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

NAME

sporfs - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite,

SYNOPSIS

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

  SUBROUTINE SPORFS_64( UPLO, N, NRHS, A, LDA, AF, LDAF, B, LDB, X, 
 *      LDX, FERR, BERR, WORK, WORK2, INFO)
  CHARACTER * 1 UPLO
  INTEGER*8 N, NRHS, LDA, LDAF, LDB, LDX, INFO
  INTEGER*8 WORK2(*)
  REAL A(LDA,*), AF(LDAF,*), B(LDB,*), X(LDX,*), FERR(*), BERR(*), WORK(*)

F95 INTERFACE

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

  SUBROUTINE PORFS_64( UPLO, [N], [NRHS], A, [LDA], AF, [LDAF], 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(:) :: WORK2
  REAL, DIMENSION(:) :: FERR, BERR, WORK
  REAL, DIMENSION(:,:) :: A, AF, B, X

C INTERFACE

#include <sunperf.h>

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

void sporfs_64(char uplo, long n, long nrhs, float *a, long lda, float *af, long ldaf, float *b, long ldb, float *x, long ldx, float *ferr, float *berr, long *info);

PURPOSE

sporfs improves the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite, 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 triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T, as computed by SPOTRF.

• LDAF (input)
  The leading dimension of the array AF. LDAF > = 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/output)
  On entry, the solution matrix X, as computed by SPOTRS. 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)
  dimension(N)

• INFO (output)
  

   = 0:  successful exit

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