cherfs

NAME

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

SYNOPSIS

  SUBROUTINE CHERFS( UPLO, N, NRHS, A, LDA, AF, LDAF, IPIVOT, B, LDB, 
 *      X, LDX, FERR, BERR, WORK, WORK2, INFO)
  CHARACTER * 1 UPLO
  COMPLEX A(LDA,*), AF(LDAF,*), B(LDB,*), X(LDX,*), WORK(*)
  INTEGER N, NRHS, LDA, LDAF, LDB, LDX, INFO
  INTEGER IPIVOT(*)
  REAL FERR(*), BERR(*), WORK2(*)
 
  SUBROUTINE CHERFS_64( UPLO, N, NRHS, A, LDA, AF, LDAF, IPIVOT, B, 
 *      LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO)
  CHARACTER * 1 UPLO
  COMPLEX A(LDA,*), AF(LDAF,*), B(LDB,*), X(LDX,*), WORK(*)
  INTEGER*8 N, NRHS, LDA, LDAF, LDB, LDX, INFO
  INTEGER*8 IPIVOT(*)
  REAL FERR(*), BERR(*), WORK2(*)

F95 INTERFACE

  SUBROUTINE HERFS( UPLO, [N], [NRHS], A, [LDA], AF, [LDAF], IPIVOT, 
 *       B, [LDB], X, [LDX], FERR, BERR, [WORK], [WORK2], [INFO])
  CHARACTER(LEN=1) :: UPLO
  COMPLEX, DIMENSION(:) :: WORK
  COMPLEX, DIMENSION(:,:) :: A, AF, B, X
  INTEGER :: N, NRHS, LDA, LDAF, LDB, LDX, INFO
  INTEGER, DIMENSION(:) :: IPIVOT
  REAL, DIMENSION(:) :: FERR, BERR, WORK2
 
  SUBROUTINE HERFS_64( UPLO, [N], [NRHS], A, [LDA], AF, [LDAF], 
 *       IPIVOT, B, [LDB], X, [LDX], FERR, BERR, [WORK], [WORK2], [INFO])
  CHARACTER(LEN=1) :: UPLO
  COMPLEX, DIMENSION(:) :: WORK
  COMPLEX, DIMENSION(:,:) :: A, AF, B, X
  INTEGER(8) :: N, NRHS, LDA, LDAF, LDB, LDX, INFO
  INTEGER(8), DIMENSION(:) :: IPIVOT
  REAL, DIMENSION(:) :: FERR, BERR, WORK2

C INTERFACE

#include <sunperf.h>

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

void cherfs_64(char uplo, long n, long nrhs, complex *a, long lda, complex *af, long ldaf, long *ipivot, complex *b, long ldb, complex *x, long ldx, float *ferr, float *berr, long *info);

PURPOSE

cherfs improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian indefinite, 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 Hermitian 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 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**H or A = L*D*L**H as computed by CHETRF.
* LDAF (input): The leading dimension of the array AF. LDAF >= max(1,N).
* IPIVOT (input): Details of the interchanges and the block structure of D as determined by CHETRF.
* 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 CHETRS. 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)