lecture7 revised

8/9/2019 Lecture7 Revised

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Numerical Computing in PythonLecture

Tuesday, October 20, 2009


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Numerical Computing in Python: Review of the Basics

Weve already seen how python can be used to compute some fairly basic mathematics.

And that the math module provides some additional functionality.



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Numerical Computing in Python: Review of the Basics

Weve already seen how python can be used to compute some fairly basic mathematics.

And that the math module provides some additional functionality.

Today were going to talk about python modules that extend its standard numerical computingabilities.



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rom numpy import*

NumPy provides fast numerical computing methodsfor Python.

http://numpy.scipy.org/http://numpy.scipy.org/


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rom numpy import*

NumPy provides fast numerical computing methodsfor Python.

Multi-dimensional arrays Standard matrix/array operations

Sophisticated random number functionality Access to the fortran-based LINPACK numerical linear algebra software library Ability to integrate Fortran & C/C++ code

NumPy can also be used as an efcient multi-dimensional container, and has threefundamental objects:

[1] the ndarray itself [2] the data-type objects describing the layoutof a single xed-size element of the array.[3] the array-scalar Python object that isreturned when a single element is accessed.



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rom numpy import*

NumPy is primarily used for array functionality:

Create array like a nested list



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rom numpy import*



Obtain dimensions of a (rows, columns)



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Obtain dimensions of a (rows, columns)

Array slicing is a natural extension of list slicing



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rom numpy import*

Vectors, matrices, and tensors are all arrays.

vector: [1, 2, 3]matrix:

[[1, 2, 3],[ 4, 5, 6]]

tensor:[[[1, 2, 3], [ 4, 5, 6]],[[1, 2, 3], [ 4, 5, 6]]]



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rom numpy import*

Vectors, matrices, and tensors are all arrays.

...but why would we want our data in an array, rather than something else?

vector: [1, 2, 3]matrix:

[[1, 2, 3],[ 4, 5, 6]]

tensor:[[[1, 2, 3], [ 4, 5, 6]],[[1, 2, 3], [ 4, 5, 6]]]



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rom numpy import*

Main Advantage : a single command can be used to perform basic math operations.

This can substantially increase the efciency of your code.

NumPy arrays haveseveral attributes:

dot(a, b) Matrix product of a and b

More in the linalg submodule...



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rom numpy import*

In addition to normal slicing, there are several other array methods for item selection& manipulation

an order for the indices that would lead to sorting



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rom numpy import*

abbreviated command summary



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Random numbers

abbreviated summary of array methods



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Random numbers

Two solutions:

>>> import random

>>> import numpy.random

One often needs to generaterandom numbers in scientic

scripting.



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Random numbers

Two solutions:

>>> import random

One often needs to generaterandom numbers in scientic

scripting. We already saw that therandom module can do this.



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Random numbers

Two solutions:

>>> import random



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Random numbers

Two solutions: The random module within NumPyProvides vectorized drawing of randomnumbers, in addition to a variety ofadditional methods.



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Random numbers

Two solutions:

The NumPy random module allowsus to take advantage of powerfularray methods!

The random module within NumPyProvides vectorized drawing of randomnumbers, in addition to a variety ofadditional methods.



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Random numbers

Watch out for namespace collision!



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rom scipy import*

SciPy provides a variety of scientic tools, and is built to specically work withNumPy arrays


l l


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rom scipy import linalgSciPys linalg submodule provides most of the matrix algebra-related operations youll

want.

In linear algebra, one frequently needs to solve systems of equations taking the form

Xb = yusing a procedure called Gaussian Elimination. This becomes verystraightforward with our Python library extensions. For example, if

we could determine the values in b by


i i li l
http://docs.scipy.org/doc/scipy/reference/linalg.htmlhttp://docs.scipy.org/doc/scipy/reference/linalg.htmlhttp://docs.scipy.org/doc/scipy/reference/linalg.html


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rom scipy import linalg

linalg.inv(a) Returns the inverse of matrix a

linalg.pinv(a) Returns the pseudoinverse of singular matrix a linalg.svd(a) Returns U, s, V--results from singular value decomposition

SciPys linalg submodule provides most of the matrix algebra-related operations youll want.

Compute the inverse

Singular Value Decomposition

Matrix multiplication isincluded in the NumPy module


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http://docs.scipy.org/doc/scipy/reference/linalg.htmlhttp://docs.scipy.org/doc/scipy/reference/linalg.html


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import xlrd

http://www.python-excel.org/

Sometimes we need to get dataout of/into excel directly.

The xlrd & xlwt modules provide this functionality. Both have to be downloaded from their websites and installed.

On macintosh, youll have toinstall it manually from the zip ortar.gz source le:

Computery:~ ambertk$ cd DesktopComputery:~ ambertk$ gunzip xlrd-0.7.1.tar.gzComputery:~ ambertk$ tar -xvf xlrd-0.7.1.tarComputery:~ ambertk$ python xlrd-0.7.1/setup.py install

(for .zip, just unzipand do this line)


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http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/


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import xlrd

http://www.python-excel.org/

Lets say weneeded to

work withan .xlsspreadsheet

like thisone...

http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/http://www.python-excel.org/


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Scenario


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Scenario.

Projecting from three dimensions to two is one type of linear transformation. We canuse a 2x3 matrix P whose columns dictate where the transformed x, y, and z will be

located in two dimensions ( u, v).

Kerl, 2009Tuesday, October 20, 2009

Scenario


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Scenario.

Projecting from three dimensions to two is one type of linear transformation. We canuse a 2x3 matrix P whose columns dictate where the transformed x, y, and z will be

located in two dimensions ( u, v).

Lets say we have a 50 x 3 excel le containing a set of x, y, z coordinates that we want to map to two dimensions, and write to a tab-delimited text le.


Scenario


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Scenario.


Scenario--better code


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Scenario--better code


misc


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misc.

Others that may interest you...

biopython (http://piopython.org) Bioinformatics et al.

scipy (http://www.scipy.org) Symbolic mathematics--integration FFT

matplotlib (http://matplotlib.sourceforge.net/)

Interactive 2D plotting MATLAB-like interfaceSymPy (http://code.google.com/p/sympy/)

Computer Alge bra System written in Pythonmlpy (https://mlpy.fbk.eu/)

General-purpose machine learning using numpy arraysrpy2 (http://rpy.sourceforge.net/rpy2.html)

python-R interfacing (well talk about this one on Friday...)
https://mlpy.fbk.eu/https://mlpy.fbk.eu/https://mlpy.fbk.eu/http://www.scipy.org/http://www.scipy.org/http://piopython.org/http://piopython.org/

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