LAPACK  3.8.0
LAPACK: Linear Algebra PACKage
zrqt03.f
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1 *> \brief \b ZRQT03
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 ZRQT03( 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 RESULT( * ), RWORK( * )
19 * COMPLEX*16 AF( LDA, * ), C( LDA, * ), CC( LDA, * ),
20 * $ Q( LDA, * ), TAU( * ), WORK( LWORK )
21 * ..
22 *
23 *
24 *> \par Purpose:
25 * =============
26 *>
27 *> \verbatim
28 *>
29 *> ZRQT03 tests ZUNMRQ, which computes Q*C, Q'*C, C*Q or C*Q'.
30 *>
31 *> ZRQT03 compares the results of a call to ZUNMRQ with the results of
32 *> forming Q explicitly by a call to ZUNGRQ and then performing matrix
33 *> multiplication by a call to ZGEMM.
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 COMPLEX*16 array, dimension (LDA,N)
63 *> Details of the RQ factorization of an m-by-n matrix, as
64 *> returned by ZGERQF. See CGERQF for further details.
65 *> \endverbatim
66 *>
67 *> \param[out] C
68 *> \verbatim
69 *> C is COMPLEX*16 array, dimension (LDA,N)
70 *> \endverbatim
71 *>
72 *> \param[out] CC
73 *> \verbatim
74 *> CC is COMPLEX*16 array, dimension (LDA,N)
75 *> \endverbatim
76 *>
77 *> \param[out] Q
78 *> \verbatim
79 *> Q is COMPLEX*16 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 COMPLEX*16 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 COMPLEX*16 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 *> \date December 2016
132 *
133 *> \ingroup complex16_lin
134 *
135 * =====================================================================
136  SUBROUTINE zrqt03( M, N, K, AF, C, CC, Q, LDA, TAU, WORK, LWORK,
137  $ RWORK, RESULT )
138 *
139 * -- LAPACK test routine (version 3.7.0) --
140 * -- LAPACK is a software package provided by Univ. of Tennessee, --
141 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
142 * December 2016
143 *
144 * .. Scalar Arguments ..
145  INTEGER K, LDA, LWORK, M, N
146 * ..
147 * .. Array Arguments ..
148  DOUBLE PRECISION RESULT( * ), RWORK( * )
149  COMPLEX*16 AF( lda, * ), C( lda, * ), CC( lda, * ),
150  $ q( lda, * ), tau( * ), work( lwork )
151 * ..
152 *
153 * =====================================================================
154 *
155 * .. Parameters ..
156  DOUBLE PRECISION ZERO, ONE
157  parameter( zero = 0.0d+0, one = 1.0d+0 )
158  COMPLEX*16 ROGUE
159  parameter( rogue = ( -1.0d+10, -1.0d+10 ) )
160 * ..
161 * .. Local Scalars ..
162  CHARACTER SIDE, TRANS
163  INTEGER INFO, ISIDE, ITRANS, J, MC, MINMN, NC
164  DOUBLE PRECISION CNORM, EPS, RESID
165 * ..
166 * .. External Functions ..
167  LOGICAL LSAME
168  DOUBLE PRECISION DLAMCH, ZLANGE
169  EXTERNAL lsame, dlamch, zlange
170 * ..
171 * .. External Subroutines ..
172  EXTERNAL zgemm, zlacpy, zlarnv, zlaset, zungrq, zunmrq
173 * ..
174 * .. Local Arrays ..
175  INTEGER ISEED( 4 )
176 * ..
177 * .. Intrinsic Functions ..
178  INTRINSIC dble, dcmplx, max, min
179 * ..
180 * .. Scalars in Common ..
181  CHARACTER*32 SRNAMT
182 * ..
183 * .. Common blocks ..
184  COMMON / srnamc / srnamt
185 * ..
186 * .. Data statements ..
187  DATA iseed / 1988, 1989, 1990, 1991 /
188 * ..
189 * .. Executable Statements ..
