jax_privacy.matrix_factorization.toeplitz.materialize_lower_triangular

jax_privacy.matrix_factorization.toeplitz.materialize_lower_triangular(coef, n=None)

Creates a lower-triangular Toeplitz matrix.

Example: If coef = [a, b, c] and n = 6, then this method returns:

` [a 0 0 0 0 0] [b a 0 0 0 0] [c b a 0 0 0] [0 c b a 0 0] [0 0 c b a 0] [0 0 0 c b a] `

Parameters:

• coef (Array) – The nonzero coefficients of a lower-triangular Toeplitz matrix C, that is, coef are the leading nonzero entries of C[:, 0]. C is of size n x n; if len(coef) < n, the remaining coefficients are assumed to be zero. If len(coef) > n, then only the first n coefficients are used.

• n (int | None) – Optional, the size of the matrix C (see coef above). If None, the size of the matrix is equal to the number of coefficients.

Return type:

Array

Returns:

The lower-triangular Toeplitz matrix.