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Here is an example: pattern = r"""(?x)[AB]\d+ # Match A or B followed by some digits [CD]\d+ # Match C or D followed by some digits """ **print(re.sub(pattern, '*', 'A3C9 and C1B17'))** ###### * [and ]* 21.3 Summary There is a lot to remember.
Here is a summary: Expression Description [] any of the characters inside the brackets . any character except the newline + 1 or more of the preceding - 0 or more of the preceding ?
0 or 1 of the preceding {m} exactly m of the preceding {m,n} between m and n (inclusive) of the preceding ?
following +, *, ?, {m}, and {m,n} — take as few as possible \ escape special characters | “or” ^ (at start of pattern) match just the first occurrence $ (at end of pattern) match just the last occurrence \d \D any digit (non-digit) \w \W any letter or number (non-letter or -number) \s \S any whitespace (non-whit...
match newlines, too (?x) flag to enable verbose style ----- _21.3.
SUMMARY_ 213 Here are some short examples: Expression Description 'abc' the exact string abc '[ABC]' an A, B, or C '[a-zA-Z][0-9]' match a letter followed by a digit '[a..]' a followed by any two characters (except newlines) 'a+' one or more a’s 'a*' any number of a’s, even none 'a?' zero or one a 'a{2}' exac...
All of our matching is done from the left and does not consider overlaps. For instance, we have the following: re.sub('aba', '*', 'abababa') ----- 214 _CHAPTER 21.
REGULAR EXPRESSIONS_ ###### 21.4 Groups Using parentheses around part of an expression creates a group that contains the text that matches a pattern.
You can use this to do more sophisticated substitutions.
Here is an example that converts to lowercase every capital letter that is followed by a lowercase letter: **def modify(match):** letters = match.group() **return letters.lower()** re.sub(r'([A-Z])[a-z]', modify, 'PEACH Apple ApriCot') ###### PEACH apple apricot The modify function ends up getting called three t...
The re.sub function automatically sends to the modify function a Match object, which we name match. This object contains information about the matching text.
The object’s group method returns the matching text itself. If instead of match.group, we use match.groups, then we can further break down the match according the groups defined by the parentheses.
Here is an example that matches a capital letter followed by a digit and converts each letter to lowercase and adds 10 to each number: **def modify(match):** letter, number = match.groups() **return letter.lower() + str(int(number)+10)** re.sub(r'([A-Z])(\d)', modify, 'A1 + B2 + C7') ###### a11 + b12 + c17 The g...
For instance, in the above program the tuples returned are shown below: First match: ('A', '1') Second match: ('B', '2') Third match: ('C', '7') Note also that we can get at this information by passing arguments to match.group.
For the first match, match.group(1) is 'A' and match.group(2) is 1. ###### 21.5 Other functions - sub — We have seen many examples of sub.
One thing we haven’t mentioned is that there is an optional argument count, which specifies how many matches (from the left) to make. Here is an example: re.sub(r'a', '*', 'ababababa', count=2) ----- _21.5.
OTHER FUNCTIONS_ 215 - findall — The findall function returns a list of all the matches found.
Here is an example: re.findall(r'[AB]\d', 'A3 + B2 + A9') As another example, to find all the words in a string, you can do the following: re.findall(r'\w+', s) This is better than using s.split() because split does not handle punctuation, while the regular expression does. - split — The split function is anal...
The regular expression version allows us to split on something more general than the string method does.
Here is an example that splits an algebraic expression at + or -. re.split(r'\+|\-', '3x+4y-12x^2+7') - match and search — These are useful if you just want to know if a match occurs.
The difference between these two functions is match only checks to see if the beginning of the string matches the pattern, while search searches through the string until it finds a match. Both return None if they fail to find a match and a Match object if they do find a match.
Here are examples: **if (re.match(r'ZZZ', 'abc ZZZ xyz')):** **print('Match found at beginning.')** **else:** **print('No match at beginning')** **if (re.search(r'ZZZ', 'abc ZZZ xyz')):** **print('Match found in string.')** **else:** **print('No match found.')** ###### No match at beginning.
Match found in string. The Match object returned by these functions has group information in it.
Say we have the following: a=re.search(r'([ABC])(\d)', '= A3+B2+C8') a.group() a.group(1) a.group(2) 'A3' 'A' '3' Remember that re.search will only report on the first match it finds in the string. ----- 216 _CHAPTER 21.
REGULAR EXPRESSIONS_ - finditer — This returns an iterator of Match objects that we can loop through, like below: **for s in re.finditer(r'([AB])(\d)', 'A3+B4'):** **print(s.group(1))** Note that this is a little more general than the findall function in that findall returns the matching strings, whereas findite...
