by
What advantages has it?
The Reasons for Choosing Python
Python is free
It is object-oriented
It is interpreted
It is operating-system independent
It has an excellent optimization
module
It offers modern COM modules for
interfacing with Solids Works
Getting Started with Python
Python(x,y) package from http://code.google.com/p/pythonxy
The Python(x,y) package comes with all numerical and scientific Python
modules.
Python(x,y) is a free scientific and engineering development
software for numerical computations, data analysis and data
visualization based on Python programming language. Spyder is
excellent integrated development environment (IDE).
Index for some packages related to python
http://pypi.python.org/pypi?%3Aaction=index
SfePy is a software for solving systems of coupled partial differential
equations (PDEs) by the finite element method in 2D and 3D
http://stepy.org
http://plateformesn-m2p.ensam.eu/SphinxDoc/cnem/index.html
http://femhub.org/
Since Python is an object-oriented language,
everything one creates in Python is an object, including integers, float,
strings, arrays, etc.
>>> i=4
>>> x=3.56
>>> a=“hello”
Examples
Associated with objects are methods that act on these objects. By
Typing a ‘dot’ after the object variable name, we can access a list
of methods associated with it.
Examples
>>> a=“hello”
>>> a.capitalize()
‘Hello’
Basic Objects
For integers and floats, it is interpreted as the usual addition; for
strings it is interpreted in Python as a concatenation. We can reassign
the variables.
>>> i=1+2
>>> i
3
>>>a=“hello”+“world!”
>>>a
“hello world!”
>>>a=“hello”
>>>b=a
>>>print a,b
hello hello
>>>b=“world!”
>>>print a,b
hello world!
Examples
Basic Objects
A list is a collection of other Python objects. Lists can contain a variety
of objects (integers, strings, etc). They can contain other list objects as
in b= [3,a]. Addition of lists leads to a concatenation as in c=a+a. There
is an access to individual elements of a list is through the [] operator (as
In a[2]). The indexing of individual elements f a list starts from 0.
>>> a=[1, 2, “srt”]
>>> b=[3,a]
>>> c=a+a
>>> print a,b,c
[1, 2, “str”][3, [1, 2, “str”]][1, 2, “str”,1, 2, “str”]
>>> b=a
>>>b[2]=3
>>>print a
[1, 2, 3]
>>> range(5)
[0, 1, 2, 3, 4]
Examples
Lists
Simple Python program in the Editor (e.g. within Spyder). You can give
a name, e.g. PythonObjects.py, ‘py’ extension refers to a Python file.
# Floats and integers
print 2**10 #2 to the power 10
x=0.5
print 2.5*x/3
# Strings
s=“Hello World!”
print 3*s # implies concatenation
# Lists
a=[0,1,2,3] # list, not an array or vector
b=range(4) # list, with the same contents as a
print a,b
print 3*a # implies concatenation
Python Scripts
File Edit Format Run Options Windows Help
PythonObjects.py-…
The following output appears in the Console window after running
the code PythonObjects.py
1024
0.416666666667
Hello World!Hello World!Hello World!
[0, 1, 2, 3] [0, 1, 2, 3]
[0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3]
Output
The following example illustrates the use of ‘for’, ‘if’ and ‘while’
commands in Python.
# Flow control in Python
for i in range(10): # does not include 10
if i<=4:
print i, i**2
elif i<=7:
print i,i**2+1
else:
print i,i**2+2
s='-'
while len(s)<25:
s+='-'
print s
Flow Control
File Edit Format Run Options Windows Help
FControl.py-…
The following output appears in the Console window
after running the code FControl.py
0 0
1 1
2 4
3 9
4 16
5 26
6 37
7 50
8 66
9 83
-------------------------
Output
Python provides two commands, namely ‘raw_input’ and ‘input’ for user.
The first command returns the user input as a string, while the second
Command will interpret and evaluate the input, and return
the interpreted value if the evaluation is meaningful.
>>> a=raw_input(“Enter data:”)
Enter data: 3*4-5
>>> a
'3*4-5'
>>> a=input(“Enter data:”)
Enter data: 3*4-5
>>> a
7
User Input
There are numerical objects (arrays, dot product, etc) and methods
that are not part of the core Python language, but are part of the numpy
and scipy libraries/modules. They are installed when we install Python.
However, in order to access them in a script file we must import them.
# Using Pylab
import pylab as py #(or e.g. import numpy as py)
x=py.array([0,1,2,3]) # creates an array from a list
y=x+x # this is now an addition not concatenation
print y
a=py.pi # the number 3.1415926535897931
theta=py.arange(-a,a,0.1) # sample from -pi to +pi using arange
z=py.sin(theta) # compute sin(theta) for all samples
print sz.max() # find the maximum value
Numerical Python
File Edit Format Run Options Windows Help
UsingPylab.py-…
The resulting output in the Console window is shown
[0 2 4 6]
0.999923257564
Output
Python also supports the use of complex numbers through the use of
symbol “j” that represents −1.
>>> a=3+4j
>>> a**2
‘(-7+24j)'
>>> sqrt(a) # it is needed to import Numerical Python before
‘(2+1j)
Complex Numbers
Examples
There are numerical objects (arrays, dot product, etc) and methods
that are not part of the core Python language, but are part of the numpy
and scipy libraries/modules. They are installed when we install Python.
However, in order to access them in a script file we must import them.
