, you can still use patsy's formula language to produce design matrices. Those matrices
can then be fed to the fitting funct... | import patsy
f = "Lottery ~ Literacy * Wealth"
y, X = patsy.dmatrices(f, df, return_type="matrix")
print(y[:5])
print(X[:5]) | v0.13.1/examples/notebooks/generated/formulas.ipynb | statsmodels/statsmodels.github.io | bsd-3-clause |
To generate pandas data frames: | f = "Lottery ~ Literacy * Wealth"
y, X = patsy.dmatrices(f, df, return_type="dataframe")
print(y[:5])
print(X[:5])
print(sm.OLS(y, X).fit().summary()) | v0.13.1/examples/notebooks/generated/formulas.ipynb | statsmodels/statsmodels.github.io | bsd-3-clause |
Get endpoint, host headers, and load the image from a file or from the MNIST dataset. | print('************************************************************')
print('************************************************************')
print('************************************************************')
print("starting query")
if len(sys.argv) < 3:
raise Exception("No endpoint specified. ")
endpoint = sys.... | docs/samples/explanation/aix/mnist/query_explain.ipynb | kubeflow/kfserving-lts | apache-2.0 |
Display the input image to be used. | fig0 = (inputs[:,:,0] + 0.5)*255
f, axarr = plt.subplots(1, 1, figsize=(10,10))
axarr.set_title("Original Image")
axarr.imshow(fig0, cmap="gray")
plt.show() | docs/samples/explanation/aix/mnist/query_explain.ipynb | kubeflow/kfserving-lts | apache-2.0 |
Send the image to the inferenceservice. | print("Sending Explain Query")
x = time.time()
res = requests.post(endpoint, json=input_image, headers=headers)
print("TIME TAKEN: ", time.time() - x) | docs/samples/explanation/aix/mnist/query_explain.ipynb | kubeflow/kfserving-lts | apache-2.0 |
Unwrap the response from the inferenceservice and display the explanations. | print(res)
if not res.ok:
res.raise_for_status()
res_json = res.json()
temp = np.array(res_json["explanations"]["temp"])
masks = np.array(res_json["explanations"]["masks"])
top_labels = np.array(res_json["explanations"]["top_labels"])
fig, m_axs = plt.subplots(2,5, figsize = (12,6))
for i, c_ax in enumerate(m_axs.... | docs/samples/explanation/aix/mnist/query_explain.ipynb | kubeflow/kfserving-lts | apache-2.0 |
1 Introduction
Scenario
There are 8 schools in Neighborhood Y of City X and a total of 100 microscopes for the biology classes at the 8 schools, though the microscopes are not evenly distributed across the locations. Since last academic year there has been a significant enrollment shift in the neighborhood, and at 4 of... | supply_schools = [1, 6, 7, 8]
demand_schools = [2, 3, 4, 5] | notebooks/transportation-problem.ipynb | pysal/spaghetti | bsd-3-clause |
Amount of supply and demand at each location (indexed by supply_schools and demand_schools) | amount_supply = [20, 30, 15, 35]
amount_demand = [5, 45, 10, 40] | notebooks/transportation-problem.ipynb | pysal/spaghetti | bsd-3-clause |
Solution class | class TransportationProblem:
def __init__(
self,
supply_nodes,
demand_nodes,
cij,
si,
dj,
xij_tag="x_%s,%s",
supply_constr_tag="supply(%s)",
demand_constr_tag="demand(%s)",
solver="cbc",
display=True,
):
"""Instantia... | notebooks/transportation-problem.ipynb | pysal/spaghetti | bsd-3-clause |
Plotting helper functions and constants
Note: originating shipments | shipping_colors = ["maroon", "cyan", "magenta", "orange"]
def obs_labels(o, b, s, col="id", **kwargs):
"""Label each point pattern observation."""
def _lab_loc(_x):
"""Helper for labeling observations."""
