LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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dqlt01.f
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1*> \brief \b DQLT01
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 DQLT01( M, N, A, AF, Q, L, LDA, TAU, WORK, LWORK,
12* RWORK, RESULT )
13*
14* .. Scalar Arguments ..
15* INTEGER LDA, LWORK, M, N
16* ..
17* .. Array Arguments ..
18* DOUBLE PRECISION A( LDA, * ), AF( LDA, * ), L( LDA, * ),
19* \$ Q( LDA, * ), RESULT( * ), RWORK( * ), TAU( * ),
20* \$ WORK( LWORK )
21* ..
22*
23*
24*> \par Purpose:
25* =============
26*>
27*> \verbatim
28*>
29*> DQLT01 tests DGEQLF, which computes the QL factorization of an m-by-n
30*> matrix A, and partially tests DORGQL which forms the m-by-m
31*> orthogonal matrix Q.
32*>
33*> DQLT01 compares L 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 DOUBLE PRECISION array, dimension (LDA,N)
54*> The m-by-n matrix A.
55*> \endverbatim
56*>
57*> \param[out] AF
58*> \verbatim
59*> AF is DOUBLE PRECISION array, dimension (LDA,N)
60*> Details of the QL factorization of A, as returned by DGEQLF.
61*> See DGEQLF for further details.
62*> \endverbatim
63*>
64*> \param[out] Q
65*> \verbatim
66*> Q is DOUBLE PRECISION array, dimension (LDA,M)
67*> The m-by-m orthogonal matrix Q.
68*> \endverbatim
69*>
70*> \param[out] L
71*> \verbatim
72*> L is DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (min(M,N))
85*> The scalar factors of the elementary reflectors, as returned
86*> by DGEQLF.
87*> \endverbatim
88*>
89*> \param[out] WORK
90*> \verbatim
91*> WORK is DOUBLE PRECISION 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( L - 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 double_lin
122*
123* =====================================================================
124 SUBROUTINE dqlt01( M, N, A, AF, Q, L, 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 A( LDA, * ), AF( LDA, * ), L( LDA, * ),
136 \$ q( lda, * ), result( * ), rwork( * ), tau( * ),
137 \$ work( lwork )
138* ..
139*
140* =====================================================================
141*
142* .. Parameters ..
143 DOUBLE PRECISION ZERO, ONE
144 parameter( zero = 0.0d+0, one = 1.0d+0 )
145 DOUBLE PRECISION ROGUE
146 parameter( rogue = -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, DLANGE, DLANSY
154 EXTERNAL dlamch, dlange, dlansy
155* ..
156* .. External Subroutines ..
157 EXTERNAL dgemm, dgeqlf, dlacpy, dlaset, dorgql, dsyrk
158* ..
159* .. Intrinsic Functions ..
160 INTRINSIC dble, 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 dlacpy( 'Full', m, n, a, lda, af, lda )
176*
177* Factorize the matrix A in the array AF.
178*
179 srnamt = 'DGEQLF'
180 CALL dgeqlf( m, n, af, lda, tau, work, lwork, info )
181*
182* Copy details of Q
183*
184 CALL dlaset( 'Full', m, m, rogue, rogue, q, lda )
185 IF( m.GE.n ) THEN
186 IF( n.LT.m .AND. n.GT.0 )
187 \$ CALL dlacpy( 'Full', m-n, n, af, lda, q( 1, m-n+1 ), lda )
188 IF( n.GT.1 )
189 \$ CALL dlacpy( 'Upper', n-1, n-1, af( m-n+1, 2 ), lda,
190 \$ q( m-n+1, m-n+2 ), lda )
191 ELSE
192 IF( m.GT.1 )
193 \$ CALL dlacpy( 'Upper', m-1, m-1, af( 1, n-m+2 ), lda,
194 \$ q( 1, 2 ), lda )
195 END IF
196*
197* Generate the m-by-m matrix Q
198*
199 srnamt = 'DORGQL'
200 CALL dorgql( m, m, minmn, q, lda, tau, work, lwork, info )
201*
202* Copy L
203*
204 CALL dlaset( 'Full', m, n, zero, zero, l, lda )
205 IF( m.GE.n ) THEN
206 IF( n.GT.0 )
207 \$ CALL dlacpy( 'Lower', n, n, af( m-n+1, 1 ), lda,
208 \$ l( m-n+1, 1 ), lda )
209 ELSE
210 IF( n.GT.m .AND. m.GT.0 )
211 \$ CALL dlacpy( 'Full', m, n-m, af, lda, l, lda )
212 IF( m.GT.0 )
213 \$ CALL dlacpy( 'Lower', m, m, af( 1, n-m+1 ), lda,
214 \$ l( 1, n-m+1 ), lda )
215 END IF
216*
217* Compute L - Q'*A
218*
219 CALL dgemm( 'Transpose', 'No transpose', m, n, m, -one, q, lda, a,
220 \$ lda, one, l, lda )
221*
222* Compute norm( L - Q'*A ) / ( M * norm(A) * EPS ) .
223*
224 anorm = dlange( '1', m, n, a, lda, rwork )
225 resid = dlange( '1', m, n, l, lda, rwork )
226 IF( anorm.GT.zero ) THEN
227 result( 1 ) = ( ( resid / dble( max( 1, m ) ) ) / anorm ) / eps
228 ELSE
229 result( 1 ) = zero
230 END IF
231*
232* Compute I - Q'*Q
233*
234 CALL dlaset( 'Full', m, m, zero, one, l, lda )
235 CALL dsyrk( 'Upper', 'Transpose', m, m, -one, q, lda, one, l,
236 \$ lda )
237*
238* Compute norm( I - Q'*Q ) / ( M * EPS ) .
239*
240 resid = dlansy( '1', 'Upper', m, l, lda, rwork )
241*
242 result( 2 ) = ( resid / dble( max( 1, m ) ) ) / eps
243*
244 RETURN
245*
246* End of DQLT01
247*
248 END
subroutine dlacpy(UPLO, M, N, A, LDA, B, LDB)
DLACPY copies all or part of one two-dimensional array to another.
Definition: dlacpy.f:103
subroutine dlaset(UPLO, M, N, ALPHA, BETA, A, LDA)
DLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition: dlaset.f:110
subroutine dsyrk(UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC)
DSYRK
Definition: dsyrk.f:169
subroutine dgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
DGEMM
Definition: dgemm.f:187
subroutine dqlt01(M, N, A, AF, Q, L, LDA, TAU, WORK, LWORK, RWORK, RESULT)
DQLT01
Definition: dqlt01.f:126
subroutine dgeqlf(M, N, A, LDA, TAU, WORK, LWORK, INFO)
DGEQLF
Definition: dgeqlf.f:138
subroutine dorgql(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
DORGQL
Definition: dorgql.f:128