Here is an example: pattern = re.compile(r'[AB]\d') pattern.findall('A3+B4+C9+D8',2,6) ###### ['B4'] 21.6 Examples **Roman Numerals** Here we use regular expressions to convert Roman numerals into ordinary numbers. |man Numerals Here we use regular expressions to convert Roman numerals into ordinary mbers.|Col2| ...
(CD)?(D)?(C{0,3}) (XC)?(XL)?(L)?(X{0,3}) (IX)?(IV)?(V)?(I{0,3})""") num = input('Enter Roman numeral: ').upper() m = pattern.match(num) sum = 0 for x in m.groups():|| ----- _21.6.
EXAMPLES_ 217 **if x!=None and x!='':** **if x in ['CM', 'CD', 'XC', 'XL', 'IX', 'IV']:** **sum+=d[x]** **elif x[0] in 'MDCLXVI':** **sum+=d[x[0]]*len(x)** **print(sum)** ###### Enter Roman numeral: MCMXVII 1917 The regular expression itself is fairly straightforward.
It looks for up to three M’s, followed by zero or one CM’s, followed by zero or one CD’s, etc., and stores each of those in a group.
The for loop then reads through those groups and uses a dictionary to add the appropriate values to a running sum. **Dates** Here we use a regular expression to take a date in a verbose format, like February 6, 2011, and convert it an abbreviated format, mm/dd/yy (with no leading zeroes).
Rather than depend on the user to enter the date in exactly the right way, we can use a regular expression to allow for variation and mistakes.
For instance, this program will work whether the user spells out the whole month name or abbreviates it (with or with a period).
Capitalization does not matter, and it also does not matter if they can even spell the month name correctly. They just have to get the first three letters correct.
It also does not matter how much space they use and whether or not they use a comma after the day. **import re** d = {'jan':'1', 'feb':'2', 'mar':'3', 'apr':'4', 'may':'5', 'jun':'6', 'jul':'7', 'aug':'8', 'sep':'9', 'oct':'10', 'nov':'11', 'dec':'12'} date = input('Enter date: ') m = re.match('([A-Za-z]+)\.?\s*(\d...
6, 2011 2/6/11 The first part of the regular expression, ([A-Za-z]+)\.? takes care of the month name. It matches however many letters the user gives for the month name. The \.?
matches either 0 or 1 periods after the month name, so the user can either enter a period or not. The parentheses around the letters save the result in group 1. Next we find the day: \s*(\d{1,2}).
The first part \s* matches zero or more whitespace characters, so it doesn’t matter how much space the user puts between the month and day.
The rest matches one or two digits and saves it in group 2. |iation and mistakes.
For instance, this program will work whether the user spells out the whole nth name or abbreviates it (with or with a period).
Capitalization does not matter, and it also es not matter if they can even spell the month name correctly. They just have to get the first three ers correct.
It also does not matter how much space they use and whether or not they use a mma after the day.|Col2| |---|---| ||| |import re d = {'jan':'1', 'feb':'2', 'mar':'3', 'apr':'4', 'may':'5', 'jun':'6', 'jul':'7', 'aug':'8', 'sep':'9', 'oct':'10', 'nov':'11', 'dec':'12'} date = input('Enter date: ') m = re.match('([A-Za-z]...
REGULAR EXPRESSIONS_ The rest of the expression,,?\s*(\d{4}), finds the year. Then we use the results to create the abbreviated date.
The only tricky part here is the first part, which takes the month name, changes it to all lowercase, and takes only the first three characters and uses those as keys to a dictionary. This way, as long as the user correctly spells the first three letters of the month name, the program will understand it. ----- ### C...
Here are most of them: Function Description sin, cos, tan trig functions asin, acos, atan inverse trig functions atan2(y,x) gives arctan( _y/x) with proper sign behavior_ sinh, cosh, tanh hyperbolic functions asinh, acosh, atanh inverse hyperbolic functions log, log10 natural log, log base 10 log1p log(1+x), mo...
MATH_ **Note** Note that the floor and int functions behave the same for positive numbers, but differently for negative numbers. For instance, floor(3.57) and int(3.57) both return the integer 3.
However, floor(-3.57) returns -4, the greatest integer less than or equal to -3.57, while **int(-3.57) returns -3, which is obtained by throwing away the decimal part of the number.** ###### atan2 The atan2 function is useful for telling the angle between two points.
Let x and y be the distances between the points in the x and y directions. The tangent of the angle in the picture below is given by y/x.
Then arctan( _y/x) gives the angle itself._ But if the angle were 90[◦], this would not work as x would be 0. We would also need special cases to handle when x < 0 and when y < 0.
