 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ dlqt03()

 subroutine dlqt03 ( integer M, integer N, integer K, double precision, dimension( lda, * ) AF, double precision, dimension( lda, * ) C, double precision, dimension( lda, * ) CC, double precision, dimension( lda, * ) Q, integer LDA, double precision, dimension( * ) TAU, double precision, dimension( lwork ) WORK, integer LWORK, double precision, dimension( * ) RWORK, double precision, dimension( * ) RESULT )

DLQT03

Purpose:
``` DLQT03 tests DORMLQ, which computes Q*C, Q'*C, C*Q or C*Q'.

DLQT03 compares the results of a call to DORMLQ with the results of
forming Q explicitly by a call to DORGLQ and then performing matrix
multiplication by a call to DGEMM.```
Parameters
 [in] M ``` M is INTEGER The number of rows or columns of the matrix C; C is n-by-m if Q is applied from the left, or m-by-n if Q is applied from the right. M >= 0.``` [in] N ``` N is INTEGER The order of the orthogonal matrix Q. N >= 0.``` [in] K ``` K is INTEGER The number of elementary reflectors whose product defines the orthogonal matrix Q. N >= K >= 0.``` [in] AF ``` AF is DOUBLE PRECISION array, dimension (LDA,N) Details of the LQ factorization of an m-by-n matrix, as returned by DGELQF. See SGELQF for further details.``` [out] C ` C is DOUBLE PRECISION array, dimension (LDA,N)` [out] CC ` CC is DOUBLE PRECISION array, dimension (LDA,N)` [out] Q ` Q is DOUBLE PRECISION array, dimension (LDA,N)` [in] LDA ``` LDA is INTEGER The leading dimension of the arrays AF, C, CC, and Q.``` [in] TAU ``` TAU is DOUBLE PRECISION array, dimension (min(M,N)) The scalar factors of the elementary reflectors corresponding to the LQ factorization in AF.``` [out] WORK ` WORK is DOUBLE PRECISION array, dimension (LWORK)` [in] LWORK ``` LWORK is INTEGER The length of WORK. LWORK must be at least M, and should be M*NB, where NB is the blocksize for this environment.``` [out] RWORK ` RWORK is DOUBLE PRECISION array, dimension (M)` [out] RESULT ``` RESULT is DOUBLE PRECISION array, dimension (4) The test ratios compare two techniques for multiplying a random matrix C by an n-by-n orthogonal matrix Q. RESULT(1) = norm( Q*C - Q*C ) / ( N * norm(C) * EPS ) RESULT(2) = norm( C*Q - C*Q ) / ( N * norm(C) * EPS ) RESULT(3) = norm( Q'*C - Q'*C )/ ( N * norm(C) * EPS ) RESULT(4) = norm( C*Q' - C*Q' )/ ( N * norm(C) * EPS )```

Definition at line 134 of file dlqt03.f.

136 *
137 * -- LAPACK test routine --
138 * -- LAPACK is a software package provided by Univ. of Tennessee, --
139 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
140 *
141 * .. Scalar Arguments ..
142  INTEGER K, LDA, LWORK, M, N
143 * ..
144 * .. Array Arguments ..
145  DOUBLE PRECISION AF( LDA, * ), C( LDA, * ), CC( LDA, * ),
146  \$ Q( LDA, * ), RESULT( * ), RWORK( * ), TAU( * ),
147  \$ WORK( LWORK )
148 * ..
149 *
150 * =====================================================================
151 *
152 * .. Parameters ..
153  DOUBLE PRECISION ONE
154  parameter( one = 1.0d0 )
155  DOUBLE PRECISION ROGUE
156  parameter( rogue = -1.0d+10 )
157 * ..
158 * .. Local Scalars ..
159  CHARACTER SIDE, TRANS
160  INTEGER INFO, ISIDE, ITRANS, J, MC, NC
161  DOUBLE PRECISION CNORM, EPS, RESID