return _x.geometry.coords[0]
if o.index.name != "schools":
X = o.index.name[... | notebooks/transportation-problem.ipynb | pysal/spaghetti | bsd-3-clause |
Streets | streets = geopandas.read_file(examples.get_path("streets.shp"))
streets.crs = "esri:102649"
streets = streets.to_crs("epsg:2762") | notebooks/transportation-problem.ipynb | pysal/spaghetti | bsd-3-clause |
Schools | schools = geopandas.read_file(examples.get_path("schools.shp"))
schools.index.name = "schools"
schools.crs = "esri:102649"
schools = schools.to_crs("epsg:2762") | notebooks/transportation-problem.ipynb | pysal/spaghetti | bsd-3-clause |
Schools - supply nodes | schools_supply = schools[schools["POLYID"].isin(supply_schools)]
schools_supply.index.name = "supply"
schools_supply | notebooks/transportation-problem.ipynb | pysal/spaghetti | bsd-3-clause |
Schools - demand nodes | schools_demand = schools[schools["POLYID"].isin(demand_schools)]
schools_demand.index.name = "demand"
schools_demand | notebooks/transportation-problem.ipynb | pysal/spaghetti | bsd-3-clause |
Instantiate a network object | ntw = spaghetti.Network(in_data=streets)
vertices, arcs = spaghetti.element_as_gdf(ntw, vertices=True, arcs=True) | notebooks/transportation-problem.ipynb | pysal/spaghetti | bsd-3-clause |
Plot | # plot network
base = arcs.plot(linewidth=3, alpha=0.25, color="k", zorder=0, figsize=(10, 10))
vertices.plot(ax=base, markersize=2, color="red", zorder=1)
# plot observations
schools.plot(ax=base, markersize=5, color="k", zorder=2)
schools_supply.plot(ax=base, markersize=100, alpha=0.25, color="b", zorder=2)
schools_d... | notebooks/transportation-problem.ipynb | pysal/spaghetti | bsd-3-clause |
Associate both the supply and demand schools with the network and plot | ntw.snapobservations(schools_supply, "supply")
supply = spaghetti.element_as_gdf(ntw, pp_name="supply")
supply.index.name = "supply"
supply_snapped = spaghetti.element_as_gdf(ntw, pp_name="supply", snapped=True)
supply_snapped.index.name = "supply snapped"
supply_snapped
ntw.snapobservations(schools_demand, "demand")
... | notebooks/transportation-problem.ipynb | pysal/spaghetti | bsd-3-clause |
Calculate distance matrix while generating shortest path trees | s2d, tree = ntw.allneighbordistances("supply", "demand", gen_tree=True)
s2d[:3, :3]
list(tree.items())[:4], list(tree.items())[-4:] | notebooks/transportation-problem.ipynb | pysal/spaghetti | bsd-3-clause |
3. The Transportation Problem
Create decision variables for the supply locations and amount to be supplied | supply["dv"] = supply["id"].apply(lambda _id: "s_%s" % _id)
supply["s_i"] = amount_supply
supply | notebooks/transportation-problem.ipynb | pysal/spaghetti | bsd-3-clause |
Create decision variables for the demand locations and amount to be received | demand["dv"] = demand["id"].apply(lambda _id: "d_%s" % _id)
demand["d_j"] = amount_demand
demand | notebooks/transportation-problem.ipynb | pysal/spaghetti | bsd-3-clause |
Solve the Transportation Problem
Note: shipping costs are in meters per microscope | s, d, s_i, d_j = supply["dv"], demand["dv"], supply["s_i"], demand["d_j"]
trans_prob = TransportationProblem(s, d, s2d, s_i, d_j) | notebooks/transportation-problem.ipynb | pysal/spaghetti | bsd-3-clause |
Linear program (compare to its formulation in the Introduction) | trans_prob.print_lp() | notebooks/transportation-problem.ipynb | pysal/spaghetti | bsd-3-clause |
Extract all network shortest paths | paths = ntw.shortest_paths(tree, "supply", "demand")
paths_gdf = spaghetti.element_as_gdf(ntw, routes=paths)
paths_gdf.head() | notebooks/transportation-problem.ipynb | pysal/spaghetti | bsd-3-clause |
Extract the shipping paths | shipments = trans_prob.extract_shipments(paths_gdf, "id")
shipments | notebooks/transportation-problem.ipynb | pysal/spaghetti | bsd-3-clause |
Plot optimal shipping schedule | # plot network
base = arcs.plot(alpha=0.2, linewidth=1, color="k", figsize=(10, 10), zorder=0)
vertices.plot(ax=base, markersize=1, color="r", zorder=2)
# plot observations
schools.plot(ax=base, markersize=5, color="k", zorder=2)
supply.plot(ax=base, markersize=100, alpha=0.25, color="b", zorder=3)
supply_snapped.plot(... | notebooks/transportation-problem.ipynb | pysal/spaghetti | bsd-3-clause |
1. Utwórz wektor zer o rozmiarze 10
python
np.zeros
2. Ile pamięci zajmuje tablica?
3.Utwórz wektor 10 zer z wyjątkiem 5-tego elementu równego 4
4. Utwórz wektor kolejnych liczb od 111 do 144.
np.arange
5. Odwróć kolejność elementów wektora.
6. Utwórz macierz 4x4 z wartościamy od 0 do 15
reshape
7. Znajdź wsk... | import numpy as np
x = np.linspace(0,10,23)
f = np.sin(x)
%matplotlib inline
import matplotlib.pyplot as plt
plt.plot(x,f,'o-')
plt.plot(4,0,'ro')
# f1 = f[1:-1] * f[:]
print(np.shape(f[:-1]))
print(np.shape(f[1:]))
ff = f[:-1] * f[1:]
print(ff.shape)
x_zero = x[np.where(ff < 0)]
x_zero2 = x[np.where(ff < 0)[0] +... | ML_SS2017/Numpy_cwiczenia.ipynb | marcinofulus/teaching | gpl-3.0 |
9. Utwórz macierz 3x3:
identycznościową np.eye
losową z wartościami 0,1,2
10. Znajdz minimalną wartość macierzy i jej wskaźnik
11. Znajdz średnie odchylenie od wartości średniej dla wektora | Z = np.random.random(30)
| ML_SS2017/Numpy_cwiczenia.ipynb | marcinofulus/teaching | gpl-3.0 |
12. Siatka 2d.
Utworz index-array warości współrzędnych x i y dla obszaru $(-2,1)\times(-1,3)$.