190 *
191  eps = dlamch( 'Epsilon' )
192  minmn = min( m, n )
193 *
194 * Quick return if possible
195 *
196  IF( minmn.EQ.0 ) THEN
197  result( 1 ) = zero
198  result( 2 ) = zero
199  result( 3 ) = zero
200  result( 4 ) = zero
201  RETURN
202  END IF
203 *
204 * Copy the last k rows of the factorization to the array Q
205 *
206  CALL zlaset( 'Full', n, n, rogue, rogue, q, lda )
207  IF( k.GT.0 .AND. n.GT.k )
208  $ CALL zlacpy( 'Full', k, n-k, af( m-k+1, 1 ), lda,
209  $ q( n-k+1, 1 ), lda )
210  IF( k.GT.1 )
211  $ CALL zlacpy( 'Lower', k-1, k-1, af( m-k+2, n-k+1 ), lda,
212  $ q( n-k+2, n-k+1 ), lda )
213 *
214 * Generate the n-by-n matrix Q
215 *
216  srnamt = 'ZUNGRQ'
217  CALL zungrq( n, n, k, q, lda, tau( minmn-k+1 ), work, lwork,
218  $ info )
219 *
220  DO 30 iside = 1, 2
221  IF( iside.EQ.1 ) THEN
222  side = 'L'
223  mc = n
224  nc = m
225  ELSE
226  side = 'R'
227  mc = m
228  nc = n
229  END IF
230 *
231 * Generate MC by NC matrix C
232 *
233  DO 10 j = 1, nc
234  CALL zlarnv( 2, iseed, mc, c( 1, j ) )
235  10 CONTINUE
236  cnorm = zlange( '1', mc, nc, c, lda, rwork )
237  IF( cnorm.EQ.zero )
238  $ cnorm = one
239 *
240  DO 20 itrans = 1, 2
241  IF( itrans.EQ.1 ) THEN
242  trans = 'N'
243  ELSE
244  trans = 'C'
245  END IF
246 *
247 * Copy C
248 *
249  CALL zlacpy( 'Full', mc, nc, c, lda, cc, lda )
250 *
251 * Apply Q or Q' to C
252 *
253  srnamt = 'ZUNMRQ'
254  IF( k.GT.0 )
255  $ CALL zunmrq( side, trans, mc, nc, k, af( m-k+1, 1 ), lda,
256  $ tau( minmn-k+1 ), cc, lda, work, lwork,
257  $ info )
258 *
259 * Form explicit product and subtract
260 *
261  IF( lsame( side, 'L' ) ) THEN
262  CALL zgemm( trans, 'No transpose', mc, nc, mc,
263  $ dcmplx( -one ), q, lda, c, lda,
264  $ dcmplx( one ), cc, lda )
265  ELSE
266  CALL zgemm( 'No transpose', trans, mc, nc, nc,
267  $ dcmplx( -one ), c, lda, q, lda,
268  $ dcmplx( one ), cc, lda )
269  END IF
270 *
271 * Compute error in the difference
272 *
273  resid = zlange( '1', mc, nc, cc, lda, rwork )
274  result( ( iside-1 )*2+itrans ) = resid /
275  $ ( dble( max( 1, n ) )*cnorm*eps )
276 *
277  20 CONTINUE
278  30 CONTINUE
279 *
280  RETURN
281 *
282 * End of ZRQT03
283 *
284  END
subroutine zunmrq(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
ZUNMRQ
Definition: zunmrq.f:169
subroutine zungrq(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
ZUNGRQ
Definition: zungrq.f:130
subroutine zlacpy(UPLO, M, N, A, LDA, B, LDB)
ZLACPY copies all or part of one two-dimensional array to another.
Definition: zlacpy.f:105
subroutine zgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
ZGEMM
Definition: zgemm.f:189
subroutine zlaset(UPLO, M, N, ALPHA, BETA, A, LDA)
ZLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values...
Definition: zlaset.f:108
subroutine zrqt03(M, N, K, AF, C, CC, Q, LDA, TAU, WORK, LWORK, RWORK, RESULT)
ZRQT03
Definition: zrqt03.f:138
subroutine zlarnv(IDIST, ISEED, N, X)
ZLARNV returns a vector of random numbers from a uniform or normal distribution.
Definition: zlarnv.f:101