LAPACK  3.10.0
LAPACK: Linear Algebra PACKage
zqrt02.f
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1 *> \brief \b ZQRT02
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 ZQRT02( M, N, K, A, AF, Q, R, 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, * ), Q( LDA, * ),
20 * $ R( LDA, * ), TAU( * ), WORK( LWORK )
21 * ..
22 *
23 *
24 *> \par Purpose:
25 * =============
26 *>
27 *> \verbatim
28 *>
29 *> ZQRT02 tests ZUNGQR, which generates an m-by-n matrix Q with
30 *> orthonornmal columns that is defined as the product of k elementary
31 *> reflectors.
32 *>
33 *> Given the QR factorization of an m-by-n matrix A, ZQRT02 generates
34 *> the orthogonal matrix Q defined by the factorization of the first k
35 *> columns of A; it compares R(1:n,1:k) with Q(1:m,1:n)'*A(1:m,1:k),
36 *> and checks that the columns 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 *> M >= N >= 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. N >= 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 ZQRT01.
66 *> \endverbatim
67 *>
68 *> \param[in] AF
69 *> \verbatim
70 *> AF is COMPLEX*16 array, dimension (LDA,N)
71 *> Details of the QR factorization of A, as returned by ZGEQRF.
72 *> See ZGEQRF 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] R
81 *> \verbatim
82 *> R is COMPLEX*16 array, dimension (LDA,N)
83 *> \endverbatim
84 *>
85 *> \param[in] LDA
86 *> \verbatim
87 *> LDA is INTEGER
88 *> The leading dimension of the arrays A, AF, Q and R. LDA >= M.
89 *> \endverbatim
90 *>
91 *> \param[in] TAU
92 *> \verbatim
93 *> TAU is COMPLEX*16 array, dimension (N)
94 *> The scalar factors of the elementary reflectors corresponding
95 *> to the QR 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( R - Q'*A ) / ( M * norm(A) * EPS )
119 *> RESULT(2) = norm( I - Q'*Q ) / ( M * 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 *> \ingroup complex16_lin
131 *
132 * =====================================================================
133  SUBROUTINE zqrt02( M, N, K, A, AF, Q, R, LDA, TAU, WORK, LWORK,
134  $ RWORK, RESULT )
135 *
136 * -- LAPACK test routine --
137 * -- LAPACK is a software package provided by Univ. of Tennessee, --
138 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
139 *
140 * .. Scalar Arguments ..
141  INTEGER K, LDA, LWORK, M, N
142 * ..
143 * .. Array Arguments ..
144  DOUBLE PRECISION RESULT( * ), RWORK( * )
145  COMPLEX*16 A( LDA, * ), AF( LDA, * ), Q( LDA, * ),
146  $ r( lda, * ), tau( * ), work( lwork )
147 * ..
148 *
149 * =====================================================================
150 *
151 * .. Parameters ..
152  DOUBLE PRECISION ZERO, ONE
153  parameter( zero = 0.0d+0, one = 1.0d+0 )
154  COMPLEX*16 ROGUE
155  parameter( rogue = ( -1.0d+10, -1.0d+10 ) )
156 * ..
157 * .. Local Scalars ..
158  INTEGER INFO
159  DOUBLE PRECISION ANORM, EPS, RESID
160 * ..
161 * .. External Functions ..
162  DOUBLE PRECISION DLAMCH, ZLANGE, ZLANSY
163  EXTERNAL dlamch, zlange, zlansy
164 * ..
165 * .. External Subroutines ..
166  EXTERNAL zgemm, zherk, zlacpy, zlaset, zungqr
167 * ..
168 * .. Intrinsic Functions ..
169  INTRINSIC dble, dcmplx, max
170 * ..
171 * .. Scalars in Common ..
172  CHARACTER*32 SRNAMT
173 * ..
174 * .. Common blocks ..
175  COMMON / srnamc / srnamt
176 * ..
177 * .. Executable Statements ..
178 *
179  eps = dlamch( 'Epsilon' )
180 *
181 * Copy the first k columns of the factorization to the array Q
182 *
183  CALL zlaset( 'Full', m, n, rogue, rogue, q, lda )
184  CALL zlacpy( 'Lower', m-1, k, af( 2, 1 ), lda, q( 2, 1 ), lda )
185 *
186 * Generate the first n columns of the matrix Q
187 *
188  srnamt = 'ZUNGQR'
189  CALL zungqr( m, n, k, q, lda, tau, work, lwork, info )
190 *
191 * Copy R(1:n,1:k)
192 *
193  CALL zlaset( 'Full', n, k, dcmplx( zero ), dcmplx( zero ), r,
194  $ lda )
195  CALL zlacpy( 'Upper', n, k, af, lda, r, lda )
196 *
197 * Compute R(1:n,1:k) - Q(1:m,1:n)' * A(1:m,1:k)
198 *
199  CALL zgemm( 'Conjugate transpose', 'No transpose', n, k, m,
200  $ dcmplx( -one ), q, lda, a, lda, dcmplx( one ), r,
201  $ lda )
202 *
203 * Compute norm( R - Q'*A ) / ( M * norm(A) * EPS ) .
204 *
205  anorm = zlange( '1', m, k, a, lda, rwork )
206  resid = zlange( '1', n, k, r, lda, rwork )
207  IF( anorm.GT.zero ) THEN
208  result( 1 ) = ( ( resid / dble( max( 1, m ) ) ) / anorm ) / eps
209  ELSE
210  result( 1 ) = zero
211  END IF
212 *
213 * Compute I - Q'*Q
214 *
215  CALL zlaset( 'Full', n, n, dcmplx( zero ), dcmplx( one ), r, lda )
216  CALL zherk( 'Upper', 'Conjugate transpose', n, m, -one, q, lda,
217  $ one, r, lda )
218 *
219 * Compute norm( I - Q'*Q ) / ( M * EPS ) .
220 *
221  resid = zlansy( '1', 'Upper', n, r, lda, rwork )
222 *
223  result( 2 ) = ( resid / dble( max( 1, m ) ) ) / eps
224 *
225  RETURN
226 *
227 * End of ZQRT02
228 *
229  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 zqrt02(M, N, K, A, AF, Q, R, LDA, TAU, WORK, LWORK, RWORK, RESULT)
ZQRT02
Definition: zqrt02.f:135
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 zungqr(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
ZUNGQR
Definition: zungqr.f:128