LAPACK  3.8.0
LAPACK: Linear Algebra PACKage
zrqt01.f
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1 *> \brief \b ZRQT01
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 ZRQT01( M, N, A, AF, Q, R, LDA, TAU, WORK, LWORK,
12 * RWORK, RESULT )
13 *
14 * .. Scalar Arguments ..
15 * INTEGER LDA, LWORK, M, N
16 * ..
17 * .. Array Arguments ..
18 * DOUBLE PRECISION RESULT( * ), RWORK( * )
19 * COMPLEX*16 A( LDA, * ), AF( LDA, * ), Q( LDA, * ),
20 * $ R( LDA, * ), TAU( * ), WORK( LWORK )
21 * ..
22 *
23 *
24 *> \par Purpose:
25 * =============
26 *>
27 *> \verbatim
28 *>
29 *> ZRQT01 tests ZGERQF, which computes the RQ factorization of an m-by-n
30 *> matrix A, and partially tests ZUNGRQ which forms the n-by-n
31 *> orthogonal matrix Q.
32 *>
33 *> ZRQT01 compares R with A*Q', and checks that Q is orthogonal.
34 *> \endverbatim
35 *
36 * Arguments:
37 * ==========
38 *
39 *> \param[in] M
40 *> \verbatim
41 *> M is INTEGER
42 *> The number of rows of the matrix A. M >= 0.
43 *> \endverbatim
44 *>
45 *> \param[in] N
46 *> \verbatim
47 *> N is INTEGER
48 *> The number of columns of the matrix A. N >= 0.
49 *> \endverbatim
50 *>
51 *> \param[in] A
52 *> \verbatim
53 *> A is COMPLEX*16 array, dimension (LDA,N)
54 *> The m-by-n matrix A.
55 *> \endverbatim
56 *>
57 *> \param[out] AF
58 *> \verbatim
59 *> AF is COMPLEX*16 array, dimension (LDA,N)
60 *> Details of the RQ factorization of A, as returned by ZGERQF.
61 *> See ZGERQF for further details.
62 *> \endverbatim
63 *>
64 *> \param[out] Q
65 *> \verbatim
66 *> Q is COMPLEX*16 array, dimension (LDA,N)
67 *> The n-by-n orthogonal matrix Q.
68 *> \endverbatim
69 *>
70 *> \param[out] R
71 *> \verbatim
72 *> R is COMPLEX*16 array, dimension (LDA,max(M,N))
73 *> \endverbatim
74 *>
75 *> \param[in] LDA
76 *> \verbatim
77 *> LDA is INTEGER
78 *> The leading dimension of the arrays A, AF, Q and L.
79 *> LDA >= max(M,N).
80 *> \endverbatim
81 *>
82 *> \param[out] TAU
83 *> \verbatim
84 *> TAU is COMPLEX*16 array, dimension (min(M,N))
85 *> The scalar factors of the elementary reflectors, as returned
86 *> by ZGERQF.
87 *> \endverbatim
88 *>
89 *> \param[out] WORK
90 *> \verbatim
91 *> WORK is COMPLEX*16 array, dimension (LWORK)
92 *> \endverbatim
93 *>
94 *> \param[in] LWORK
95 *> \verbatim
96 *> LWORK is INTEGER
97 *> The dimension of the array WORK.
98 *> \endverbatim
99 *>
100 *> \param[out] RWORK
101 *> \verbatim
102 *> RWORK is DOUBLE PRECISION array, dimension (max(M,N))
103 *> \endverbatim
104 *>
105 *> \param[out] RESULT
106 *> \verbatim
107 *> RESULT is DOUBLE PRECISION array, dimension (2)
108 *> The test ratios:
109 *> RESULT(1) = norm( R - A*Q' ) / ( N * norm(A) * EPS )
110 *> RESULT(2) = norm( I - Q*Q' ) / ( N * EPS )
111 *> \endverbatim
112 *
113 * Authors:
114 * ========
115 *
116 *> \author Univ. of Tennessee
117 *> \author Univ. of California Berkeley
118 *> \author Univ. of Colorado Denver
119 *> \author NAG Ltd.
120 *
121 *> \date December 2016
122 *
123 *> \ingroup complex16_lin
124 *
125 * =====================================================================
126  SUBROUTINE zrqt01( M, N, A, AF, Q, R, LDA, TAU, WORK, LWORK,
127  $ RWORK, RESULT )
128 *
129 * -- LAPACK test routine (version 3.7.0) --
130 * -- LAPACK is a software package provided by Univ. of Tennessee, --
131 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
132 * December 2016
133 *
134 * .. Scalar Arguments ..
135  INTEGER LDA, LWORK, M, N
136 * ..
137 * .. Array Arguments ..
138  DOUBLE PRECISION RESULT( * ), RWORK( * )
139  COMPLEX*16 A( lda, * ), AF( lda, * ), Q( lda, * ),
140  $ r( lda, * ), tau( * ), work( lwork )
141 * ..
142 *
143 * =====================================================================
144 *
145 * .. Parameters ..
