LAPACK  3.4.2 LAPACK: Linear Algebra PACKage
crqt01.f
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1 *> \brief \b CRQT01
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 CRQT01( 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 * REAL RESULT( * ), RWORK( * )
19 * COMPLEX A( LDA, * ), AF( LDA, * ), Q( LDA, * ),
20 * \$ R( LDA, * ), TAU( * ), WORK( LWORK )
21 * ..
22 *
23 *
24 *> \par Purpose:
25 * =============
26 *>
27 *> \verbatim
28 *>
29 *> CRQT01 tests CGERQF, which computes the RQ factorization of an m-by-n
30 *> matrix A, and partially tests CUNGRQ which forms the n-by-n
31 *> orthogonal matrix Q.
32 *>
33 *> CRQT01 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 array, dimension (LDA,N)
54 *> The m-by-n matrix A.
55 *> \endverbatim
56 *>
57 *> \param[out] AF
58 *> \verbatim
59 *> AF is COMPLEX array, dimension (LDA,N)
60 *> Details of the RQ factorization of A, as returned by CGERQF.
61 *> See CGERQF for further details.
62 *> \endverbatim
63 *>
64 *> \param[out] Q
65 *> \verbatim
66 *> Q is COMPLEX 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 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 array, dimension (min(M,N))
85 *> The scalar factors of the elementary reflectors, as returned
86 *> by CGERQF.
87 *> \endverbatim
88 *>
89 *> \param[out] WORK
90 *> \verbatim
91 *> WORK is COMPLEX 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 REAL array, dimension (max(M,N))
103 *> \endverbatim
104 *>
105 *> \param[out] RESULT
106 *> \verbatim
107 *> RESULT is REAL 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 November 2011
122 *
123 *> \ingroup complex_lin
124 *
125 * =====================================================================
126  SUBROUTINE crqt01( M, N, A, AF, Q, R, LDA, TAU, WORK, LWORK,
127  \$ rwork, result )
128 *
129 * -- LAPACK test routine (version 3.4.0) --
130 * -- LAPACK is a software package provided by Univ. of Tennessee, --
131 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
132 * November 2011
133 *
134 * .. Scalar Arguments ..
135  INTEGER lda, lwork, m, n
136 * ..
137 * .. Array Arguments ..
138  REAL result( * ), rwork( * )
139  COMPLEX a( lda, * ), af( lda, * ), q( lda, * ),
140  \$ r( lda, * ), tau( * ), work( lwork )
141 * ..
142 *
143 * =====================================================================
144 *
145 * .. Parameters ..
146  REAL zero, one
147  parameter( zero = 0.0e+0, one = 1.0e+0 )
148  COMPLEX rogue
149  parameter( rogue = ( -1.0e+10, -1.0e+10 ) )
150 * ..
151 * .. Local Scalars ..
152  INTEGER info, minmn
153  REAL anorm, eps, resid
154 * ..
155 * .. External Functions ..
156  REAL clange, clansy, slamch
157  EXTERNAL clange, clansy, slamch
158 * ..
159 * .. External Subroutines ..
160  EXTERNAL cgemm, cgerqf, cherk, clacpy, claset, cungrq
161 * ..
162 * .. Intrinsic Functions ..
163  INTRINSIC cmplx, max, min, real
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 = slamch( 'Epsilon' )
175 *
176 * Copy the matrix A to the array AF.
177 *
178  CALL clacpy( 'Full', m, n, a, lda, af, lda )
179 *
180 * Factorize the matrix A in the array AF.
181 *
182  srnamt = 'CGERQF'
183  CALL cgerqf( m, n, af, lda, tau, work, lwork, info )
184 *
185 * Copy details of Q
186 *
187  CALL claset( 'Full', n, n, rogue, rogue, q, lda )
188  IF( m.LE.n ) THEN
189  IF( m.GT.0 .AND. m.LT.n )
190  \$ CALL clacpy( 'Full', m, n-m, af, lda, q( n-m+1, 1 ), lda )
191  IF( m.GT.1 )
192  \$ CALL clacpy( '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 clacpy( '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 = 'CUNGRQ'
203  CALL cungrq( n, n, minmn, q, lda, tau, work, lwork, info )
204 *
205 * Copy R
206 *
207  CALL claset( 'Full', m, n, cmplx( zero ), cmplx( zero ), r, lda )
208  IF( m.LE.n ) THEN
209  IF( m.GT.0 )
210  \$ CALL clacpy( 'Upper', m, m, af( 1, n-m+1 ), lda,
211  \$ r( 1, n-m+1 ), lda )
212  ELSE
213  IF( m.GT.n .AND. n.GT.0 )
214  \$ CALL clacpy( 'Full', m-n, n, af, lda, r, lda )
215  IF( n.GT.0 )
216  \$ CALL clacpy( 'Upper', n, n, af( m-n+1, 1 ), lda,
217  \$ r( m-n+1, 1 ), lda )
218  END IF
219 *
220 * Compute R - A*Q'
221 *
222  CALL cgemm( 'No transpose', 'Conjugate transpose', m, n, n,
223  \$ cmplx( -one ), a, lda, q, lda, cmplx( one ), r, lda )
224 *
225 * Compute norm( R - Q'*A ) / ( N * norm(A) * EPS ) .
226 *
227  anorm = clange( '1', m, n, a, lda, rwork )
228  resid = clange( '1', m, n, r, lda, rwork )
229  IF( anorm.GT.zero ) THEN
230  result( 1 ) = ( ( resid / REAL( MAX( 1, N ) ) ) / anorm ) / eps
231  ELSE
232  result( 1 ) = zero
233  END IF
234 *
235 * Compute I - Q*Q'
236 *
237  CALL claset( 'Full', n, n, cmplx( zero ), cmplx( one ), r, lda )
238  CALL cherk( 'Upper', 'No transpose', n, n, -one, q, lda, one, r,
239  \$ lda )
240 *
241 * Compute norm( I - Q*Q' ) / ( N * EPS ) .
242 *
243  resid = clansy( '1', 'Upper', n, r, lda, rwork )
244 *
245  result( 2 ) = ( resid / REAL( MAX( 1, N ) ) ) / eps
246 *
247  return
248 *
249 * End of CRQT01
250 *
251  END