sporfs

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)
* 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)
* INFO (output)