LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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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*> \ingroup complex_lin
122*
123* =====================================================================
124 SUBROUTINE crqt01( 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 REAL RESULT( * ), RWORK( * )
136 COMPLEX A( LDA, * ), AF( LDA, * ), Q( LDA, * ),
137 \$ r( lda, * ), tau( * ), work( lwork )
138* ..
139*
140* =====================================================================
141*
142* .. Parameters ..
143 REAL ZERO, ONE
144 parameter( zero = 0.0e+0, one = 1.0e+0 )
145 COMPLEX ROGUE
146 parameter( rogue = ( -1.0e+10, -1.0e+10 ) )
147* ..
148* .. Local Scalars ..
149 INTEGER INFO, MINMN
150 REAL ANORM, EPS, RESID
151* ..
152* .. External Functions ..
153 REAL CLANGE, CLANSY, SLAMCH
154 EXTERNAL clange, clansy, slamch
155* ..
156* .. External Subroutines ..
157 EXTERNAL cgemm, cgerqf, cherk, clacpy, claset, cungrq
158* ..
159* .. Intrinsic Functions ..
160 INTRINSIC cmplx, max, min, real
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 = slamch( 'Epsilon' )
172*
173* Copy the matrix A to the array AF.
174*
175 CALL clacpy( 'Full', m, n, a, lda, af, lda )
176*
177* Factorize the matrix A in the array AF.
178*
179 srnamt = 'CGERQF'
180 CALL cgerqf( m, n, af, lda, tau, work, lwork, info )
181*
182* Copy details of Q
183*
184 CALL claset( 'Full', n, n, rogue, rogue, q, lda )
185 IF( m.LE.n ) THEN
186 IF( m.GT.0 .AND. m.LT.n )
187 \$ CALL clacpy( 'Full', m, n-m, af, lda, q( n-m+1, 1 ), lda )
188 IF( m.GT.1 )
189 \$ CALL clacpy( '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 clacpy( '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 = 'CUNGRQ'
200 CALL cungrq( n, n, minmn, q, lda, tau, work, lwork, info )
201*
202* Copy R
203*
204 CALL claset( 'Full', m, n, cmplx( zero ), cmplx( zero ), r, lda )
205 IF( m.LE.n ) THEN
206 IF( m.GT.0 )
207 \$ CALL clacpy( 'Upper', m, m, af( 1, n-m+1 ), lda,
208 \$ r( 1, n-m+1 ), lda )
209 ELSE
210 IF( m.GT.n .AND. n.GT.0 )
211 \$ CALL clacpy( 'Full', m-n, n, af, lda, r, lda )
212 IF( n.GT.0 )
213 \$ CALL clacpy( 'Upper', n, n, af( m-n+1, 1 ), lda,
214 \$ r( m-n+1, 1 ), lda )
215 END IF
216*
217* Compute R - A*Q'
218*
219 CALL cgemm( 'No transpose', 'Conjugate transpose', m, n, n,
220 \$ cmplx( -one ), a, lda, q, lda, cmplx( one ), r, lda )
221*
222* Compute norm( R - Q'*A ) / ( N * norm(A) * EPS ) .
223*
224 anorm = clange( '1', m, n, a, lda, rwork )
225 resid = clange( '1', m, n, r, lda, rwork )
226 IF( anorm.GT.zero ) THEN
227 result( 1 ) = ( ( resid / real( max( 1, n ) ) ) / anorm ) / eps
228 ELSE
229 result( 1 ) = zero
230 END IF
231*
232* Compute I - Q*Q'
233*
234 CALL claset( 'Full', n, n, cmplx( zero ), cmplx( one ), r, lda )
235 CALL cherk( 'Upper', 'No transpose', n, n, -one, q, lda, one, r,
236 \$ lda )
237*
238* Compute norm( I - Q*Q' ) / ( N * EPS ) .
239*
240 resid = clansy( '1', 'Upper', n, r, lda, rwork )
241*
242 result( 2 ) = ( resid / real( max( 1, n ) ) ) / eps
243*
244 RETURN
245*
246* End of CRQT01
247*
248 END
subroutine cgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
CGEMM
Definition: cgemm.f:187
subroutine cherk(UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC)
CHERK
Definition: cherk.f:173
subroutine crqt01(M, N, A, AF, Q, R, LDA, TAU, WORK, LWORK, RWORK, RESULT)
CRQT01
Definition: crqt01.f:126
subroutine cgerqf(M, N, A, LDA, TAU, WORK, LWORK, INFO)
CGERQF
Definition: cgerqf.f:139
subroutine claset(UPLO, M, N, ALPHA, BETA, A, LDA)
CLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition: claset.f:106
subroutine clacpy(UPLO, M, N, A, LDA, B, LDB)
CLACPY copies all or part of one two-dimensional array to another.
Definition: clacpy.f:103
subroutine cungrq(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
CUNGRQ
Definition: cungrq.f:128