LAPACK  3.8.0
LAPACK: Linear Algebra PACKage
zlqt02.f
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1 *> \brief \b ZLQT02
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 ZLQT02( M, N, K, A, AF, Q, L, 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 A( LDA, * ), AF( LDA, * ), L( LDA, * ),
20 * $ Q( LDA, * ), TAU( * ), WORK( LWORK )
21 * ..
22 *
23 *
24 *> \par Purpose:
25 * =============
26 *>
27 *> \verbatim
28 *>
29 *> ZLQT02 tests ZUNGLQ, which generates an m-by-n matrix Q with
30 *> orthonornmal rows that is defined as the product of k elementary
31 *> reflectors.
32 *>
33 *> Given the LQ factorization of an m-by-n matrix A, ZLQT02 generates
34 *> the orthogonal matrix Q defined by the factorization of the first k
35 *> rows of A; it compares L(1:k,1:m) with A(1:k,1:n)*Q(1:m,1:n)', and
36 *> checks that the rows of Q are orthonormal.
37 *> \endverbatim
38 *
39 * Arguments:
40 * ==========
41 *
42 *> \param[in] M
43 *> \verbatim
44 *> M is INTEGER
45 *> The number of rows of the matrix Q to be generated. M >= 0.
46 *> \endverbatim
47 *>
48 *> \param[in] N
49 *> \verbatim
50 *> N is INTEGER
51 *> The number of columns of the matrix Q to be generated.
52 *> N >= M >= 0.
53 *> \endverbatim
54 *>
55 *> \param[in] K
56 *> \verbatim
57 *> K is INTEGER
58 *> The number of elementary reflectors whose product defines the
59 *> matrix Q. M >= K >= 0.
60 *> \endverbatim
61 *>
62 *> \param[in] A
63 *> \verbatim
64 *> A is COMPLEX*16 array, dimension (LDA,N)
65 *> The m-by-n matrix A which was factorized by ZLQT01.
66 *> \endverbatim
67 *>
68 *> \param[in] AF
69 *> \verbatim
70 *> AF is COMPLEX*16 array, dimension (LDA,N)
71 *> Details of the LQ factorization of A, as returned by ZGELQF.
72 *> See ZGELQF for further details.
73 *> \endverbatim
74 *>
75 *> \param[out] Q
76 *> \verbatim
77 *> Q is COMPLEX*16 array, dimension (LDA,N)
78 *> \endverbatim
79 *>
80 *> \param[out] L
81 *> \verbatim
82 *> L is COMPLEX*16 array, dimension (LDA,M)
83 *> \endverbatim
84 *>
85 *> \param[in] LDA
86 *> \verbatim
87 *> LDA is INTEGER
88 *> The leading dimension of the arrays A, AF, Q and L. LDA >= N.
89 *> \endverbatim
90 *>
91 *> \param[in] TAU
92 *> \verbatim
93 *> TAU is COMPLEX*16 array, dimension (M)
94 *> The scalar factors of the elementary reflectors corresponding
95 *> to the LQ factorization in AF.
96 *> \endverbatim
97 *>
98 *> \param[out] WORK
99 *> \verbatim
100 *> WORK is COMPLEX*16 array, dimension (LWORK)
101 *> \endverbatim
102 *>
103 *> \param[in] LWORK
104 *> \verbatim
105 *> LWORK is INTEGER
106 *> The dimension of the array WORK.
107 *> \endverbatim
108 *>
109 *> \param[out] RWORK
110 *> \verbatim
111 *> RWORK is DOUBLE PRECISION array, dimension (M)
112 *> \endverbatim
113 *>
114 *> \param[out] RESULT
115 *> \verbatim
116 *> RESULT is DOUBLE PRECISION array, dimension (2)
117 *> The test ratios:
118 *> RESULT(1) = norm( L - A*Q' ) / ( N * norm(A) * EPS )
119 *> RESULT(2) = norm( I - Q*Q' ) / ( N * EPS )
120 *> \endverbatim
121 *
122 * Authors:
123 * ========
124 *
125 *> \author Univ. of Tennessee
126 *> \author Univ. of California Berkeley
127 *> \author Univ. of Colorado Denver
128 *> \author NAG Ltd.
