Writing scientific application in Python

Writing scientific application in Python

K.I.A Derouiche

June 03 th 2013

Introduction Basics Python Modules for Science Faster Python and Glueing Summary

Outline

1 Introduction

2 Basics

3 Python Modules for Science

4 Faster Python and Glueing

5 Summary


Me !

Membre in AADEMTIDeveloppeur-Maintainer in NetBSD ProjectFree Software Research EngPromise Theory


Outline

1 Introduction

2 Basics



5 Summary


Who uses...

We all use computers to generate or process data

Question to the audience: who uses...

C/C++?Fortran?Ada?Java?Matlab/Octave?

IDL?Perl?Ruby?Python?


What is Python?

Python is/has...

a scripting languagegeneral purposeinterpretedeasy to learnclean syntax

multi-paradigmopen-sourceavailable for all majorplatformsgreat community


The best of all:

Python comes...... with batteries included!

Libraries available for...

daily IT needs...

networksOS interactiontemporary fileszip filesweb API

science!

efficient array operations (NumPy)general numerical algorithms (SciPy)2D visualization (matplotlib)3D visualization (Mayavi, Paraview)special problems (e.g. finite elements withFEniCS, SfePy,quntum optics with QuTiP,EMpy)symbolic math (SageMath, SymPy)


Outline

1 Introduction

2 Basics



5 Summary


Scientific Hello, World!

import sysfrom math import sin, pi

def sincSquare(x):"""Return sinc(x)^2."""if(x <> 0.0):

return (sin(pi*x)/(pi*x))**2else:

return 1.0

x = sys.argv[1]y = sincSquare(float(x))print("sinc(%s)^2 = %s"%(x, y))

cmp. H.-P. Langtangen,"Python Scripting forComputational Science"

run with:

python HelloWorld.py 0.0


Control structures

# if statements:if(divisor == 0):

...elif(divisor > 1E20):

...else:

...

# loops:for i in range(10): # i = 0, 1, ..., 9

print("i = %s"%i)

# while loops:while(True):

...


Functions

# functions:def f(x, a=1.0, b=2.0):

"""Return a/x and a/x^b"""

return a/x, a/x**b

# somewhere else:y1, y2 = f(x, 5.0)y3, y4 = f(2, b=3.0)


Functions (cont)#def sentence(**words):

print(’Receve %d word(s)’ %len(words))print(’List of words: %s’ % ’ ’.join(words.values()))print(’Parameter name: %s’ % ’ ’.join(words.keys()))

sentence(word1=’word1’, word2=’word2’, word3=’word3’)

#Combine parameter:def sentence(name, firstword=’none_word’, **words):

pass

#Arbitray parametresdef sum (sentence, *args):

print(sentence % args)format(’%d more the %s at possible’, 2, ’combinaison’)


Example: λ − calculs!

c = lambda x, y: x**2 + y**2print c(3,4)


Enumerate, Itertools

from itertools import chain

import numpy as np

lst = np.arange(7)for idx, ele in enumerate(lst):

print idx, ele

list(chain(xrange(11), xrange(15, 21), xrange(30, 46)))


Data types: List, Tuple

a = 2 # integerb = 2.0 # floatc = "3.0" # stringd = [1, 2, "three"] # liste = "1"print(a*b) # valid, upcastingprint(a*c) # valid, but probably not desired: ’3.03.0’print(b*c) # invalidprint(d[1]) # prints 2for item in d: # lists are "iterable"

print(item)for character in c: # strings are iterable

print(character) # prints 3\n.\n0f = e + c # + joins strings: f = ’13.0’g = d + [someObj, "foobar"] # + joins lists


Data types: Stacks, Queues, Dictionariesstack = [3, 4, 5]stack.append(6)stack.append(7)stack.pop()

from collections import dequequeue = deque(["1", "2", "pi"])queue.append("Terry")queue.popleft()

pole = {’j’: 40.98, ’s’: 41.39}pole[’g’] = 41.27; pole[’j’]40.98del pole[’s’]pole.keys()’g’ in pole


