Which linear function of SciPy is used to solve Toeplitz matrix using Levinson Recursion?

The linear function named scipy.linalg.solve_toeplitz is used to solve the Toeplitz matrix equation. The form of this function is as follows −

scipy.linalg.solve_toeplitz(c_or_cr, b, check_finite=True)

This linear function will solve the equation Tx = b for x where T is the Toeplitz matrix.


Below are given the parameters of the function scipy.linalg.solve_toeplitz()

  • c_or_cr− array_like or tuple of (array_like, array_like)

This parameter is the vector c or tuple of arrays (c, r). Despite the actual shape of c, it will always be converted to a one-dimensional array. If r is not given, the assumption made is r = conjugate(c). Below are given two cases −

                  v If c[0] is real, the Toeplitz matrix is Hermitian.

                  v If r[0] is ignored, the first row of this matrix will be [c[0], r[1:]].

Despite the actual shape of r, it will also be converted to a one-dimensional array.

  • b− (M,) or (M, K)array_like

This parameter represents the right-hand side matrix in the equation Tx = b.

check_finite− bool, optional

This parameter is used to check whether the input matrices contain only finite numbers or not. We may get some performance gain after disabling it. It may result in problems if the inputs do not contain infinities.


  • x− (M,) or (M, K) ndarray

    It returns the solution of the the Toeplitz matrix equation Tx = b. The shape of the output will depend on the shape of b.