dsprfs

NAME

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

SYNOPSIS

  SUBROUTINE DSPRFS( UPLO, N, NRHS, A, AF, IPIVOT, B, LDB, X, LDX, 
 *      FERR, BERR, WORK, WORK2, INFO)
  CHARACTER * 1 UPLO
  INTEGER N, NRHS, LDB, LDX, INFO
  INTEGER IPIVOT(*), WORK2(*)
  DOUBLE PRECISION A(*), AF(*), B(LDB,*), X(LDX,*), FERR(*), BERR(*), WORK(*)
 
  SUBROUTINE DSPRFS_64( UPLO, N, NRHS, A, AF, IPIVOT, B, LDB, X, LDX, 
 *      FERR, BERR, WORK, WORK2, INFO)
  CHARACTER * 1 UPLO
  INTEGER*8 N, NRHS, LDB, LDX, INFO
  INTEGER*8 IPIVOT(*), WORK2(*)
  DOUBLE PRECISION A(*), AF(*), B(LDB,*), X(LDX,*), FERR(*), BERR(*), WORK(*)

F95 INTERFACE

  SUBROUTINE SPRFS( UPLO, N, NRHS, A, AF, IPIVOT, B, [LDB], X, [LDX], 
 *       FERR, BERR, [WORK], [WORK2], [INFO])
  CHARACTER(LEN=1) :: UPLO
  INTEGER :: N, NRHS, LDB, LDX, INFO
  INTEGER, DIMENSION(:) :: IPIVOT, WORK2
  REAL(8), DIMENSION(:) :: A, AF, FERR, BERR, WORK
  REAL(8), DIMENSION(:,:) :: B, X
 
  SUBROUTINE SPRFS_64( UPLO, N, NRHS, A, AF, IPIVOT, B, [LDB], X, [LDX], 
 *       FERR, BERR, [WORK], [WORK2], [INFO])
  CHARACTER(LEN=1) :: UPLO
  INTEGER(8) :: N, NRHS, LDB, LDX, INFO
  INTEGER(8), DIMENSION(:) :: IPIVOT, WORK2
  REAL(8), DIMENSION(:) :: A, AF, FERR, BERR, WORK
  REAL(8), DIMENSION(:,:) :: B, X

C INTERFACE

#include <sunperf.h>

void dsprfs(char uplo, int n, int nrhs, double *a, double *af, int *ipivot, double *b, int ldb, double *x, int ldx, double *ferr, double *berr, int *info);

void dsprfs_64(char uplo, long n, long nrhs, double *a, double *af, long *ipivot, double *b, long ldb, double *x, long ldx, double *ferr, double *berr, long *info);

PURPOSE

dsprfs improves the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite and packed, 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 upper or lower triangle of the symmetric matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array A as follows: if UPLO = 'U', A(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', A(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=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 SSPTRF, stored as a packed triangular matrix.
* IPIVOT (input): Details of the interchanges and the block structure of D as determined by SSPTRF.
* 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 SSPTRS. 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)