• NAME
• SYNOPSIS
• F95 INTERFACE
• C INTERFACE
• PURPOSE
• ARGUMENTS

NAME

dtbrfs - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coefficient matrix

SYNOPSIS

  SUBROUTINE DTBRFS( UPLO, TRANSA, DIAG, N, NDIAG, NRHS, A, LDA, B, 
 *      LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO)
  CHARACTER * 1 UPLO, TRANSA, DIAG
  INTEGER N, NDIAG, NRHS, LDA, LDB, LDX, INFO
  INTEGER WORK2(*)
  DOUBLE PRECISION A(LDA,*), B(LDB,*), X(LDX,*), FERR(*), BERR(*), WORK(*)

  SUBROUTINE DTBRFS_64( UPLO, TRANSA, DIAG, N, NDIAG, NRHS, A, LDA, B, 
 *      LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO)
  CHARACTER * 1 UPLO, TRANSA, DIAG
  INTEGER*8 N, NDIAG, NRHS, LDA, LDB, LDX, INFO
  INTEGER*8 WORK2(*)
  DOUBLE PRECISION A(LDA,*), B(LDB,*), X(LDX,*), FERR(*), BERR(*), WORK(*)

F95 INTERFACE

  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
  INTEGER :: N, NDIAG, NRHS, LDA, LDB, LDX, INFO
  INTEGER, DIMENSION(:) :: WORK2
  REAL(8), DIMENSION(:) :: FERR, BERR, WORK
  REAL(8), DIMENSION(:,:) :: A, B, X

  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
  INTEGER(8) :: N, NDIAG, NRHS, LDA, LDB, LDX, INFO
  INTEGER(8), DIMENSION(:) :: WORK2
  REAL(8), DIMENSION(:) :: FERR, BERR, WORK
  REAL(8), DIMENSION(:,:) :: A, B, X

C INTERFACE

#include <sunperf.h>

void dtbrfs(char uplo, char transa, char diag, int n, int ndiag, int nrhs, double *a, int lda, double *b, int ldb, double *x, int ldx, double *ferr, double *berr, int *info);

void dtbrfs_64(char uplo, char transa, char diag, long n, long ndiag, long nrhs, double *a, long lda, double *b, long ldb, double *x, long ldx, double *ferr, double *berr, long *info);

PURPOSE

dtbrfs 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 STBTRS or some other means before entering this routine. STBRFS does not do iterative refinement because doing so cannot improve the backward error.

ARGUMENTS

• UPLO (input)
  

   = 'U':  A is upper triangular;

   = 'L':  A is lower triangular.

• TRANSA (input)
  Specifies the form of the system of equations:

   = 'N':  A * X  = B  (No transpose)

   = 'T':  A**T * X  = B  (Transpose)

   = 'C':  A**H * X  = B  (Conjugate transpose  = Transpose)

• DIAG (input)
  

   = 'N':  A is non-unit triangular;

   = 'U':  A is unit triangular.

• N (input)
  The order of the matrix A. N > = 0.

• NDIAG (input)
  The number of superdiagonals or subdiagonals of the triangular band matrix A. NDIAG > = 0.

• NRHS (input)
  The number of right hand sides, i.e., the number of columns of the matrices B and X. NRHS > = 0.

• A (input)
  The upper or lower triangular band matrix A, stored in the first kd+1 rows of the array. The j-th column of A is stored in the j-th column of the array A as follows: if UPLO = 'U', 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.

• LDA (input)
  The leading dimension of the array A. LDA > = NDIAG+1.

• B (input)
  The right hand side matrix B.

• LDB (input)
  The leading dimension of the array B. LDB > = max(1,N).

• X (input)
  The solution matrix X.

• LDX (input)
  The leading dimension of the array X. LDX > = max(1,N).

• FERR (output)
  The estimated forward error bound for each solution vector 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.

• BERR (output)
  The componentwise relative backward error of each solution vector X(j) (i.e., the smallest relative change in any element of A or B that makes X(j) an exact solution).

• WORK (workspace)
  dimension(3*N)

• WORK2 (workspace)
  dimension(N)

• INFO (output)
  

   = 0:  successful exit

   < 0:  if INFO  = -i, the i-th argument had an illegal value