The atan2 function handles all of this. Doing atan2(y,x) will return arctan( _y/x) with all of the cases handled properly._ The atan2 function returns the result in radians.
If you would like degrees, do the following: angle = math.degrees(atan2(y,x)) The resulting angle from atan2 is between _π and π (_ 180[◦] and 180[◦]).
If you would like it between _−_ _−_ 0 and 360[◦], do the following: angle = math.degrees(atan2(y,x)) angle = (angle+360) % 360 ###### 22.2 Scientific notation Look at the following code: 100.1**10 ###### 1.0100451202102516e+20 The resulting value is displayed in scientific notation.
It is 1.0100451202102516 10[20]. The e+20 _×_ stands for 10[20]. Here is another example: _×_ .15**10 ###### 5.7665039062499975e-09 This is 5.7665039062499975 10[−][9]. _×_ ----- _22.3.
COMPARING FLOATING POINT NUMBERS_ 221 ###### 22.3 Comparing floating point numbers In Section 3.1 we saw that some numbers, like .1, are not represented exactly on a computer.
Mathematically, after the code below executes, x should be 1, but because of accumulated errors, it is actually 0.9999999999999999. x = 0 **for i in range(10):** x+=.1 This means that the following if statement will turn out False: **if x==1:** A more reliable way to compare floating point numbers x and y is to ...
Here is a simple example of it in action: **from fractions import Fraction** r = Fraction(3, 4) s = Fraction(1, 4) **print(r+s)** ###### Fraction(1, 1) You can do basic arithmetic with Fraction objects, as well as compare them, take their absolute values, etc.
Here are some further examples: r = Fraction(3, 4) s = Fraction(2, 8) **print(s)** **print(abs(2*r-3))** **if r>s:** **print('r is larger')** ###### Fraction(1,4) Fraction(3,2) r is larger Note that Fraction automatically converts things to lowest terms.
The example below shows how to get the numerator and denominator: r = Fraction(3,4) r.numerator r.denominator ----- 222 _CHAPTER 22.
MATH_ ###### 3 4 **Converting to and from floats** To convert a fraction to a floating point number, use float, like below: **float(Fraction(1, 8))** ###### 0.125 On the other hand, say we want to convert 0.3 to a fraction.
Unfortunately, we should not do Fraction(.3) because, as mentioned, some numbers, including .3, are not represented exactly on the computer.
In fact, Fraction(.3) returns the following Fraction object: ###### Fraction(5404319552844595, 18014398509481984) Instead, use string notation, like below: Fraction('.3') **Limiting the denominator** One useful method is limit_denominator.
For a given Fraction object, limit_denominator(x) finds the closest fraction to that value whose denominator does not exceed x.
Here is some examples: Fraction('.333').limit_denominator(100) Fraction('.333').limit_denominator(1000) Fraction('3.14159').limit_denominator(1000) ###### Fraction(1, 3) Fraction(333, 1000) Fraction(355, 113) The last example returns a pretty close fractional approximation to π.
It is off by less than 0.0000003. **Greatest common divisor** The fractions module contains a useful function called gcd that returns the greatest common divisor of two numbers.
Here is an example: **from fractions import gcd** **print('The largest factor 35 and 21 have in common is', gcd(35, 21))** ###### The largest factor 35 and 21 have in common is 7 22.5 The decimal module Python has a module called decimal for doing exact calculations with decimal numbers.
As we’ve noted a few times now, some numbers, such as .3, cannot be represented exactly as a float. Here is ----- _22.5.
THE DECIMAL MODULE_ 223 how to get an exact decimal representation of .3: **from decimal import Decimal** Decimal('.3') ###### Decimal('0.3') The string here is important.
If we leave it out, we get a decimal that corresponds with the inexact floating point representation of .3: Decimal(.3) **Math** You can use the usual math operators to work with Decimal objects.
For example: Decimal(.34) + Decimal(.17) Here is another example: Decimal(1) / Decimal(17) The mathematical functions exp, ln, log10, and sqrt are methods of decimal objects.
For instance, the following gives the square root of 2: Decimal(2).sqrt() Decimal objects can also be used with the built in max, min, and sum functions, as well as converted to floats with float and strings with str. **Precision** By default Decimal objects have 28-digit precision.
To change it to, say, five digitprecision, use the getcontext function. **from decimal import getcontext** getcontext().prec = 5 _�_ Here is an example that prints out 100 digits of getcontext().prec = 100 Decimal(2).sqrt() 2: ----- 224 _CHAPTER 22.
MATH_ There is theoretically no limit to the precision you can use, but the higher the precision, the more memory is required and the slower things will run.
In general, even with small precisions, Decimal objects are slower than floating point numbers.
