LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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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:188
subroutine zgerqf(m, n, a, lda, tau, work, lwork, info)
ZGERQF
Definition zgerqf.f:139
subroutine zherk(uplo, trans, n, k, alpha, a, lda, beta, c, ldc)
ZHERK
Definition zherk.f:173
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
subroutine zrqt01(m, n, a, af, q, r, lda, tau, work, lwork, rwork, result)
ZRQT01
Definition zrqt01.f:126