Pythonize Yourself 1/74

Pythonize Yourself

Integrated Circuits and Systems (ICAS) Instituto de Microelectrónica de Barcelona, IMB-CNM(CSIC)

This work ’as-is’ we provide. No warranty express or implied. May 2016 We’ve done our best, to debug and test. Liability for damages denied.

Permission is granted hereby, to copy, share, and modify. Use as is fit, free or for profit. These rights, on this notice, rely. Image credit: V (1983 miniseries)

M, Dei, IMB-CNM(CSIC) ICAS Tutorials Pythonize Yourself 2/74IntroTools Language Packages4Science Examples

1 Introduction: Matlabholics Anonymous - How to redeem

2 Tools: How to get things done: Tools, IDEs, Installation

3 Language: Enjoy the Lego R

4 Packages4Science: Four Horsemen of the Apocalypse: NumPy, SciPy, Matplotlib, Sympy

5 Examples: Dirty work (but someone has to do it)

M, Dei, IMB-CNM(CSIC) ICAS Tutorials Pythonize Yourself 2/74Intro Tools Language Packages4Science Examples

1 Introduction: Matlabholics Anonymous - How to redeem

2 Tools: How to get things done: Tools, IDEs, Installation

3 Language: Enjoy the Lego R

4 Packages4Science: Four Horsemen of the Apocalypse: NumPy, SciPy, Matplotlib, Sympy

5 Examples: Dirty work (but someone has to do it)

M, Dei, IMB-CNM(CSIC) ICAS Tutorials Pythonize Yourself 3/74Intro Tools Language Packages4Science Examples

Targeting my audience, being a target too

You already know what is a(n): I 15 algorithm, array, argument, assignment, boolean, code, conditional statement (if-then-else), function, program, 25 variable

10 10 I Don’t expect me to: 20 be formal, be unbiased, be a guru I 15 I port your MATLAB/GNU Octave scripts. Some tools already have been designed to it, for ex.: https://github.com/victorlei/smop 10 https://sourceforge.net/projects/libermate/ You can also run your M-ﬁle directly into Python: https://pypi.python.org/pypi/oct2py

M, Dei, IMB-CNM(CSIC) ICAS Tutorials Pythonize Yourself 4/74Intro Tools Language Packages4Science Examples

What is this about?

I Introduce Python and its core scientiﬁc packages

I Promote open source for scientiﬁc computing

I Present a Python integrated development environment (IDE) similar to that of MATLAB R

I Discuss the potentiality of Python through some practical examples of common tasks in the scientiﬁc routine

The content of this presentation is inspired on: I ”Python for MATLAB Users” material by Kitware Staff http://www.kitware.com/cvpr2012.html I Python Course by Bernd Klein http://www.python-course.eu/

M, Dei, IMB-CNM(CSIC) ICAS Tutorials Pythonize Yourself 5/74Intro Tools Language Packages4Science Examples

Ethics!

”Universalism requires that science be independent of race, color, or creed and that it should be essentially international”

”Communalism requires that sci- entiﬁc knowledge should be pub- lic knowledge; [...] there should be freedom of exchange of sci- entiﬁc information between scientists everywhere”

”Disinterestedness requires that the results of bona fide scien- tific research should not be ma- nipulated to serve [...] personal profit, ideology, or expediency” ”Organized skepticism requires that statements should not be accepted on the word of author- ity, but that scientists should be R.H. Brown. The Wisdom of Science. free to question them [...]” Cambridge University Press. 1986.

M, Dei, IMB-CNM(CSIC) ICAS Tutorials Pythonize Yourself 5/74Intro Tools Language Packages4Science Examples

1 from mpl_toolkits.mplot3d import Axes3D 2 import matplotlib.pyplot as pp 3 4 fig = pp.figure(figsize=(5,5)) 5 ax = Axes3D(fig) 6 7 # https://en.wikipedia.org/wiki/Tetrahedron 8 X = ( 1, 1, 1), ( 1, -1, -1),\ 9 (-1, 1, -1), (-1, -1, 1) 10 11 keys =’s’,’color’,’ha’,’va’,’size’,’bbox’ 12 bbox_props = dict(boxstyle="round4,pad=0.3",\ 13 fc="w", ec="1.0", alpha=0.7) 14 labels =’Universalism’,’Communalism’,\ 15 ’Desiterestedness’,’Organized\n skeptisism’ 16 17 def pt2ln(p1, p2, **kwargs): 18 s = (’xs’,’ys’,’zs’,’color’,’linewidth’,’alpha’) 19 p = lambda i: [p1[i], p2[i]] 20 return dict(zip(s, [p(0),p(1),p(2),’g’,8,0.5])) 21 22 for i1 in range(len(X)): 23 for i2 in range(i1+1, len(X)): 24 ax.plot(**pt2ln(X[i1], X[i2])) 25 ax.text(*X[i1], **dict(zip(keys, [labels[i1], 26 ’g’,’center’,’center’, 18, bbox_props]))) 27 28 pp. title (’Mertonian paradigm’,fontsize=16,fontweight=’bold’) 29 ax.xaxis.set_ticklabels([]) 30 ax.yaxis.set_ticklabels([]) 31 ax.zaxis.set_ticklabels([]) 32 pp. show () mertonian paradigm.py M, Dei, IMB-CNM(CSIC) ICAS Tutorials Pythonize Yourself 6/74Intro Tools Language Packages4Science Examples

Why not MATLAB R ? Nor MATLAB-like programs I Expensive I Inﬂuential establishment held by a private company ”MATLAB R , the language of technical computing, is a programming environment for algorithm development, data analysis, visualization, and numeric computation.”

> 5000 academias as customers > 1 million users of MATLAB worldwide > 500 third-party solutions built on MATLAB/Simulink > 1700 MATLAB based books in 28 languages

I Structurally poor language A major ﬂaw is that promotes cut+paste coding by:

Function-name = file-name. Ok for small code bases but discourages writing modular programs suitable for grown up projects, and at last the capability of your code to be shared and be useful for the rest of the community

http://www.mathworks.com/company/factsheet.pdf http://www.mathworks.com/company/aboutus/index.html?s_tid=gn_loc_drop

M, Dei, IMB-CNM(CSIC) ICAS Tutorials Pythonize Yourself 7/74Intro Tools Language Packages4Science Examples

Why not MATLAB R ? Nor MATLAB-like programs

I Exercise #1

Provided that I have convinced you that MATLAB R is: 1. an inﬂuential establishment hold by a private company; 2. a structurally poor language; 3. expensive, in which sense its use in science offends the Mertonian paradigm: universalism, communalism, disinterestedness, organized skeptisism? I Exercise #2 Given that GNU Octave:

1. treats incompatibility with MATLAB R as a bug; 2. is distributed under a GLPv3-”Free as in Freedom” licence, discuss the following statement:

GNU Octave is a free-MATLAB, but not MATLAB-free

http://wiki.octave.org/FAQ

M, Dei, IMB-CNM(CSIC) ICAS Tutorials Pythonize Yourself 8/74Intro Tools Language Packages4Science Examples

The Python remedy

I Holistic (not just domain speciﬁc) I Open and encouraging your vocation to share (algorithms, methods, results...) I Exhibits excellent readability (if you can read it you can reuse it) I Implement modular programming since functions and classes are organized in namespaces I Has powerful built-in data structures I Scientiﬁc modules (and not only) are supported by a large and active community

1 #-*- coding: utf-8-*- 2 import numpy as np 3 import matplotlib.pyplot as pp 4 5 x = np.linspace(0, 2, 1000) 6 pp. xkcd () 7 pp.figure(figsize=(3.5,3.5)) 8 pp.plot(x, np.sqrt(x),color=’m’,\ 9 label =r"Skiing:$\sqrt{t}$") 10 pp.plot(x,x**2,color=’g’,\ 11 label =r"Snowboarding: $t^2$") 12 Side effects? pp. xlabel ("Time $t$") ; pp.ylabel("Skill") 13 pp.legend(loc=’upper center’,fontsize=14,\ 14 fancybox=True,framealpha=0.25) 15 pp. show () learning curve.py

https://www.stat.washington.edu/~hoytak/blog/whypython.html

M, Dei, IMB-CNM(CSIC) ICAS Tutorials Pythonize Yourself 9/74Intro Tools Language Packages4Science Examples

More & less

I Cython: optimising static compiler for Python, allows calls back and forth from and to C or C++ code natively at any point. easily tune readable Python code into plain C performance by adding static type declarations I Python can be integrated with other languages too (Fortran, Java, PHP ...): https://wiki.python.org/moin/IntegratingPythonWithOtherLanguages I What is Python used for? Google, Yahoo, Youtube, gaming... https://wiki.python.org/moin/OrganizationsUsingPython I Is used as extension language in Inkscape, Freecad, Klayout, Glade, Pymol: https://en.wikipedia.org/wiki/List_of_Python_software#Embedded_as_a_scripting_language I Build a compiled application optimizing speed and simplifying dependencies: https://sourcecontribute.com/2015/05/02/compiling-python-to-standalone-executables-on-linux-using-nuitka/

There is no 1 to 1 replacement of Simulink in Python

Anyway we can take advantage of the interoperability of Scilab/Python and use the Xcos to design dynamical systems models. https://www.scilab.org/scilab/features/xcos The last example in this presentation is focused on this issue.

