CVXMOD – Matrices

Matrices are represented using the matrix class provided by CVXOPT. Matrices are created by specifying a list of (column-by-column) entries, followed by a tuple describing the matrix size. Omitting the size will result in a column vector.

There is currently no support for sparse or complex-valued matrices. This will be addressed at some stage.

>>> matrix((1.1, 2, 3.8, 4, 5, 6), (3, 2))

[   1.100    4.000]
[   2.000    5.000]
[   3.800    6.000]

>>> matrix((1.1, 2, 3.8, 4))

[   1.100]
[   2.000]
[   3.800]
[   4.000]

Automatic conversions to and from the NumPy type array are supported.

>>> from numpy import array
>>> array(matrix((1.1, 2, 3.8, 4, 5, 6), (3, 2)))

array([[ 1.1,  4. ],
       [ 2. ,  5. ],
       [ 3.8,  6. ]])

>>> matrix(array((3.2, 4)))

[   3.200]
[   4.000]

Matrix functions

Matrices can be used in:

• Arithmetic operations +, - or * between two matrices of appropriate sizes,

• Elementwise scalar arithmetic operations +, -, * or /, and

• Elementwise scalar exponentiation .

Various other functions may be applied to matrices, too.

• transpose(mat) returns the matrix transpose of mat. (Also available as tp(mat).)

• rows(mat) returns the number of rows of mat.

• cols(mat) returns the number of columns of mat.

• size(mat) returns a tuple equal to (rows(mat), cols(mat)).

• is1x1(mat) returns True if mat is a scalar or a size (1, 1) matrix.

• concathoriz(mat1, mat2) returns a horizontal concatenation of two matrices.

• concatvert(mat1, mat2) returns a vertical concatenation of two matrices.

Matrix indexing and slicing

Matrices are indexed or sliced with one or two indices. Indices begin at 0.

>>> A = matrix((1.1, 2, 3.8, 4, 5, 6), (3, 2))

>>> A

[   1.100    4.000]
[   2.000    5.000]
[   3.800    6.000]

>>> A[1]
2.0

>>> A[2,1]
6.0

>>> A[2:4]

[   3.800]
[   4.000]

>>> A[0,:]

[   1.100    4.000]

>>> A[:,1]

[   4.000]
[   5.000]
[   6.000]

Randomly generated matrices

CVXMOD provides wrappers to CVXOPT’s random number generators:

• rand(rows, cols=rows, lowerlim=0, upperlim=1) returns a matrix with entries uniformly distributed between lowerlim and upperlim.

• randn(rows, cols=rows, mean=0, std=1) returns a matrix with individual entries normally distributed with mean mean and standard deviation std.

• randseed(s) seeds the random number generator. Omitting s uses a seed value from the system clock.

>>> randseed(14)
>>> randn(3)

[   1.219   -1.939  -0.1466]
[  0.9686  -0.1017   -1.458]
[  -1.371   0.7619  -0.4962]

>>> rand(5, 1, -2, 0.5)

[  -1.008]
[-0.05621]
[  -1.704]
[  -1.442]
[  0.2537]

Utility functions

CVXMOD provides functions for producing various special matrices.

• eye(n) returns the size (n, n) identity matrix.

• ones(rows, cols=rows) returns an all-ones matrix.

• zeros(rows, cols=rows) returns an all-zeros matrix.

• zm() returns a matrix with size (0, 0), which can be useful when building a matrix with the concathoriz or concatvert functions.

• linspace(start, end, N, includeend=True) returns a column matrix with N evenly spaced entries from start (inclusive) to stop (inclusive or exclusive).