LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ zhst01()

 subroutine zhst01 ( integer N, integer ILO, integer IHI, complex*16, dimension( lda, * ) A, integer LDA, complex*16, dimension( ldh, * ) H, integer LDH, complex*16, dimension( ldq, * ) Q, integer LDQ, complex*16, dimension( lwork ) WORK, integer LWORK, double precision, dimension( * ) RWORK, double precision, dimension( 2 ) RESULT )

ZHST01

Purpose:
``` ZHST01 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 ZGEHRD + ZUNGHR.

In this version, ILO and IHI are not used, but they could be used
to save some work if this is desired.```
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 COMPLEX*16 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 COMPLEX*16 array, dimension (LDH,N) The upper Hessenberg matrix H from the reduction A = Q*H*Q' as computed by ZGEHRD. 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 COMPLEX*16 array, dimension (LDQ,N) The orthogonal matrix Q from the reduction A = Q*H*Q' as computed by ZGEHRD + ZUNGHR.``` [in] LDQ ``` LDQ is INTEGER The leading dimension of the array Q. LDQ >= max(1,N).``` [out] WORK ` WORK is COMPLEX*16 array, dimension (LWORK)` [in] LWORK ``` LWORK is INTEGER The length of the array WORK. LWORK >= 2*N*N.``` [out] RWORK ` RWORK is DOUBLE PRECISION array, dimension (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 )```

Definition at line 138 of file zhst01.f.

140*
141* -- LAPACK test routine --
142* -- LAPACK is a software package provided by Univ. of Tennessee, --
143* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
144*
145* .. Scalar Arguments ..
146 INTEGER IHI, ILO, LDA, LDH, LDQ, LWORK, N
147* ..
148* .. Array Arguments ..
149 DOUBLE PRECISION RESULT( 2 ), RWORK( * )
150 COMPLEX*16 A( LDA, * ), H( LDH, * ), Q( LDQ, * ),
151 \$ WORK( LWORK )
152* ..
153*
154* =====================================================================
155*
156* .. Parameters ..
157 DOUBLE PRECISION ONE, ZERO
158 parameter( one = 1.0d+0, zero = 0.0d+0 )
159* ..
160* .. Local Scalars ..
161 INTEGER LDWORK
162 DOUBLE PRECISION ANORM, EPS, OVFL, SMLNUM, UNFL, WNORM
163* ..
164* .. External Functions ..
165 DOUBLE PRECISION DLAMCH, ZLANGE
166 EXTERNAL dlamch, zlange
167* ..
168* .. External Subroutines ..
169 EXTERNAL dlabad, zgemm, zlacpy, zunt01
170* ..
171* .. Intrinsic Functions ..
172 INTRINSIC dcmplx, max, min
173* ..
174* .. Executable Statements ..
175*
176* Quick return if possible
177*
178 IF( n.LE.0 ) THEN
179 result( 1 ) = zero
180 result( 2 ) = zero
181 RETURN
182 END IF
183*
184 unfl = dlamch( 'Safe minimum' )
185 eps = dlamch( 'Precision' )
186 ovfl = one / unfl
187 CALL dlabad( unfl, ovfl )
188 smlnum = unfl*n / eps
189*
190* Test 1: Compute norm( A - Q*H*Q' ) / ( norm(A) * N * EPS )
191*
192* Copy A to WORK
193*
194 ldwork = max( 1, n )
195 CALL zlacpy( ' ', n, n, a, lda, work, ldwork )
196*
197* Compute Q*H
198*
199 CALL zgemm( 'No transpose', 'No transpose', n, n, n,
200 \$ dcmplx( one ), q, ldq, h, ldh, dcmplx( zero ),
201 \$ work( ldwork*n+1 ), ldwork )
202*
203* Compute A - Q*H*Q'
204*
205 CALL zgemm( 'No transpose', 'Conjugate transpose', n, n, n,
206 \$ dcmplx( -one ), work( ldwork*n+1 ), ldwork, q, ldq,
207 \$ dcmplx( one ), work, ldwork )
208*
209 anorm = max( zlange( '1', n, n, a, lda, rwork ), unfl )
210 wnorm = zlange( '1', n, n, work, ldwork, rwork )
211*
212* Note that RESULT(1) cannot overflow and is bounded by 1/(N*EPS)
213*
214 result( 1 ) = min( wnorm, anorm ) / max( smlnum, anorm*eps ) / n
215*
216* Test 2: Compute norm( I - Q'*Q ) / ( N * EPS )
217*
218 CALL zunt01( 'Columns', n, n, q, ldq, work, lwork, rwork,
219 \$ result( 2 ) )
220*
221 RETURN
222*
223* End of ZHST01
224*
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
subroutine zgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
ZGEMM
Definition: zgemm.f:187
subroutine zunt01(ROWCOL, M, N, U, LDU, WORK, LWORK, RWORK, RESID)
ZUNT01
Definition: zunt01.f:126
double precision function zlange(NORM, M, N, A, LDA, WORK)
ZLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: zlange.f:115
subroutine zlacpy(UPLO, M, N, A, LDA, B, LDB)
ZLACPY copies all or part of one two-dimensional array to another.
Definition: zlacpy.f:103
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