M, Dei, IMB-CNM(CSIC) ICAS Tutorials Pythonize Yourself 10/74Intro Tools Language Packages4Science Examples

1 Introduction: Matlabholics Anonymous - How to redeem

2 Tools: How to get things done: Tools, IDEs, Installation

3 Language: Enjoy the Lego R

4 Packages4Science: Four Horsemen of the Apocalypse: NumPy, SciPy, Matplotlib, Sympy

5 Examples: Dirty work (but someone has to do it)

M, Dei, IMB-CNM(CSIC) ICAS Tutorials Pythonize Yourself 11/74Intro Tools Language Packages4Science Examples

Get the tools

DIE HARD Build Python (latest version) , conﬁg Vi(m) or Emacs https://docs.python.org/2/using/unix.html

apt-get install python, than pip modules. Get Ipython qt-console and conﬁgure it with fancy text editors

The same as above but using Synaptic (Ubuntu based Linux) or other software manager. Main modules can also be installed from there (Numpy, Scipy, Matplotlib, Sympy...) Spyder is a complete IDE that can be used, integrating both: an editor tool and Ipython qt-console(s).

You can rely on a Python package distribution provided by third par- ties: Continuum R Analytics Anaconda, Pyzo or Enthought Canopy. Download, Install and Launch. (Batteries included) Marshmallow https://www.continuum.io/downloads

M, Dei, IMB-CNM(CSIC) ICAS Tutorials Pythonize Yourself 12/74Intro Tools Language Packages4Science Examples

IDE = Editor + Console

I Python on terminal you may want to use it as command line tool

M, Dei, IMB-CNM(CSIC) ICAS Tutorials Pythonize Yourself 12/74Intro Tools Language Packages4Science Examples

IDE = Editor + Console

I Python on terminal you may want to use it as command line tool

I IPython on terminal Interactive with graphical capabilities, shell syntax, tab completion, and his- tory. It has %magic commands

M, Dei, IMB-CNM(CSIC) ICAS Tutorials Pythonize Yourself 12/74Intro Tools Language Packages4Science Examples

IDE = Editor + Console

I Python on terminal you may want to use it as command line tool

I IPython on terminal Interactive with graphical capabilities, shell syntax, tab completion, and his- tory. It has %magic commands

I IDLE Syntax highlighting, debugger

M, Dei, IMB-CNM(CSIC) ICAS Tutorials Pythonize Yourself 12/74Intro Tools Language Packages4Science Examples

IDE = Editor + Console

I Python on terminal you may want to use it as command line tool

I IPython on terminal Interactive with graphical capabilities, shell syntax, tab completion, and his- tory. It has %magic commands

I IDLE Syntax highlighting, debugger

I Spyder Syntax highlighting, debugger, intro- spection for code completion, support for multiple Python consoles (including IPython), has the ability to explore and edit variables from a GUI

IDE >Editor + Console A plenty of IDEs: https://wiki.python.org/moin/IntegratedDevelopmentEnvironments

M, Dei, IMB-CNM(CSIC) ICAS Tutorials Pythonize Yourself 13/74IntroTools Language Packages4Science Examples

1 Introduction: Matlabholics Anonymous - How to redeem

2 Tools: How to get things done: Tools, IDEs, Installation

3 Language: Enjoy the Lego R

4 Packages4Science: Four Horsemen of the Apocalypse: NumPy, SciPy, Matplotlib, Sympy

5 Examples: Dirty work (but someone has to do it)

M, Dei, IMB-CNM(CSIC) ICAS Tutorials Pythonize Yourself 14/74IntroTools Language Packages4Science Examples

About the language

1 2 I It is interpreted and dynamically typed I It is case sensitive and indentation sensitive. I Python has two basic modes: Script: as a command line tool to run scripts Interactive (>>>, [1]:): immediate feedback for each statement. The user provides statements line by line. quit() or Ctrl-D to exit

Let’s start to scratch the surface...

1Not compiled, like C. The interpreter executes instructions directly, without previously compiling a program into machine-language instructions. The interpreter executes the program directly, translating each statement into a sequence of one or more subroutines already compiled into machine code.

2Variables do not have a ﬁxed type. Differently from statically typed languages, variables are not a segment of the memory where some value is written, they are tags or names pointing to objects. It is therefore possible for the variable a to be set to the value 1, then to the value "a string", then to a function.

M, Dei, IMB-CNM(CSIC) ICAS Tutorials Pythonize Yourself 15/74IntroTools Language Packages4Science Examples

Calculator

>>> 17 / 3 # Comment: int/ int -> int 5 >>> 17 / 3.0 # int/ float -> float 5.666666666666667 >>> 17 // 3.0 # explicit floor division discards the fractional part 5.0 >>> 17 % 3 # the% operator returns the remainder of the division 2 >>> _ ** 3 # Exponentiation, the underscore is the last returned value 8 >>> (-1 + 3j)*2j # Complex numbers, natively supported (-6-2j)

Numerical Special Container

int,(long) str limited, unlimited bool values: True or False string of characters precision (Python 2) float tuple Floating point, None ﬁxed sequence of Null object (Some) Built-in Types: double precision objects

complex list mutable sequence of real and imaginary ﬂoats objects dict maps one set of objects to another The world ”object” here appears several times, please be patient...

M, Dei, IMB-CNM(CSIC) ICAS Tutorials Pythonize Yourself 16/74IntroTools Language Packages4Science Examples

Playing around

>>> type(’float’) # String using single quotes >>> type(8), type(8.1) #A sequence of inputs separated bya comma (, ) >>> bool(-3), bool(0.0) # How much truth ina number? (True, False) >>> float(7), complex(3.1) # Conversion of numerical types (7.0, (3.1+0j)) >>> a = complex(3, -4) # Assignment using complex() constructor >>> abs(a) # Absolute function, consistent with the argument type 5.0 >>> int(a) # Will throw an exception’TypeError’ since it is ambiguous Traceback (most recent call last): File"", line 1, in TypeError: can’t convert complex to int ’ >>> str(0.278), str(True), int(’23’) # Back and forth from str (’0.278’,’True’, 23)

Boolean operators: and, or, not Comparisons: <, <=, >, >=, ==, !=, is, is not

>>> x, y = 3, 4.4 >>> x == y , x is y, id(x), id(y) (False, False, 35246376, 35317432) >>> x = y >>> x == y , x is y, id(x), id(y) Multiple assignment (True, True, 35317432, 35317432) >>> z = 4.4 Identity: >>> z == y, z isy Every Python object has an identity. The function (True, False) id(object) returns a unique identifying integer

M, Dei, IMB-CNM(CSIC) ICAS Tutorials Pythonize Yourself 17/74IntroTools Language Packages4Science Examples

Lists & Tuples Sequences of items, of any type, mutable and immutable, respectively. I Tuple: comma separated items, enclosed in parentheses (), sometimes omitted I List: comma separated items, enclosed in square brackets [], mandatory

>>> t0 = 5,’ciao’, (3.14, None) # The last item isa tuple of two items >>> t0[0], t0[2] # can be accessed by indexing (0-based) (5, (3.14, None)) >>> t0 [1] =’hola’ # They are immutable! Traceback (most recent call last): File"", line 1, in TypeError :’tuple’ object does not support item assignment >>> l0 = list(t0) # Cast the tuple intoa list >>> l0 [1] =’hola’ # No complaints now >>> l0 # Note the output: [5,’hola’, (3.14, None)] Common operations and functions Lists have more capabilities (methodsa) to both: than tuples: >>>’hola’ in t0,’hola’ in l0 # test inclusion >>> dir([]) (False, True) [’append’,’count’,’extend’,’index’, >>> t0 + (’hola’,) # Concatenate item ’insert’,’pop’,’remove’,’reverse’, (5,’ciao’, (3.14, None),’hola’) ’sort’] >>> t0 * 2 # Concatenate shallow copies (5,’ciao’, (3.14, None), 5,’ciao’, (3.14, None)) Tuples don’t, but simplicity makes them >>> len(l0) # Length of sequence computationally efﬁcient. 3 aAgain, be patient

M, Dei, IMB-CNM(CSIC) ICAS Tutorials Pythonize Yourself 18/74IntroTools Language Packages4Science Examples

Indexing and slicing Zero based indexing3. >>> a = range(1,6) # Createa sequence of integers >>> a[0], a[-1] # Indexing Index: (1, 5) 0 1 2 3 4 5 >>> a [1:3] # Slicing: index1 to 3, all within [2, 3] Item: 1 2 3 4 5 >>> a[: -1] # Slicing: index0 to last-1 [1, 2, 3, 4] >>> a[:-1:2] # Slicing: same as above, step2 -5 -1-2-3-4 [1, 3] range(stop), return a list of integers in the >>> a[-3:-1] # Slicing: index -3 to -1, all within half open interval [0; stop) [3, 4] range(start, stop[, step]) list of integers in >>> a[3:1:-1] # Beware! the half open interval [start; stop), step [4, 3] speciﬁes the increment/decrement Slice objects: >>> s = slice(1, 4, 2) >>> a[s] slice(stop) [2, 4] slice(start, stop[, step]) >>> s = slice(3, len(a)) >>> a[s] len [4, 5] number of items of a sequence or collection

a.index(x) index of the ﬁrst occurrence of x in a Very usefull methods: a.count(x) total number of occurrences of x in a

3http://www.cs.utexas.edu/users/EWD/transcriptions/EWD08xx/EWD831.html

M, Dei, IMB-CNM(CSIC) ICAS Tutorials Pythonize Yourself 19/74IntroTools Language Packages4Science Examples

Strings

I Immutable sequences of characters I Many built-in methods: >>> s ="Hello World" >>> s.upper() # upper case ’HELLOWORLD’ >>> s[::-1].split() # splitting [’dlroW’,’olleH’] >>>"_".join((s,s[::-1])) # join witha given separator ’Hello World_dlroW olleH’ >>> s.replace("Hello","Goodbye") # substring replacement ’Goodbye World’ >>> s +’%g’%(1/3.0) # sprintf-like formatter ’Hello World 0.333333’ >>> s ="""# triple quotes string ... This is typically used in docstrings ... to documenta segment of code. ... They are important metada! ..."""