* Oblicz na nim wartości funkcji $sin(x^2+y^2)$
* narysuj wynik za pomocą imshow i countour | x = np.linspace(0,3,64)
y = np.linspace(0,3,64)
X,Y = np.meshgrid(x,y)
X
Y
np.sin(X**2+Y**2)
plt.contourf(X,Y,np.sin(X**2+Y**2))
| ML_SS2017/Numpy_cwiczenia.ipynb | marcinofulus/teaching | gpl-3.0 |
Quantum Clustering with Schrödinger's equation
Background
This method starts off by creating a Parzen-window density estimation of the input data by associating a Gaussian with each point, such that
$$ \psi (\mathbf{x}) = \sum ^N _{i=1} e^{- \frac{\left \| \mathbf{x}-\mathbf{x}_i \right \| ^2}{2 \sigma ^2}} $$
where $N... | def fineCluster2(xyData,pV,minD):
n = xyData.shape[0]
clust = np.zeros(n)
# index of points sorted by potential
sortedUnclust=pV.argsort()
# index of unclestered point with lowest potential
i=sortedUnclust[0]
# fist cluster index is 1
clustInd=1
while np.min(clust)==0:
x=xyData[i]
# euclidean di... | notebooks/Horn accuracy.ipynb | Chiroptera/QCThesis | mit |
Iris
The iris dataset (available at the UCI ML repository) has 3 classes each with 50 datapoints each. There are 4 features. The data is preprocessed using PCA. | # load data
#dataset='/home/chiroptera/workspace/datasets/iris/iris.csv'
dataset='https://archive.ics.uci.edu/ml/machine-learning-databases/iris/iris.data'
irisPCA=True
normalize=False
irisData=np.genfromtxt(dataset,delimiter=',')
irisData_o=irisData[:,:-1] # remove classification column
iN,iDims=irisData_o.shape
# ... | notebooks/Horn accuracy.ipynb | Chiroptera/QCThesis | mit |
I choose $\sigma=\frac{1}{4}$ to reproduce the experiments in [3]. We use only the first two PC here. For more complete results the algorithm is also executed using all PC. | #%%timeit
sigma=0.25
steps=80
irisD1,iV1,iE=HornAlg.graddesc(irisData_c[:,0:2],sigma=sigma,steps=steps)
#%%timeit
sigma=0.9
steps=80
irisD2,iV2,iE=HornAlg.graddesc(irisData_c,sigma=sigma,steps=steps) | notebooks/Horn accuracy.ipynb | Chiroptera/QCThesis | mit |
Comments
The results shown above distinguish cluster assignment by colour. However, the colours might not be consistent throughout all figures. They serve only as a visual way to see how similar clusters are. This is due to the cluster assignment algorithm being used. Two methods may be used and differ only in the orde... | dist=1.8
irisClustering=HornAlg.fineCluster(irisD1,dist)#,potential=iV)
print 'Number of clusters:',max(irisClustering)
iFig2=plt.figure(figsize=(16,12))
iAx1=iFig2.add_subplot(2,2,1)
iAx2=iFig2.add_subplot(2,2,2)
iAx3=iFig2.add_subplot(2,2,4)
iAx1.set_title('Final quantum system')
iAx1.set_xlabel('PC1')
iAx1.set_yl... | notebooks/Horn accuracy.ipynb | Chiroptera/QCThesis | mit |
Turning to the results, in the first case (clustering on the 2 first PC), the results show the clustering algorithm was able to cluster well one of the clusters (the one that is linearly seperable from the other two) but struggled with outliers present in the space of the other 2 clusters. Furthermore, the separation b... | dist=4.5
irisClustering=HornAlg.fineCluster(irisD2,dist,potential=iV2)
print 'Number of clusters:',max(irisClustering)
iFig2=plt.figure(figsize=(16,6))
iAx1=iFig2.add_subplot(1,2,1)
iAx2=iFig2.add_subplot(1,2,2)
#iAx3=iFig2.add_subplot(2,2,4)
iAx1.set_title('Final quantum system')
iAx1.set_xlabel('PC1')
iAx1.set_yla... | notebooks/Horn accuracy.ipynb | Chiroptera/QCThesis | mit |
In this case, we use all PC. In the final quantum system, the number of minima is the same. However, some of the minima are very close to others and have less datapoints assigned which suggest that they might be local minima and should probably be annexed to the bigger minima close by. Once again the outliers were not ... | crabsPCA=True
crabsNormalize=False
crabs=np.genfromtxt('/home/chiroptera/workspace/datasets/crabs/crabs.dat')
crabsData=crabs[1:,3:]
# PCA
if crabsPCA:
ncrabsData1, cComps,cEigs=HornAlg.pcaFun(crabsData,whiten=True,center=False,
method='eig',type='cov',normalize=crabsN... | notebooks/Horn accuracy.ipynb | Chiroptera/QCThesis | mit |
We're visualizing the data projected on the second and third principal components to replicate the results presented on [3]. They use PCA with the correlation matrix. Below we can see the data on different representations. The closest representation of the data is using the covariance matrix with uncentered data (uncon... | cFig1=plt.figure(figsize=(16,12))
cF1Ax1=cFig1.add_subplot(2,2,1)
cF1Ax2=cFig1.add_subplot(2,2,2)
cF1Ax3=cFig1.add_subplot(2,2,3)
cF1Ax4=cFig1.add_subplot(2,2,4)
cF1Ax1.set_title('Original crab data')
for i in range(len(crabsAssign)):
cF1Ax1.plot(crabsData[i,2],crabsData[i,1],marker='.',c=tableau20[int(crabsAssign... | notebooks/Horn accuracy.ipynb | Chiroptera/QCThesis | mit |
Cluster
We're clustering according to the second and third PC to try to replicate [3], along with the same $\sigma$. | #%%timeit
sigma=1.0/sqrt(2)
steps=80
crab2cluster=ncrabsData1
crabD,V,E=HornAlg.graddesc(crab2cluster[:,1:3],sigma=sigma,steps=steps)
dist=1
crabClustering=HornAlg.fineCluster(crabD,dist,potential=V)
print 'Number of clusters:',max(crabClustering)
print 'Unclestered points:', np.count_nonzero(crabClustering==0)
cF... | notebooks/Horn accuracy.ipynb | Chiroptera/QCThesis | mit |
The 'Final quantum system' shows how the points evolved in 80 steps. We can see that they all converged to 4 minima of the potential for $\sigma=\frac{1}{\sqrt{2}}$, making it easy to identify the number of clusters to choose. However, this is only clear observing the results. The distance used to actually assign the p... | sigma=1.0/sqrt(2)
steps=80
crab2cluster=ncrabsData3
crabD,V,E=HornAlg.graddesc(crab2cluster[:,1:3],sigma=sigma,steps=steps)
#%%debug
dist=1
crabClustering=HornAlg.fineCluster(crabD,dist,potential=V)
print 'Number of clusters:',max(crabClustering)
print 'Unclestered points:', np.count_nonzero(crabClustering==0)
cFig2... | notebooks/Horn accuracy.ipynb | Chiroptera/QCThesis | mit |
Using conventional PCA, clustering results are better.
