cpprfs

NAME

cpprfs - improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and packed, and provides error bounds and backward error estimates for the solution

SYNOPSIS

  SUBROUTINE CPPRFS( UPLO, N, NRHS, A, AF, B, LDB, X, LDX, FERR, BERR, 
 *      WORK, WORK2, INFO)
  CHARACTER * 1 UPLO
  COMPLEX A(*), AF(*), B(LDB,*), X(LDX,*), WORK(*)
  INTEGER N, NRHS, LDB, LDX, INFO
  REAL FERR(*), BERR(*), WORK2(*)
 
  SUBROUTINE CPPRFS_64( UPLO, N, NRHS, A, AF, B, LDB, X, LDX, FERR, 
 *      BERR, WORK, WORK2, INFO)
  CHARACTER * 1 UPLO
  COMPLEX A(*), AF(*), B(LDB,*), X(LDX,*), WORK(*)
  INTEGER*8 N, NRHS, LDB, LDX, INFO
  REAL FERR(*), BERR(*), WORK2(*)

F95 INTERFACE

  SUBROUTINE PPRFS( UPLO, N, [NRHS], A, AF, B, [LDB], X, [LDX], FERR, 
 *       BERR, [WORK], [WORK2], [INFO])
  CHARACTER(LEN=1) :: UPLO
  COMPLEX, DIMENSION(:) :: A, AF, WORK
  COMPLEX, DIMENSION(:,:) :: B, X
  INTEGER :: N, NRHS, LDB, LDX, INFO
  REAL, DIMENSION(:) :: FERR, BERR, WORK2
 
  SUBROUTINE PPRFS_64( UPLO, N, [NRHS], A, AF, B, [LDB], X, [LDX], 
 *       FERR, BERR, [WORK], [WORK2], [INFO])
  CHARACTER(LEN=1) :: UPLO
  COMPLEX, DIMENSION(:) :: A, AF, WORK
  COMPLEX, DIMENSION(:,:) :: B, X
  INTEGER(8) :: N, NRHS, LDB, LDX, INFO
  REAL, DIMENSION(:) :: FERR, BERR, WORK2

C INTERFACE

#include <sunperf.h>

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

void cpprfs_64(char uplo, long n, long nrhs, complex *a, complex *af, complex *b, long ldb, complex *x, long ldx, float *ferr, float *berr, long *info);

PURPOSE

cpprfs improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite 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 Hermitian 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)*(2n-j)/2) = A(i,j) for j<=i<=n.
* AF (input): The triangular factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H, as computed by SPPTRF/CPPTRF, packed columnwise in a linear array in the same format as A (see A).
* 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 CPPTRS. 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)