129 *
130 *> \date December 2016
131 *
132 *> \ingroup complex16_lin
133 *
134 * =====================================================================
135  SUBROUTINE zlqt02( M, N, K, A, AF, Q, L, LDA, TAU, WORK, LWORK,
136  $ RWORK, RESULT )
137 *
138 * -- LAPACK test routine (version 3.7.0) --
139 * -- LAPACK is a software package provided by Univ. of Tennessee, --
140 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
141 * December 2016
142 *
143 * .. Scalar Arguments ..
144  INTEGER K, LDA, LWORK, M, N
145 * ..
146 * .. Array Arguments ..
147  DOUBLE PRECISION RESULT( * ), RWORK( * )
148  COMPLEX*16 A( lda, * ), AF( lda, * ), L( lda, * ),
149  $ q( lda, * ), tau( * ), work( lwork )
150 * ..
151 *
152 * =====================================================================
153 *
154 * .. Parameters ..
155  DOUBLE PRECISION ZERO, ONE
156  parameter( zero = 0.0d+0, one = 1.0d+0 )
157  COMPLEX*16 ROGUE
158  parameter( rogue = ( -1.0d+10, -1.0d+10 ) )
159 * ..
160 * .. Local Scalars ..
161  INTEGER INFO
162  DOUBLE PRECISION ANORM, EPS, RESID
163 * ..
164 * .. External Functions ..
165  DOUBLE PRECISION DLAMCH, ZLANGE, ZLANSY
166  EXTERNAL dlamch, zlange, zlansy
167 * ..
168 * .. External Subroutines ..
169  EXTERNAL zgemm, zherk, zlacpy, zlaset, zunglq
170 * ..
171 * .. Intrinsic Functions ..
172  INTRINSIC dble, dcmplx, max
173 * ..
174 * .. Scalars in Common ..
175  CHARACTER*32 SRNAMT
176 * ..
177 * .. Common blocks ..
178  COMMON / srnamc / srnamt
179 * ..
180 * .. Executable Statements ..
181 *
182  eps = dlamch( 'Epsilon' )
183 *
184 * Copy the first k rows of the factorization to the array Q
185 *
186  CALL zlaset( 'Full', m, n, rogue, rogue, q, lda )
187  CALL zlacpy( 'Upper', k, n-1, af( 1, 2 ), lda, q( 1, 2 ), lda )
188 *
189 * Generate the first n columns of the matrix Q
190 *
191  srnamt = 'ZUNGLQ'
192  CALL zunglq( m, n, k, q, lda, tau, work, lwork, info )
193 *
194 * Copy L(1:k,1:m)
195 *
196  CALL zlaset( 'Full', k, m, dcmplx( zero ), dcmplx( zero ), l,
197  $ lda )
198  CALL zlacpy( 'Lower', k, m, af, lda, l, lda )
199 *
200 * Compute L(1:k,1:m) - A(1:k,1:n) * Q(1:m,1:n)'
201 *
202  CALL zgemm( 'No transpose', 'Conjugate transpose', k, m, n,
203  $ dcmplx( -one ), a, lda, q, lda, dcmplx( one ), l,
204  $ lda )
205 *
206 * Compute norm( L - A*Q' ) / ( N * norm(A) * EPS ) .
207 *
208  anorm = zlange( '1', k, n, a, lda, rwork )
209  resid = zlange( '1', k, m, l, lda, rwork )
210  IF( anorm.GT.zero ) THEN
211  result( 1 ) = ( ( resid / dble( max( 1, n ) ) ) / anorm ) / eps
212  ELSE
213  result( 1 ) = zero
214  END IF
215 *
216 * Compute I - Q*Q'
217 *
218  CALL zlaset( 'Full', m, m, dcmplx( zero ), dcmplx( one ), l, lda )
219  CALL zherk( 'Upper', 'No transpose', m, n, -one, q, lda, one, l,
220  $ lda )
221 *
222 * Compute norm( I - Q*Q' ) / ( N * EPS ) .
223 *
224  resid = zlansy( '1', 'Upper', m, l, lda, rwork )
225 *
226  result( 2 ) = ( resid / dble( max( 1, n ) ) ) / eps
227 *
228  RETURN
229 *
230 * End of ZLQT02
231 *
232  END
subroutine zlqt02(M, N, K, A, AF, Q, L, LDA, TAU, WORK, LWORK, RWORK, RESULT)
ZLQT02
Definition: zlqt02.f:137
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
subroutine zunglq(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
ZUNGLQ
Definition: zunglq.f:129