Other preprocessing
Let's now consider clustering on data projected on all principal components (with centered data) and on original data. | #1.0/np.sqrt(2)
sigma_allpc=0.5
steps_allpc=200
crabD_allpc,V_allpc,E=HornAlg.graddesc(ncrabsData1[:,:3],sigma=sigma_allpc,steps=steps_allpc)
sigma_origin=1.0/sqrt(2)
steps_origin=80
crabD_origin,V_origin,E=HornAlg.graddesc(crabsData,sigma=sigma_origin,steps=steps_origin)
dist_allpc=12
dist_origin=15
crabClustering_... | notebooks/Horn accuracy.ipynb | Chiroptera/QCThesis | mit |
The results of the last experimens show considerably worse results. The final quantum system suggests a great ammount of minima and bigger variance on the final convergence of the points. Furthermore the distribution of the minima doesn't suggest any natural clustering for the user, contrary to what happened before.
Th... | n_samples=400
n_features=5
centers=4
x_Gauss,x_assign=sklearn.datasets.make_blobs(n_samples=n_samples,n_features=n_features,centers=centers)
#nX=sklearn.preprocessing.normalize(x_Gauss,axis=0)
x_2cluster=x_Gauss
gMix_fig=plt.figure()
plt.title('Gaussian Mix, '+str(n_features)+' features')
for i in range(x_Gauss.shape... | notebooks/Horn accuracy.ipynb | Chiroptera/QCThesis | mit |
PCA Mix | pcaX,gaussComps,gaussEigs=HornAlg.pcaFun(x_Gauss,whiten=True,center=True,
method='eig',type='cov',normalize=False)
gPCAf=plt.figure()
plt.title('PCA')
for i in range(x_Gauss.shape[0]):
plt.plot(pcaX[i,0],pcaX[i,1],marker='.',c=tableau20[int(x_assign[i])*2])
sigma=2.
ste... | notebooks/Horn accuracy.ipynb | Chiroptera/QCThesis | mit |
Testing params
The following params are introduced to test the new param.imag parametrization by going back to three channels for the existing modelzoo models | def arbitrary_channels_to_rgb(*args, channels=None, **kwargs):
channels = channels or 10
full_im = param.image(*args, channels=channels, **kwargs)
r = tf.reduce_mean(full_im[...,:channels//3]**2, axis=-1)
g = tf.reduce_mean(full_im[...,channels//3:2*channels//3]**2, axis=-1)
b = tf.reduce_mean(full_... | notebooks/feature-visualization/any_number_channels.ipynb | tensorflow/lucid | apache-2.0 |
Arbitrary channels parametrization
param.arbitrary_channels calls param.image and then reduces the arbitrary number of channels to 3 for visualizing with modelzoo models. | _ = render.render_vis(model, "mixed4a_pre_relu:476", param_f=lambda:arbitrary_channels_to_rgb(128, channels=10)) | notebooks/feature-visualization/any_number_channels.ipynb | tensorflow/lucid | apache-2.0 |
Grayscale parametrization
param.grayscale_image creates param.image with a single channel and then tiles them 3 times for visualizing with modelzoo models. | _ = render.render_vis(model, "mixed4a_pre_relu:476", param_f=lambda:grayscale_image_to_rgb(128)) | notebooks/feature-visualization/any_number_channels.ipynb | tensorflow/lucid | apache-2.0 |
Testing different objectives
Different objectives applied to both parametrizations. | _ = render.render_vis(model, objectives.deepdream("mixed4a_pre_relu"), param_f=lambda:arbitrary_channels_to_rgb(128, channels=10))
_ = render.render_vis(model, objectives.channel("mixed4a_pre_relu", 360), param_f=lambda:arbitrary_channels_to_rgb(128, channels=10))
_ = render.render_vis(model, objectives.neuron("mixed4a... | notebooks/feature-visualization/any_number_channels.ipynb | tensorflow/lucid | apache-2.0 |
variable definitions
figure directory | figure_directory = "" | figures/Figure 3 - noise removal.ipynb | jacobdein/alpine-soundscapes | mit |
example recording 1 | site1 = Site.objects.get(name='Höttinger Rain')
sound_db1 = Sound.objects.get(id=147) | figures/Figure 3 - noise removal.ipynb | jacobdein/alpine-soundscapes | mit |
example recording 2 | site2 = Site.objects.get(name='Pfaffensteig')
sound_db2 = Sound.objects.get(id=158) | figures/Figure 3 - noise removal.ipynb | jacobdein/alpine-soundscapes | mit |