I Many more sophisticated ways to format strings: https://docs.python.org/2/library/string.html

M, Dei, IMB-CNM(CSIC) ICAS Tutorials Pythonize Yourself 20/74IntroTools Language Packages4Science Examples

Dictionaries

I Mutable mapping of one object to another I key:value pairs are comma separated and enclosed in curly braces {} I Can be created using the dict() constructor

>>> a = dict(one=1, two=2, three=3) >>> b = {’one’: 1,’two’: 2,’three’: 3} >>> c = dict(zip([’one’,’two’,’three’], [1, 2, 3])) >>> d = dict([(’two’, 2), (’one’, 1), (’three’, 3)]) >>> e = dict({’three’: 3,’one’: 1,’two’: 2}) >>> a == b == c == d == e True >>>’four’ in a,’one’ inb (False, True) >>> c[’two’] = 22 >>> c.values() [3, 22, 1] >>> c.keys() [’three’,’two’,’one’]

M, Dei, IMB-CNM(CSIC) ICAS Tutorials Pythonize Yourself 21/74IntroTools Language Packages4Science Examples

Flow control4 if : for in : while : ...... elif : ... for in : while : ...... elif : if : if : ... continue continue else: ...... for in : while : ...... if : if : break break ......

Iterable: An object capable of returning its members one at a time. Examples: Error handling all sequence types (list, str, and tuple) and some non-sequence types like Sometimes: ”it’s better to beg forgive- dict and file. ness than ask permission” XRange Type: The xrange type is an immutable sequence which is commonly try: used for looping. The advantage of the xrange type over range is that the former 1/0 will always take the same amount of memory, no matter the size of the range it except ZeroDivisionError: represents. range(100000), is list of 100000 elements! xrange(100000) not. print(’1/0!’) >>> tuple(enumerate([6, 4, 5, 9])) assert(1 > 0) ((0, 6), (1, 4), (2, 5), (3, 9)) Enumerate: >>> fori,v in enumerate([6, 4, 5, 9]): assert for checking inputs or interme- ... print(i, v) diate results. If not asserted, raises an AssertionError

4https://docs.python.org/2/tutorial/controlflow.html https://docs.python.org/2/tutorial/errors.html

M, Dei, IMB-CNM(CSIC) ICAS Tutorials Pythonize Yourself 22/74IntroTools Language Packages4Science Examples

Functions Suppose you want a function that calculates the roots of ax2 + bx + c = 0.

1 def quadratic_formula(a, b, c): >>> quadratic_formula(1, -3, 2) 2 dis = (b**2 - 4*a*c)**0.5 (1.0 , 2.0) 3 return (-dis-b)/(2*a), (dis-b)/(2*a) quadratic0.py >>> quadratic_formula(1, 3, 3) Traceback (most recent call last): ... ValueError: negative number cannot be raised to a fractional power

NOTE: def, :, 4-spaces indentation, return. When the return statement is not declared, the function returns a Null object. Let’s ﬁx the ValueError:

1 def quadratic_formula(a, b, c): >>> quadratic_formula(1, 3, 3) 2 dis = (b**2 - 4*a*c + 0j)**0.5 ((-1.5-0.8660254037844386j), 3 return (-dis-b)/(2*a), (dis-b)/(2*a) (-1.5+0.8660254037844386j)) quadratic1.py >>> quadratic_formula(1, -3, 2) ((1-0j), (2+0j))

I What if we want only real solutions?

M, Dei, IMB-CNM(CSIC) ICAS Tutorials Pythonize Yourself 23/74IntroTools Language Packages4Science Examples

Functions ... Optional arguments:

1 def quadratic_formula(a, b, c, real=False): >>> quadratic_formula(1, -3, 2) 2 dis = (b**2 - 4*a*c + 0j)**0.5 ((1-0j), (2+0j)) 3 if real: 4 if dis.imag == 0: >>> quadratic_formula(1, -3, 2, real=True) 5 return (-dis.real-b)/(2*a), (1.0 , 2.0) 6 (dis.real-b)/(2*a) 7 else: a, b, c are positional arguments 8 return (-dis-b)/(2*a), (dis-b)/(2*a) real is a keyword argument quadratic2.py keyword arguments come always after positional arguments

I Exercise: What is returned by quadratic_formula(1, 3, 3, real=True)?

Before continuing let’s do the following experiment on a new python console: dir() >>> dir() If called without an argument, return the names in [’__builtins__’,’__doc__’,’__name__’,’__package__’] the current scope.

>>> __name__ ’__main__’

I The variable name is already deﬁned, and set to the value ’ main ’. I This allows the programmer to control the behaviour of the script whether it is the main program executed or not.

M, Dei, IMB-CNM(CSIC) ICAS Tutorials Pythonize Yourself 24/74IntroTools Language Packages4Science Examples

Script behaviours: !# #! 1 #!/usr/bin/env python 2 def quadratic_formula(a, b, c, real=False): (shebang) directive: 3 """ instructs the loader which program to look 4 Returns the roots of:a*x**2+b*x+c=0 for executing the current script. 5 Only real solutions are returned if real is True 6 """ For Python scripts: 7 dis = (b**2 - 4*a*c + 0j)**0.5 #!/usr/bin/python 8 if real: 9 if dis.imag == 0: or, even bettera 10 return (-dis.real-b)/(2*a), (dis.real-b)/(2*a) 11 else: #!/usr/bin/env python 12 return (-dis-b)/(2*a), (dis-b)/(2*a) 13 The interpreter ignores it, as it is a com- 14 if __name__ ==’__main__’: ment 15 print(’This script contains the definition ofa function’) ahttps://mail.python.org/pipermail/tutor/ 16 else: 2007-June/054816.html 17 print(__name__) quadratic3.py

Your script is now ready to be used in a shell, once you have changed its privileges to be executable:

$ chmod a+x quadratic3.py $ ./quadratic3.py This script contains the definition of a function $_

What about the else part?

M, Dei, IMB-CNM(CSIC) ICAS Tutorials Pythonize Yourself 25/74IntroTools Language Packages4Science Examples

Script behaviours: import

>>> import quadratic3 quadratic3 On import the else part is executed.

>>> dir(quadratic3) [’__builtins__’,’__doc__’,’__file__’, quadratic3 has its own attributes: ’__name__’,’__package__’,’quadratic_formula’] it has a name...

>>> quadratic3.__name__ ’quadratic3’

>>> quadratic3.__file__ ’quadratic3.py’

>>> help(quadratic_formula) The docstrings allows the help() function to Help on function quadratic_formula in module __main__: return them if queried quadratic_formula(a, b, c, real=False) Returns the roots of: a*x**2 + b*x + c = 0 Only real solutions are returned if real is True

>>> quadratic_formula(1, -2, 1, True) quadratic_formula() is now available for (1.0 , 1.0) use

Functions, classes, and more generally, objects, can be deﬁned and reused im- porting them. From now on cut+paste code from/to your scripts is capital crime!

M, Dei, IMB-CNM(CSIC) ICAS Tutorials Pythonize Yourself 26/74IntroTools Language Packages4Science Examples import is very important

I How to use simultaneously the deﬁnition of quadratic formula() from quadratic1.py and quadratic3.py? from ... import ... as ... In [1]: from quadratic1 import quadratic_formula as qf1 In [2]: from quadratic3 import quadratic_formula as qf3 %timeit This magic command provided quadratic3 by the IPython interactive interpreter pro- In [3]: %timeit [qf1(1,0,i) fori in xrange(1000)] vide a simple way to time small bits of 1000 loops, best of 3: 1.69 ms per loop Python code In [4]: %timeit [qf3(1,0,i) fori in xrange(1000)] [... for ...] ? Be patient! 1000 loops, best of 3: 1.76 ms per loop

The import quadratic1 statement will look for the proper ﬁle, which is quadratic1.py in the same directory as the caller. If it is not found, the Python interpreter will search “path” recursively and raise an ImportError exception if it is not found. from some_module import* Very bad: [...] Is some function part of some module? A built-in? Deﬁned above? x = some_function(4)

from some_module import some_function Better: [...] some function may be part of some module, if not redeﬁned in between x = some_function(4)

import some_module Best: [...] some function visibility as part of some module namespace x = some_module.some_function(4)

I as allows renaming in the local namespace http://docs.python-guide.org/en/latest/writing/structure/ https://ipython.org/ipython-doc/dev/interactive/magics.html

M, Dei, IMB-CNM(CSIC) ICAS Tutorials Pythonize Yourself 27/74IntroTools Language Packages4Science Examples

Scripts, passing arguments

I Suppose you want your script with quadratic formula() be accessible directly at command line level. You may want to pass additional arguments to the interpreter. $ python script_name.py argument(s) The script name and additional arguments thereafter are turned into a list of strings and assigned to the argv variable in the sys module.

