zhprfs.f File Reference

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Functions/Subroutines
subroutine	ZHPRFS (UPLO, N, NRHS, AP, AFP, IPIV, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO)
	ZHPRFS

---

Function/Subroutine Documentation

subroutine ZHPRFS	(	CHARACTER	UPLO,
		INTEGER	N,
		INTEGER	NRHS,
		COMPLEX*16, dimension( * )	AP,
		COMPLEX*16, dimension( * )	AFP,
		INTEGER, dimension( * )	IPIV,
		COMPLEX*16, dimension( ldb, * )	B,
		INTEGER	LDB,
		COMPLEX*16, dimension( ldx, * )	X,
		INTEGER	LDX,
		DOUBLE PRECISION, dimension( * )	FERR,
		DOUBLE PRECISION, dimension( * )	BERR,
		COMPLEX*16, dimension( * )	WORK,
		DOUBLE PRECISION, dimension( * )	RWORK,
		INTEGER	INFO
	)

ZHPRFS

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Purpose:

 ZHPRFS improves the computed solution to a system of linear
 equations when the coefficient matrix is Hermitian indefinite
 and packed, and provides error bounds and backward error estimates
 for the solution.
 

Parameters:

[in]	UPLO	UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored.
[in]	N	N is INTEGER The order of the matrix A. N >= 0.
[in]	NRHS	NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrices B and X. NRHS >= 0.
[in]	AP	AP is COMPLEX*16 array, dimension (N*(N+1)/2) 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 AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
[in]	AFP	AFP is COMPLEX*16 array, dimension (N*(N+1)/2) The factored form of the matrix A. AFP 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 ZHPTRF, stored as a packed triangular matrix.
[in]	IPIV	IPIV is INTEGER array, dimension (N) Details of the interchanges and the block structure of D as determined by ZHPTRF.
[in]	B	B is COMPLEX*16 array, dimension (LDB,NRHS) The right hand side matrix B.
[in]	LDB	LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).
[in,out]	X	X is COMPLEX*16 array, dimension (LDX,NRHS) On entry, the solution matrix X, as computed by ZHPTRS. On exit, the improved solution matrix X.
[in]	LDX	LDX is INTEGER The leading dimension of the array X. LDX >= max(1,N).
[out]	FERR	FERR is DOUBLE PRECISION array, dimension (NRHS) 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.
[out]	BERR	BERR is DOUBLE PRECISION array, dimension (NRHS) 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).
[out]	WORK	WORK is COMPLEX*16 array, dimension (2*N)
[out]	RWORK	RWORK is DOUBLE PRECISION array, dimension (N)
[out]	INFO	INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value

Internal Parameters:

  ITMAX is the maximum number of steps of iterative refinement.
 

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2011

Definition at line 180 of file zhprfs.f.

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