scipy.linalg.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)

The vector c, or a tuple of arrays (c, 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[0] is real, the Toeplitz matrix is Hermitian. r[0] is ignored; the first row of the Toeplitz matrix is [c[0], 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.