1 #!/usr/bin/env python 2 import sys $ python quadratic4.py 4 0 -100 3 import quadratic3 as q3 quadratic3 4 ((-5+0j), (5+0j)) 5 if __name__ ==’__main__’: 6 arg = sys.argv $ python quadratic4.py 4 0 -100 True 7 try: quadratic3 8 assert (len(arg) >= 4) ( -5.0 , 5.0) 9 a,b,c = float(arg[1]),float(arg[2]),float(arg[3]) 10 real = False $ python quadratic4.py 4 Z -100 True 11 if len(arg) > 4: quadratic3 12 real = True if arg[4] ==’True’ else’False’ Invalid arguments 13 if a == 0: 14 try: $ python quadratic4.py 15 print(-c/b) Help on function quadratic_formula in 16 except ZeroDivisionError: module quadratic3: 17 print(’No unknown to solve for’) 18 else: quadratic_formula(a, b, c, real=False) 19 print(q3.quadratic_formula(a, b, c, real)) Returns the roots of: a*x**2 + b*x 20 except AssertionError: + c = 0 21 help(q3.quadratic_formula) Only real solutions are returned 22 except ValueError: if real is True 23 print(’Invalid arguments’) (END) quadratic4.py

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More on passing arguments Argument: value passed to a function (or method) when calling the function. There are two types of arguments: I Keyword argument: an argument preceded by an identiﬁer (e.g. name=) in a function call >>> complex(real=3, imag=5) or passed as a value in a dictionary preceded by **. For example, 3 and 5 are both keyword arguments in the following >>> complex(**{’real’: 3,’imag’: 5}) calls to complex():

I Positional argument: an argument that is not a keyword argument. Positional arguments can appear at the beginning of an argument list and/or be passed as >>> complex(3, 5) elements of an iterable preceded by *. For example, 3 and 5 are both positional arguments in the following >>> complex(*(3, 5)) calls:

Some remarks:

>>> def fun0(*args, **kwargs): >>> x, y = (1,2,3), (4,5,6) ... print(args) >>> z = zip(x,y); print(z) ... print(kwargs) [(1, 4), (2, 5), (3, 6)] >>> xx , yy = zip(*z) >>> fun0(1, 2, third=3, forth=4) >>> print(xx, yy) (1, 2) ((1, 2, 3), (4, 5, 6)) {’forth’: 4,’third’: 3} zip() Note nor args neither kwargs are known previously from function side. args, kwargs are conventional names.

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Functional programming5

I a, b, c = float(arg[1]), float(arg[2]), float(arg[3]) : yuck! List comprehensions: [ expression for item in list (if conditional) ]

>>> o = [i*i fori in range(10)]  Adding a simple condition: >>> o = []  >>> fori in range(10) −→ >>> o = [i*i fori in range(10) if i%2==0] ... o.append(i*i)  Adding a multiple condition: >>> o = [i*i if i%2==0 else -i*i fori in range(10)]

Mapping a function to a sequence: map() and the lambda operator

>>> sq = lambda x: x*x Beware! >>> o = map(sq, range(10)) >>> cb = lambda x: x*x*x >>> f = [sq, cb] >>> o = map(lambda x: x*x, range(10)) >>> o2 = [map(lambda y: y(x), f) forx in range(10)]

What about the if? filter() o = filter(lambda x: x%2-1, range(10)) o = map(lambda x: x*x, filter(lambda x: x%2-1, range(10))) # Beware! Want more? reduce(), applies a function to a sequence iteratively. See for ex. http://www.python-course.eu/lambda.php 5However this is a controversial topic: http://stackoverflow.com/questions/1017621/why-isnt-python-very-good-for-functional-programming

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Classes I What is a class? It’s about the definition of things. def: defines a function, class defines a logical grouping of data and functions. We refer to them as attributes and methods, respectively.

A rapid search in the web for ”class examples in Python” gives: bank accounts, vehicles, persons, pets... that’s because objects created from a class aim to mimic real world ”objects”.

How to spot the usefulness of classes in a (probably) more familiar context?

https://xkcd.com/26/ You have a big database of signals: I some of them are represented in the time domain, others in frequency domain. Each of them comes with its time (∆t) or frequency resolution (∆f), for simplicity uniformly spaced. You may wish to switch from one representation to another. Direct and inverse fft() I you may want to analyse them from a power spectral density (psd) point of view, and associate to each signal its proper windowing function, or more advanced ﬁltering to extract the signal from unwanted interference. psd(), window, averages number, filt(), filt params = { ... } I you may also want some specialized visualization tools for your data: psd plot, an histogram plotting the statistical distribution of amplitudes, etc. psd plot(), histo()

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Classes ... A skecth of your class would look like: After deﬁning your class you would use it simply 1 class Signal(): like: 2 def __init__(self, x, domain, res): 3 assert(domain in[’time’,’freq’]) >>> x = Signal(raw_data, 1e2, 4 TF = domain ==’time’ ’freq’) 5 self.xt = x ifTF else self.fft(x, res, -1) >>> x.filt(5e3, 50e3) 6 self.xf = self.fft(x, res) ifTF elsex >>> x.histo() 7 ... 8 def fft(self, x, dx, direction = 1): 9 pass # to be implemented! x is now an object with all its attributes (x.xt, x.xf 10 ...) tidily bundled and organized. 11 def psd(self, window): It has capabilities (methods) like histo(), psd(), etc. 12 self.window = window that operates on it, and are specialized functions that 13 pass # to be implemented! operate in a well deﬁned environment. 14 15 def filt(self, **filt_params): __init__()? Initialization method, needed to initial- 16 pass # to be implemented! ize the instance. 17 18 def psd_plot(self): self? 19 pass # to be implemented! used to declare a method or an a attribute of the 20 instance! Without it all would look like local variables 21 def histo(self): and the code would be ambiguous 22 pass # to be implemented!

Inheritance? Operator overloading? Polymorphism? You can dig more6!

6For example: http://python-textbok.readthedocs.io/en/1.0/Classes.html https://jeffknupp.com/blog/2014/06/18/improve-your-python-python-classes-and-object-oriented-programming/

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1 Introduction: Matlabholics Anonymous - How to redeem

2 Tools: How to get things done: Tools, IDEs, Installation

3 Language: Enjoy the Lego R

4 Packages4Science: Four Horsemen of the Apocalypse: NumPy, SciPy, Matplotlib, Sympy

5 Examples: Dirty work (but someone has to do it)

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Stack/Ecosystem

NumPy, the fundamental package for numerical computation. It deﬁnes the numerical array and matrix types and basic operations on them.

The SciPy library, a collection of numerical algorithms and domain-speciﬁc toolboxes, including signal processing, optimization, statistics and much more.

Matplotlib, a mature and popular plotting package, that provides publication-quality 2D plotting as well as rudimentary 3D plotting.

SymPy, for symbolic mathematics and computer algebra.

Anyway the ”ecosystem” includes much more tools, for ex.: Pandas (high-performance data structures), Mayavi (3D visualization), Cython (C extensions and integration), etc.

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Numpy

I Open source extension module for Python: import numpy as np I Provides fast precompiled numerical routines for (large) multi-dimensional arrays Create

>>> a = np.array([[1, 2, 3], [4, 5, 6]]) arange([start,] stop[, step,], dtype=None) array([[1, 2, 3], array of evenly spaced values within the half-open in- [4, 5, 6]]) terval [start, stop) >>> np.arange(1,10,2) linspace(start, stop, num=50, endpoint=True, array([1, 3, 5, 7, 9]) retstep=False) Returns num evenly spaced samples, calculated over >>> np.linspace(0, 10, 4, endpoint=False) the interval [start, stop] array([ 0. , 2.5, 5. , 7.5]) >>> np.linspace(0, 10, 4, endpoint=True) logspace(start, stop, num=50, endpoint=True, array([ 0. , 3.33333333, 6.66666667, 10. ]) base=10.0) samples uniformly distributed in log space >>> np.logspace(0, 3, 4) array([ 1., 10., 100., 1000.]) meshgrid N-dimensional coordinate arrays useful to evaluate >>> x, y = np.arange(-5, 5, .1), np.arange(-5, 5, .1) functions on a grid >>> xx , yy = meshgrid(x, y, sparse=True) >>> z = np.sin(xx**2 + yy**2) / (xx**2 + yy**2)