# Linear Algebra
import pylab as py #(or e.g. import numpy as py)
A=py.array([[2,-1],[-1,2]]) # creates an array from a list
B=py.array([1,1])
x=py.solve(A,b)
print “Solution for 2x2 problem is” +str(x)
Linear Algebra
File Edit Format Run Options Windows Help
LinearAlgebra.py-…
# Linear Algebra (continuation)
Lambda, V=py.eig(A)
print “Eigenvalues of matrix are” +str(Lambda)
Print “Eigenvectors of matrix are \n” +str(V)
A=py.rand(50,50)
xIn=py.rand(50,1)
B=py.dot(A,xIn)
xOut=py.solve(A,b)
Err=py.norm(xIn-xOut)
print “Error for a random matrix solve is “ +str(err)
Linear Algebra (cont.)
File Edit Format Run Options Windows Help
LinearAlgebra.py-…
Pylab supports 2D and 3D plotting via matlibplot
(http://matplot.souceforge.net) package that can be
Accessed through pylab.
Plots
MatLibPlot.py-…
File Edit Format Run Options Windows Help
# 2-D plots using Python/Pylab
import pylab as py
pi=py.pi
x=py.arrange(0,2*pi,pi/50)
y=py.sin(x)
Z=py.cos(x)
py.plot(x,y)
py.plot(x,z)
py.xlabel(“x”)
py.ylabel(“sin(x)&cos(x)”)
py.legend(“sin(x)’,’cos(x)”))
py.savefig(“Fig2.png”)
py.show()
The resulting output in the Console window is shown
Plots
One can include multiple functions within a single Python file, and
Access each one of them individually (a distinct advantage over Matlab).
Modules
Example: a file containing multiple functions
SampleFunctions.py-…
File Edit Format Run Options Windows Help
# Module consists of 1-D functions, and derivatives of some of these funcs.
import pylab as py
def f1(x):
f=-x*py.exp(-x**2) # returns -x*exp(-x**2)
return f
def f1_gradient(x):
g=-py.exp(x**2)+2*x*x*py.exp(-x**2) # returns the derivative of f
return g
def f2_hessian(x):
h=6*x*py.exp(x**2)-4*x**3*py.exp(-x**2) # return the second derivative of f
The resulting output in the Console window is shown below
>>> import SimpleFunctions
>>> SimpleFunctions.f1(2)
-0.036631277777468357
Modules
Python offers a rich set language features for passing arguments into
Functions. We consider the function f1 (together with a testing script)
Function Arguments
FunctionsArguments.py-…
File Edit Format Run Options Windows Help
# Example to illustrate function arguments
def f1(x, a=4, s=‘hello’):
print x, a, s
if __name__==“__main__”:
f1(0.3)
f1(x=0.4)
f1(x=0.5,a=5)
f1(0.5, a=5)
f1(x=0.6,s=“world”)
f1(0.6,s=“world”)
f1(s=“world”,a=7,x=0.7)
The resulting output in the Console window is shown below
0.3 4 hello
0.4 4 hello
0.5 5 hello
0.5 5 hello
0.6 4 world
0.6 4 world
0.7 7 world
Function Arguments
There are a few Python ‘quirks’ that one must keep in mind
>>> 5.0/2
2.5
>>> 5/2
2
>>> from __future__ import division
>>> 5/2
2.5
>>> A=array([[2,1],[1,2]]); x=array([1,-1])
>>> b=A*x
>>> b
array([[2,-1],
[1,-2]]]) # the ‘*’operator is interpreted as 𝑏𝑖𝑗 = 𝐴𝑖𝑗𝑥𝑗
>>> b=dot(A,x)
>>> b
array([1,-1]) # the ‘dot’ operator is interpreted as 𝑏𝑖𝑗 = 𝐴𝑖𝑗𝑥𝑗 𝑗
Python Quirks
Examples
An important concept “class”, in object oriented languages such Python,
Is a collection of objects and methods that are closely related.
import pylab as py
class Polynomial:
def __init__ (self,aIn):
self.a=py.array(aIn)
Python Class
def evaluate(x):
#v=a[0]+a[1]*x+a[2]*x**2+...
v,temp=0.0,1.0
for coeff in a:
v+=coeff*temp
temp*=x
return v
if __name__=="__main__":
p=Polynomial([1,-1,2])
a=p.a
print a
st=__str__();
print st
p1=evaluate(2.0)
print p1
import PolynomialClass
from PolynomialClass import Polynomial
def __str__():
string=str(a[0])
for i, coeff in enumerate(a[1:]):
if coeff == 0.0:
continue
elif (coeff<0):
sign=' - '
else:
sign=' + '
string+=sign+str(abs(coeff))+’*x^’+str(i+1)
return string
PolynomialClass.py
SfePy - software for solving PDEs in Python
SfePy is a software for solving systems of coupled partial differential equations (PDEs) by the finite element method in 2D and 3D
SfePy can use many terms to build systems of partial differential equations (PDEs) to be solved
SfePy comes with a number of examples that can get you started
Sources :http://sfepy.org , http://femhub.org/
http://plateformesn- m2p.ensam.eu/SphinxDoc/cnem/index.html
Biot problem - deformable
porous mediumm
With using modules/lib.:
numpy, sfepy
Biot problem - deformable porous medium with the no-penetration boundary condition on boundary region With using modules/libraries: sfepy.linalg, sfepy.mechanics.matcoefs
Linear viscoelasticity with pressure traction load on surface and constrained to one-dimensional motion. The fading memory terms require an unloaded initial configuration, so the load starts in the second time step. With using modules/libraries
sfepy.base.base sfepy.mechanics.matcoefs sfepy.homogenization.utils
References
Mark Lutz & David Ascher, Learning
Python, O’Reilly, 1999 (Help for
Programmers)
Mark Lutz, Programming Python,
O’Reilly, 2001 (Solutions for Python
Programmers)
Documentations from internet sources
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