dhst01()

subroutine dhst01	(	integer	N,
		integer	ILO,
		integer	IHI,
		double precision, dimension( lda, * )	A,
		integer	LDA,
		double precision, dimension( ldh, * )	H,
		integer	LDH,
		double precision, dimension( ldq, * )	Q,
		integer	LDQ,
		double precision, dimension( lwork )	WORK,
		integer	LWORK,
		double precision, dimension( 2 )	RESULT
	)

DHST01

Purpose:

 DHST01 tests the reduction of a general matrix A to upper Hessenberg
 form:  A = Q*H*Q'.  Two test ratios are computed;

 RESULT(1) = norm( A - Q*H*Q' ) / ( norm(A) * N * EPS )
 RESULT(2) = norm( I - Q'*Q ) / ( N * EPS )

 The matrix Q is assumed to be given explicitly as it would be
 following DGEHRD + DORGHR.

 In this version, ILO and IHI are not used and are assumed to be 1 and
 N, respectively.

Parameters

[in]	N	N is INTEGER The order of the matrix A. N >= 0.
[in]	ILO	ILO is INTEGER
[in]	IHI	IHI is INTEGER A is assumed to be upper triangular in rows and columns 1:ILO-1 and IHI+1:N, so Q differs from the identity only in rows and columns ILO+1:IHI.
[in]	A	A is DOUBLE PRECISION array, dimension (LDA,N) The original n by n matrix A.
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).
[in]	H	H is DOUBLE PRECISION array, dimension (LDH,N) The upper Hessenberg matrix H from the reduction A = Q*H*Q' as computed by DGEHRD. H is assumed to be zero below the first subdiagonal.
[in]	LDH	LDH is INTEGER The leading dimension of the array H. LDH >= max(1,N).
[in]	Q	Q is DOUBLE PRECISION array, dimension (LDQ,N) The orthogonal matrix Q from the reduction A = Q*H*Q' as computed by DGEHRD + DORGHR.
[in]	LDQ	LDQ is INTEGER The leading dimension of the array Q. LDQ >= max(1,N).
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (LWORK)
[in]	LWORK	LWORK is INTEGER The length of the array WORK. LWORK >= 2*N*N.
[out]	RESULT	RESULT is DOUBLE PRECISION array, dimension (2) RESULT(1) = norm( A - Q*H*Q' ) / ( norm(A) * N * EPS ) RESULT(2) = norm( I - Q'*Q ) / ( N * EPS )

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.