ztbrfs

NAME

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

SYNOPSIS

  SUBROUTINE ZTBRFS( UPLO, TRANSA, DIAG, N, NDIAG, NRHS, A, LDA, B, 
 *      LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO)
  CHARACTER * 1 UPLO, TRANSA, DIAG
  DOUBLE COMPLEX A(LDA,*), B(LDB,*), X(LDX,*), WORK(*)
  INTEGER N, NDIAG, NRHS, LDA, LDB, LDX, INFO
  DOUBLE PRECISION FERR(*), BERR(*), WORK2(*)
 
  SUBROUTINE ZTBRFS_64( UPLO, TRANSA, DIAG, N, NDIAG, NRHS, A, LDA, B, 
 *      LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO)
  CHARACTER * 1 UPLO, TRANSA, DIAG
  DOUBLE COMPLEX A(LDA,*), B(LDB,*), X(LDX,*), WORK(*)
  INTEGER*8 N, NDIAG, NRHS, LDA, LDB, LDX, INFO
  DOUBLE PRECISION FERR(*), BERR(*), WORK2(*)

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

C INTERFACE

#include <sunperf.h>

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

void ztbrfs_64(char uplo, char transa, char diag, long n, long ndiag, long nrhs, doublecomplex *a, long lda, doublecomplex *b, long ldb, doublecomplex *x, long ldx, double *ferr, double *berr, long *info);

PURPOSE

ztbrfs 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.

ARGUMENTS

* UPLO (input)
* TRANSA (input): Specifies the form of the system of equations:
* DIAG (input)
* 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(2*N)
* WORK2 (workspace)
* INFO (output)