# scipy.linalg.solve_toeplitz¶

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.

Parameters: 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 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.

Notes

The solution is computed using Levinson-Durbin recursion, which is faster than generic least-squares methods, but can be less numerically stable.

#### Previous topic

scipy.linalg.solve_triangular

scipy.linalg.det