LAPACK  3.8.0 LAPACK: Linear Algebra PACKage
zqrt01p.f
Go to the documentation of this file.
1 *> \brief \b ZQRT01P
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 ZQRT01P( 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 *> ZQRT01P tests ZGEQRFP, which computes the QR factorization of an m-by-n
30 *> matrix A, and partially tests ZUNGQR which forms the m-by-m
31 *> orthogonal matrix Q.
32 *>
33 *> ZQRT01P compares R with Q'*A, 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 QR factorization of A, as returned by ZGEQRFP.
61 *> See ZGEQRFP for further details.
62 *> \endverbatim
63 *>
64 *> \param[out] Q
65 *> \verbatim
66 *> Q is COMPLEX*16 array, dimension (LDA,M)
67 *> The m-by-m 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 R.
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 ZGEQRFP.
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 (M)
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 - Q'*A ) / ( M * norm(A) * EPS )
110 *> RESULT(2) = norm( I - Q'*Q ) / ( M * 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 zqrt01p( 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, zgeqrfp, zherk, zlacpy, zlaset, zungqr
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 = 'ZGEQRFP'
183  CALL zgeqrfp( m, n, af, lda, tau, work, lwork, info )
184 *
185 * Copy details of Q
186 *
187  CALL zlaset( 'Full', m, m, rogue, rogue, q, lda )
188  CALL zlacpy( 'Lower', m-1, n, af( 2, 1 ), lda, q( 2, 1 ), lda )
189 *
190 * Generate the m-by-m matrix Q
191 *
192  srnamt = 'ZUNGQR'
193  CALL zungqr( m, m, minmn, q, lda, tau, work, lwork, info )
194 *
195 * Copy R
196 *
197  CALL zlaset( 'Full', m, n, dcmplx( zero ), dcmplx( zero ), r,
198  \$ lda )
199  CALL zlacpy( 'Upper', m, n, af, lda, r, lda )
200 *
201 * Compute R - Q'*A
202 *
203  CALL zgemm( 'Conjugate transpose', 'No transpose', m, n, m,
204  \$ dcmplx( -one ), q, lda, a, lda, dcmplx( one ), r,
205  \$ lda )
206 *
207 * Compute norm( R - Q'*A ) / ( M * norm(A) * EPS ) .
208 *
209  anorm = zlange( '1', m, n, a, lda, rwork )
210  resid = zlange( '1', m, n, r, lda, rwork )
211  IF( anorm.GT.zero ) THEN
212  result( 1 ) = ( ( resid / dble( max( 1, m ) ) ) / anorm ) / eps
213  ELSE
214  result( 1 ) = zero
215  END IF
216 *
217 * Compute I - Q'*Q
218 *
219  CALL zlaset( 'Full', m, m, dcmplx( zero ), dcmplx( one ), r, lda )
220  CALL zherk( 'Upper', 'Conjugate transpose', m, m, -one, q, lda,
221  \$ one, r, lda )
222 *
223 * Compute norm( I - Q'*Q ) / ( M * EPS ) .
224 *
225  resid = zlansy( '1', 'Upper', m, r, lda, rwork )
226 *
227  result( 2 ) = ( resid / dble( max( 1, m ) ) ) / eps
228 *
229  RETURN
230 *
231 * End of ZQRT01P
232 *
233  END
subroutine zgeqrfp(M, N, A, LDA, TAU, WORK, LWORK, INFO)
ZGEQRFP
Definition: zgeqrfp.f:141
subroutine zqrt01p(M, N, A, AF, Q, R, LDA, TAU, WORK, LWORK, RWORK, RESULT)
ZQRT01P
Definition: zqrt01p.f:128
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 zungqr(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
ZUNGQR
Definition: zungqr.f:130
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