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

NAME

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

SYNOPSIS

  SUBROUTINE CTRRFS( UPLO, TRANSA, DIAG, N, 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, NRHS, LDA, LDB, LDX, INFO
  REAL FERR(*), BERR(*), WORK2(*)

  SUBROUTINE CTRRFS_64( UPLO, TRANSA, DIAG, N, 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, NRHS, LDA, LDB, LDX, INFO
  REAL FERR(*), BERR(*), WORK2(*)

F95 INTERFACE

  SUBROUTINE TRRFS( UPLO, [TRANSA], DIAG, [N], [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, NRHS, LDA, LDB, LDX, INFO
  REAL, DIMENSION(:) :: FERR, BERR, WORK2

  SUBROUTINE TRRFS_64( UPLO, [TRANSA], DIAG, [N], [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, NRHS, LDA, LDB, LDX, INFO
  REAL, DIMENSION(:) :: FERR, BERR, WORK2

C INTERFACE

#include <sunperf.h>

void ctrrfs(char uplo, char transa, char diag, int n, int nrhs, complex *a, int lda, complex *b, int ldb, complex *x, int ldx, float *ferr, float *berr, int *info);

void ctrrfs_64(char uplo, char transa, char diag, long n, long nrhs, complex *a, long lda, complex *b, long ldb, complex *x, long ldx, float *ferr, float *berr, long *info);

PURPOSE

ctrrfs provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix.

The solution matrix X must be computed by CTRTRS or some other means before entering this routine. CTRRFS 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)

• DIAG (input)
  

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

   = 'U':  A is unit triangular.

• N (input)
  The order of the matrix A. N > = 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 triangular matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of the array A contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading N-by-N lower triangular part of the array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced. If DIAG = 'U', the diagonal elements of A are also not referenced and are assumed to be 1.

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

• 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)
  dimension(N)

• INFO (output)
  

   = 0:  successful exit

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