RandomMatrix

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RandomMatrix#

class xesn.RandomMatrix(n_rows, n_cols, factor, distribution, normalization='multiply', random_seed=None)#

Creates a random numpy or cupy based matrix via __call__(). Use input arguments to control the shape, generator distribution, normalization, and the random number generator seed.

Parameters:

  • n_rows (int) – number of rows in the matrix

  • n_cols (int) – number of columns in the matrix

  • distribution (str) – distribution to draw elements of the matrix from, either “uniform”, or “gaussian” and “normal” are recognized

  • normalization (str, optional) – method used to rescale the matrix, see normalize()

  • factor (float, optional) – factor to rescale the matrix with after it’s been normalized

  • random_seed (int, optional) – used to control the RNG for matrix generation

Example

Create a 2x2 random matrix with entries from a uniform distribution ranging from -5 to 5

>>> from xesn import RandomMatrix
>>> mat = RandomMatrix(2, 2, factor=5, distribution="uniform", random_seed=0)
>>> A = mat()
>>> A
array([[0.48813504, 2.15189366],
       [1.02763376, 0.44883183]])

Note that every time the object is called, a new matrix is generated

>>> B = mat()
>>> B
array([[-0.76345201,  1.45894113],
       [-0.62412789,  3.91773001]])

Example

Create a 2x2 random matrix with entries from a Gaussian distribution with its spectral radius set to 0.9

>>> from xesn import RandomMatrix ; from scipy.linalg import eigvals
>>> mat = RandomMatrix(2, 2, factor=0.9, distribution="gaussian", normalization="eig", random_seed=0)

or equivalently…

>>> mat = RandomMatrix(2, 2, factor=0.9, distribution="normal", normalization="eig", random_seed=0)
>>> A = mat()
>>> A
array([[0.59414168, 0.13477495],
       [0.32964386, 0.75474407]])
>>> max(abs(eigvals(A)))
0.9000000000000001

Example

Create a 2x2 random matrix with entries from a Gaussian distribution with its induced 2-norm set to 1.0

>>> from xesn import RandomMatrix ; from scipy.linalg import svd
>>> mat = RandomMatrix(2, 2, factor=1.0, distribution="gaussian", normalization="svd", random_seed=0)
>>> A = mat()
>>> A
array([[0.64082821, 0.14536532],
       [0.35554665, 0.81405043]])
>>> max(abs(svd(A, compute_uv=False, full_matrices=False)))
1.0

Methods

RandomMatrix.__call__()

The main routine to use.

RandomMatrix.create_matrix()

Create either a uniform or normal random matrix.

RandomMatrix.normalize(A)

Rescale a random matrix either through simple multiplication, or by first normalizing by the matrix's spectral radius or induced 2 norm.

Attributes

RandomMatrix.n_rows

RandomMatrix.n_cols

RandomMatrix.distribution

RandomMatrix.normalization

RandomMatrix.factor

RandomMatrix.random_seed

RandomMatrix.random_state

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