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== Starting the IPython shell as a Notebook == {{{ # On the ZMAW system you have to select the newest version with notebooks available module load python/2.7-ve2 # Start the notebook server in the background ipython notebook --pylab inline & }}} {{{ # The notebook server provides some information about where to find the dashboard [NotebookApp] Serving notebooks from /home/zmaw/u242023/sync/python/notebooks [NotebookApp] The IPython Notebook is running at: http://127.0.0.1:8888/ }}} The dashboard is the central place to collect your scripts (notebooks). Different ports (here :8888) are used if there are additional notebook servers running on the same machine. You should use firefox to interact with the notebook server. Make sure the Java script is enable when you want to use other browsers. * [[http://code.google.com/p/pythonxy/|Try this at home and download Python(x,y)]] |
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== Unix basics == The ampersand {{{&}}} at the end of a line starts a process in the background. You can get the process in the foreground by typing {{{fg}}}. You can stop a process in the foreground by pressing Control-C. Within the IPython shell you can use the exclamation mark ! to spawn unix commands. E.g. {{{ # List directory content !ls # Make new directory !mkdir new_name # Change to directory !cd new_name # Change to an upper level !cd .. # Move or rename file or directory !mv filename_old filename_new }}} |
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| = Python basic data types = One step back: here we look at the built-in data types which are available without loading any modules. == Built-in data types and operations == There are four distinct numeric types: * plain integers {{{int}}} * long integers {{{long}}} * floating point numbers {{{float}}} * complex numbers {{{complex}}} In addition, Booleans are a subtype of plain integers === Boolean === Boolean (logical) types * True * False === Operations === {{{ x + y sum of x and y x - y difference of x and y x * y product of x and y x / y quotient of x and y x // y (floored) quotient of x and y x % y remainder of x / y -x x negated +x x unchanged abs(x) absolute value or magnitude of x int(x) x converted to integer long(x) x converted to long integer float(x) x converted to floating point complex(re,im) a complex number with real part re, imaginary part im. im defaults to zero c.conjugate() conjugate of the complex number c x ** y x to the power y }}} Boolean Operations: {{{and}}}, {{{or}}}, {{{not}}} {{{ x or y if x is false, then y, else x x and y if x is false, then x, else y not x if x is false, then True, else False }}} === Comparisons === {{{ < strictly less than <= less than or equal > strictly greater than >= greater than or equal == equal != not equal is object identity }}} === Sequence types === * String {{{str}}} * List {{{list}}} * Tuple {{{tuple}}} === Operations === {{{ x in s True if an item of s is equal to x, else False x not in s False if an item of s is equal to x, else True s + t the concatenation of s and t s[i] i'th item of s s[i:j] slice of s from i to j s[i:j:k] slice of s from i to j with step k len(s) length of s min(s) smallest item of s max(s) largest item of s }}} == Variables, assignment == The assignment statement = creates new variables and gives them values {{{ a=2 l=9**1000L S='Hello' f=1e5 }}} == Lists and tuples == * Lists {{{[]}}} are mutable sequences of values * Tuples {{{()}}} can not be changed (immutable) {{{ In [5]: a=[1,2,3] In [6]: b=(1,2,3) In [7]: a[0] Out[7]: 1 In [8]: b[0] Out[8]: 1 In [9]: a[0]=4 In [10]: a Out[10]: [4, 2, 3] In [11]: b[0]=4 --------------------------------------------------------------------------- exceptions.TypeError }}} == Indexing and slicing == * Indices {{{[]}}} select elements of variables * Indices start from zero * {{{x[a:b]}}} selects a slice of elements from variable x {{{ In [1]: a=range(10) In [2]: a Out[2]: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9] In [3]: a[0:4] Out[3]: [0, 1, 2, 3] In [4]: a[4:] Out[4]: [4, 5, 6, 7, 8, 9] In [5]: a[:4] Out[5]: [0, 1, 2, 3] In [6]: a[:-1] Out[6]: [0, 1, 2, 3, 4, 5, 6, 7, 8] In [7]: s='Hello world' In [8]: s[:5] Out[8]: 'Hello' In [9]: a=tuple(range(10)) In [10]: a[0:4] Out[10]: (0, 1, 2, 3) }}} === List built-in functions (methods) === * {{{L.append(object)}}} -- append object to end * {{{L.count(value)}}} -> integer -- return number of occurrences of value * {{{L.extend(iterable)}}} -- extend list by appending elements from the iterable * {{{L.index(value, [start, [stop]])}}} -> integer -- return first index of value * {{{L.insert(index, object)}}} -- insert object before index * {{{L.pop([index])}}} -> item -- remove and return item at index (default last) * {{{L.reverse()}}} -- reverse *IN PLACE* * {{{L.sort()}}} -- sort *IN PLACE* {{{ In [72]: L=['C','A','B'] In [73]: L.sort() In [74]: L Out[74]: ['A', 'B', 'C'] In [75]: L.pop() Out[75]: 'C' In [76]: L Out[76]: ['A', 'B'] In [77]: L.insert(1,'C') In [78]: L Out[78]: ['A', 'C', 'B'] }}} Nested data structures {{{ In [84]: a=range(10) In [85]: b=range(0,10,2) In [86]: b Out[86]: [0, 2, 4, 6, 8] In [87]: c=[a,b] In [88]: c Out[88]: [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 2, 4, 6, 8]] In [91]: c[0] Out[91]: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9] In [92]: c[1] Out[92]: [0, 2, 4, 6, 8] In [93]: c[0][0:4] Out[93]: [0, 1, 2, 3] In [94]: c[1][0:4] Out[94]: [0, 2, 4, 6] }}} == Dictionary == * A dictionary is like a list, but more general. * In a list, the indices have to be integers; in a dictionary they can be (almost) any type. * {{{d={} }}} creates empty dictionary * {{{ d[key]=value }}} add a key, value pair to dictionary * {{{ d.keys() }}} returns list of keys {{{ In [95]: D={} In [96]: D['a']=range(10) In [97]: D['b']=range(0,10,2) In [98]: D Out[98]: {'a': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 'b': [0, 2, 4, 6, 8]} In [99]: D['a'] Out[99]: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9] In [100]: D.keys() Out[100]: ['a', 'b'] }}} == Loops == * Looping over a list is done for the {{{ for }}} statement * {{{ enumerate() }}} returns an enumerated object {{{ In [106]: a=['Hund','Katze','Maus'] In [108]: for i in a: .....: print i .....: Hund Katze Maus In [111]: for i,j in enumerate(a): .....: print i,j .....: 0 Hund 1 Katze 2 Maus }}} == Control statements == * Conditions can be checked with {{{if-else}}} statement * {{{ if }}} condition: indented block * {{{ else: }}} {{{ In [116]: if a==1: .....: print 'a=1' .....: else: .....: print 'a != 1' .....: a=1 }}} |
== Pure Python essentials == [[/Python basics|Python basic data types]] === Loop === {{{ #!python for i in range(3): print i }}} == Symbolic math == Use isympy or import sympy to obtain a computer algebra system {{{ isympy IPython console for SymPy 0.7.1 (Python 2.7.0-64-bit) (ground types: python) These commands were executed: >>> from __future__ import division >>> from sympy import * >>> x, y, z, t = symbols('x y z t') >>> k, m, n = symbols('k m n', integer=True) >>> f, g, h = symbols('f g h', cls=Function) Documentation can be found at http://www.sympy.org }}} Derivatives {{{ In [1]: f=sin(x) In [2]: diff(f,x) Out[2]: cos(x) }}} Series expansion {{{ In [3]: f.series() Out[3]: 3 5 x x x - ── + ─── + O(x**6) 6 120 }}} Simplification {{{ In [4]: g=sin(x)**2+cos(x)**2 In [5]: simplify(g) Out[5]: 1 }}} Integration {{{ In [7]: F=sin(x) In [8]: f=diff(F,x) In [9]: f.integrate() Out[9]: sin(x) }}} Calculus {{{ In [12]: Rational(1,3)+Rational(1,4) Out[12]: 7/12 }}} |
Python Quick Start
Why Python?
