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

NAME

zsyrfs - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite, and provides error bounds and backward error estimates for the solution

SYNOPSIS

  SUBROUTINE ZSYRFS( UPLO, N, NRHS, A, LDA, AF, LDAF, IPIVOT, B, LDB, 
 *      X, LDX, FERR, BERR, WORK, WORK2, INFO)
  CHARACTER * 1 UPLO
  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 ZSYRFS_64( UPLO, N, NRHS, A, LDA, AF, LDAF, IPIVOT, B, 
 *      LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO)
  CHARACTER * 1 UPLO
  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 SYRFS( UPLO, [N], [NRHS], A, [LDA], AF, [LDAF], IPIVOT, 
 *       B, [LDB], X, [LDX], FERR, BERR, [WORK], [WORK2], [INFO])
  CHARACTER(LEN=1) :: UPLO
  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 SYRFS_64( UPLO, [N], [NRHS], A, [LDA], AF, [LDAF], 
 *       IPIVOT, B, [LDB], X, [LDX], FERR, BERR, [WORK], [WORK2], [INFO])
  CHARACTER(LEN=1) :: UPLO
  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 zsyrfs(char uplo, 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 zsyrfs_64(char uplo, 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

zsyrfs improves the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite, and provides error bounds and backward error estimates for the solution.

ARGUMENTS

• UPLO (input)
  

   = 'U':  Upper triangle of A is stored;

   = 'L':  Lower triangle of A is stored.

• 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 symmetric matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced.

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

• AF (input)
  The factored form of the matrix A. AF contains the block diagonal matrix D and the multipliers used to obtain the factor U or L from the factorization A = U*D*U**T or A = L*D*L**T as computed by CSYTRF.

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

• IPIVOT (input)
  Details of the interchanges and the block structure of D as determined by CSYTRF.

• 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 CSYTRS. 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