formating | style.set_font() | figures/Figure 3 - noise removal.ipynb | jacobdein/alpine-soundscapes | mit |
remove noise
remove noise from example recordings 1 and 2 using the adaptive level equalization algorithm | # example recording 1
wave1 = Wave(sound_db1.get_filepath())
wave1.read()
wave1.normalize()
samples1 = wave1.samples[(100 * wave1.rate):(160 * wave1.rate)]
duration = 60
f, t, a_pass = psd(samples1, rate=wave1.rate, window_length=512)
ale_pass = remove_background_noise(a_pass, N=0.18, iterations=3)
b_pass = remove_anth... | figures/Figure 3 - noise removal.ipynb | jacobdein/alpine-soundscapes | mit |
plot | # create figure
figure3 = pyplot.figure()
#figure3.subplots_adjust(left=0.04, bottom=0.12, right=0.96, top=0.97, wspace=0, hspace=0)
figure3.subplots_adjust(left=0.04, bottom=0.04, right=0.96, top=0.99, wspace=0, hspace=0)
figure3.set_figwidth(6.85)
figure3.set_figheight(9.21)
# specify frequency bins (width of 1 kilo... | figures/Figure 3 - noise removal.ipynb | jacobdein/alpine-soundscapes | mit |
save figure | #figure3.savefig(path.join(figure_directory, "figure3.png"), dpi=300) | figures/Figure 3 - noise removal.ipynb | jacobdein/alpine-soundscapes | mit |
Line plot | ts = np.linspace(0,16*np.pi,1000)
xs = np.sin(ts)
ys = np.cos(ts)
zs = ts
fig = plt.figure()
ax = fig.add_subplot(111, projection ='3d')
ax.plot(xs,ys,zs, zdir = 'z') | 3D_Plots_01.ipynb | AdrianoValdesGomez/Master-Thesis | cc0-1.0 |
Esta es la manera "canónica" de generar una gráfica en la que habrá una curva en $\mathbb{R}^3$. Las xs, ys, zs son las coordenadas de la curva, en este caso están dadas por arreglos de numpy. zdir hace alusión a la dirección que se considerará como la dirección z en caso de introducir una gráfica 2D en esta misma.
Sca... | ts = np.linspace(0,8*np.pi,1000)
xs = np.sin(ts)
ys = np.cos(ts)
zs = ts
fig = plt.figure()
ax = fig.add_subplot(111, projection ='3d')
ax.scatter(xs,ys,zs, zdir = 'z', alpha = 0.3) | 3D_Plots_01.ipynb | AdrianoValdesGomez/Master-Thesis | cc0-1.0 |
Wireframe Plot
En este caso necesitamos arreglos bidimensionales para las xs y las ys, para ello usamos la función meshgrid, de la siguiente forma | x = np.linspace(-1.5,1.5,100)
y = np.linspace(-1.5,1.5,100)
Xs, Ys = np.meshgrid(x,y)
Zs = np.sin(2*Xs)*np.sin(2*Ys)
fig = plt.figure(figsize=(5.9,5.9))
ax = fig.add_subplot(111, projection ='3d')
ax.plot_wireframe(Xs,Ys,Zs, rstride=3, cstride=3, alpha = 0.4)
#plt.figure? | 3D_Plots_01.ipynb | AdrianoValdesGomez/Master-Thesis | cc0-1.0 |
Quiver Plot | pts_x_ini = np.array([0])
pts_y_ini = np.array([0])
pts_z_ini = np.array([0])
pts_x_fin = np.array([0])
pts_y_fin = np.array([0])
pts_z_fin = np.array([1])
fig = plt.figure()
ax = fig.add_subplot(111, projection = '3d')
ax.quiver(0,0,0,0,0,10,length=1.0, arrow_length_ratio = .1)
ax.set_xlim(-1,1)
ax.set_ylim(-1,1)
ax.... | 3D_Plots_01.ipynb | AdrianoValdesGomez/Master-Thesis | cc0-1.0 |
Vector FIeld | xc, yc, zc = np.meshgrid(np.arange(-0.8, 1, 0.2),
np.arange(-0.8, 1, 0.2),
np.arange(-0.8, 1, 0.8))
u = np.sin(np.pi * xc) * np.cos(np.pi * yc) * np.cos(np.pi * zc)
v = -np.cos(np.pi * xc) * np.sin(np.pi * yc) * np.cos(np.pi * zc)
w = (np.sqrt(2.0 / 3.0) * np.cos(np.pi * xc)... | 3D_Plots_01.ipynb | AdrianoValdesGomez/Master-Thesis | cc0-1.0 |
Campo vectorial Eléctroestático | xr,yr,zr = np.meshgrid(np.arange(-1,1,.1),np.arange(-1,1,.1),np.arange(-1,1,.1))
theta = np.linspace(0,np.pi,100)
phi = np.linspace(0,2*np.pi,100)
r = 1/np.sqrt(xr**2+yr**2+zr**2)
fig = plt.figure()
U,V,W = np.sin(theta)*np.cos(phi), np.sin(theta)*np.sin(phi), np.cos(theta)
ax = fig.add_subplot(111,projection = '3d')
a... | 3D_Plots_01.ipynb | AdrianoValdesGomez/Master-Thesis | cc0-1.0 |
2D plots inside 3D plots | fig = plt.figure()
ax = fig.gca(projection='3d')