Ordinary floating point arithmetic is enough for most problems, but it is nice to know that you can get higher precision if you ever need it. There is a lot more to the decimal module.
See the Python documentation [1]. ###### 22.6 Complex numbers Python has a data type for complex numbers. _�_ In math, we have i = _−1. The number i is called an imaginary number.
A complex number is a_ number of the form a + bi, where a and b are real numbers. The value a is called the real part, and _b is the imaginary part.
In electrical engineering, the symbol j is used in place of i, and in Python j_ is used for imaginary numbers.
Here are a couple of examples of creating complex numbers: x = 7j x = 1j x = 3.4 + .3j x = complex(3.4, .3) If a number ends in a j or J, Python treats it as a complex number. Complex numbers have methods real() and imag() which return the real and imaginary parts of the number.
The conjugate method returns the complex conjugate (the conjugate of a + bi is _a_ _bi)._ _−_ The cmath module contains many of the same functions as the math module, except that they work with complex arguments.
The functions include regular, inverse, and hyperbolic trigonometric functions, logarithms and the exponential function.
It also contains two functions, polar and rect, for converting between rectangular and polar coordinates: cmath.polar(3j) cmath.rect(3.0, 1.5707963267948966) ###### (3.0, 1.5707963267948966) (1.8369701987210297e-16+3j) Complex numbers are fascinating, though not all that useful in day-to-day life.
One nice application, however, is fractals. Here is a program that draws the famous Mandelbrot set.
The program requires the PIL and Python 2.6 or 2.7. |mplex numbers are fascinating, though not all that useful in day-to-day life. One nice applica- n, however, is fractals.
Here is a program that draws the famous Mandelbrot set.
The program uires the PIL and Python 2.6 or 2.7.|Col2| |---|---| ||| |from Tkinter import * from PIL import Image, ImageTk, ImageDraw def color_convert(r, g, b): return '#{0:02x}{1:02x}{2:02x}'.format(int(r*2.55),int(g*2.55), int(b*2.55)) max_iter=75|| ----- _22.6.
COMPLEX NUMBERS_ 225 xtrans=-.5 ytrans=0 xzoom=150 yzoom=-150 root = Tk() canvas = Canvas(width=300, height=300) canvas.grid() image=Image.new(mode='RGB',size=(300,300)) draw = ImageDraw.Draw(image) **for x in range(300):** c_x = (x-150)/float(xzoom)+xtrans **for y in range(300):** c = complex(c_x, (y-150)/float(y...
There are ways to speed it up somewhat, but Python is unfortunately slow for these kinds of things. ----- 226 _CHAPTER 22.
MATH_ ###### 22.7 More with lists and arrays **Sparse lists** A 10,000,000 10,000,000 list of integers requires several hundred terabytes of storage, _×_ far more than most hard drives can store.
However, in many practical applications, most of the entries of a list are 0. This allows us to save a lot of memory by just storing the nonzero values along with their locations.
We can do this using a dictionary whose keys are the locations of the nonzero elements and whose values are the values stored in the array at those locations.
For example, suppose we have a two-dimensional list L whose entries are all zero except that L[10][12] is 47 and L[100][245] is 18.
Here is a the dictionary that we would use: d = {(10,12): 47, (100,245): 18} **The array module** Python has a module called array that defines an array object that behaves a lot like a list, except that its elements must all be the same type.
The benefit of array over lists is more efficient memory usage and faster performance.
See the Python documentation [1] for more about arrays. **The NumPy and SciPy libraries** If you have any serious mathematical or scientific calculations [to do on arrays, you may want to consider the NumPy library.
It is easy to download and install.](http://numpy.scipy.org/) From the NumPy user’s guide: NumPy is the fundamental package for scientific computing in Python.
It is a Python library that provides a multidimensional array object, various derived objects (such as masked arrays and matrices), and an assortment of routines for fast operations on arrays, including mathematical, logical, shape manipulation, sorting, selecting, I/O, discrete Fourier transforms, basic linear algebra...
This time from the SciPy user’s guide:](http://scipy.org/) SciPy is a collection of mathematical algorithms and convenience functions built on the NumPy extension for Python.
It adds significant power to the interactive Python session by exposing the user to high-level commands and classes for the manipulation and visualization of data.
With SciPy, an interactive Python session becomes a data-processing and system-prototyping environment rivaling sytems such as MATLAB, IDL, Octave, R-Lab, and SciLab. ###### 22.8 Random numbers **How Python generates random numbers** The random number generator that Python uses is called the Mersenne Twister.
It is reliable and well-tested. It is a deterministic generator, meaning ----- _22.8. RANDOM NUMBERS_ 227 that it uses a mathematical process to generate random numbers.