jax_privacy.matrix_factorization.toeplitz.inverse_coef

jax_privacy.matrix_factorization.toeplitz.inverse_coef(coef, n=None)[source]

Finds the inverse coefficients of a lower-triangularToeplitz matrix.

If C is a lower-triangular Toeplitz matrix, then so is C^{-1}; this function returns the Toeplitz coefficients of this inverse.

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 Toeplitz coefficients of C^{-1}, of length n.