solve_toeplitz(c_or_cr, b, check_finite=True)[source]¶
Solve a Toeplitz system using Levinson Recursion
The Toeplitz matrix has constant diagonals, with c as its first column and r as its first row. If r is not given,
r == conjugate(c)is assumed.
c_or_cr : array_like or tuple of (array_like, array_like)
c, or a tuple of arrays (
r). Whatever the actual shape of
c, it will be converted to a 1-D array. If not supplied,
r = conjugate(c)is assumed; in this case, if c is real, the Toeplitz matrix is Hermitian. r is ignored; the first row of the Toeplitz matrix is
[c, r[1:]]. Whatever the actual shape of
r, it will be converted to a 1-D array.
b : (M,) or (M, K) array_like
Right-hand side in
T x = b.
check_finite : bool, optional
Whether to check that the input matrices contain only finite numbers. Disabling may give a performance gain, but may result in problems (result entirely NaNs) if the inputs do contain infinities or NaNs.
x : (M,) or (M, K) ndarray
The solution to the system
T x = b. Shape of return matches shape of b.
The solution is computed using Levinson-Durbin recursion, which is faster than generic least-squares methods, but can be less numerically stable.