LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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drqt03.f
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1*> \brief \b DRQT03
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8* Definition:
9* ===========
10*
11* SUBROUTINE DRQT03( M, N, K, AF, C, CC, Q, LDA, TAU, WORK, LWORK,
12* RWORK, RESULT )
13*
14* .. Scalar Arguments ..
15* INTEGER K, LDA, LWORK, M, N
16* ..
17* .. Array Arguments ..
18* DOUBLE PRECISION AF( LDA, * ), C( LDA, * ), CC( LDA, * ),
19* \$ Q( LDA, * ), RESULT( * ), RWORK( * ), TAU( * ),
20* \$ WORK( LWORK )
21* ..
22*
23*
24*> \par Purpose:
25* =============
26*>
27*> \verbatim
28*>
29*> DRQT03 tests DORMRQ, which computes Q*C, Q'*C, C*Q or C*Q'.
30*>
31*> DRQT03 compares the results of a call to DORMRQ with the results of
32*> forming Q explicitly by a call to DORGRQ and then performing matrix
33*> multiplication by a call to DGEMM.
34*> \endverbatim
35*
36* Arguments:
37* ==========
38*
39*> \param[in] M
40*> \verbatim
41*> M is INTEGER
42*> The number of rows or columns of the matrix C; C is n-by-m if
43*> Q is applied from the left, or m-by-n if Q is applied from
44*> the right. M >= 0.
45*> \endverbatim
46*>
47*> \param[in] N
48*> \verbatim
49*> N is INTEGER
50*> The order of the orthogonal matrix Q. N >= 0.
51*> \endverbatim
52*>
53*> \param[in] K
54*> \verbatim
55*> K is INTEGER
56*> The number of elementary reflectors whose product defines the
57*> orthogonal matrix Q. N >= K >= 0.
58*> \endverbatim
59*>
60*> \param[in] AF
61*> \verbatim
62*> AF is DOUBLE PRECISION array, dimension (LDA,N)
63*> Details of the RQ factorization of an m-by-n matrix, as
64*> returned by DGERQF. See SGERQF for further details.
65*> \endverbatim
66*>
67*> \param[out] C
68*> \verbatim
69*> C is DOUBLE PRECISION array, dimension (LDA,N)
70*> \endverbatim
71*>
72*> \param[out] CC
73*> \verbatim
74*> CC is DOUBLE PRECISION array, dimension (LDA,N)
75*> \endverbatim
76*>
77*> \param[out] Q
78*> \verbatim
79*> Q is DOUBLE PRECISION array, dimension (LDA,N)
80*> \endverbatim
81*>
82*> \param[in] LDA
83*> \verbatim
84*> LDA is INTEGER
85*> The leading dimension of the arrays AF, C, CC, and Q.
86*> \endverbatim
87*>
88*> \param[in] TAU
89*> \verbatim
90*> TAU is DOUBLE PRECISION array, dimension (min(M,N))
91*> The scalar factors of the elementary reflectors corresponding
92*> to the RQ factorization in AF.
93*> \endverbatim
94*>
95*> \param[out] WORK
96*> \verbatim
97*> WORK is DOUBLE PRECISION array, dimension (LWORK)
98*> \endverbatim
99*>
100*> \param[in] LWORK
101*> \verbatim
102*> LWORK is INTEGER
103*> The length of WORK. LWORK must be at least M, and should be
104*> M*NB, where NB is the blocksize for this environment.
105*> \endverbatim
106*>
107*> \param[out] RWORK
108*> \verbatim
109*> RWORK is DOUBLE PRECISION array, dimension (M)
110*> \endverbatim
111*>
112*> \param[out] RESULT
113*> \verbatim
114*> RESULT is DOUBLE PRECISION array, dimension (4)
115*> The test ratios compare two techniques for multiplying a
116*> random matrix C by an n-by-n orthogonal matrix Q.
117*> RESULT(1) = norm( Q*C - Q*C ) / ( N * norm(C) * EPS )
118*> RESULT(2) = norm( C*Q - C*Q ) / ( N * norm(C) * EPS )
119*> RESULT(3) = norm( Q'*C - Q'*C )/ ( N * norm(C) * EPS )
120*> RESULT(4) = norm( C*Q' - C*Q' )/ ( N * norm(C) * EPS )
121*> \endverbatim
122*
123* Authors:
124* ========
125*
126*> \author Univ. of Tennessee
127*> \author Univ. of California Berkeley
128*> \author Univ. of Colorado Denver
129*> \author NAG Ltd.