162 * ..
163 * .. External Functions ..
164  LOGICAL LSAME
165  DOUBLE PRECISION DLAMCH, DLANGE
166  EXTERNAL lsame, dlamch, dlange
167 * ..
168 * .. External Subroutines ..
169  EXTERNAL dgemm, dlacpy, dlarnv, dlaset, dorglq, dormlq
170 * ..
171 * .. Local Arrays ..
172  INTEGER ISEED( 4 )
173 * ..
174 * .. Intrinsic Functions ..
175  INTRINSIC dble, max
176 * ..
177 * .. Scalars in Common ..
178  CHARACTER*32 SRNAMT
179 * ..
180 * .. Common blocks ..
181  COMMON / srnamc / srnamt
182 * ..
183 * .. Data statements ..
184  DATA iseed / 1988, 1989, 1990, 1991 /
185 * ..
186 * .. Executable Statements ..
187 *
188  eps = dlamch( 'Epsilon' )
189 *
190 * Copy the first k rows of the factorization to the array Q
191 *
192  CALL dlaset( 'Full', n, n, rogue, rogue, q, lda )
193  CALL dlacpy( 'Upper', k, n-1, af( 1, 2 ), lda, q( 1, 2 ), lda )
194 *
195 * Generate the n-by-n matrix Q
196 *
197  srnamt = 'DORGLQ'
198  CALL dorglq( n, n, k, q, lda, tau, work, lwork, info )
199 *
200  DO 30 iside = 1, 2
201  IF( iside.EQ.1 ) THEN
202  side = 'L'
203  mc = n
204  nc = m
205  ELSE
206  side = 'R'
207  mc = m
208  nc = n
209  END IF
210 *
211 * Generate MC by NC matrix C
212 *
213  DO 10 j = 1, nc
214  CALL dlarnv( 2, iseed, mc, c( 1, j ) )
215  10 CONTINUE
216  cnorm = dlange( '1', mc, nc, c, lda, rwork )
217  IF( cnorm.EQ.0.0d0 )
218  \$ cnorm = one
219 *
220  DO 20 itrans = 1, 2
221  IF( itrans.EQ.1 ) THEN
222  trans = 'N'
223  ELSE
224  trans = 'T'
225  END IF
226 *
227 * Copy C
228 *
229  CALL dlacpy( 'Full', mc, nc, c, lda, cc, lda )
230 *
231 * Apply Q or Q' to C
232 *
233  srnamt = 'DORMLQ'
234  CALL dormlq( side, trans, mc, nc, k, af, lda, tau, cc, lda,
235  \$ work, lwork, info )
236 *
237 * Form explicit product and subtract
238 *
239  IF( lsame( side, 'L' ) ) THEN
240  CALL dgemm( trans, 'No transpose', mc, nc, mc, -one, q,
241  \$ lda, c, lda, one, cc, lda )
242  ELSE
243  CALL dgemm( 'No transpose', trans, mc, nc, nc, -one, c,
244  \$ lda, q, lda, one, cc, lda )
245  END IF
246 *
247 * Compute error in the difference
248 *
249  resid = dlange( '1', mc, nc, cc, lda, rwork )
250  result( ( iside-1 )*2+itrans ) = resid /
251  \$ ( dble( max( 1, n ) )*cnorm*eps )
252 *
253  20 CONTINUE
254  30 CONTINUE
255 *
256  RETURN
257 *
258 * End of DLQT03
259 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
subroutine dlarnv(IDIST, ISEED, N, X)
DLARNV returns a vector of random numbers from a uniform or normal distribution.
Definition: dlarnv.f:97
subroutine dlacpy(UPLO, M, N, A, LDA, B, LDB)
DLACPY copies all or part of one two-dimensional array to another.
Definition: dlacpy.f:103
subroutine dlaset(UPLO, M, N, ALPHA, BETA, A, LDA)
DLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition: dlaset.f:110
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine dgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
DGEMM
Definition: dgemm.f:187
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:114
subroutine dorglq(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
DORGLQ
Definition: dorglq.f:127
subroutine dormlq(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
DORMLQ
Definition: dormlq.f:167
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