vsip_dcovsol_p - Solve a Covariance System of Equations

Core

This manual is preliminary and incomplete.
While our Core implementation implements all functions given in the standard we are still working on completing this documentation.

Please refer to the VSIPL standard for a complete function reference of the Core profile until we have completed work on this documentation.

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6.2.2 vsip_dcovsol_p - Solve a Covariance System of Equations

int vsip_covsol_f(const vsip_vview_f* r, const vsip_vview_f* b, const vsip_vview_f* x); 
int vsip_ccovsol_f(const vsip_cvview_f* r, const vsip_cvview_f* b, const vsip_cvview_f* x);

Description

This function solves a covariance system of linear equations $Tx =b$ , where T is a symmetric positive definite Toeplitz covariance matrix defined by its first column r, b is the right-hand side vector, and x is the solution vector. The covariance matrix is a special type of Toeplitz matrix where the first column r completely defines the matrix structure.

This function is particularly useful in signal processing applications such as linear prediction and Wiener filtering, where covariance matrices frequently appear.

Parameters

const vsip_dvview_p* r: Pointer to the vector view containing the first column of the covariance matrix (autocorrelation sequence). The length of this vector determines the size of the covariance matrix.
const vsip_dvview_p* b: Pointer to the vector view containing the right-hand side vector.
const vsip_dvview_p* x: Pointer to the vector view where the solution will be stored.

Return Value

Returns 0 on success.
Returns a non-zero value on error (e.g., if the covariance matrix is singular or not positive definite).

Example

vsip_vview_f *covariance_vector; 
vsip_vview_f *rhs_vector; 
vsip_vview_f *solution_vector; 
int result; 
 
// Assuming all vector views have been properly initialized 
// and covariance_vector contains the autocorrelation sequence 
result = vsip_covsol_f(covariance_vector, rhs_vector, solution_vector); 
 
if (result != 0) { 
    // Handle error (e.g., singular or non-positive definite matrix) 
}

Notes

The covariance matrix is assumed to be symmetric and positive definite.
The length of the covariance vector r should be one more than the length of vectors b and x.
This function uses a Levinson-Durbin recursion algorithm for efficient solution of the covariance system.

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