130*
131*> \ingroup double_lin
132*
133* =====================================================================
134 SUBROUTINE drqt03( M, N, K, AF, C, CC, Q, LDA, TAU, WORK, LWORK,
135 \$ RWORK, RESULT )
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 ZERO, ONE
154 parameter( zero = 0.0d0, 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, MINMN, 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, dorgrq, dormrq
170* ..
171* .. Local Arrays ..
172 INTEGER ISEED( 4 )
173* ..
174* .. Intrinsic Functions ..
175 INTRINSIC dble, max, min
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 minmn = min( m, n )
190*
191* Quick return if possible
192*
193 IF( minmn.EQ.0 ) THEN
194 result( 1 ) = zero
195 result( 2 ) = zero
196 result( 3 ) = zero
197 result( 4 ) = zero
198 RETURN
199 END IF
200*
201* Copy the last k rows of the factorization to the array Q
202*
203 CALL dlaset( 'Full', n, n, rogue, rogue, q, lda )
204 IF( k.GT.0 .AND. n.GT.k )
205 \$ CALL dlacpy( 'Full', k, n-k, af( m-k+1, 1 ), lda,
206 \$ q( n-k+1, 1 ), lda )
207 IF( k.GT.1 )
208 \$ CALL dlacpy( 'Lower', k-1, k-1, af( m-k+2, n-k+1 ), lda,
209 \$ q( n-k+2, n-k+1 ), lda )
210*
211* Generate the n-by-n matrix Q
212*
213 srnamt = 'DORGRQ'
214 CALL dorgrq( n, n, k, q, lda, tau( minmn-k+1 ), work, lwork,
215 \$ info )
216*
217 DO 30 iside = 1, 2
218 IF( iside.EQ.1 ) THEN
219 side = 'L'
220 mc = n
221 nc = m
222 ELSE
223 side = 'R'
224 mc = m
225 nc = n
226 END IF
227*
228* Generate MC by NC matrix C
229*
230 DO 10 j = 1, nc
231 CALL dlarnv( 2, iseed, mc, c( 1, j ) )
232 10 CONTINUE
233 cnorm = dlange( '1', mc, nc, c, lda, rwork )
234 IF( cnorm.EQ.0.0d0 )
235 \$ cnorm = one
236*
237 DO 20 itrans = 1, 2
238 IF( itrans.EQ.1 ) THEN
239 trans = 'N'
240 ELSE
241 trans = 'T'
242 END IF
243*
244* Copy C
245*
246 CALL dlacpy( 'Full', mc, nc, c, lda, cc, lda )
247*
248* Apply Q or Q' to C
249*
250 srnamt = 'DORMRQ'
251 IF( k.GT.0 )
252 \$ CALL dormrq( side, trans, mc, nc, k, af( m-k+1, 1 ), lda,
253 \$ tau( minmn-k+1 ), cc, lda, work, lwork,
254 \$ info )
255*
256* Form explicit product and subtract
257*
258 IF( lsame( side, 'L' ) ) THEN
259 CALL dgemm( trans, 'No transpose', mc, nc, mc, -one, q,
260 \$ lda, c, lda, one, cc, lda )
261 ELSE
262 CALL dgemm( 'No transpose', trans, mc, nc, nc, -one, c,
263 \$ lda, q, lda, one, cc, lda )
264 END IF
265*
266* Compute error in the difference
267*
268 resid = dlange( '1', mc, nc, cc, lda, rwork )
269 result( ( iside-1 )*2+itrans ) = resid /
270 \$ ( dble( max( 1, n ) )*cnorm*eps )
271*
272 20 CONTINUE
273 30 CONTINUE
274*
275 RETURN
276*
277* End of DRQT03
278*
279 END
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
subroutine dgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
DGEMM
Definition: dgemm.f:187
subroutine drqt03(M, N, K, AF, C, CC, Q, LDA, TAU, WORK, LWORK, RWORK, RESULT)
DRQT03
Definition: drqt03.f:136
subroutine dorgrq(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
DORGRQ
Definition: dorgrq.f:128
subroutine dormrq(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
DORMRQ
Definition: dormrq.f:167