Files

readFile = open("infile", mode="r")writeFile = open("outfile", mode="w")

for line in readFile: # iterate over file’s linesxString, yString = line.split() # split the linex = float(xString); y = float(yString)print("x = %s, y = %s"%(x, y))writeFile.write("%s * %s = %s\n"%(x, y, x*y))

readFile.close(); writeFile.close()

infile:

1.0 2.03.0 4.0

outfile:

1.0 * 2.0 = 2.03.0 * 4.0 = 12.0


Class, Method, Composition, Polymorphisme,Inheritancee

import random

class sales_normal(object):def __init__(self):

pass

def A(self):"""This commente """return random.randint (0, 1)

def B(self):s = 0for i in range(0, 100):

s += self.A ()return s


Class, Method, Composition, Inheritancee

class false_device(sales_normal):def A(self):

t = random.randint(0, 10)if t >=3 :

return 1else:

return 0

if __name__ == "__main__":p = sales_normal()print p.B()p2 = false_device()print p2.B()


Reusing code: modules

Place code to be reused in Module.py:

"""A Python module for illustration."""

def printData():print(data)

data = 2

In somewhereElse.py, do something like:

import Module

Module.data = 3Module.printData()


Some Python magic

x, y = y, x # swapping

print(1 > 2 > 3) # prints False

# filtering (there is also reduce(), map())numbers = range(50)evenNumbers = filter(lambda x: x % 2 == 0, numbers)print("All even numbers in [0; 50): %s"%evenNumbers)

# list comprehensions:squares = [x**2 for x in numbers]

a += 2 # a = a + 2

print("string" in "Long string") # prints True


Pitfalls

☇ Common pitfalls:

slicing: last index is exclusive, not inclusive as in e.g. Fortranx = [1, 2, 3, 4]print(x[0:2]) # prints [1, 2], not [1, 2, 3]

What looks like performing an assignment is actually setting areference:a = []b = aa.append(2)print(a) # prints [2]print(b) # prints [2], not []!


Outline

1 Introduction

2 Basics



5 Summary


Scientific Python Application Stack


The IPython shellIPythonAn interactive shell - may replace MatLab [tm] for interactive work

SyntaxhighlightingTabcompletionInline docu-mentationEasyprofiling,timing...IPython ≥

0.13.x:inlineplots...


NumPy: Python meets an array data type

NumPyFast and convenient array operations

Lists: + does join, not add!NumPy array: basic vector/matrix data typeConvenience functions (e.g. linspace(), zeros(),loadtxt()...)Array slicingelement-wise operationsCode using NumPy reads and writes very similar to modernFortran (slicing, vector valued indices...)


NumPy by examples(1)

import numpy as np

a = np.array([1.0, 2.0, 3.0, 4.0])b = np.array([4.0, 3.0, 2.0, 1.0])for item in a: # arrays are iterable

print(item)c = a + b # c = [5, 5, 5, 5]print(a[0:3:2]) # 1.0, 3.0; last element not included!a[0:3] = b[0:-1]

print(a*b) # prints [4, 6, 6, 4], not the scalar product!


NumPy by examples(2)

import numpy as np

#Creation:a = np.arange(10)a = np.zeros((2, 4), dtype=’f’)a = np.ones((3, 5))*np.nana = np.identity(3)a = np.mat([1, 0], [0, 1])a = np.indices((2, 5))c = a.flat # view

# Dimensiona = np.array([0.1, 0.0, 0.2]) #a.ndim; a.dtype; a.sizeb = np.array([1, 2, 3], [4, 5, 6]) #b.ndim; b.dtype; b.size


NumPy by examples (3)#shapeimport numpy as np

a = np.ones((3, 5, 7)).shapenp.shape(a)# reshape change shapea = np.arange(105).reshape((3, 5, 7))# Fortran implementationa = np.ones((2, 3, 4), order=’Fortran’); np.isfortran(a)#Transpos:a.T#index:a = np.arange(24).reshape(2, 3, 4)a[0][2][1]a[0][0:-1]a = np.arange(24).reshape(2, 3, 2, 2)a.tolist()##


NumPy by examples (4)

import numpy as np

a= np.arange(6).reshape(3, 2)1+np.sin(a)*1/2a>3a.max() #max valuea.sum() #sommea.mean # Moyenne#Matrixb = np.matrix(a); b[0]


