Estimates the error in the solution of a system of linear equations with a triangular band coefficient matrix.

Syntax

lapack_int LAPACKE_stbrfs( int matrix_layout, char uplo, char trans, char diag, lapack_int n, lapack_int kd, lapack_int nrhs, const float* ab, lapack_int ldab, const float* b, lapack_int ldb, const float* x, lapack_int ldx, float* ferr, float* berr );

lapack_int LAPACKE_dtbrfs( int matrix_layout, char uplo, char trans, char diag, lapack_int n, lapack_int kd, lapack_int nrhs, const double* ab, lapack_int ldab, const double* b, lapack_int ldb, const double* x, lapack_int ldx, double* ferr, double* berr );

lapack_int LAPACKE_ctbrfs( int matrix_layout, char uplo, char trans, char diag, lapack_int n, lapack_int kd, lapack_int nrhs, const lapack_complex_float* ab, lapack_int ldab, const lapack_complex_float* b, lapack_int ldb, const lapack_complex_float* x, lapack_int ldx, float* ferr, float* berr );

lapack_int LAPACKE_ztbrfs( int matrix_layout, char uplo, char trans, char diag, lapack_int n, lapack_int kd, lapack_int nrhs, const lapack_complex_double* ab, lapack_int ldab, const lapack_complex_double* b, lapack_int ldb, const lapack_complex_double* x, lapack_int ldx, double* ferr, double* berr );

Include Files

  • mkl.h

Description

The routine estimates the errors in the solution to a system of linear equations A*X = B or AT*X = B or AH*X = B with a triangular band 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).

The routine also 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 solver routine ?tbtrs.

Input Parameters

matrix_layout

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

uplo

Must be 'U' or 'L'.

Indicates whether A is upper or lower triangular:

If uplo = 'U', then A is upper triangular.

If uplo = 'L', then A is lower triangular.

trans

Must be 'N' or 'T' or 'C'.

Indicates the form of the equations:

If trans = 'N', the system has the form A*X = B.

If trans = 'T', the system has the form AT*X = B.

If trans = 'C', the system has the form AH*X = B.

diag

Must be 'N' or 'U'.

If diag = 'N', A is not a unit triangular matrix.

If diag = 'U', A is unit triangular: diagonal elements of A are assumed to be 1 and not referenced in the array ab.

n

The order of the matrix A; n 0.

kd

The number of super-diagonals or sub-diagonals in the matrix A; kd 0.

nrhs

The number of right-hand sides; nrhs 0.

ab, b, x

Arrays:

ab(size max(1, ldab*n)) contains the upper or lower triangular matrix A, as specified by uplo, in band storage format.

bof size max(1, ldb*nrhs) for column major layout and max(1, ldb*n) for row major layout contains the right-hand side matrix B.

xof size max(1, ldx*nrhs) for column major layout and max(1, ldx*n) for row major layout contains the solution matrix X.

ldab

The leading dimension of the array ab; ldabkd +1.

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; ldb max(1, n) for column major layout and ldbnrhs for row major layout.

Output Parameters

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.

Application Notes

The bounds returned in ferr are not rigorous, but in practice they almost always overestimate the actual error.

A call to this routine involves, for each right-hand side, solving a number of systems of linear equations A*x = b; the number of systems is usually 4 or 5 and never more than 11. Each solution requires approximately 2n*kd floating-point operations for real flavors or 8n*kd operations for complex flavors.

Para obter informações mais completas sobre otimizações do compilador, consulte nosso aviso de otimização.
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