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Create

>>> np.ones((2,3)) ones(shape, dtype=None, ...) array([[ 1., 1., 1.], zeros(shape, dtype=None, ...) [ 1., 1., 1.]]) ones_like(a, dtype=None, ...) >>> np.ones(4) zeros_like(a, dtype=None, ...) array([ 1., 1., 1., 1.]) >>> a = np.zeros(3) >>> np.ones_like(a) eye(N, M=None, k=0, dtype=) array([ 1., 1., 1.]) Return a 2-D array with ones on the diagonal and ... zeros elsewhere. M columns, k index of diagonal. >>> np.eye(3) array([[ 1., 0., 0.], k: 0 1-1 [ 0., 1., 0.], [ 0., 0., 1.]]) 11 12 13 >>> np.eye(3, k=-2) + np.eye(3, k=1) 21 22 23 array([[ 0., 1., 0.], [ 0., 0., 1.], 31 32 33 [ 1., 0., 0.]]) Simple tests

>>> a = np.array([[1, 2], [3, 4]]) dtype >>> type(a), a.dtype, len(a), np.shape(a), np.size(a) shape (, dtype(’int64’), 2, (2, 2), 4) size

>>> np.unique(a) unique array([1, 2, 3, 4]) Extraction of unique elements >>> a.diagonal() diagonal array([1, 4])

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Simple manipulation

>>> a.transpose() >>> a transpose In multidimensional arrays array([[1, 3], array([[1, 2], both as method and function you have the axis optional [2, 4]]) [3, 4]]) argument: >>> np.transpose(a) array([[1, 3], >>> a.sum()

[2, 4]]) 10 axis=0 >>> a.T >>> a.sum(axis=0) array([[1, 3], array([4, 6]) [2, 4]]) >>> a.prod(axis=1) array([ 2, 12]) axis=2 >>> a.reshape(4,1) reshape, flatten axis=1 both as methods and func- array([[1], >>> a.mean(axis=1) sum, prod [2] , tions array([ 1.5, 3.5]) [3] , mean, var, std, max, min [4]]) >>> a.argmin(axis=1) >>> a.flatten() array([0, 0]) argmax, argmin array([1, 2, 3, 4]) >>> a.argmax(axis=0) array indices of the minimum array([1, 1]) and maximum values >>> a.clip(2,3) clip, fill array([[2, 2], >>> b = a copy [3, 3]]) >>> b.fill(0); a >>> a.fill(9); a array([[0, 0], array([[9, 9], [0, 0]]) [9, 9]]) >>> a = np.copy(b) >>> a = np.eye(2); b array([[0, 0], [0, 0]])

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More reﬁned manipulation and testing

>>> a = np.where(a>2, 0, a) where array([[1, 2], Tests returning boolean values: [0, 0]]) any() checks if at least one element of the array is True or >>> 2 ina in greater than zero True all() checks if all elements are True of greater than zero >>> np.nonzero(a) nonzero isnan() checks if the element if (array([0, 0]), array([0, 1])) Return the indices of the ele- not-a-number NaN >>> a.nonzero() ments that are non-zero isinf() inﬁnity check (array([0, 0]), array([0, 1]))

Element wise agebra and broadcasting Element wise functions + - * / % ** == != > >= < <= abs, sign, sqrt, log, log10, exp, sin, cos, tan, arcsin, arccos, arctan, 11 12 13 1 2 3 12 14 16 sinh, cosh, tanh, arcsinh, arccosh, andarctanh. 21 22 23 1 2 3 22 24 26 floor ceil, rint 31 32 33 1 2 3 32 34 36

11 12 13 1 1 1 12 13 14 21 22 23 2 2 2 23 24 25 Exercises 31 32 33 3 3 3 34 35 36 Which is the result of:

111 1 1 1 2 3 2 3 4 I np.array([[1, 2, 3]]).T*np.array([1, 2, 3])? 2 2 2 1 2 3 3 4 5 I np.arange(1,10).reshape((3,3))**2? 3 3 3 1 2 3 4 5 6

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A simple speed test

Using the IPython console, we have the %timeit command 1 #-*- coding: utf-8-*- which returns also statistical information: 2 import time 3 import numpy as np In [1]: %timeit fahrenheit = 4 [x *9/5 + 32 forx in Tl] 5 Tm = 25.0 # mean temperature 1000 loops, best of 3: 717 us per loop 6 Td = 5.0 # temperature standard deviation 7 ns = 1000 # number of samples In [2]: %timeit fahrenheit = T*9/5 + 32 8 100000 loops, best of 3: 14.1 us per loop 9 # Generate thea normally distributed array 10 # of temperatures 11 T = np.random.normal(Tm, Td, ns) 12 Tl = list(T) # convert to list 13 14 # list approach: 15 t0 = time.time() 16 fahrenheit = [x*9/5 + 32 forx in Tl] 17 t_list = time.time() - t0 18 19 # numpy approach: 20 t0 = time.time() 21 fahrenheit = T*9/5 + 32 22 t_array = time.time() - t0 23 24 # print ratio 25 print str(t_list/t_array) list vs nparray.py

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Indexing and slicing

>>> a = np.arange(10); a a[start:stop:step] array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])

>>> a[0] 0-based indexing 0

>>> a[-1] The -1,(-2, -3, ...) 9

>>> a[2:6] Slicing array([2, 3, 4, 5])

>>> a[::-1] Reverse ordering array([9, 8, 7, 6, 5, 4, 3, 2, 1, 0])

>>> b = a[1:].reshape((3,3)) Indexing multidimensional arrays >>> b[1][1], b[1,1] 5, 5

I Whereas slicings on lists and tuples create new objects, a slicing operation on an array creates a view on the original array. So we get an another possibility to access the array, or better a part of the array. From this follows that if we modify a view, the original array will be modiﬁed as well.

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Array selectors I Selection by booleans I Selection by indexes >>> a = np.array([[6, 4], [5, 9]], float) >>> a = np.array([2, 4, 6, 8], float) >>> a >= 6 >>> b = np.array([0, 0, 1, 3, 2, 1], int) array([[ True, False], >>> a[b] [False, True]], dtype=bool) array([ 2., 2., 4., 8., 6., 4.]) >>> a[a >= 6] array([ 6., 9.]) >>> a[np.where(a>5)] >>> a[np.logical_and(a > 5, a < 9)] array([6, 9])

>>> a[np.nonzero(a>5)] array([6, 9])

Structured arrays

>>> dtype = np.dtype([(’month’,’S10’),(’day’,’S10’),(’number’,’i4’)])

>>> calendar = np.array([(’April’,’Saturday’, 30),(’May’,’Sunday’, 1)], dtype=dtype) >>> calendar[’month’] array ([’April’,’May’], dtype =’|S10’) dtype() declares a data type. ’S10’ stands for a string of 10 characters, ’i4’ stands for integer of 4 bytes. Detailed description of primitive types: http://docs.scipy.org/doc/numpy-1.5.x/reference/arrays.scalars.html

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Array algebra

>>> a, b = np.array([1, 2, 3]), np.array([0, 1, 1]) dot() >>> np.dot(a,b) dot product 5

NumPy also comes with a number of built-in routines for linear algebra calculations. These can be found in the sub-module linalg.

>>> a = np.eye(8) - 4*np.ones((8,8)) det() >>> np.linalg.det(a) Determinant -31.0 eig() Eigenvectors, eigenvalues >>> vals, vecs = np.linalg.eig(a) inv() Inverse >>> b = np.linalg.inv(a) (+ Singular value decomposition, and more)

Polynomials poly() Given a set of roots, returns the polynomial >>> np.poly([-1, 1, 1, 10]) coefﬁcients poly() Given a set of polynomial coefﬁcients, returns >>> np.roots([1, 4, -2, 3]) the roots polyadd(), polysub(), polymul(), polydiv() Polyno- >>> np.polyint([1, 1, 1, 1]) mial algebra polyder(), polyint() Derivation, integration (constant >>> np.polyder([1./4., 1./3., 1./2., 1., 0.]) of unknown term is 0) polyval() Evaluates a polynomial at a particular point ... polyfot() fot data to polynomial (least-squares error)

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Random numbers: random submodule

>>> np.random.seed(293423) random() Return random floats in the half-open inter- >>> np.random.random() val [0.0, 1.0) rand() An array of random numbers in the half-open >>> np.random.rand(5) interval [0.0, 1.0) >>> np.random.rand(2, 3) randint() An array of random integers in the half open specified interval >>> np.random.randint(5, 10) normal() Gaussian probability distribution with µ mean and σ standard deviation >>> np.random.normal(1.5, 4.0) uniform() Uniform probability distribution in the specified half-open interval >>> np.random.uniform(1.5, 4.0) %

NumPy also includes generators for many other distributions: Beta, binomial, chi-square, Dirichlet, exponential, F, Gamma, geometric, Gumbel, hyper- geometric, Laplace, logistic, log- normal, logarithmic, multinomial, multivariate, negative binomial, noncentral chi-square, noncentral F, normal, Pareto, Poisson, power, Rayleigh, Cauchy, Student’s t, triangular, von Mises, Wald, Weibull, and Zipf distributions.

It also allows: (Weigthed) Random Choices Random Intervals Random Samples http://www.python-course.eu/python_numpy_probability.php

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Scipy?

