jax_privacy.matrix_factorization.toeplitz.multiply

jax_privacy.matrix_factorization.toeplitz.multiply(lhs_coef, rhs_coef, n=None)

Computes the matrix product of two lower-triangular Toeplitz matrices.

Parameters:

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

• rhs_coef (Array) – The nonzero coefficients of a lower-triangular Toeplitz matrix R, under the same conventions as lhs_coef.

• n (int | None) – Optional, the size of the matrices L and R (see coef above). If None, the size of the matrices is equal to the number of coefficients.

Return type:

Array

Returns:

The coefficients of the lower-triangular Toeplitz matrix L @ R where L = materialize_lower_triangular(lhs_coef, n) and R = materialize_lower_triangular(rhs_coef, n).