146  DOUBLE PRECISION ZERO, ONE
147  parameter( zero = 0.0d+0, one = 1.0d+0 )
148  COMPLEX*16 ROGUE
149  parameter( rogue = ( -1.0d+10, -1.0d+10 ) )
150 * ..
151 * .. Local Scalars ..
152  INTEGER INFO, MINMN
153  DOUBLE PRECISION ANORM, EPS, RESID
154 * ..
155 * .. External Functions ..
156  DOUBLE PRECISION DLAMCH, ZLANGE, ZLANSY
157  EXTERNAL dlamch, zlange, zlansy
158 * ..
159 * .. External Subroutines ..
160  EXTERNAL zgemm, zgerqf, zherk, zlacpy, zlaset, zungrq
161 * ..
162 * .. Intrinsic Functions ..
163  INTRINSIC dble, dcmplx, max, min
164 * ..
165 * .. Scalars in Common ..
166  CHARACTER*32 SRNAMT
167 * ..
168 * .. Common blocks ..
169  COMMON / srnamc / srnamt
170 * ..
171 * .. Executable Statements ..
172 *
173  minmn = min( m, n )
174  eps = dlamch( 'Epsilon' )
175 *
176 * Copy the matrix A to the array AF.
177 *
178  CALL zlacpy( 'Full', m, n, a, lda, af, lda )
179 *
180 * Factorize the matrix A in the array AF.
181 *
182  srnamt = 'ZGERQF'
183  CALL zgerqf( m, n, af, lda, tau, work, lwork, info )
184 *
185 * Copy details of Q
186 *
187  CALL zlaset( 'Full', n, n, rogue, rogue, q, lda )
188  IF( m.LE.n ) THEN
189  IF( m.GT.0 .AND. m.LT.n )
190  $ CALL zlacpy( 'Full', m, n-m, af, lda, q( n-m+1, 1 ), lda )
191  IF( m.GT.1 )
192  $ CALL zlacpy( 'Lower', m-1, m-1, af( 2, n-m+1 ), lda,
193  $ q( n-m+2, n-m+1 ), lda )
194  ELSE
195  IF( n.GT.1 )
196  $ CALL zlacpy( 'Lower', n-1, n-1, af( m-n+2, 1 ), lda,
197  $ q( 2, 1 ), lda )
198  END IF
199 *
200 * Generate the n-by-n matrix Q
201 *
202  srnamt = 'ZUNGRQ'
203  CALL zungrq( n, n, minmn, q, lda, tau, work, lwork, info )
204 *
205 * Copy R
206 *
207  CALL zlaset( 'Full', m, n, dcmplx( zero ), dcmplx( zero ), r,
208  $ lda )
209  IF( m.LE.n ) THEN
210  IF( m.GT.0 )
211  $ CALL zlacpy( 'Upper', m, m, af( 1, n-m+1 ), lda,
212  $ r( 1, n-m+1 ), lda )
213  ELSE
214  IF( m.GT.n .AND. n.GT.0 )
215  $ CALL zlacpy( 'Full', m-n, n, af, lda, r, lda )
216  IF( n.GT.0 )
217  $ CALL zlacpy( 'Upper', n, n, af( m-n+1, 1 ), lda,
218  $ r( m-n+1, 1 ), lda )
219  END IF
220 *
221 * Compute R - A*Q'
222 *
223  CALL zgemm( 'No transpose', 'Conjugate transpose', m, n, n,
224  $ dcmplx( -one ), a, lda, q, lda, dcmplx( one ), r,
225  $ lda )
226 *
227 * Compute norm( R - Q'*A ) / ( N * norm(A) * EPS ) .
228 *
229  anorm = zlange( '1', m, n, a, lda, rwork )
230  resid = zlange( '1', m, n, r, lda, rwork )
231  IF( anorm.GT.zero ) THEN
232  result( 1 ) = ( ( resid / dble( max( 1, n ) ) ) / anorm ) / eps
233  ELSE
234  result( 1 ) = zero
235  END IF
236 *
237 * Compute I - Q*Q'
238 *
239  CALL zlaset( 'Full', n, n, dcmplx( zero ), dcmplx( one ), r, lda )
240  CALL zherk( 'Upper', 'No transpose', n, n, -one, q, lda, one, r,
241  $ lda )
242 *
243 * Compute norm( I - Q*Q' ) / ( N * EPS ) .
244 *
245  resid = zlansy( '1', 'Upper', n, r, lda, rwork )
246 *
247  result( 2 ) = ( resid / dble( max( 1, n ) ) ) / eps
248 *
249  RETURN
250 *
251 * End of ZRQT01
252 *
253  END
subroutine zrqt01(M, N, A, AF, Q, R, LDA, TAU, WORK, LWORK, RWORK, RESULT)
ZRQT01
Definition: zrqt01.f:128
subroutine zungrq(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
ZUNGRQ
Definition: zungrq.f:130
subroutine zgerqf(M, N, A, LDA, TAU, WORK, LWORK, INFO)
ZGERQF
Definition: zgerqf.f:140
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 zherk(UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC)
ZHERK
Definition: zherk.f:175