Utilities in cr.sparse module

Some checks and utilities for matrices (2D arrays)

transpose(A)	Returns the transpose of an array
hermitian(a)	Returns the conjugate transpose of an array
is_matrix(A)	Checks if an array is a matrix
is_square(A)	Checks if an array is a square matrix
is_symmetric(A)	Checks if an array is a symmetric matrix
is_hermitian(A)	Checks if an array is a Hermitian matrix
is_positive_definite(A)	Checks if an array is a symmetric positive definite matrix
has_orthogonal_columns(A)	Checks if a matrix has orthogonal columns
has_orthogonal_rows(A)	Checks if a matrix has orthogonal rows
has_unitary_columns(A)	Checks if a matrix has unitary columns
has_unitary_rows(A)	Checks if a matrix has unitary rows

Row wise and column wise norms for signal/representation matrices

norms_l1_cw(X)	Computes the l_1 norm of each column of a matrix
norms_l1_rw(X)	Computes the l_1 norm of each row of a matrix
norms_l2_cw(X)	Computes the l_2 norm of each column of a matrix
norms_l2_rw(X)	Computes the l_2 norm of each row of a matrix
norms_linf_cw(X)	Computes the l_inf norm of each column of a matrix
norms_linf_rw(X)	Computes the l_inf norm of each row of a matrix
sqr_norms_l2_cw(X)	Computes the squared l_2 norm of each column of a matrix
sqr_norms_l2_rw(X)	Computes the l_2 norm of each row of a matrix
normalize_l1_cw(X)	Normalize each column of X per l_1-norm
normalize_l1_rw(X)	Normalize each row of X per l_1-norm
normalize_l2_cw(X)	Normalize each column of X per l_2-norm
normalize_l2_rw(X)	Normalize each row of X per l_2-norm

Sparse representations

Following functions analyze or construct representation vectors which are known to be sparse.

nonzero_values(x)	Returns the values of non-zero entries in x
nonzero_indices(x)	Returns the indices of non-zero entries in x
randomize_rows(key, X)	Randomizes the rows in X
randomize_cols(key, X)	Randomizes the columns in X
largest_indices(x, K)	Returns the indices of K largest entries in x by magnitude
hard_threshold(x, K)	Returns the indices and corresponding values of largest K non-zero entries in a vector x
hard_threshold_sorted(x, K)	Returns the sorted indices and corresponding values of largest K non-zero entries in a vector x
sparse_approximation(x, K)	Keeps only largest K non-zero entries by magnitude in a vector x
build_signal_from_indices_and_values(length, …)	Builds a sparse signal from its non-zero entries (specified by their indices and values)
dynamic_range(x)	Returns the ratio of largest and smallest values (by magnitude) in x (dB)
nonzero_dynamic_range(x)	Returns the ratio of largest and smallest non-zero values (by magnitude) in x (dB)

Sparse representation matrices (row-wise)

largest_indices_rw(X, K)	Returns the indices of K largest entries by magnitude in each row of X
take_along_rows(X, indices)	Picks K entries from each row of X specified by indices matrix
sparse_approximation_rw(X, K)	Keeps only largest K non-zero entries by magnitude in each row of X

Sparse representation matrices (column-wise)

largest_indices_cw(X, K)	Returns the indices of K largest entries by magnitude in each column of X
take_along_cols(X, indices)	Picks K entries from each column of X specified by indices matrix
sparse_approximation_cw(X, K)	Keeps only largest K non-zero entries by magnitude in each column of X