LAPACK  3.10.1
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 *> \ingroup complex16_lin
122 *
123 * =====================================================================
124  SUBROUTINE zrqt01( M, N, A, AF, Q, R, LDA, TAU, WORK, LWORK,
125  $ RWORK, RESULT )
126 *
127 * -- LAPACK test routine --
128 * -- LAPACK is a software package provided by Univ. of Tennessee, --
129 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
130 *
131 * .. Scalar Arguments ..
132  INTEGER LDA, LWORK, M, N
133 * ..
134 * .. Array Arguments ..
135  DOUBLE PRECISION RESULT( * ), RWORK( * )
136  COMPLEX*16 A( LDA, * ), AF( LDA, * ), Q( LDA, * ),
137  $ r( lda, * ), tau( * ), work( lwork )
138 * ..
139 *
140 * =====================================================================
141 *
142 * .. Parameters ..
143  DOUBLE PRECISION ZERO, ONE
144  parameter( zero = 0.0d+0, one = 1.0d+0 )
145  COMPLEX*16 ROGUE
146  parameter( rogue = ( -1.0d+10, -1.0d+10 ) )
147 * ..
148 * .. Local Scalars ..
149  INTEGER INFO, MINMN
150  DOUBLE PRECISION ANORM, EPS, RESID
151 * ..
152 * .. External Functions ..
153  DOUBLE PRECISION DLAMCH, ZLANGE, ZLANSY
154  EXTERNAL dlamch, zlange, zlansy
155 * ..
156 * .. External Subroutines ..
157  EXTERNAL zgemm, zgerqf, zherk, zlacpy, zlaset, zungrq
158 * ..
159 * .. Intrinsic Functions ..
160  INTRINSIC dble, dcmplx, max, min
161 * ..
162 * .. Scalars in Common ..
163  CHARACTER*32 SRNAMT
164 * ..
165 * .. Common blocks ..
166  COMMON / srnamc / srnamt
167 * ..
168 * .. Executable Statements ..
169 *
170  minmn = min( m, n )
171  eps = dlamch( 'Epsilon' )
172 *
173 * Copy the matrix A to the array AF.
174 *
175  CALL zlacpy( 'Full', m, n, a, lda, af, lda )
176 *
177 * Factorize the matrix A in the array AF.
178 *
179  srnamt = 'ZGERQF'
180  CALL zgerqf( m, n, af, lda, tau, work, lwork, info )
181 *
182 * Copy details of Q
183 *
184  CALL zlaset( 'Full', n, n, rogue, rogue, q, lda )
185  IF( m.LE.n ) THEN
186  IF( m.GT.0 .AND. m.LT.n )
187  $ CALL zlacpy( 'Full', m, n-m, af, lda, q( n-m+1, 1 ), lda )
188  IF( m.GT.1 )
189  $ CALL zlacpy( 'Lower', m-1, m-1, af( 2, n-m+1 ), lda,
190  $ q( n-m+2, n-m+1 ), lda )
191  ELSE
192  IF( n.GT.1 )
193  $ CALL zlacpy( 'Lower', n-1, n-1, af( m-n+2, 1 ), lda,
194  $ q( 2, 1 ), lda )
195  END IF
196 *
197 * Generate the n-by-n matrix Q
198 *
199  srnamt = 'ZUNGRQ'
200  CALL zungrq( n, n, minmn, q, lda, tau, work, lwork, info )
201 *
202 * Copy R
203 *
204  CALL zlaset( 'Full', m, n, dcmplx( zero ), dcmplx( zero ), r,
205  $ lda )
206  IF( m.LE.n ) THEN
207  IF( m.GT.0 )
208  $ CALL zlacpy( 'Upper', m, m, af( 1, n-m+1 ), lda,
209  $ r( 1, n-m+1 ), lda )
210  ELSE
211  IF( m.GT.n .AND. n.GT.0 )
212  $ CALL zlacpy( 'Full', m-n, n, af, lda, r, lda )
213  IF( n.GT.0 )
214  $ CALL zlacpy( 'Upper', n, n, af( m-n+1, 1 ), lda,
215  $ r( m-n+1, 1 ), lda )
216  END IF
217 *
218 * Compute R - A*Q'
219 *
220  CALL zgemm( 'No transpose', 'Conjugate transpose', m, n, n,
221  $ dcmplx( -one ), a, lda, q, lda, dcmplx( one ), r,
222  $ lda )
223 *
224 * Compute norm( R - Q'*A ) / ( N * norm(A) * EPS ) .
225 *
226  anorm = zlange( '1', m, n, a, lda, rwork )
227  resid = zlange( '1', m, n, r, lda, rwork )
228  IF( anorm.GT.zero ) THEN
229  result( 1 ) = ( ( resid / dble( max( 1, n ) ) ) / anorm ) / eps
230  ELSE
231  result( 1 ) = zero
232  END IF
233 *
234 * Compute I - Q*Q'
235 *
236  CALL zlaset( 'Full', n, n, dcmplx( zero ), dcmplx( one ), r, lda )
237  CALL zherk( 'Upper', 'No transpose', n, n, -one, q, lda, one, r,
238  $ lda )
239 *
240 * Compute norm( I - Q*Q' ) / ( N * EPS ) .
241 *
242  resid = zlansy( '1', 'Upper', n, r, lda, rwork )
243 *
244  result( 2 ) = ( resid / dble( max( 1, n ) ) ) / eps
245 *
246  RETURN
247 *
248 * End of ZRQT01
249 *
250  END
subroutine zgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
ZGEMM
Definition: zgemm.f:187
subroutine zherk(UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC)
ZHERK
Definition: zherk.f:173
subroutine zrqt01(M, N, A, AF, Q, R, LDA, TAU, WORK, LWORK, RWORK, RESULT)
ZRQT01
Definition: zrqt01.f:126
subroutine zgerqf(M, N, A, LDA, TAU, WORK, LWORK, INFO)
ZGERQF
Definition: zgerqf.f:139
subroutine zlacpy(UPLO, M, N, A, LDA, B, LDB)
ZLACPY copies all or part of one two-dimensional array to another.
Definition: zlacpy.f:103
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:106
subroutine zungrq(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
ZUNGRQ
Definition: zungrq.f:128