Scipy is composed of task-speciﬁc sub-modules:

scipy.cluster Vector quantization / Kmeans scipy.constants Physical and mathematical constants scipy.fftpack Fourier transform scipy.integrate Integration routines scipy.interpolate Interpolation scipy.io Data input and output scipy.linalg Linear algebra routines scipy.ndimage n-dimensional image package scipy.odr Orthogonal distance regression scipy.optimize Optimization scipy.signal Signal processing scipy.sparse Sparse matrices scipy.spatial Spatial data structures and algorithms scipy.special Any special mathematical functions scipy.stats Statistics http://docs.scipy.org/doc/scipy/reference/

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Matplotlib Van der Pol phase portrait #1

1 #-*- coding: utf-8-*- 8 # Computation part: Van der Pol equation 2 from numpy import* 9 def vanderpol(u, t=0., mu=.5): 3 from scipy import* 10 x = u[0] 4 from scipy.integrate import odeint 11 v = u[1] 5 from matplotlib.pyplot import* 12 dx = v 6 matplotlib.rc(’axes’, edgecolor =’black’) 13 dv = mu*(1. - x**2)*v - x van der pol mod1.py 14 return dx, dv With respect to the original codea here the computa- 15 tional and the graphical parts are separated. 16 t = linspace(-5.5, 5.5, 300) 17 u0 = array([1. , 1.]) I numpy, scipy, matplotlib.pyplot imported di- 18 mu = [ .25, .5, 1., 1.5, 2.0] rectly into the main namespace. 19 u = [] 20 form in mu: I The odeint solve numerically systems of ordi- 21 u.append(odeint(vanderpol, u0, t, args=(m,))) nary differential equation: 22 dx 23 # Computational part: attractors = f(x, t0,...) 24 x = linspace(-3, 3, 15) dt 25 y = linspace(-4, 4, 15) 26 x, y = meshgrid(x, y) I The Van der Pol equation is: 27 X, Y = vanderpol([x, y]) 2 ( dx 28 M = (hypot(X, Y)) d x 2 dx dt = v −µ(1−x ) +x = 0 −→ 29 M[M == 0] = 1. dt2 dt dv = µ(1 − x2)v − x dt 30 X, Y = X/M, Y/M ahttps://commons.wikimedia.org/wiki/File: van der pol mod1.py Van_der_pols_equation_phase_portrait.svg

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Matplotlib Van der Pol phase portrait #1 (...)

32 # Graphical part: Van der Pol equation 33 fig = figure(figsize=(5.5, 7)) 34 ax = subplot(111) 35 fori,m in enumerate(mu): 36 ax.plot(u[i][:,0], u[i][:,1], lw=1.5, label=r’$\mu=%.2f$’%m) 37 fig.savefig("van_der_pol_equation_phase_portrait_1_p1.svg", 38 bbox_inches="tight", pad_inches=.15) van der pol mod1.py

I Declaration of the ﬁgure object, and its size I Declaration of subplot: (111), 1 row, 1 column, start at 1 I Each plot will be referenced in the legend, being label attached individually

I The ﬁgure is saved as svg in this case, most backends support also png, pdf, ps, eps

savefig (fname, dpi=None, facecolor=’w’, edgecolor=’w’, orientation=’portrait’, papertype=None, format=None, transparent=False, bbox inches=None, pad inches=0.1, frameon=None)

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Matplotlib Van der Pol phase portrait #1 (...)

40 # Graphical part: attractors 41 ax.quiver(x, y, X, Y, M, pivot =’mid’, cmap = cm.Pastel1) 42 fig.savefig("van_der_pol_equation_phase_portrait_1_p2.svg", 43 bbox_inches="tight", pad_inches=.15) van der pol mod1.py

I Quiver plot, using the previously calculated vanderpol on the meshgrid

I Arrow length normalization (see line 23-30) I Color map: cmap http://matplotlib.org/examples/color/ colormaps_reference.html

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Matplotlib Van der Pol phase portrait #1 (...)

I legend() http://matplotlib.org/users/legend_guide. html

I It is also possible to have multiple legends on the same axes

I setp() is used to set the properties of graphical objects. To get a list of settable line properties, call the setp() function with a line or lines as argument. For example in this case: >>> setp(ax) adjustable: [’box’|’datalim’ | ... agg_filter: unknown alpha : float (0.0 transparent through ... anchor: unknown animated: [True | False] aspect: unknown autoscale_on: unknown autoscalex_on: unknown autoscaley_on: unknown axes : an :class : matplotlib.axes.Axes ... axes_locator: unknown ...

45 # Legend 46 ax.legend(loc =’upper left’) 47 setp(ax.get_legend().get_texts(), fontsize = 14) 48 fig.savefig("van_der_pol_equation_phase_portrait_1_p3.svg", 49 bbox_inches="tight", pad_inches=.15) van der pol mod1.py

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Matplotlib Van der Pol phase portrait #1 (...)

I grid(): True or False I text(): position text on ﬁgure with given coordinates, text properties have been passed using a dictionary and the ** operator

50 # Grids 51 ax.grid(True) 52 ax.minorticks_on() 53 54 # Text on figure 55 txt_dic = {’fontsize’: 18,’backgroundcolor’:’w’} 56 text(0.0, -3.2,r’$\dot{x}= v$’, **txt_dic) 57 text(0.0, -3.7,r’$\dot{v}=\mu(1-x^2)v- x$’, **txt_dic) 58 fig.savefig("van_der_pol_equation_phase_portrait_1_p4.svg", 59 bbox_inches="tight", pad_inches=.15) van der pol mod1.py

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Matplotlib Van der Pol phase portrait #1 (...)

I xlabel(), ylabel(): axis labels I title(): title

61 # Lables and title 62 xlabel (r’$\dot{x}$’, fontsize = 18) 63 ylabel (r’$\dot{v}$’, fontsize = 18) 64 title (’Van der Pol\’s Phase portrait’) 65 fig.savefig("van_der_pol_equation_phase_portrait_1.svg", 66 bbox_inches="tight", pad_inches=.15) van der pol mod1.py

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Matplotlib Van der Pol phase portrait #2

van der pol mod2.py

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Matplotlib Van der Pol phase portrait #3

van der pol mod3.py Plotting contest: http://nellev.github.io/tmp/jhepc/gallery.html

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Sympy7

I Sympy adds symbolic math for a Maple or Mathematica alternative. In conjunction with $ ipython notebook --profile=sympy a IPython Notebook, it has similar functional- >>> from sympy import* ity. However we will explore its features im- porting it as a module. 8 I Regarding Sage : – Sage includes Sympy – Sage is huge and glues together many mathematical open source packages (also non-Python) – Sympy is a lightweight normal Python module. No external dependencies.

 Geometry Module  Linear Algebra Module   Numerics Module  I It has various submodules: Plotting Module Concrete Mathematics Module   Polynomials Module   Statistics Module Pretty Printing

7Extensive documentation: http://sympy.googlecode.com/svn/api/sympy.html 8https://github.com/sympy/sympy/wiki/SymPy-vs.-Sage

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SymPy: Symbols Built-in numeric types: Real for arbitrary-precision ﬂoating-point numbers, Rational Rep- resents integers and rational numbers p/q of any size >>> Rational(3), Rational(1,2) (3, 1/2) >>> Rational("3/5"), Rational("1.23") # froma string (3/5, 123/100) >>> Rational("1.23").p, Rational("1.23").q # Access nominator and denominator as.p and.q (123 , 100)

Complex numbers >>> exp(I*x).expand(complex=True) I*exp(-im(x))*sin(re(x)) + exp(-im(x))*cos(re(x)) >>> x = Symbol("x", real=True) >>> exp(I*x).expand(complex=True) I*sin(x) + cos(x)

Explicit declaration of symbolic variables:

>>> x = Symbol(’x’) >>> symbols(’a0:3’) >>> y = Symbol(’y’) (a0 , a1 , a2) >>> ((x+y)**2).expand() x**2 + 2*x*y + y**2 Note: an arbitrary number of symbols can be created at >>> ((x+y)**2).subs(x, 1) runtime without knowing them in advance by manipulat- (y + 1)**2 >>> ((x+y)**2).subs(x, y) ing the string ’a0:3’. 4*y**2

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SymPy: Calculus Limits Algebraic equations >>> limit(sin(x)/x, x, 0) In [19]: solve(Eq(x**4, 1), x) 1 Out[19]: [1, -1, -I, I] >>> limit(1/x, x, oo) # infinity symbol: oo 0 Integration >>> integrate(log(x), x) # indefinite Differentiation x*log(x) - x >>> diff(tan(x), x) >>> integrate(sin(x), (x, 0, pi/2)) # definite tan(x)**2 + 1 1 >>> limit((tan(x+y)-tan(x))/y, y, 0) >>> integrate(exp(-x), (x, 0, oo)) # improper tan(x)**2 + 1 1 # Higher derivatives diff(func, var,n): >>> diff(sin(2*x), x, 2) Series expansion -4*sin(2*x) >>> cos(x).series(x, 0, 10) 1 - x**2/2 + x**4/24 - x**6/720 + x**8/40320 + + O(x **10) Differential equations In [2]: Eq(f(x).diff(x, x) + f(x), 0) Out [2]: 2 d -----(f(x)) + f(x) = 0 dx dx

In [3]: dsolve(Eq(f(x).diff(x, x) + f(x), 0), f(x)) Out[3]: C1*sin(x) + C2*cos(x)

