SparseRandomMatrix#

class xesn.SparseRandomMatrix(n_rows, n_cols, factor, distribution, normalization='multiply', density=None, sparsity=None, connectedness=None, format='coo', random_seed=None)#

Similar to RandomMatrix, but used to create a sparse random matrix. Additional controls are the density and sparse array layout.

Example

Create a sparse 100x100 random matrix with entries from a Gaussian distribution with its spectral radius set to 0.9

>>> from xesn import SparseRandomMatrix ; from scipy.sparse.linalg import eigs
>>> mat = SparseRandomMatrix(100, 100, factor=0.9, distribution="normal", normalization="eig", connectedness=1, random_seed=0)
>>> A = mat()
>>> A
<100x100 sparse matrix of type '<class 'numpy.float64'>'
    with 100 stored elements in COOrdinate format>
>>> A.nnz
100
>>> mat.density
0.01
>>> max(abs(eigs(A, k=1, which="LM", return_eigenvectors=False)))
0.9000000000000011

Parameters:

n_rows (int) – number of rows in the matrix
n_cols (int) – number of columns in the matrix
factor (float, optional) – factor to rescale the matrix with after it’s been normalized
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()
density (float) – use ‘density’, ‘sparsity’ or ‘connectedness’ to specify the number of nonzero values in the matrix, where ‘density’ sets the fraction of nonzero values, sparsity=1 - density, and density = connectedness / n_rows, but note that ‘connectedness’ only makes sense for square matrices
sparsity (float) – use ‘density’, ‘sparsity’ or ‘connectedness’ to specify the number of nonzero values in the matrix, where ‘density’ sets the fraction of nonzero values, sparsity=1 - density, and density = connectedness / n_rows, but note that ‘connectedness’ only makes sense for square matrices
connectedness (float) – use ‘density’, ‘sparsity’ or ‘connectedness’ to specify the number of nonzero values in the matrix, where ‘density’ sets the fraction of nonzero values, sparsity=1 - density, and density = connectedness / n_rows, but note that ‘connectedness’ only makes sense for square matrices
random_seed (int, optional) – used to control the RNG for matrix generation

Methods

`SparseRandomMatrix.__call__`()	The main routine to use.
`SparseRandomMatrix.create_matrix`()	Create either a uniform or normal random matrix.
`SparseRandomMatrix.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

`SparseRandomMatrix.density`
`SparseRandomMatrix.format`
`SparseRandomMatrix.distribution`
`SparseRandomMatrix.factor`
`SparseRandomMatrix.n_cols`
`SparseRandomMatrix.n_rows`
`SparseRandomMatrix.normalization`
`SparseRandomMatrix.random_seed`
`SparseRandomMatrix.random_state`

SparseRandomMatrix

Contents

SparseRandomMatrix#