LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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zqrt01.f
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1*> \brief \b ZQRT01
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 ZQRT01( 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*> ZQRT01 tests ZGEQRF, 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*> ZQRT01 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 ZGEQRF.
61*> See ZGEQRF 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 ZGEQRF.
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*> \ingroup complex16_lin
122*
123* =====================================================================
124 SUBROUTINE zqrt01( 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, zgeqrf, zherk, zlacpy, zlaset, zungqr
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 = 'ZGEQRF'
180 CALL zgeqrf( m, n, af, lda, tau, work, lwork, info )
181*
182* Copy details of Q
183*
184 CALL zlaset( 'Full', m, m, rogue, rogue, q, lda )
185 CALL zlacpy( 'Lower', m-1, n, af( 2, 1 ), lda, q( 2, 1 ), lda )
186*
187* Generate the m-by-m matrix Q
188*
189 srnamt = 'ZUNGQR'
190 CALL zungqr( m, m, minmn, q, lda, tau, work, lwork, info )
191*
192* Copy R
193*
194 CALL zlaset( 'Full', m, n, dcmplx( zero ), dcmplx( zero ), r,
195 \$ lda )
196 CALL zlacpy( 'Upper', m, n, af, lda, r, lda )
197*
198* Compute R - Q'*A
199*
200 CALL zgemm( 'Conjugate transpose', 'No transpose', m, n, m,
201 \$ dcmplx( -one ), q, lda, a, lda, dcmplx( one ), r,
202 \$ lda )
203*
204* Compute norm( R - Q'*A ) / ( M * norm(A) * EPS ) .
205*
206 anorm = zlange( '1', m, n, a, lda, rwork )
207 resid = zlange( '1', m, n, r, lda, rwork )
208 IF( anorm.GT.zero ) THEN
209 result( 1 ) = ( ( resid / dble( max( 1, m ) ) ) / anorm ) / eps
210 ELSE
211 result( 1 ) = zero
212 END IF
213*
214* Compute I - Q'*Q
215*
216 CALL zlaset( 'Full', m, m, dcmplx( zero ), dcmplx( one ), r, lda )
217 CALL zherk( 'Upper', 'Conjugate transpose', m, m, -one, q, lda,
218 \$ one, r, lda )
219*
220* Compute norm( I - Q'*Q ) / ( M * EPS ) .
221*
222 resid = zlansy( '1', 'Upper', m, r, lda, rwork )
223*
224 result( 2 ) = ( resid / dble( max( 1, m ) ) ) / eps
225*
226 RETURN
227*
228* End of ZQRT01
229*
230 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 zqrt01(M, N, A, AF, Q, R, LDA, TAU, WORK, LWORK, RWORK, RESULT)
ZQRT01
Definition: zqrt01.f:126
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
subroutine zgeqrf(M, N, A, LDA, TAU, WORK, LWORK, INFO)
ZGEQRF VARIANT: left-looking Level 3 BLAS of the algorithm.
Definition: zgeqrf.f:152