Utilities in cr.sparse module

Array data type utilities

promote_arg_dtypes(*args)	Promotes args to a common inexact type.
check_shapes_are_equal(array1, array2)	Raise an error if the shapes of the two arrays do not match.

Utilities for vectors

is_scalar(x)	Returns if x is a scalar
is_vec(x)	Returns if x is a line vector or row vector or column vector
is_line_vec(x)	Returns if x is a line vector
is_row_vec(x)	Returns if x is a row vector
is_col_vec(x)	Returns if x is a column vector
to_row_vec(x)	Converts a line vector to a row vector
to_col_vec(x)	Converts a line vector to a column vector
vec_unit(n, i)	Returns a unit vector in i-th dimension for the standard coordinate system
vec_shift_right(x)	Right shift the contents of the vector
vec_rotate_right(x)	Circular right shift the contents of the vector
vec_shift_left(x)	Left shift the contents of the vector
vec_rotate_left(x)	Circular left shift the contents of the vector
vec_shift_right_n(x, n)	Right shift the contents of the vector by n places
vec_rotate_right_n(x, n)	Circular right shift the contents of the vector by n places
vec_shift_left_n(x, n)	Left shift the contents of the vector by n places
vec_rotate_left_n(x, n)	Circular left shift the contents of the vector by n places
vec_repeat_at_end(x, p)	Extends a vector by repeating it at the end (periodic extension)
vec_repeat_at_start(x, p)	Extends a vector by repeating it at the start (periodic extension)
vec_centered(x, length)	Returns the central part of a vector of a specified length
vec_unit_jit(n, i)	Returns a unit vector in i-th dimension for the standard coordinate system
vec_repeat_at_end_jit(x, p)	Extends a vector by repeating it at the end (periodic extension)
vec_repeat_at_start_jit(x, p)	Extends a vector by repeating it at the start (periodic extension)
vec_centered_jit(x, length)	Returns the central part of a vector of a specified length

Metrics for measuring signal and error levels

These functions are available under cr.sparse.metrics.

mean_squared(array)	Returns the mean squared value of an array
mean_squared_error(array1, array2)	Returns the mean square error between two arrays
root_mean_squared(array)	Returns the root mean squared value of an array
root_mse(array1, array2)	Returns the root mean square error between two arrays
normalized_root_mse(reference_arr, test_arr)	Returns the normalized root mean square error between two arrays
peak_signal_noise_ratio(reference_arr, test_arr)	Returns the Peak Signal to Noie Ratio between two arrays
signal_noise_ratio(reference_arr, test_arr)	Returns the signal to noise ratio between a reference array and a test array

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[, atol])	Checks if a matrix has orthogonal columns
has_orthogonal_rows(A[, atol])	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
off_diagonal_elements(A)	Returns the off diagonal elements of a matrix A
off_diagonal_min(A)	Returns the minimum of the off diagonal elements
off_diagonal_max(A)	Returns the maximum of the off diagonal elements
off_diagonal_mean(A)	Returns the maximum of the off diagonal elements

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

Pairwise Distances

pairwise_sqr_l2_distances_rw(A, B)	Computes the pairwise squared distances between points in A and points in B where each point is a row vector
pairwise_sqr_l2_distances_cw(A, B)	Computes the pairwise squared distances between points in A and points in B where each point is a column vector
pairwise_l2_distances_rw(A, B)	Computes the pairwise distances between points in A and points in B where each point is a row vector
pairwise_l2_distances_cw(A, B)	Computes the pairwise distances between points in A and points in B where each point is a column vector
pdist_sqr_l2_rw(A)	Computes the pairwise squared distances between points in A where each point is a row vector
pdist_sqr_l2_cw(A)	Computes the pairwise squared distances between points in A where each point is a column vector
pdist_l2_rw(A)	Computes the pairwise distances between points in A where ach point is a row vector
pdist_l2_cw(A)	Computes the pairwise distances between points in A where each point is a column vector
pairwise_l1_distances_rw(A, B)	Computes the pairwise city-block distances between points in A and points in B where each point is a row vector
pairwise_l1_distances_cw(A, B)	Computes the pairwise city-block distances between points in A and points in B where each point is a column vector
pdist_l1_rw(A)	Computes the pairwise city-block distances between points in A where each point is a row vector
pdist_l1_cw(A)	Computes the pairwise city-block distances between points in A where each point is a column vector
pairwise_linf_distances_rw(A, B)	Computes the pairwise Chebyshev distances between points in A and points in B where each point is a row vector
pairwise_linf_distances_cw(A, B)	Computes the pairwise Chebyshev distances between points in A and points in B where each point is a column vector
pdist_linf_rw(A)	Computes the pairwise Chebyshev distances between points in A where each point is a row vector
pdist_linf_cw(A)	Computes the pairwise Chebyshev distances between points in A where each point is a column vector

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

Utilities for ND-Arrays

arr_largest_index(x)

Returns the unraveled index of the largest entry (by magnitude) in an n-d array