LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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dqlt02.f
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1*> \brief \b DQLT02
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 DQLT02( M, N, K, A, AF, Q, L, LDA, TAU, WORK, LWORK,
12* RWORK, RESULT )
13*
14* .. Scalar Arguments ..
15* INTEGER K, 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*> DQLT02 tests DORGQL, which generates an m-by-n matrix Q with
30*> orthonormal columns that is defined as the product of k elementary
31*> reflectors.
32*>
33*> Given the QL factorization of an m-by-n matrix A, DQLT02 generates
34*> the orthogonal matrix Q defined by the factorization of the last k
35*> columns of A; it compares L(m-n+1:m,n-k+1:n) with
36*> Q(1:m,m-n+1:m)'*A(1:m,n-k+1:n), and checks that the columns of Q are
37*> orthonormal.
38*> \endverbatim
39*
40* Arguments:
41* ==========
42*
43*> \param[in] M
44*> \verbatim
45*> M is INTEGER
46*> The number of rows of the matrix Q to be generated. M >= 0.
47*> \endverbatim
48*>
49*> \param[in] N
50*> \verbatim
51*> N is INTEGER
52*> The number of columns of the matrix Q to be generated.
53*> M >= N >= 0.
54*> \endverbatim
55*>
56*> \param[in] K
57*> \verbatim
58*> K is INTEGER
59*> The number of elementary reflectors whose product defines the
60*> matrix Q. N >= K >= 0.
61*> \endverbatim
62*>
63*> \param[in] A
64*> \verbatim
65*> A is DOUBLE PRECISION array, dimension (LDA,N)
66*> The m-by-n matrix A which was factorized by DQLT01.
67*> \endverbatim
68*>
69*> \param[in] AF
70*> \verbatim
71*> AF is DOUBLE PRECISION array, dimension (LDA,N)
72*> Details of the QL factorization of A, as returned by DGEQLF.
73*> See DGEQLF for further details.
74*> \endverbatim
75*>
76*> \param[out] Q
77*> \verbatim
78*> Q is DOUBLE PRECISION array, dimension (LDA,N)
79*> \endverbatim
80*>
81*> \param[out] L
82*> \verbatim
83*> L is DOUBLE PRECISION array, dimension (LDA,N)
84*> \endverbatim
85*>
86*> \param[in] LDA
87*> \verbatim
88*> LDA is INTEGER
89*> The leading dimension of the arrays A, AF, Q and L. LDA >= M.
90*> \endverbatim
91*>
92*> \param[in] TAU
93*> \verbatim
94*> TAU is DOUBLE PRECISION array, dimension (N)
95*> The scalar factors of the elementary reflectors corresponding
96*> to the QL factorization in AF.
97*> \endverbatim
98*>
99*> \param[out] WORK
100*> \verbatim
101*> WORK is DOUBLE PRECISION array, dimension (LWORK)
102*> \endverbatim
103*>
104*> \param[in] LWORK
105*> \verbatim
106*> LWORK is INTEGER
107*> The dimension of the array WORK.
108*> \endverbatim
109*>
110*> \param[out] RWORK
111*> \verbatim
112*> RWORK is DOUBLE PRECISION array, dimension (M)
113*> \endverbatim
114*>
115*> \param[out] RESULT
116*> \verbatim
117*> RESULT is DOUBLE PRECISION array, dimension (2)
118*> The test ratios:
119*> RESULT(1) = norm( L - Q'*A ) / ( M * norm(A) * EPS )
120*> RESULT(2) = norm( I - Q'*Q ) / ( M * EPS )
121*> \endverbatim
122*
123* Authors:
124* ========
125*
126*> \author Univ. of Tennessee
127*> \author Univ. of California Berkeley
128*> \author Univ. of Colorado Denver
129*> \author NAG Ltd.
130*
131*> \ingroup double_lin
132*
133* =====================================================================
134 SUBROUTINE dqlt02( M, N, K, A, AF, Q, L, LDA, TAU, WORK, LWORK,
135 \$ RWORK, RESULT )
136*
137* -- LAPACK test routine --
138* -- LAPACK is a software package provided by Univ. of Tennessee, --
139* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
140*
141* .. Scalar Arguments ..
142 INTEGER K, LDA, LWORK, M, N
143* ..
144* .. Array Arguments ..
145 DOUBLE PRECISION A( LDA, * ), AF( LDA, * ), L( LDA, * ),
146 \$ q( lda, * ), result( * ), rwork( * ), tau( * ),
147 \$ work( lwork )
148* ..
