LAPACK 3.12.0 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 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 smlnum = unfl*n / eps
188*
189* Test 1: Compute norm( A - Q*H*Q' ) / ( norm(A) * N * EPS )
190*
191* Copy A to WORK
192*
193 ldwork = max( 1, n )
194 CALL zlacpy( ' ', n, n, a, lda, work, ldwork )
195*
196* Compute Q*H
197*
198 CALL zgemm( 'No transpose', 'No transpose', n, n, n,
199 \$ dcmplx( one ), q, ldq, h, ldh, dcmplx( zero ),
200 \$ work( ldwork*n+1 ), ldwork )
201*
202* Compute A - Q*H*Q'
203*
204 CALL zgemm( 'No transpose', 'Conjugate transpose', n, n, n,
205 \$ dcmplx( -one ), work( ldwork*n+1 ), ldwork, q, ldq,
206 \$ dcmplx( one ), work, ldwork )
207*
208 anorm = max( zlange( '1', n, n, a, lda, rwork ), unfl )
209 wnorm = zlange( '1', n, n, work, ldwork, rwork )
210*
211* Note that RESULT(1) cannot overflow and is bounded by 1/(N*EPS)
212*
213 result( 1 ) = min( wnorm, anorm ) / max( smlnum, anorm*eps ) / n
214*
215* Test 2: Compute norm( I - Q'*Q ) / ( N * EPS )
216*
217 CALL zunt01( 'Columns', n, n, q, ldq, work, lwork, rwork,
218 \$ result( 2 ) )
219*
220 RETURN
221*
222* End of ZHST01
223*
subroutine zgemm(transa, transb, m, n, k, alpha, a, lda, b, ldb, beta, c, ldc)
ZGEMM
Definition zgemm.f:188
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
double precision function dlamch(cmach)
DLAMCH
Definition dlamch.f:69
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 zunt01(rowcol, m, n, u, ldu, work, lwork, rwork, resid)
ZUNT01
Definition zunt01.f:126
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