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SymPy Linear Algebra: Matrix >>> from sympy.matrices import Matrix >>> A = Matrix([[1,x], [y,1]]) >>> A [1, x] [y, 1]

>>> A**2 [x*y+1, 2*x] [ 2*y,x*y+1]

Printing Python build-in way to print an expression is simply through the use of str(expression) or repr(expression). More readable printing is available through the Pretty printing submodule:

I pretty(expr), pretty print(expr), pprint(expr) Return or print, respectively, a pretty representation of expr. I latex(expr), print latex(expr) Return or print, respectively, a LATEX representation of expr. I To enable LATEX output directly on the qt console: >>> init_printing(pretty_print=True)

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SymPy Simpliﬁcations Simplify: uses heuristics to determine the ”simplest” result. Combinations of expand(), factor(), collect(), cancel() may return the desired result9. >>> simplify(sin(x)**2 + cos(x)**2) 1 Partial fractions >>> f = 1/(x**2*(x**2 + 1)) >>> f 1 x2(x2 + 1) >>> apart(f) 1 1 − + x2 + 1 x2 >>> together(_) 1 x2(x2 + 1)

Evaluations: evalf evaluates a sympy expression numerically with arbitrary number of digits. lambdify transform sympy expressions to lambda functions which can be used to calculate numerical values very fast. Example: >>> pi.evalf(n=30) 3.14159265358979323846264338328

9http://docs.sympy.org/latest/tutorial/simplification.html#simplify

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SymPy, Plot The plotting module allows you to make 2-dimensional and 3-dimensional plots. Plots are rendered using matplotlib as a backend. The following functions are available: I plot: Plots 2D line plots. I plot parametric: Plots 2D parametric plots.

I plot implicit: Plots 2D implicit and 15 region plots. 10 I plot3d: Plots 3D plots of functions in 5 two variables. 0 I plot3d parametric line: Plots 3D 5 line plots, deﬁned by a parameter. 10 I plot3d parametric surface: Plots 15 3D parametric surface plots. 10 5 Example: 10 0 5 0 5 5 >>> from sympy.plotting import plot3d 10 10 >>> x, y = symbols(’xy’) >>> plot3d(cos(x*3)*cos(y*5)-y*cos(x))

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1 Introduction: Matlabholics Anonymous - How to redeem

2 Tools: How to get things done: Tools, IDEs, Installation

3 Language: Enjoy the Lego R

4 Packages4Science: Four Horsemen of the Apocalypse: NumPy, SciPy, Matplotlib, Sympy

5 Examples: Dirty work (but someone has to do it)

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Gini Coefﬁcient, part #1: gini coeff.py This example is designed to show how: I Import data from a simple CSV ﬁle to a structured array I Play with list comprehensions and some Numpy array methods

Suppose we are interested in the socio-economic inequality issue, we ﬁnd some data on the internet10 and we propose to analyse them.

We save our CSV ﬁle, with its prediﬁned name DP LIVE 26042016225351582.csv locally into a data subfolder relative to our script path.

The data we found comes as a comma-separated-value file (CSV). There is no well-defined standard for CSV files, but we know how many lines form the header, how many columns and the structure of the data. $ head DP_LIVE_26042016225351582.csv -n 3 "LOCATION","INDICATOR","SUBJECT","MEASURE","FREQUENCY","TIME","Value","Flag Codes" "AUT","INCOMEINEQ","GINI","INEQ","A","2007",0.285, "AUT","INCOMEINEQ","GINI","INEQ","A","2008",0.281,

We want to be able to view the data by country (LOCATION), by year (TIME), and of course by the value of the Gini coefﬁcient (VALUE).

10https://data.oecd.org/inequality/income-inequality.htm

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Gini Coefﬁ5cient, part #1: gini coeff.py ...

1 #-*- coding: utf-8-*- 2 import numpy as np 3 import os 4 import csv

6 csv_file = ( 7 ’DP_LIVE_26042016225351582.csv’, 8 ’data’, 9 os.path.dirname(os.path.abspath(__file__)) 10 ) 11 data_struct = { 12 ’field’:(’Country’,’Year’,’Value’), 13 ’dtype’:(’S3’, np.int16, np.float16), 14 ’ncol’ : (0, 5, 6), 15 ’heads’:1 16 }

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Gini Coefﬁcient, part #1: gini coeff.py ...

18 # Createa void structured array 19 dtype = zip(data_struct[’field’], data_struct[’dtype’]) 20 data = np.array( [], dtype=dtype )

22 # Open the file to fecth the data 23 f = os.sep.join(csv_file[::-1]) 24 with open(f,’rb’) as fopen: 25 reader = csv.reader(fopen, delimiter=’,’) 26 skip_header_count = data_struct[’heads’] 27 for row in reader: 28 # skip the header 29 if skip_header_count > 0: 30 skip_header_count -= 1 31 # fill the data array 32 else: 33 data0 = np.zeros(1, dtype=dtype) 34 fori,f in enumerate(data_struct[’field’]): 35 data0[f] = row[data_struct[’ncol’][i]] 36 data = np.hstack( (data, data0) )

>>> print(data[1:8]) [(’AUT’, 2008, 0.281005859375) (’AUT’, 2009, 0.2890625) (’AUT’, 2010, 0.280029296875) (’AUT’, 2011, 0.281982421875) (’AUT’, 2012, 0.27587890625) (’BEL’, 2005, 0.280029296875) (’BEL’, 2006, 0.27099609375)]

I data could be large and difﬁcult to read

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Gini Coefﬁcient, part #1: gini coeff.py ...

38 def filter_data(key, key_value): 39 # dtype, data, data_struct: outside the scope of this function 40 fdata = np.array( [], dtype=dtype ) 41 ford in data: 42 if d[key] == key_value: 43 fdata = np.hstack( (fdata, d) ) 44 return fdata

>>> d = filter_data(’Year’, 2005); print(d) [(’BEL’, 2005, 0.280029296875) (’CZE’, 2005, 0.260986328125) (’FIN’, 2005, 0.264892578125) (’GRC’, 2005, 0.345947265625) (’IRL’, 2005, 0.323974609375) (’ITA’, 2005, 0.324951171875) (’LUX’, 2005, 0.283935546875) (’POL’, 2005, 0.326904296875) (’PRT’, 2005, 0.37890625) (’SVK’, 2005, 0.2890625) (’GBR’, 2005, 0.35009765625) (’EST’, 2005, 0.337890625) (’SVN’, 2005, 0.239990234375)]

I filter data() helps fetching interesting data, but it looks redundant

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Gini Coefﬁcient, part #1: gini coeff.py ...

46 def extract_data(key, key_value): 47 # dtype, data, data_struct: outside the scope of this function 48 fields = data_struct[’field’] 49 field0 = [f forf in fields if f != key] 50 type0 = [data_struct[’dtype’][fields.index(f)] forf in field0] 51 dtype0 = zip(field0, type0) 52 53 fdata = filter_data(key, key_value) 54 data0 = np.zeros(len(fdata), dtype=dtype0) 55 forf in field0: 56 data0[f] = fdata[f] 57 return data0

>>> d = extract_data(’Year’, 2005); print(d) [(’BEL’, 0.280029296875) (’CZE’, 0.260986328125) (’FIN’, 0.264892578125) (’GRC’, 0.345947265625) (’IRL’, 0.323974609375) (’ITA’, 0.324951171875) (’LUX’, 0.283935546875) (’POL’, 0.326904296875) (’PRT’, 0.37890625) (’SVK’, 0.2890625) (’GBR’, 0.35009765625) (’EST’, 0.337890625) (’SVN’, 0.239990234375)]

Looks ok, but: I This script is tailored to a specific CSV file I How do I reuse this code without committing the cut+paste capital crime for a (not so) different CSV file?

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Gini Coefﬁcient, part #2: csv2data.py This example is designed to show how: I Organize code in a class for reusability

1 #-*- coding: utf-8-*- 2 import numpy as np 3 import csv 4 5 class csv2data(): 6 7 def __init__(self, csv_file, data_struct): 8 self.csv_file = csv_file 9 self.data_struct = data_struct 10 self.dtype = zip(data_struct[’field’], data_struct[’dtype’]) 11 self.data = np.array( [], dtype=self.dtype )

We want csv file, data struct, dtype, data to be accessible for all the methods in the csv2data class, hence they are created at init as class attributes. Now the class could be organized with the following functionalities (methods): I fetch data in the given csv file, corresponding to the code between lines 22-26 of gini coeff.py I capability to ﬁlter by key, key value analogously to the function filter data() I capability to extract data, as in extract data()

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Gini Coefﬁcient, part #2: csv2data.py ...

13 def fetch_data(self): 14 f = self.csv_file 15 try: 16 with open(f,’rb’) as fopen: 17 reader = csv.reader(fopen, delimiter=’,’) 18 skip_header_count = self.data_struct[’heads’] 19 for row in reader: 20 # skip the header 21 if skip_header_count > 0: 22 skip_header_count -= 1 23 # fill the data array 24 else: 25 data0 = np.zeros(1, dtype=self.dtype) 26 fori,f in enumerate(self.data_struct[’field’]): 27 data0[f] = row[self.data_struct[’ncol’][i]] 28 self.data = np.hstack( (self.data, data0) ) 29 except IOError: 30 print(’Cannot open’+ f)

With respect to the gini coeff.py we added here a try/except construct to handle input/output errors of the ﬁle (for example, ﬁle not found, etc.)

