Refines the solution of a system of linear equations with a symmetric (Hermitian) positive-definite tridiagonal coefficient matrix and estimates its error.

Syntax

lapack_int LAPACKE_sptrfs( int matrix_layout, lapack_int n, lapack_int nrhs, const float* d, const float* e, const float* df, const float* ef, const float* b, lapack_int ldb, float* x, lapack_int ldx, float* ferr, float* berr );

lapack_int LAPACKE_dptrfs( int matrix_layout, lapack_int n, lapack_int nrhs, const double* d, const double* e, const double* df, const double* ef, const double* b, lapack_int ldb, double* x, lapack_int ldx, double* ferr, double* berr );

lapack_int LAPACKE_cptrfs( int matrix_layout, char uplo, lapack_int n, lapack_int nrhs, const float* d, const lapack_complex_float* e, const float* df, const lapack_complex_float* ef, const lapack_complex_float* b, lapack_int ldb, lapack_complex_float* x, lapack_int ldx, float* ferr, float* berr );

lapack_int LAPACKE_zptrfs( int matrix_layout, char uplo, lapack_int n, lapack_int nrhs, const double* d, const lapack_complex_double* e, const double* df, const lapack_complex_double* ef, const lapack_complex_double* b, lapack_int ldb, lapack_complex_double* x, lapack_int ldx, double* ferr, double* berr );

Include Files

  • mkl.h

Description

The routine performs an iterative refinement of the solution to a system of linear equations A*X = B with a symmetric (Hermitian) positive definite tridiagonal matrix A, with multiple right-hand sides. For each computed solution vector x, the routine computes the component-wise backward errorβ. This error is the smallest relative perturbation in elements of A and b such that x is the exact solution of the perturbed system:

|δaij| β|aij|, |δbi| β|bi| such that (A + δA)x = (b + δb).

Finally, the routine estimates the component-wise forward error in the computed solution ||x - xe||/||x|| (here xe is the exact solution).

Before calling this routine:

  • call the factorization routine ?pttrf

  • call the solver routine ?pttrs.

Input Parameters

matrix_layout

Specifies whether matrix storage layout is row major (LAPACK_ROW_MAJOR) or column major (LAPACK_COL_MAJOR).

uplo

Used for complex flavors only. Must be 'U' or 'L'.

Specifies whether the superdiagonal or the subdiagonal of the tridiagonal matrix A is stored and how A is factored:

If uplo = 'U', the array e stores the superdiagonal of A, and A is factored as UH*D*U.

If uplo = 'L', the array e stores the subdiagonal of A, and A is factored as L*D*LH.

n

The order of the matrix A; n 0.

nrhs

The number of right-hand sides; nrhs 0.

d

The array d (size n) contains the n diagonal elements of the tridiagonal matrix A.

df

The array df (size n) contains the n diagonal elements of the diagonal matrix D from the factorization of A as computed by ?pttrf.

e,ef,b,x

The array e (size n -1) contains the (n - 1) off-diagonal elements of the tridiagonal matrix A (see uplo).

The array ef (size n -1) contains the (n - 1) off-diagonal elements of the unit bidiagonal factor U or L from the factorization computed by ?pttrf (see uplo).

The array b of size max(1, ldb*nrhs) for column major layout and max(1, ldb*n) for row major layout contains the matrix B whose columns are the right-hand sides for the systems of equations.

The array x of size max(1, ldx*nrhs) for column major layout and max(1, ldx*n) for row major layout contains the solution matrix X as computed by ?pttrs.

ldb

The leading dimension of b; ldb max(1, n) for column major layout and ldbnrhs for row major layout.

ldx

The leading dimension of x; ldx max(1, n) for column major layout and ldxnrhs for row major layout.

Output Parameters

x

The refined solution matrix X.

ferr, berr

Arrays, size at least max(1, nrhs). Contain the component-wise forward and backward errors, respectively, for each solution vector.

Return Values

This function returns a value info.

If info = 0, the execution is successful.

If info = -i, parameter i had an illegal value.

For more complete information about compiler optimizations, see our Optimization Notice.
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