149*
150* =====================================================================
151*
152* .. Parameters ..
153 DOUBLE PRECISION ZERO, ONE
154 parameter( zero = 0.0d+0, one = 1.0d+0 )
155 DOUBLE PRECISION ROGUE
156 parameter( rogue = -1.0d+10 )
157* ..
158* .. Local Scalars ..
159 INTEGER INFO
160 DOUBLE PRECISION ANORM, EPS, RESID
161* ..
162* .. External Functions ..
163 DOUBLE PRECISION DLAMCH, DLANGE, DLANSY
164 EXTERNAL dlamch, dlange, dlansy
165* ..
166* .. External Subroutines ..
167 EXTERNAL dgemm, dlacpy, dlaset, dorgql, dsyrk
168* ..
169* .. Intrinsic Functions ..
170 INTRINSIC dble, max
171* ..
172* .. Scalars in Common ..
173 CHARACTER*32 SRNAMT
174* ..
175* .. Common blocks ..
176 COMMON / srnamc / srnamt
177* ..
178* .. Executable Statements ..
179*
180* Quick return if possible
181*
182 IF( m.EQ.0 .OR. n.EQ.0 .OR. k.EQ.0 ) THEN
183 result( 1 ) = zero
184 result( 2 ) = zero
185 RETURN
186 END IF
187*
188 eps = dlamch( 'Epsilon' )
189*
190* Copy the last k columns of the factorization to the array Q
191*
192 CALL dlaset( 'Full', m, n, rogue, rogue, q, lda )
193 IF( k.LT.m )
194 \$ CALL dlacpy( 'Full', m-k, k, af( 1, n-k+1 ), lda,
195 \$ q( 1, n-k+1 ), lda )
196 IF( k.GT.1 )
197 \$ CALL dlacpy( 'Upper', k-1, k-1, af( m-k+1, n-k+2 ), lda,
198 \$ q( m-k+1, n-k+2 ), lda )
199*
200* Generate the last n columns of the matrix Q
201*
202 srnamt = 'DORGQL'
203 CALL dorgql( m, n, k, q, lda, tau( n-k+1 ), work, lwork, info )
204*
205* Copy L(m-n+1:m,n-k+1:n)
206*
207 CALL dlaset( 'Full', n, k, zero, zero, l( m-n+1, n-k+1 ), lda )
208 CALL dlacpy( 'Lower', k, k, af( m-k+1, n-k+1 ), lda,
209 \$ l( m-k+1, n-k+1 ), lda )
210*
211* Compute L(m-n+1:m,n-k+1:n) - Q(1:m,m-n+1:m)' * A(1:m,n-k+1:n)
212*
213 CALL dgemm( 'Transpose', 'No transpose', n, k, m, -one, q, lda,
214 \$ a( 1, n-k+1 ), lda, one, l( m-n+1, n-k+1 ), lda )
215*
216* Compute norm( L - Q'*A ) / ( M * norm(A) * EPS ) .
217*
218 anorm = dlange( '1', m, k, a( 1, n-k+1 ), lda, rwork )
219 resid = dlange( '1', n, k, l( m-n+1, n-k+1 ), lda, rwork )
220 IF( anorm.GT.zero ) THEN
221 result( 1 ) = ( ( resid / dble( max( 1, m ) ) ) / anorm ) / eps
222 ELSE
223 result( 1 ) = zero
224 END IF
225*
226* Compute I - Q'*Q
227*
228 CALL dlaset( 'Full', n, n, zero, one, l, lda )
229 CALL dsyrk( 'Upper', 'Transpose', n, m, -one, q, lda, one, l,
230 \$ lda )
231*
232* Compute norm( I - Q'*Q ) / ( M * EPS ) .
233*
234 resid = dlansy( '1', 'Upper', n, l, lda, rwork )
235*
236 result( 2 ) = ( resid / dble( max( 1, m ) ) ) / eps
237*
238 RETURN
239*
240* End of DQLT02
241*
242 END
subroutine dqlt02(m, n, k, a, af, q, l, lda, tau, work, lwork, rwork, result)
DQLT02
Definition dqlt02.f:136
subroutine dgemm(transa, transb, m, n, k, alpha, a, lda, b, ldb, beta, c, ldc)
DGEMM
Definition dgemm.f:188
subroutine dsyrk(uplo, trans, n, k, alpha, a, lda, beta, c, ldc)
DSYRK
Definition dsyrk.f:169
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 dorgql(m, n, k, a, lda, tau, work, lwork, info)
DORGQL
Definition dorgql.f:128