Numeric Programming in Python (Brief Overview, 2011)

A large Python application domain

� Scientific: Lawrence Livermore, Los Alamos, Fermi, �

� Engineering: NASA, JPL, �

� Financial: UBS, JP Morgan Chase, Getco, DRW, �

� Movie animation (ILM), weather forecasts (NOAA), hydrology models (SFWMD), GIS (ESRI), NSA, �

Based on third-party open source extensions

Three primary packages

� NumPy:�� efficient matrix processing and numeric libraries

� SciPy: �� adds additional numeric libs, statistics, tools

� matplotlib: � 2D plotting tools for rendering NumPy/SciPy results

Other popular packages

� Parallel computation: pypar (MPI, NumPy, openmpi), pp (SMP), pypvm (PVM), pyMPI

� Graphics: Maya, Blender, OpenGL

� Visualization: VPython, VTK

� Compiled code linkage: SWIG, F2PY, Cython (PyRex), Weave

� IPython shell (MATLAB-like), BioPython, ScientificPython, cluster computing, �

NumPy

� http://numpy.scipy.org/

� Extends Python with high-performance vector/matrix tools

� Python + NumPy = free, open source alternative to MATLAB

� Effieciency of NumPy arrays� + flexibility, power, and libs of Python

� Numeric processing, + GUIs, networking, databases, sys admin, text, Web, �

� Also being used as an alternative to FORTRAN (no, really)

From NumPy�s example pages�

>>> import numpy as np

# many ways to create arrays

>>> x = np.array([[1, 2, 3], [4, 5, 6]], np.int32)

>>> type(x)

>>> x.shape

(2, 3)

>>> x.dtype

dtype('int32')

>>> np.array([1, 2, 3], dtype='f')

array([ 1.,� 2.,� 3.], dtype=float32)

>>> np.indices((3,3))

array([[[0, 0, 0], [1, 1, 1], [2, 2, 2]], [[0, 1, 2], [0, 1, 2], [0, 1, 2]]])

# plus pairwise, vector-wide operations and expressions

>>> a = np.array((1, 2))

>>> a * 3.

array([3., 6.])

>>> a = np.array([1, 2, 3, 4])

>>> b = np.array([2, 3, 4, 5])

>>> a + b

array([3, 5, 7, 9])

See also:

Matrix code in the core Python language (after you�ve learned about loops and comprehensions!):

�� Extras\Code\Misc\matrix-code.py

As a rule, NumPy supports arrays which are much more efficient in space and speed for larger data sets

SciPy

� http://www.scipy.org/

� Builds on NumPy base to add additional libraries and tools

� Numerical integration, optimization, statistics, interpolation, �

� Includes Weave, a tool for including C/C++ code in Python scripts

� A central �clearinghouse� for other scientific tools: IPython shell, �

From SciPy�s example pages�

# Bessel functions, circular drum head vibrational modes

>>> from scipy import *

>>> from scipy.special import jn, jn_zeros

>>>

>>> def drumhead_height(n, k, distance, angle, t):

...�� nth_zero = jn_zeros(n, k)

...�� return cos(t)*cos(n*angle)*jn(n, distance*nth_zero)

...

>>> theta = r_[0:2*pi:50j]

>>> radius = r_[0:1:50j]

>>>

>>> x = array([r*cos(theta) for r in radius])

>>> y = array([r*sin(theta) for r in radius])

>>> z = array([drumhead_height(1, 1, r, theta, 0.5) for r in radius])

matplotlib

� http://matplotlib.sourceforge.net/

� A popular Python 2D plotting library

� Can be used in python scripts, the python and IPython shell (like MATLAB, Mathematica)

� Also supports web servers and 6 GUI toolkits for rendering

From matplotlib�s example pages�

# histogram plotting demo, one of many at the web site!

import numpy as np

import matplotlib.mlab as mlab

import matplotlib.pyplot as plt

mu, sigma = 100, 15

x = mu + sigma*np.random.randn(10000)

# the histogram of the data

n, bins, patches = plt.hist(x, 50, normed=1, facecolor='green', alpha=0.75)

# add a 'best fit' line

y = mlab.normpdf( bins, mu, sigma)

l = plt.plot(bins, y, 'r--', linewidth=1)

plt.xlabel('Smarts')

plt.ylabel('Probability')

plt.title(r'$\mathrm{Histogram\ of\ IQ:}\ \mu=100,\ \sigma=15$')

plt.axis([40, 160, 0, 0.03])

plt.grid(True)

plt.show()

For More Details

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