ctbrfs - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coefficient matrix
SUBROUTINE CTBRFS( UPLO, TRANSA, DIAG, N, NDIAG, NRHS, A, LDA, B, * LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER * 1 UPLO, TRANSA, DIAG COMPLEX A(LDA,*), B(LDB,*), X(LDX,*), WORK(*) INTEGER N, NDIAG, NRHS, LDA, LDB, LDX, INFO REAL FERR(*), BERR(*), WORK2(*)
SUBROUTINE CTBRFS_64( UPLO, TRANSA, DIAG, N, NDIAG, NRHS, A, LDA, B, * LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER * 1 UPLO, TRANSA, DIAG COMPLEX A(LDA,*), B(LDB,*), X(LDX,*), WORK(*) INTEGER*8 N, NDIAG, NRHS, LDA, LDB, LDX, INFO REAL FERR(*), BERR(*), WORK2(*)
SUBROUTINE TBRFS( UPLO, [TRANSA], DIAG, [N], NDIAG, [NRHS], A, [LDA], * B, [LDB], X, [LDX], FERR, BERR, [WORK], [WORK2], [INFO]) CHARACTER(LEN=1) :: UPLO, TRANSA, DIAG COMPLEX, DIMENSION(:) :: WORK COMPLEX, DIMENSION(:,:) :: A, B, X INTEGER :: N, NDIAG, NRHS, LDA, LDB, LDX, INFO REAL, DIMENSION(:) :: FERR, BERR, WORK2
SUBROUTINE TBRFS_64( UPLO, [TRANSA], DIAG, [N], NDIAG, [NRHS], A, * [LDA], B, [LDB], X, [LDX], FERR, BERR, [WORK], [WORK2], [INFO]) CHARACTER(LEN=1) :: UPLO, TRANSA, DIAG COMPLEX, DIMENSION(:) :: WORK COMPLEX, DIMENSION(:,:) :: A, B, X INTEGER(8) :: N, NDIAG, NRHS, LDA, LDB, LDX, INFO REAL, DIMENSION(:) :: FERR, BERR, WORK2
#include <sunperf.h>
void ctbrfs(char uplo, char transa, char diag, int n, int ndiag, int nrhs, complex *a, int lda, complex *b, int ldb, complex *x, int ldx, float *ferr, float *berr, int *info);
void ctbrfs_64(char uplo, char transa, char diag, long n, long ndiag, long nrhs, complex *a, long lda, complex *b, long ldb, complex *x, long ldx, float *ferr, float *berr, long *info);
ctbrfs provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coefficient matrix.
The solution matrix X must be computed by CTBTRS or some other means before entering this routine. CTBRFS does not do iterative refinement because doing so cannot improve the backward error.
= 'U': A is upper triangular;
= 'L': A is lower triangular.
= 'N': A * X = B (No transpose)
= 'T': A**T * X = B (Transpose)
= 'C': A**H * X = B (Conjugate transpose)
= 'N': A is non-unit triangular;
= 'U': A is unit triangular.
A(kd+1+i-j,j)
= A(i,j)
for max(1,j-kd)
< =i < =j;
if UPLO = 'L', A(1+i-j,j)
= A(i,j)
for j < =i < =min(n,j+kd).
If DIAG = 'U', the diagonal elements of A are not referenced
and are assumed to be 1.
X(j)
(the j-th column of the solution matrix X).
If XTRUE is the true solution corresponding to X(j), FERR(j)
is an estimated upper bound for the magnitude of the largest
element in (X(j) - XTRUE) divided by the magnitude of the
largest element in X(j). The estimate is as reliable as
the estimate for RCOND, and is almost always a slight
overestimate of the true error.
X(j)
(i.e., the smallest relative change in
any element of A or B that makes X(j)
an exact solution).
dimension(2*N)
dimension(N)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value