SciPy

SciPyNumerical algorithms using NumPy arrays

Wrappers around well-established libraries

Submodules:

linalg: linear algebra(lapack)io: MATLAB FILE, NetCDF,HDF5 futur managersparse: sparse matricesfft: FFT (fftpack)optimize: optimization,zeros (minpack)

integration: integration(quadpack, odepack)special: special functions(amos...)signal: signal processing


p(x) = x4

5 + 3x2− 7x + 5

#derivationfrom scipy import poly1dq = poly1d([0.5, 0.3, -7, 5])q.deriv()poly1d([ 1.5, 0.6, -7. ])print q

#integrationfrom scipy import *q.integ()poly1d([0.1, 0., 1., -3.5, 5., 0.])


Van der Pol oscillator:

import scipy as spfrom scipy.integrate import odeintimport pylab as plt

def vdp1000(y, t):dy=sp.zeros(2)dy[0] = y[1]dy[1] = 1000.*(1.-y[0]**2)*y[1]-y[0]return dy

t0 = 0 ;tf = 3000; N = 300000dt = (tf-t0)/Ntgrid=sp.linspace(t0, tf, num=N)y= odeint(vdp1000, [2., 0.], tgrid)plt.plot(tgrid, y[:, 0])plt.show()


d2x(t)dt2 − εω0(1 − x2(t))

dx(t)dt + ω

20x(t) = 0

Already used here: Matplotlib


SymPy: CAS pure Python


Matplotlib(mostly) 2D plots

Pylab: MatLab alternative for interactive work


Lorenz system

⎧⎪⎪⎪⎪⎨⎪⎪⎪⎪⎩

dx(t)dt = σ(y(t) − x(t))

dy(t)dt = ρx(t) − y(t) − x(t)z(t)

dz(t)dt = x(t)y(t) − βz(t)


Outline

1 Introduction

2 Basics



5 Summary


Using Python as glue

Python can wrap different different other programming languages

Cython

compiled, typed Python - interface C/C++ code

f2py

Fortran wrapper, included in NumPy

Why do that?

Python can be slowPython loops are slowcalling Python functions isslow

Wrap external C/Fortran...librariesHappily/unfortunately (?)there is legacy code


Problem: sinc(x)2import numpy as npfrom math import sin, pi

def sincSquare(x):"""Return the sinc(x) = (sin(x)/x)**2 of the arrayargument x."""retVal = np.zeros_like(x)for i in range(len(x)):

retVal[i] = (sin(pi*x[i]) / (pi*x[i]))**2

return retVal

#b = np.random.uniform(-10, 10, size=1000)#sincSquare(b)106 array elements: 1 loops, best of 3: 4.91 s per loop


Problem: sinc(x)2import numpy as npfrom math import sin, pi

def sincSquare(x):"""Return the sinc(x) = (sin(x)/x)**2 of the arrayargument x."""retVal = np.zeros_like(x)for i in range(len(x)):

retVal[i] = (sin(pi*x[i]) / (pi*x[i]))**2

return retVal

#b = np.random.uniform(-10, 10, size=1000)#sincSquare(b)106 array elements: 1 loops, best of 3: 4.91 s per loop


First attempt: use NumPy array operations

import numpy as np

def sincSquareNumPy1(x):

return (np.sin(np.pi*x[:])/(np.pi*x[:]))**2


return np.sinc(x[:])**2

106 array elements: first function: 10 loops, best of 3: 73 msper loop, second function: 10 loops, best of 3: 92.9 msper loop


First attempt: use NumPy array operations

import numpy as np


return (np.sin(np.pi*x[:])/(np.pi*x[:]))**2


return np.sinc(x[:])**2

106 array elements: first function: 10 loops, best of 3: 73 msper loop, second function: 10 loops, best of 3: 92.9 msper loop


How Cython works

Cythoncompiled, possibly typed Python:

.pyx fileCythonÔ⇒ .c file

C compilerÔ⇒ .so/.dll file

various levels of typing possibleC output and Cython’s opinion on code speed can easily beinspected (optional .html output)interfacing C libraries is easy


sinc(x)2 - Cython, Version 1

cdef extern from "math.h":double sin(double)double pow(double, int)

def sincSquareCython1(x):

pi = 3.1415926535897932384626433retVal = np.zeros_like(x)

for i in range(len(x)):retVal[i] = (sin(pi*x[i]) / (pi*x[i]))**2

return retVal

106 array elements: 1 loops, best of 3: 4.39 s per loop



cdef extern from "math.h":double sin(double)double pow(double, int)

def sincSquareCython1(x):

pi = 3.1415926535897932384626433retVal = np.zeros_like(x)

for i in range(len(x)):retVal[i] = (sin(pi*x[i]) / (pi*x[i]))**2

return retVal

106 array elements: 1 loops, best of 3: 4.39 s per loop



cimport numpy as np # also C-import types

cpdef np.ndarray[double] sincSquareCython2\(np.ndarray[double] x):

cdef int icdef double pi = 3.1415926535897932384626433cdef np.ndarray[double] retVal = np.zeros_like(x)

for i in range(len(x)):retVal[i] = pow(sin(pi*x[i]) / (pi*x[i]), 2)

106 array elements: 10 loops, best of 3: 49.1 ms per loopThat’s a speedup by a factor ≈ 100!



cimport numpy as np # also C-import types

cpdef np.ndarray[double] sincSquareCython2\(np.ndarray[double] x):

cdef int icdef double pi = 3.1415926535897932384626433cdef np.ndarray[double] retVal = np.zeros_like(x)

for i in range(len(x)):retVal[i] = pow(sin(pi*x[i]) / (pi*x[i]), 2)

106 array elements: 10 loops, best of 3: 49.1 ms per loopThat’s a speedup by a factor ≈ 100!


How f2py works

f2pywrap Fortran code in Python:

.f/.f90 filef2pyÔ⇒ .so/.dll file

f2py is included in NumPyexposes NumPy arrays to Fortran codeonce ’Fortran space’ is entered, you run at full Fortran speed


sinc(x)2 - f2py, Version 1

subroutine sincsquaref2py1(x, n, outVal)implicit none

double precision, dimension(n), intent(in) :: xinteger, intent(in) :: ndouble precision, dimension(n), intent(out) :: outValdouble precision, parameter :: pi = 4.0d0 * atan(1.0d0)

outVal(:) = (sin(pi*x(:)) / (pi*x(:)))**2

end subroutine sincsquaref2py1

106 array elements: 10 loops, best of 3: 47.4 ms per loopAgain, a speedup by a factor of ≈ 100!


sinc(x)2 - f2py, Version 1

subroutine sincsquaref2py1(x, n, outVal)implicit none

double precision, dimension(n), intent(in) :: xinteger, intent(in) :: ndouble precision, dimension(n), intent(out) :: outValdouble precision, parameter :: pi = 4.0d0 * atan(1.0d0)

outVal(:) = (sin(pi*x(:)) / (pi*x(:)))**2

end subroutine sincsquaref2py1

106 array elements: 10 loops, best of 3: 47.4 ms per loopAgain, a speedup by a factor of ≈ 100!


Techniques for faster Scripts

After you have written a prototype in Python with NumPy andSciPy, check if your code is already fast enough. If not,

profile your script (IPython’s run -p or cProfile module...)to find bottlenecksif a large numbers of function calls is the bottleneck, typing andusing Cython’s cdef/cpdef for C calling conventions speedsyour code up at the cost of flexibilityloops greatly benefit from typing, tooconsider moving heavy computations to Fortran/C completely -f2py and Cython will help you wrapping


Outline

1 Introduction

2 Basics



5 Summary


Python in teaching

Python/Pylab should be used in teaching because

it is easy...and yet powerful;it may be used specialized to numerical computing...and also serve students as a general purpose language;it is safe;and best of all, it is free!

Take home message 1Python is ideal for teaching


Summary

We have...

introduced basic Python scriptingshown some basic modules for scientific computingdemonstrated how to wrap other languageslearned how to speed Python up

Take home message 2Python is a very valuable tool for Physicists

Slides, LATEX and Python Sources available athttp://github.com/aeberspaecher

http://github.com/aeberspaecher

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Writing scientific application in Python

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