Ex = np.linspace(0, 2*np.pi, 100)
Ey = np.sin(Ex * 2 * np.pi) / 2 + 0.5
ax.plot(Ex, Ey, zs=0, zdir='z', label='zs=0, zdir=z')
Bx = np.linspace(0, 2*np.pi, 100)
By = np.sin(Bx * 2 * np.pi) / 2 + 0.5
ax.plot(Bx, By, zs=0, zdir='y', label='zs=0, zdir=z')
#colors = ('r... | 3D_Plots_01.ipynb | AdrianoValdesGomez/Master-Thesis | cc0-1.0 |
Fill_Between in 3D plots | import math as mt
import matplotlib.pyplot as pl
import numpy as np
import random as rd
from mpl_toolkits.mplot3d import Axes3D
from mpl_toolkits.mplot3d.art3d import Poly3DCollection
# Parameter (reference height)
h = 0.0
# Code to generate the data
n = 200
alpha = 0.75 * mt.pi
theta = [alpha + 2.0 * mt.pi * (floa... | 3D_Plots_01.ipynb | AdrianoValdesGomez/Master-Thesis | cc0-1.0 |
Putting text inside the plots | fig = plt.figure()
ax = fig.gca(projection='3d')
plt.rc('text', usetex=True)
zdirs = (None, 'x', 'y', 'z', (1, 1, 0), (1, 1, 1))
xs = (1, 4, 4, 9, 4, 1)
ys = (2, 5, 8, 10, 1, 2)
zs = (10, 3, 8, 9, 1, 8)
for zdir, x, y, z in zip(zdirs, xs, ys, zs):
label = '(%d, %d, %d), dir=%s' % (x, y, z, zdir)
ax.text(x, y, ... | 3D_Plots_01.ipynb | AdrianoValdesGomez/Master-Thesis | cc0-1.0 |
Then we load the modules, some issues remain with matplotlib on Jupyter, but we'll fix them later. | # NN
import keras
# Descriptor (unused)
import dscribe
# Custom Libs
import cpmd
import filexyz
# Maths
import numpy as np
from scipy.spatial.distance import cdist
# Plots
import matplotlib
matplotlib.use('nbAgg')
import matplotlib.pyplot as plt
# Scalers
from sklearn.preprocessing import StandardScaler, MinMaxScaler
f... | Projects/Moog_2016-2019/CO2/CO2_NN/forces.ipynb | CondensedOtters/PHYSIX_Utils | gpl-3.0 |
Then we write some functions that are not yet on LibAtomicSim, but should be soon(ish) | def getDistance1Dsq( position1, position2, length):
dist = position1-position2
half_length = length*0.5
if dist > half_length :
dist -= length
elif dist < -half_length:
dist += length
return dist*dist
def getDistanceOrtho( positions, index1, index2, cell_lengths ):
dist=0
for... | Projects/Moog_2016-2019/CO2/CO2_NN/forces.ipynb | CondensedOtters/PHYSIX_Utils | gpl-3.0 |
Data Parameters | volume=8.82
temperature=3000
nb_type=2
nbC=32
nbO=64
run_nb=1
nb_atoms=nbC+nbO
path_sim = str( "/Users/mathieumoog/Documents/CO2/" + str(volume) + "/" + str(temperature) + "K/" + str(run_nb) + "-run/") | Projects/Moog_2016-2019/CO2/CO2_NN/forces.ipynb | CondensedOtters/PHYSIX_Utils | gpl-3.0 |
Loading Trajectory
Here we load the trajectory, including forces and velocities, and convert the positions back into angstroms, while the forces are still in a.u (although we could do everything in a.u.). | cell_lengths = np.ones(3)*volume
ftraj_path = str( path_sim + "FTRAJECTORY" )
positions, velocities, forces = cpmd.readFtraj( ftraj_path, True )
nb_step = positions.shape[0]
ang2bohr = 0.529177
positions = positions*ang2bohr
for i in range(3):
positions[:,:,i] = positions[:,:,i] % cell_lengths[i] | Projects/Moog_2016-2019/CO2/CO2_NN/forces.ipynb | CondensedOtters/PHYSIX_Utils | gpl-3.0 |
Data parametrization
Setting up the parameters for the data construction. | sigma_C = 0.9
sigma_O = 0.9
size_data = nb_step*nbC
dx = 0.1
positions_offset = np.zeros( (6,3), dtype=float )
size_off = 6
n_features=int(2*(size_off+1))
for i,ival in enumerate(np.arange(0,size_off,2)):
positions_offset[ ival , i ] += dx
positions_offset[ ival+1 , i ] -= dx | Projects/Moog_2016-2019/CO2/CO2_NN/forces.ipynb | CondensedOtters/PHYSIX_Utils | gpl-3.0 |
Building complete data set, with the small caveat that we don't seek to load all of the positions for time constraints (for now at least). | max_step = 1000
start_step = 1000
stride = 10
size_data = max_step*nbC
data = np.zeros( (max_step*nbC, size_off+1, nb_type ), dtype=float )
for step in np.arange(start_step,stride*max_step+start_step,stride):