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Gini Coefﬁcient, part #2: csv2data.py ...

32 def filter_data(self, key, key_value): 33 fdata = np.array( [], dtype=self.dtype ) 34 ford in self.data: 35 if d[key] == key_value: 36 fdata = np.hstack( (fdata, d) ) 37 return fdata 38 39 def extract_data(self, key, key_value): 40 fields = self.data_struct[’field’] 41 field0 = [f forf in fields if f != key] 42 type0 = [self.data_struct[’dtype’][fields.index(f)] forf in field0] 43 dtype0 = zip(field0, type0) 44 fdata = self.filter_data(key, key_value) 45 data0 = np.zeros(len(fdata), dtype=dtype0) 46 forf in field0: 47 data0[f] = fdata[f] 48 return data0 Finally we add a call method to let any instance of the csv2data class to be used as they were functions: 50 def __call__(self, key, key_value): 51 if len(self.data)==0: 52 self.fetch_data() 53 return self.extract_data(key, key_value)

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Gini Coefﬁcient, part #2: test csv2data.py Simple test of the csv2data class: 1 #-*- coding: utf-8-*- 2 import os ﬁrst an instance is created 3 import numpy as np I 4 from csv2data import csv2data as c2d ( init ()) 5 import matplotlib.pyplot as plt 6 I then is used through its 7 csv_file = ( call () method 8 ’DP_LIVE_26042016225351582.csv’, 9 ’data’, 10 os.path.dirname(os.path.abspath(__file__)) 11 ) 12 data_struct = { 13 ’field’:(’Country’,’Year’,’Value’), 14 ’dtype’:(’S3’, np.int16, np.float16), 15 ’ncol’ : (0, 5, 6), 16 ’heads’:1 17 } 18 19 f = os.sep.join(csv_file[::-1]) 20 gini = c2d(f, data_struct)

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Gini Coefﬁcient, part #2: test csv2data.py ...

SVN LUX ITA PRT 22 countries = [’SVN’,’LUX’,’ITA’,’PRT’] 0.40 23 colors = [’cyan’,’blue’,’magenta’,’red’] 24 25 fig = plt.figure(figsize=(4,4)) 0.35 26 ax = fig.add_subplot(111) 27 props = dict(width=0.3, alpha=0.5, linewidth=0) 28 29 for i, country in enumerate(countries): 0.30 30 g = gini (’Country’, country) 31 x = g[’Year’] Gini coefficient 32 y = g[’Value’] 0.25 33 ax.bar(x+i*0.2, y, color=colors[i], label=country, **props) 34 35 plt.legend(bbox_to_anchor=(0., 1.02, 1., .102), loc=3, 36 ncol=4, mode="expand", borderaxespad=0., fontsize=10) 0.20 37 ax.set_ylim([0.2,0.4]) 2005 2006 2007 2008 2009 2010 2011 2012 38 ax.set_ylabel(’Gini coefficient’) 39 xTickMarks = [str(i) fori in range(min(g[’Year’]),max(g[’Year’])+1)] 40 xtickNames = ax.set_xticklabels(xTickMarks) 41 plt.setp(xtickNames, rotation=45) 42 plt.subplots_adjust(right=0.5) 43 plt.tight_layout() test csv2data.py

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Multiprocessing: multiproc.py This example is designed to show how: I include a very basic multiprocessing capability in Python scripts

When parallel processing has an How many parallel process is optimum advantage over sequential processing? for performances? I CPU-limited vs. I/O-limited I CPU cores processes I Inter-process communication I Independent processes vs. pipelined processes f(x) will be the target function of the 1 #-*- coding: utf-8-*- test: it will be executed independently 2 import multiprocessing as mp by the processes. 3 import time 4 5 def f(x): 6 "simple test function" 7 result = 0 8 fori in xrange(x): 9 result += x*x 10 return result

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Multiprocessing: multiproc.py ...

I Heuristically: 12 if __name__ ==’__main__’: Number of processes ∝ Number of proces- 13 sor units 14 # Inputs tof: 15 num_iter = 1000 I .cpu_count(): counts the number of process- 16 f_inputs = range(num_iter) ing units 17 .Pool() deﬁnes a pool of workers: each 18 # Parallel process: worker will start an independent parallel job 19 num_workers = mp.cpu_count()*4 .map() gives to the pool of workers what to do 20 pool = mp.Pool(num_workers) and with which arguments 21 t0 = time.time() 22 res_parallel = pool.map(f, f_inputs) The main is protected by an if statement: 23 dt_parallel = time.time() - t0 I due to the way the new processes are 24 print("parallel[s]:".rjust(18) + str(dt_parallel)) started, the child process needs to be able to 25 import the script containing the target func- 26 # Serial process: tion. 27 res_series = [] Wrapping the main part of the application in 28 t0 = time.time() a check for main ensures that it is not run 29 forx in f_inputs: recursively in each child as the module is im- 30 res_series.append(f(x)) ported. 31 dt_serial = time.time() - t0 32 print("serial[s]:".rjust(18) + str(dt_serial)) 33 I This script sketches a very basic parallel pro- 34 # Resume cessing example that could be useful in a 35 check = all([res_parallel[i]==res_series[i]\ Monte Carlo simulation batch, where each 36 fori in xrange(len(res_parallel))]) worker (a Monte Carlo try) does not share 37 print(’_’*36) data with other workers. Much more compli- 38 print("Results check:".rjust(18) + str(check)) cated (and interesting) parallel processing in- 39 print("Speed up:".rjust(18) + str(dt_serial/dt_parallel)) volving inter process communication can ac- tually be implemented!

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Interfacing with Xcos: deltasigma1ct.py This example is designed to show how: I Use the capability of Scilab-Xcos inside Python

I Xcos, like Simulink provides a graphical programming environment for modelling, sim- ulating and analysing multi-domain dynamic systems. 11 I You can script Xcos directly within the Scilab environment without Python. Anyway Scilab and Python has a certain grade of interoperability 12 I From the Python-side, to interact with Scilab-Xcos, you need the scilab2py module . It is not present in the Anaconda bundle by default, but it is easy to install by pip: $ pip install scilab2py

Useful links: How to simulate a Xcos model from the scilab command window (batch mode): https://help.scilab.org/docs/5.5.0/fr_FR/xcos_simulate.html A (very short) documentation on how to use the scilab2py API can be found here: http://blink1073.github.io/scilab2py/source/api.html

11http://www.scilab.org/ 12https://pypi.python.org/pypi/scilab2py

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Interfacing with Xcos: deltasigma1ct.py ...

The model can be set up from the Scilab graphical interface side: A very basic Scilab script to simulate the Xcos model: 1 importXcosDiagram(filename) 2 scs_m.props.context = 3 ["Ain=0.01""fs=1""fin=0.01"]; 4 xcos_simulate(scs_m, 4);

We wish to have the scripting control from the Python side with the ability to:

I Set model parameters (for ex.: Ain, fs, fin) I Recollect data (for ex.: DOUT) to be post pro- cessed

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Interfacing with Xcos: deltasigma1ct.py ...

1 from scilab2py import Scilab2Py 33 # psd plot 2 import os 34 f, Pxx = signal.periodogram(dout.T, 1, 3 from scipy import signal 35 ’flattop’, scaling=’spectrum’) 4 import matplotlib.pyplot as plt 36 fig = plt.figure(figsize=(4,4)) 5 37 plt.semilogy(f, Pxx[0]) 6 sci = Scilab2Py() 38 plt.grid(True) 7 39 plt.xlabel(r’frequency$[Hz]$’) 8 xcos_file_path = ( 40 plt.ylabel(r’PSD$[V^2/Hz]$’) 9 ’CT_DS_1.zcos’, 10 ’xcos’, 11 os.path.dirname(\ 12 os.path.abspath(__file__)) 13 ) 101 14 filename =’/’.join(xcos_file_path[::-1]) 15 100 16 # Puta variable or variables into the -1 17 # Scilab session: 10 18 sci. push (’filename’, filename) 10-2

19 # import Xcos diagram into Scilab session: ] 20 sci.eval("importXcosDiagram(filename)") 10-3 /Hz 21 # set Xcos parameters(context): 2 V 22 sci.eval(’scs_m.props.context=’+ [ 10-4 23 ’["Ain=0.01""fs=1""fin=0.01""nclocks= 2048"];’) PSD PSD 10-5 24 # simulate: 25 sci.eval(’xcos_simulate(scs_m, 4);’) 10-6 26 # retrieveDOUT from scilab workscape: 27 dout = sci.pull(’DOUT.values’) 10-7 28 # Close session: -8 29 sci.close() 10 0.0 0.1 0.2 0.3 0.4 0.5 frequency [Hz]

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Resources

This document is downloadable at: http://www.cnm.es/~mdei/pythonize_yourself/pythonize_yourself.pdf All the scripts presented are located at: http://www.cnm.es/~mdei/pythonize_yourself/scripts/

Web resources:

I http://stackoverflow.com/ I https://docs.python.org/2/ I https://wiki.python.org/moin/FrontPage

(and many many more)

M, Dei, IMB-CNM(CSIC) ICAS Tutorials