LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ 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 )```
Date
December 2016

Definition at line 136 of file dhst01.f.

136 *
137 * -- LAPACK test routine (version 3.7.0) --
138 * -- LAPACK is a software package provided by Univ. of Tennessee, --
139 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
140 * December 2016
141 *
142 * .. Scalar Arguments ..
143  INTEGER ihi, ilo, lda, ldh, ldq, lwork, n
144 * ..
145 * .. Array Arguments ..
146  DOUBLE PRECISION a( lda, * ), h( ldh, * ), q( ldq, * ),
147  \$ result( 2 ), work( lwork )
148 * ..
149 *
150 * =====================================================================
151 *
152 * .. Parameters ..
153  DOUBLE PRECISION one, zero
154  parameter( one = 1.0d+0, zero = 0.0d+0 )
155 * ..
156 * .. Local Scalars ..
157  INTEGER ldwork
158  DOUBLE PRECISION anorm, eps, ovfl, smlnum, unfl, wnorm
159 * ..
160 * .. External Functions ..
161  DOUBLE PRECISION dlamch, dlange
162  EXTERNAL dlamch, dlange
163 * ..
164 * .. External Subroutines ..
165  EXTERNAL dgemm, dlabad, dlacpy, dort01
166 * ..
167 * .. Intrinsic Functions ..
168  INTRINSIC max, min
169 * ..
170 * .. Executable Statements ..
171 *
172 * Quick return if possible
173 *
174  IF( n.LE.0 ) THEN
175  result( 1 ) = zero
176  result( 2 ) = zero
177  RETURN
178  END IF
179 *
180  unfl = dlamch( 'Safe minimum' )
181  eps = dlamch( 'Precision' )
182  ovfl = one / unfl
183  CALL dlabad( unfl, ovfl )
184  smlnum = unfl*n / eps
185 *
186 * Test 1: Compute norm( A - Q*H*Q' ) / ( norm(A) * N * EPS )
187 *
188 * Copy A to WORK
189 *
190  ldwork = max( 1, n )
191  CALL dlacpy( ' ', n, n, a, lda, work, ldwork )
192 *
193 * Compute Q*H
194 *
195  CALL dgemm( 'No transpose', 'No transpose', n, n, n, one, q, ldq,
196  \$ h, ldh, zero, work( ldwork*n+1 ), ldwork )
197 *
198 * Compute A - Q*H*Q'
199 *
200  CALL dgemm( 'No transpose', 'Transpose', n, n, n, -one,
201  \$ work( ldwork*n+1 ), ldwork, q, ldq, one, work,
202  \$ ldwork )
203 *
204  anorm = max( dlange( '1', n, n, a, lda, work( ldwork*n+1 ) ),
205  \$ unfl )
206  wnorm = dlange( '1', n, n, work, ldwork, work( ldwork*n+1 ) )
207 *
208 * Note that RESULT(1) cannot overflow and is bounded by 1/(N*EPS)
209 *
210  result( 1 ) = min( wnorm, anorm ) / max( smlnum, anorm*eps ) / n
211 *
212 * Test 2: Compute norm( I - Q'*Q ) / ( N * EPS )
213 *
214  CALL dort01( 'Columns', n, n, q, ldq, work, lwork, result( 2 ) )
215 *
216  RETURN
217 *
218 * End of DHST01
219 *
subroutine dlacpy(UPLO, M, N, A, LDA, B, LDB)
DLACPY copies all or part of one two-dimensional array to another.
Definition: dlacpy.f:105
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65
subroutine dgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
DGEMM
Definition: dgemm.f:189
double precision function dlange(NORM, M, N, A, LDA, WORK)
DLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: dlange.f:116