naginterfaces.library.linsys.real_toeplitz_solve(n, t, b, wantp)[source]

real_toeplitz_solve solves the equations , where is a real symmetric positive definite Toeplitz matrix.

For full information please refer to the NAG Library document for f04ff


The order of the Toeplitz matrix .

tfloat, array-like, shape

must contain the value , for .

bfloat, array-like, shape

The right-hand side vector .


Must be set to if the reflection coefficients are required, and must be set to otherwise.

xfloat, ndarray, shape

The solution vector .

pfloat, ndarray, shape

With as , the th element of contains the reflection coefficient, , for the th step, for . (See Further Comments.) If is , is not referenced.

(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

(errno )

Principal minor is not positive definite. Value of the reflection coefficient is .


No equivalent traditional C interface for this routine exists in the NAG Library.

real_toeplitz_solve solves the equations

where is the symmetric positive definite Toeplitz matrix

and is an -element vector.

The function uses the method of Levinson (see Levinson (1947) and Golub and Van Loan (1996)). Optionally, the reflection coefficients for each step may also be returned.


Bunch, J R, 1985, Stability of methods for solving Toeplitz systems of equations, SIAM J. Sci. Statist. Comput. (6), 349–364

Bunch, J R, 1987, The weak and strong stability of algorithms in numerical linear algebra, Linear Algebra Appl. (88/89), 49–66

Cybenko, G, 1980, The numerical stability of the Levinson–Durbin algorithm for Toeplitz systems of equations, SIAM J. Sci. Statist. Comput. (1), 303–319

Golub, G H and Van Loan, C F, 1996, Matrix Computations, (3rd Edition), Johns Hopkins University Press, Baltimore

Levinson, N, 1947, The Weiner RMS error criterion in filter design and prediction, J. Math. Phys. (25), 261–278