# Distance from all atoms (saves time?)
matrix = computeDistanceMatrix( positions[step,:,:], cell_lengt... | Projects/Moog_2016-2019/CO2/CO2_NN/forces.ipynb | CondensedOtters/PHYSIX_Utils | gpl-3.0 |
Creating test and train set
Here we focus on the carbon atoms, and we create the input and output shape of the data. The input is created by reshaping the positions array, while the output is simply the forces reshaped. Once this is done, we chose the train et test set by making sure that there is no overlap between th... | nb_data_train = 30000
nb_data_test = 1000
size_data = max_step*nbC
if nb_data_train + nb_data_test > data.shape[0]:
print("Datasets larger than amount of available data")
data = data.reshape( size_data, int(2*(size_off+1)) )
choice = np.random.choice( size_data, nb_data_train+nb_data_test, replace=False)
choice_tr... | Projects/Moog_2016-2019/CO2/CO2_NN/forces.ipynb | CondensedOtters/PHYSIX_Utils | gpl-3.0 |
Here we reshape the data and choose the point for the train and test set making sure that they do not overlap | input_train = data[ choice_train ]
input_test = data[ choice_test ]
output_total = forces[start_step:start_step+max_step*stride:stride,0:nbC,0].reshape(size_data,1)
output_train = output_total[ choice_train ]
output_test = output_total[ choice_test ] | Projects/Moog_2016-2019/CO2/CO2_NN/forces.ipynb | CondensedOtters/PHYSIX_Utils | gpl-3.0 |
Scaling input and output for the Neural Net | # Creating Scalers
scaler = []
scaler.append( StandardScaler() )
scaler.append( StandardScaler() )
# Fitting Scalers
scaler[0].fit( input_train )
scaler[1].fit( output_train )
# Scaling input and output
input_train_scale = scaler[0].transform( input_train )
input_test_scale = scaler[0].transform( input_test)... | Projects/Moog_2016-2019/CO2/CO2_NN/forces.ipynb | CondensedOtters/PHYSIX_Utils | gpl-3.0 |
Neural Net Structure
Here we set the NN parameters | # Iteration parameters
loss_fct = 'mean_squared_error' # Loss function in the NN
optimizer = 'Adam' # Choice of optimizers for training of the NN weights
learning_rate = 0.001
n_epochs = 5000 # Number of epoch for optimization?
patience = 100 # Patience for converge... | Projects/Moog_2016-2019/CO2/CO2_NN/forces.ipynb | CondensedOtters/PHYSIX_Utils | gpl-3.0 |
Here we create the neural net structure and compile it | # Individual net structure
force_net = keras.Sequential(name='force_net')
#force_net.add( keras.layers.Dropout( dropout_rate_init ) )
for node in nodes:
force_net.add( keras.layers.Dense( node, activation=activation_fct, kernel_constraint=keras.constraints.maxnorm(3)))
#force_net.add( keras.layers.Dropout( drop... | Projects/Moog_2016-2019/CO2/CO2_NN/forces.ipynb | CondensedOtters/PHYSIX_Utils | gpl-3.0 |
The layout property can be shared between multiple widgets and assigned directly. | Button(description='Another button with the same layout', layout=b.layout) | docs/source/examples/Widget Styling.ipynb | cornhundred/ipywidgets | bsd-3-clause |
Description
You may have noticed that the widget's length is shorter in presence of a description. This because the description is added inside of the widget's total length. You cannot change the width of the internal description field. If you need more flexibility to layout widgets and captions, you should use a combi... | from ipywidgets import HBox, Label, IntSlider
HBox([Label('A too long description'), IntSlider()]) | docs/source/examples/Widget Styling.ipynb | cornhundred/ipywidgets | bsd-3-clause |
Natural sizes, and arrangements using HBox and VBox
Most of the core-widgets have
- a natural width that is a multiple of 148 pixels
- a natural height of 32 pixels or a multiple of that number.
- a default margin of 2 pixels
which will be the ones used when it is not specified in the layout attribute.
This allows sim... | from ipywidgets import Button, HBox, VBox
words = ['correct', 'horse', 'battery', 'staple']
items = [Button(description=w) for w in words]
HBox([VBox([items[0], items[1]]), VBox([items[2], items[3]])]) | docs/source/examples/Widget Styling.ipynb | cornhundred/ipywidgets | bsd-3-clause |
Latex
Widgets such as sliders and text inputs have a description attribute that can render Latex Equations. The Label widget also renders Latex equations. | from ipywidgets import IntSlider, Label
IntSlider(description='$\int_0^t f$')
Label(value='$e=mc^2$') | docs/source/examples/Widget Styling.ipynb | cornhundred/ipywidgets | bsd-3-clause |
Number formatting
Sliders have a readout field which can be formatted using Python's Format Specification Mini-Language. If the space available for the readout is too narrow for the string representation of the slider value, a different styling is applied to show that not all digits are visible.
The Flexbox layout
In f... | from ipywidgets import Layout, Button, Box
items_layout = Layout(flex='1 1 auto',
width='auto') # override the default width of the button to 'auto' to let the button grow
box_layout = Layout(display='flex',
flex_flow='column',
align_items='stretch', ... | docs/source/examples/Widget Styling.ipynb | cornhundred/ipywidgets | bsd-3-clause |
Three buttons in an HBox. Items flex proportionaly to their weight. | from ipywidgets import Layout, Button, Box
items = [
Button(description='weight=1'),
Button(description='weight=2', layout=Layout(flex='2 1 auto', width='auto')),
Button(description='weight=1'),
]
box_layout = Layout(display='flex',
flex_flow='row',
align_items='s... | docs/source/examples/Widget Styling.ipynb | cornhundred/ipywidgets | bsd-3-clause |
A more advanced example: a reactive form.
