random_sparse_spd_matrix¶

probnum.problems.zoo.linalg.random_sparse_spd_matrix(dim, density, chol_entry_min=0.1, chol_entry_max=1.0, random_state=None)[source]¶

Random sparse symmetric positive definite matrix.

Constructs a random sparse symmetric positive definite matrix for a given degree of sparsity. The matrix is constructed from its Cholesky factor \(L\). Its diagonal is set to one and all other entries of the lower triangle are sampled from a uniform distribution with bounds [chol_entry_min, chol_entry_max]. The resulting sparse matrix is then given by \(A=LL^\top\).

Parameters

dim (Integral) – Matrix dimension.
density (float) – Degree of sparsity of the off-diagonal entries of the Cholesky factor. Between 0 and 1 where 1 represents a dense matrix.
chol_entry_min (float) – Lower bound on the entries of the Cholesky factor.
chol_entry_max (float) – Upper bound on the entries of the Cholesky factor.
random_state (Union[None, int, RandomState, Generator]) – Random state of the random variable. If None (or np.random), the global numpy.random state is used. If integer, it is used to seed the local RandomState instance.

See also

random_spd_matrix(): Generate a random symmetric positive definite matrix.

Examples

>>> from probnum.problems.zoo.linalg import random_sparse_spd_matrix
>>> sparsemat = random_sparse_spd_matrix(dim=5, density=0.1, random_state=42)
>>> sparsemat
array([[1.        , 0.        , 0.        , 0.        , 0.        ],
       [0.        , 1.        , 0.        , 0.        , 0.        ],
       [0.        , 0.        , 1.        , 0.        , 0.24039507],
       [0.        , 0.        , 0.        , 1.        , 0.        ],
       [0.        , 0.        , 0.24039507, 0.        , 1.05778979]])

Return type: ndarray