Starting the IPython shell as a Notebook
# On the ZMAW system you have to select the newest version with notebooks available module load python/2.7-ve2 # Start the notebook server in the background ipython notebook --pylab inline &
# The notebook server provides some information about where to find the dashboard [NotebookApp] Serving notebooks from /home/zmaw/u242023/sync/python/notebooks [NotebookApp] The IPython Notebook is running at: http://127.0.0.1:8888/
The dashboard is the central place to collect your scripts (notebooks). Different ports (here :8888) are used if there are additional notebook servers running on the same machine.
You should use firefox to interact with the notebook server. Make sure the Java script is enable when you want to use other browsers.
Starting the IPython shell
module load python/2.7-ve2 ipython --pylab
loads matplotlib module and enables interactive plotting
module load is a ZMAW specific environment setting! Version 2.7-ve2 is needed for the notebook version (see below).
Quit with CTRL-D
Getting help
help() help modules
list available modules
Features of IPython:
- Command history (up, down)
- Word completion by typing TAB
- System commands through magic functions cd, ls, env, pwd
Access to Unix shell by prefix !, e.g. !ls -s | sort -g
- Debugging and profiling
Program control: run
Print interactive variables who, whos
Are you a Matlab user?
The exercise is to plot a sine wave:
Matlab/Octave:
>> x=linspace(0,2*pi,100) >> y=sin(x) >> plot(x,y)
Python
In [1]: x=linspace(0,2*pi,100) In [2]: y=sin(x) In [3]: plot(x,y)
So, it works pretty much the same way!
Of course there are some differences but many similarities.
Unix basics
The ampersand & at the end of a line starts a process in the background. You can get the process in the foreground by typing fg. You can stop a process in the foreground by pressing Control-C.
Within the IPython shell you can use the exclamation mark ! to spawn unix commands. E.g.
# List directory content !ls # Make new directory !mkdir new_name # Change to directory !cd new_name # Change to an upper level !cd .. # Move or rename file or directory !mv filename_old filename_new
Python modules
There a several modules which are already included in the standard Python distribution:
Other modules for scientific computing have to be installed separately, e.g. Numpy, Scipy, Pylab, IPython.
Some distributions including precompiled modules are available, e.g.
http://www.pythonxy.com/ Python(x,y) is a scientific python distribution with many modules included
It is important to know where to find the functions that you need. We will go through some useful examples.
Numpy
Numpy is the core library for multidimensional array objects (ndarray) and linear algebra. Most other scientific modules use the numpy array object. Numpy arrays and standard Python sequences have important differences:
- Numpy arrays have a fixed size at creation, unlike Python lists
- Numpy arrays facilitate mathematical operations on large numbers of data efficiently
The User's guide PDF provides a good introduction.
Scipy
The Scipy module is built on Numpy and offers a collection of mathematical algorithms such as
- Clustering algorithms
- Fast Fourier Transform routines
- Integration and ordinary differential equation solvers
- Interpolation and smoothing splines
- Linear algebra
- Maximum entropy methods
- N-dimensional image processing and signal processing
- Optimization and root-finding routines
- Statistical distributions and functions
Furthermore it includes very handy routines for data input and output of binary and ASCII-tables, Matlab and Netcdf data files
Pylab
Pylab (aka Matplotlib) uses Numpy and Scipy and offers high-level functions that are similar in the name and syntax to those offered by Matlab. Matplotlib is the name of the core library and pylab provides the Matlab similarity. Pylab produces figures of great quality suitable for publications.
Making plots is easy. Start reading the User's guide. For a specific problem look at the Gallery for a similar plot you would like to have and learn from the source code.
IPython
IPython is an environment for interactive and exploratory computing. Useful features are TAB-completion, magic commands, e.g. %run, %whos, input cache and many more convenient functions that are not available in the standard Python shell.
