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

NAME

zgerfs - improve the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solution

SYNOPSIS

  SUBROUTINE ZGERFS( TRANSA, N, NRHS, A, LDA, AF, LDAF, IPIVOT, B, 
 *      LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO)
  CHARACTER * 1 TRANSA
  DOUBLE COMPLEX A(LDA,*), AF(LDAF,*), B(LDB,*), X(LDX,*), WORK(*)
  INTEGER N, NRHS, LDA, LDAF, LDB, LDX, INFO
  INTEGER IPIVOT(*)
  DOUBLE PRECISION FERR(*), BERR(*), WORK2(*)

  SUBROUTINE ZGERFS_64( TRANSA, N, NRHS, A, LDA, AF, LDAF, IPIVOT, B, 
 *      LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO)
  CHARACTER * 1 TRANSA
  DOUBLE COMPLEX A(LDA,*), AF(LDAF,*), B(LDB,*), X(LDX,*), WORK(*)
  INTEGER*8 N, NRHS, LDA, LDAF, LDB, LDX, INFO
  INTEGER*8 IPIVOT(*)
  DOUBLE PRECISION FERR(*), BERR(*), WORK2(*)

F95 INTERFACE

  SUBROUTINE GERFS( [TRANSA], [N], [NRHS], A, [LDA], AF, [LDAF], 
 *       IPIVOT, B, [LDB], X, [LDX], FERR, BERR, [WORK], [WORK2], [INFO])
  CHARACTER(LEN=1) :: TRANSA
  COMPLEX(8), DIMENSION(:) :: WORK
  COMPLEX(8), DIMENSION(:,:) :: A, AF, B, X
  INTEGER :: N, NRHS, LDA, LDAF, LDB, LDX, INFO
  INTEGER, DIMENSION(:) :: IPIVOT
  REAL(8), DIMENSION(:) :: FERR, BERR, WORK2

  SUBROUTINE GERFS_64( [TRANSA], [N], [NRHS], A, [LDA], AF, [LDAF], 
 *       IPIVOT, B, [LDB], X, [LDX], FERR, BERR, [WORK], [WORK2], [INFO])
  CHARACTER(LEN=1) :: TRANSA
  COMPLEX(8), DIMENSION(:) :: WORK
  COMPLEX(8), DIMENSION(:,:) :: A, AF, B, X
  INTEGER(8) :: N, NRHS, LDA, LDAF, LDB, LDX, INFO
  INTEGER(8), DIMENSION(:) :: IPIVOT
  REAL(8), DIMENSION(:) :: FERR, BERR, WORK2

C INTERFACE

#include <sunperf.h>

void zgerfs(char transa, int n, int nrhs, doublecomplex *a, int lda, doublecomplex *af, int ldaf, int *ipivot, doublecomplex *b, int ldb, doublecomplex *x, int ldx, double *ferr, double *berr, int *info);

void zgerfs_64(char transa, long n, long nrhs, doublecomplex *a, long lda, doublecomplex *af, long ldaf, long *ipivot, doublecomplex *b, long ldb, doublecomplex *x, long ldx, double *ferr, double *berr, long *info);

PURPOSE

zgerfs improves the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solution.

ARGUMENTS

• 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)

• 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 original N-by-N matrix A.

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

• AF (input)
  The factors L and U from the factorization A = P*L*U as computed by CGETRF.

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

• IPIVOT (input)
  The pivot indices from CGETRF; for 1 < =i < =N, row i of the matrix was interchanged with row IPIVOT(i).

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

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

• X (input/output)
  On entry, the solution matrix X, as computed by CGETRS. On exit, the improved 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