zsprfs

NAME

zsprfs - 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 ZSPRFS( UPLO, N, NRHS, A, AF, IPIVOT, B, LDB, X, LDX, 
 *      FERR, BERR, WORK, WORK2, INFO)
  CHARACTER * 1 UPLO
  DOUBLE COMPLEX A(*), AF(*), B(LDB,*), X(LDX,*), WORK(*)
  INTEGER N, NRHS, LDB, LDX, INFO
  INTEGER IPIVOT(*)
  DOUBLE PRECISION FERR(*), BERR(*), WORK2(*)
 
  SUBROUTINE ZSPRFS_64( UPLO, N, NRHS, A, AF, IPIVOT, B, LDB, X, LDX, 
 *      FERR, BERR, WORK, WORK2, INFO)
  CHARACTER * 1 UPLO
  DOUBLE COMPLEX A(*), AF(*), B(LDB,*), X(LDX,*), WORK(*)
  INTEGER*8 N, NRHS, LDB, LDX, INFO
  INTEGER*8 IPIVOT(*)
  DOUBLE PRECISION FERR(*), BERR(*), WORK2(*)

F95 INTERFACE

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

C INTERFACE

#include <sunperf.h>

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

void zsprfs_64(char uplo, long n, long nrhs, doublecomplex *a, doublecomplex *af, long *ipivot, doublecomplex *b, long ldb, doublecomplex *x, long ldx, double *ferr, double *berr, long *info);

PURPOSE

zsprfs 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 CSPTRF, stored as a packed triangular matrix.
* IPIVOT (input): Details of the interchanges and the block structure of D as determined by CSPTRF.
* 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 CSPTRS. 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)
* INFO (output)