Importing the scientific environment
The statement
from pylab import *
imports the most important functions/objects for numerical computation and plotting. When using the interactive IPyhon shell this import is already done with
ipython --pylab
For more complex applications it is useful but not necessary to follow the conventions that the community has adopted:
Arrays
Numpy provides a multidimensional array data type. An array can hold arbitrary Python objects but usually they are used for N-dimensional numeric data types.
Array creation
empty((d1,d2),dtype) returns uninitialized array of shape d1,d2.
zeros((d1,d2),dtype) returns array of shape d1,d2 filled with zeros
ones((d1,d2),dtype) returns array of shape d1,d2 filled with ones
array(object,dtype) returns an array from an object, e.g. a list
dtype fundamental C data type e.g. uint8, int16, int64, float32, float64
Arrays can also be created from special functions, e.g. random
randn((d1,d2,..,dn) returns Gaussian random numbers in an array of shape (d0, d1, ..., dn).
arange([start,] stop[, step,]) returns evenly spaced values within a given interval.
Array indexing
A[y,x] returns (y,x) element of the array
A[:,x] returns all elements of the y-dimension at x
A[y1:y2,x]
A[:,:] returns a copy of two dimensional array A
A[:,:,0] returns the first sub-image of a 3-dimensional array
Example and exercise
Write two programs, a test and a plotting program. The test program shall create a simulated dataset and the plotting routine shall read and display the data on the screen.
We start with a simple linear relation of two variables x and y. The measurement y shall be influenced by noise with a Gaussian distribution.
Generate test data
We first would like to generate x including 11 numbers in the intervall [-5,5]
x=linspace(-5,5,11)
The variable y depends on x and includes the random noise
y=x+randn(x.size)
We write both variables in a file
save('data.txt',(x,y))Now we combine this in a script. First we open an editor (xemacs, nedit, geany, vi or whatever you like) from the Unix shell
nedit generate_test_data.py &
Create a new file, copy and paste the sourcode, and save (Ctrl-S).
Now you can run the script from IPython
In [7]: run generate_test_data.py Finished!
Have a look at the variables (objects):
In [3]: whos
Variable Type Data/Info
-------------------------------
x ndarray 11: 11 elems, type `float64`, 88 bytes
y ndarray 11: 11 elems, type `float64`, 88 bytes
In [5]: x
Out[5]: array([-5., -4., -3., -2., -1., 0., 1., 2., 3., 4., 5.])
In [6]: y
Out[6]:
array([-5.0387728 , -4.28591892, -3.30766546, -1.65761351, -0.19178245,
-1.52643416, 0.52628016, 0.74130426, 2.99303495, 4.91713939,
5.13835735])
Plot test data
The following code can be used as a template
Exercise
- Add a line of identity (y=x) (solid line style)
- Add a linear regression line with dashed line style
- Add a legend
Hints:
- Look up help(plot) for style options
slope,offset=polyfit(x,y,1) can be used for the linear regression
- Use plot labels and legend(), e.g. plot(x,y,'ko',label='Simulated data')
Pure Python essentials
Loop
Symbolic math
Use isympy or import sympy to obtain a computer algebra system
isympy
IPython console for SymPy 0.7.1 (Python 2.7.0-64-bit) (ground types: python)
These commands were executed:
>>> from __future__ import division
>>> from sympy import *
>>> x, y, z, t = symbols('x y z t')
>>> k, m, n = symbols('k m n', integer=True)
>>> f, g, h = symbols('f g h', cls=Function)
Documentation can be found at http://www.sympy.orgDerivatives
In [1]: f=sin(x) In [2]: diff(f,x) Out[2]: cos(x)
Series expansion
In [3]: f.series()
Out[3]:
3 5
x x
x - ── + ─── + O(x**6)
6 120 Simplification
In [4]: g=sin(x)**2+cos(x)**2 In [5]: simplify(g) Out[5]: 1
Integration
In [7]: F=sin(x) In [8]: f=diff(F,x) In [9]: f.integrate() Out[9]: sin(x)
Calculus
In [12]: Rational(1,3)+Rational(1,4) Out[12]: 7/12
Documentation and tutorials
Matplotlib/pylab for interactive plotting