NAME

SYNOPSIS

  SUBROUTINE SSYRFS( UPLO, N, NRHS, A, LDA, AF, LDAF, IPIVOT, B, LDB, 
 *      X, LDX, FERR, BERR, WORK, WORK2, INFO)
  CHARACTER * 1 UPLO
  INTEGER N, NRHS, LDA, LDAF, LDB, LDX, INFO
  INTEGER IPIVOT(*), WORK2(*)
  REAL A(LDA,*), AF(LDAF,*), B(LDB,*), X(LDX,*), FERR(*), BERR(*), WORK(*)
 
  SUBROUTINE SSYRFS_64( UPLO, N, NRHS, A, LDA, AF, LDAF, IPIVOT, B, 
 *      LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO)
  CHARACTER * 1 UPLO
  INTEGER*8 N, NRHS, LDA, LDAF, LDB, LDX, INFO
  INTEGER*8 IPIVOT(*), WORK2(*)
  REAL A(LDA,*), AF(LDAF,*), B(LDB,*), X(LDX,*), FERR(*), BERR(*), WORK(*)
 

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
  INTEGER :: N, NRHS, LDA, LDAF, LDB, LDX, INFO
  INTEGER, DIMENSION(:) :: IPIVOT, WORK2
  REAL, DIMENSION(:) :: FERR, BERR, WORK
  REAL, DIMENSION(:,:) :: A, AF, B, X
 
  SUBROUTINE SYRFS_64( UPLO, N, NRHS, A, [LDA], AF, [LDAF], IPIVOT, B, 
 *       [LDB], X, [LDX], FERR, BERR, [WORK], [WORK2], [INFO])
  CHARACTER(LEN=1) :: UPLO
  INTEGER(8) :: N, NRHS, LDA, LDAF, LDB, LDX, INFO
  INTEGER(8), DIMENSION(:) :: IPIVOT, WORK2
  REAL, DIMENSION(:) :: FERR, BERR, WORK
  REAL, DIMENSION(:,:) :: A, AF, B, X
 

C INTERFACE

void ssyrfs(char uplo, int n, int nrhs, float *a, int lda, float *af, int ldaf, int *ipivot, float *b, int ldb, float *x, int ldx, float *ferr, float *berr, int *info);

void ssyrfs_64(char uplo, long n, long nrhs, float *a, long lda, float *af, long ldaf, long *ipivot, float *b, long ldb, float *x, long ldx, float *ferr, float *berr, long *info);

PURPOSE

ARGUMENTS

* UPLO (input)

* 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 SSYTRF.

* 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 SSYTRF.

* 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 SSYTRS. 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(3*N)

* WORK2 (workspace)

* INFO (output)