NumPy/SciPy Cheat Sheet

This cheat sheet is a quick reference for NumPy / SciPy beginners and gives an overview about the most important commands and functions of NumPy and SciPy that you might need on solving the exercise sheets about Linear Algebra in Information Retrieval. It doesn't claim to be complete and will be extended continuously. If you think that some important thing is missing or if you find any errors, please let us know.

General

What is NumPy?

A library that allows to work with arrays and matrices in Python.

What is SciPy?

Another library built upon NumPy that provides advanced Linear Algebra stuff.

Install

The routine to install NumPy and SciPy depends on your operating system.

Linux (Ubuntu, Debian)

apt-get install python-numpy python-scipy

Other systems (Windows, Mac, etc.)

For all other systems (Windows, Mac, etc.) see the instructions given on the offical SciPy website.

Matrix construction

We distinguish between dense matrices and sparse matrices. Dense matrices store every entry in the matrix, while sparse matrices only store the non-zero entries (together with their row and column index). Dense matrices are more feature-rich, but may consume more memory space than sparse matrices (in particular if most of the entries in a matrix are zero).

Dense matrices

In NumPy, there are two concepts of dense matrices: matrices and arrays. Matrices are strictly 2-dimensional, while arrays are n-dimensional (the term array is a bit misleading here).

Construct a matrix:

numpy.matrix(arg, dtype=None)

arg:
   The data to construct the matrix from, given as
     * a standard Python array; or
     * a string with columns separated by commas or spaces and rows separated by semicolons.
dtype (str, optional):
   The type of the entries in the matrix (e.g., 'integer', 'float', 'string', etc.).

----------
Examples:

>>> numpy.matrix("1 2; 3 4")
[[1 2]
 [3 4]]

>>> numpy.matrix([[1, 2], [3, 4]], dtype='float')
[[1.0 2.0]
 [3.0 4.0]]

numpy.matrix

Construct an array:

numpy.array(arg, dtype=None, ndmin=0)

arg:
   The data to construct the matrix from, given as
      * a standard array; or
      * a function that returns an array.
dtype (str, optional):
   The type of the entries in the matrix ('integer', 'float', 'string', etc.).
ndmin (int, optional):
   The minimum number of dimensions that the array should have.

----------
Examples:

>>> numpy.array([[1, 2], [3, 4]])
[[1 2]
 [3 4]]

>>> numpy.array([[1, 2], [3, 4]], dtype='float')
[[1.0 2.0]
 [3.0 4.0]]

>>> numpy.array([[1, 2], [3, 4]], ndmin=3)
[[[1 2]
  [3 4]]]

numpy.array

There are some utility functions to create special-structured arrays:

(1) Construct an array filled with zeros:

numpy.zeros(shape, dtype=float)

shape (int or sequence of ints):
   The dimensions of the array to create.
dtype (str, optional):
   The type of the entries in the matrix ('integer', 'float', 'string', etc.).

----------
Examples:

>>> numpy.zeros(3)
[0.0, 0.0, 0.0]

>>> numpy.zeros([3, 2], dtype='int')
[[0 0]
 [0 0]
 [0 0]]

numpy.zeros

(2) Construct an array without initializing the entries (an array with random entries):

numpy.empty(shape, dtype=float)

shape (int or sequence of ints):
   The dimensions of the array to create.
dtype (str, optional):
   The type of the entries in the matrix ('integer', 'float', 'string', etc.).

----------
Examples:

>>> numpy.empty(3)
[6.95052181e-310 1.74512682e-316 1.58101007e-322]

>>> numpy.empty([3, 2], dtype='int')
[[140045355821992 140045355821992]
 [140045136216840 140045136244784]
 [140045125643544 140045153116544]]

numpy.empty

Sparse matrices

There are two principle concepts of sparse matrices:

• Compressed Sparse Row matrix (CSR matrix): entries are stored row by row (sorted by row index first)

• Compressed Sparse Column matrix (CSC matrix): entries are stored column by column (sorted by column index first)

Construct a CSR/CSC matrix:

scipy.sparse.csr_matrix(arg, shape=None, dtype=None)
scipy.sparse.csc_matrix(arg, shape=None, dtype=None)

arg:
   The data to create the CSR matrix from, given as 
     * a dense matrix; or
     * another sparse matrix; or
     * a tuple (m, n), to construct an empty matrix with shape (n, m); or
     * a tuple (data, (rows, cols), to construct a matrix A where A[rows[k], cols[k]] = data[k]; or
     * a tuple (data, indices, indptr)
shape (int or sequence of ints):
   The dimensions of the matrix to create.
dtype (str, optional):
   The type of the entries in the matrix ('integer', 'float', 'string', etc.).

----------
Examples:

>>> scipy.sparse.csr_matrix([[1, 2, 3], [0, 0, 1], [0, 1, 3]])
[[1 2 3]
 [0 0 1]
 [0 1 3]]  # (transformed to a dense matrix for visualization).

>>> scipy.sparse.csc_matrix([[1, 2, 3], [0, 0, 1], [0, 1, 3]])
[[1 2 3]
 [0 0 1]
 [0 1 3]]  # (transformed to a dense matrix for visualization).

>>> values = [1, 2, 3]
>>> rows   = [0, 0, 1]
>>> cols   = [0, 1, 3]
>>> scipy.sparse.csr_matrix((values, (rows, columns)), shape=[5, 5], dtype=int)
[[1 1 0 0]
 [0 0 0 3]
 [0 0 0 0]
 [0 0 0 0]]  # (transformed to a dense matrix for visualization).

>>> values = [1, 2, 3]
>>> rows   = [0, 0, 1]
>>> cols   = [0, 1, 3]
>>> scipy.sparse.csc_matrix((values, (rows, columns)), shape=[5, 5], dtype=int)
[[1 1 0 0]
 [0 0 0 3]
 [0 0 0 0]
 [0 0 0 0]]  # (transformed to a dense matrix for visualization).

scipy.sparse.csr_matrix
scipy.sparse.csc_matrix

... to be continued ...