The form is a VBox of width '50%'. Each row in the VBox is an HBox, that justifies the content with space between.. | from ipywidgets import Layout, Button, Box, FloatText, Textarea, Dropdown, Label, IntSlider
form_item_layout = Layout(
display='flex',
flex_flow='row',
justify_content='space-between'
)
form_items = [
Box([Label(value='Age of the captain'), IntSlider(min=40, max=60)], layout=form_item_layout),
Box... | docs/source/examples/Widget Styling.ipynb | cornhundred/ipywidgets | bsd-3-clause |
A more advanced example: a carousel. | from ipywidgets import Layout, Button, Box
item_layout = Layout(height='100px', min_width='40px')
items = [Button(layout=item_layout, description=str(i), button_style='warning') for i in range(40)]
box_layout = Layout(overflow_x='scroll',
border='3px solid black',
width='500px',... | docs/source/examples/Widget Styling.ipynb | cornhundred/ipywidgets | bsd-3-clause |
Predefined styles
If you wish the styling of widgets to make use of colors and styles defined by the environment (to be consistent with e.g. a notebook theme), many widgets enable choosing in a list of pre-defined styles.
For example, the Button widget has a button_style attribute that may take 5 different values:
'pr... | from ipywidgets import Button
Button(description='Danger Button', button_style='danger') | docs/source/examples/Widget Styling.ipynb | cornhundred/ipywidgets | bsd-3-clause |
The style attribute
While the layout attribute only exposes layout-related CSS properties for the top-level DOM element of widgets, the
style attribute is used to expose non-layout related styling attributes of widgets.
However, the properties of the style atribute are specific to each widget type. | b1 = Button(description='Custom color')
b1.style.button_color = 'lightgreen'
b1 | docs/source/examples/Widget Styling.ipynb | cornhundred/ipywidgets | bsd-3-clause |
Just like the layout attribute, widget styles can be assigned to other widgets. | b2 = Button()
b2.style = b1.style
b2 | docs/source/examples/Widget Styling.ipynb | cornhundred/ipywidgets | bsd-3-clause |
Widget styling attributes are specific to each widget type. | s1 = IntSlider(description='Blue handle')
s1.style.handle_color = 'lightblue'
s1 | docs/source/examples/Widget Styling.ipynb | cornhundred/ipywidgets | bsd-3-clause |
1) Fit the Model Using Data Augmentation
Here is some code to set up some ImageDataGenerators. Run it, and then answer the questions below about it. | from tensorflow.keras.applications.resnet50 import preprocess_input
from tensorflow.keras.preprocessing.image import ImageDataGenerator
image_size = 224
# Specify the values for all arguments to data_generator_with_aug.
data_generator_with_aug = ImageDataGenerator(preprocessing_function=preprocess_input,
... | notebooks/deep_learning/raw/ex5_data_augmentation.ipynb | Kaggle/learntools | apache-2.0 |
Why do we need both a generator with augmentation and a generator without augmentation? After thinking about it, check out the solution below. | # Check your answer (Run this code cell to receive credit!)
q_1.solution() | notebooks/deep_learning/raw/ex5_data_augmentation.ipynb | Kaggle/learntools | apache-2.0 |
2) Choosing Augmentation Types
ImageDataGenerator offers many types of data augmentation. For example, one argument is rotation_range. This rotates each image by a random amount that can be up to whatever value you specify.
Would it be sensible to use automatic rotation for this problem? Why or why not? | # Check your answer (Run this code cell to receive credit!)
q_2.solution() | notebooks/deep_learning/raw/ex5_data_augmentation.ipynb | Kaggle/learntools | apache-2.0 |
3) Code
Fill in the missing pieces in the following code. We've supplied some boilerplate. You need to think about what ImageDataGenerator is used for each data source. | # Specify which type of ImageDataGenerator above is to load in training data
train_generator = data_generator_with_aug.flow_from_directory(
directory = '../input/dogs-gone-sideways/images/train',
target_size=(image_size, image_size),
batch_size=12,
class_mode='categorical')
# Specify wh... | notebooks/deep_learning/raw/ex5_data_augmentation.ipynb | Kaggle/learntools | apache-2.0 |
4) Did Data Augmentation Help?
How could you test whether data augmentation improved your model accuracy? | # Check your answer (Run this code cell to receive credit!)
q_4.solution() | notebooks/deep_learning/raw/ex5_data_augmentation.ipynb | Kaggle/learntools | apache-2.0 |
Magnetic isochrones were computed earlier. Details can be found in this notebook entry on a small magnetic stellar grid. I'll focus on those computed with the Grevesse, Asplund, & Sauval (2007; henceforth GAS07) solar abundance distribution. Three ages will be examined: 5 Myr, 12 Myr, and 30 Myr, in line with the previ... | std_iso_05 = np.genfromtxt('files/dmestar_00005.0myr_z+0.00_a+0.00_gas07_t010.iso')
std_iso_12 = np.genfromtxt('files/dmestar_00012.0myr_z+0.00_a+0.00_gas07_t010.iso')
std_iso_30 = np.genfromtxt('files/dmestar_00030.0myr_z+0.00_a+0.00_gas07_t010.iso')
mag_iso_05 = np.genfromtxt('files/dmestar_00005.0myr_gas07_z+0.00_a... | Daily/20150729_young_magnetic_models.ipynb | gfeiden/Notebook | mit |
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