LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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slqt02.f
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1*> \brief \b SLQT02
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 SLQT02( 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* REAL 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*> SLQT02 tests SORGLQ, which generates an m-by-n matrix Q with
30*> orthonormal rows that is defined as the product of k elementary
31*> reflectors.
32*>
33*> Given the LQ factorization of an m-by-n matrix A, SLQT02 generates
34*> the orthogonal matrix Q defined by the factorization of the first k
35*> rows of A; it compares L(1:k,1:m) with A(1:k,1:n)*Q(1:m,1:n)', and
36*> checks that the rows of Q are orthonormal.
37*> \endverbatim
38*
39* Arguments:
40* ==========
41*
42*> \param[in] M
43*> \verbatim
44*> M is INTEGER
45*> The number of rows of the matrix Q to be generated. M >= 0.
46*> \endverbatim
47*>
48*> \param[in] N
49*> \verbatim
50*> N is INTEGER
51*> The number of columns of the matrix Q to be generated.
52*> N >= M >= 0.
53*> \endverbatim
54*>
55*> \param[in] K
56*> \verbatim
57*> K is INTEGER
58*> The number of elementary reflectors whose product defines the
59*> matrix Q. M >= K >= 0.
60*> \endverbatim
61*>
62*> \param[in] A
63*> \verbatim
64*> A is REAL array, dimension (LDA,N)
65*> The m-by-n matrix A which was factorized by SLQT01.
66*> \endverbatim
67*>
68*> \param[in] AF
69*> \verbatim
70*> AF is REAL array, dimension (LDA,N)
71*> Details of the LQ factorization of A, as returned by SGELQF.
72*> See SGELQF for further details.
73*> \endverbatim
74*>
75*> \param[out] Q
76*> \verbatim
77*> Q is REAL array, dimension (LDA,N)
78*> \endverbatim
79*>
80*> \param[out] L
81*> \verbatim
82*> L is REAL array, dimension (LDA,M)
83*> \endverbatim
84*>
85*> \param[in] LDA
86*> \verbatim
87*> LDA is INTEGER
88*> The leading dimension of the arrays A, AF, Q and L. LDA >= N.
89*> \endverbatim
90*>
91*> \param[in] TAU
92*> \verbatim
93*> TAU is REAL array, dimension (M)
94*> The scalar factors of the elementary reflectors corresponding
95*> to the LQ factorization in AF.
96*> \endverbatim
97*>
98*> \param[out] WORK
99*> \verbatim
100*> WORK is REAL array, dimension (LWORK)
101*> \endverbatim
102*>
103*> \param[in] LWORK
104*> \verbatim
105*> LWORK is INTEGER
106*> The dimension of the array WORK.
107*> \endverbatim
108*>
109*> \param[out] RWORK
110*> \verbatim
111*> RWORK is REAL array, dimension (M)
112*> \endverbatim
113*>
114*> \param[out] RESULT
115*> \verbatim
116*> RESULT is REAL array, dimension (2)
117*> The test ratios:
118*> RESULT(1) = norm( L - A*Q' ) / ( N * norm(A) * EPS )
119*> RESULT(2) = norm( I - Q*Q' ) / ( N * EPS )
120*> \endverbatim
121*
122* Authors:
123* ========
124*
125*> \author Univ. of Tennessee
126*> \author Univ. of California Berkeley
127*> \author Univ. of Colorado Denver
128*> \author NAG Ltd.
129*
130*> \ingroup single_lin
131*
132* =====================================================================
133 SUBROUTINE slqt02( M, N, K, A, AF, Q, L, LDA, TAU, WORK, LWORK,
134 \$ RWORK, RESULT )
135*
136* -- LAPACK test routine --
137* -- LAPACK is a software package provided by Univ. of Tennessee, --
138* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
139*
140* .. Scalar Arguments ..
141 INTEGER K, LDA, LWORK, M, N
142* ..
143* .. Array Arguments ..
144 REAL A( LDA, * ), AF( LDA, * ), L( LDA, * ),
145 \$ q( lda, * ), result( * ), rwork( * ), tau( * ),
146 \$ work( lwork )
147* ..
148*
149* =====================================================================
150*
151* .. Parameters ..
152 REAL ZERO, ONE
153 parameter( zero = 0.0e+0, one = 1.0e+0 )
154 REAL ROGUE
155 parameter( rogue = -1.0e+10 )
156* ..
157* .. Local Scalars ..
158 INTEGER INFO
159 REAL ANORM, EPS, RESID
160* ..
161* .. External Functions ..
162 REAL SLAMCH, SLANGE, SLANSY
163 EXTERNAL slamch, slange, slansy
164* ..
165* .. External Subroutines ..
166 EXTERNAL sgemm, slacpy, slaset, sorglq, ssyrk
167* ..
168* .. Intrinsic Functions ..
169 INTRINSIC max, real
170* ..
171* .. Scalars in Common ..
172 CHARACTER*32 SRNAMT
173* ..
174* .. Common blocks ..
175 COMMON / srnamc / srnamt
176* ..
177* .. Executable Statements ..
178*
179 eps = slamch( 'Epsilon' )
180*
181* Copy the first k rows of the factorization to the array Q
182*
183 CALL slaset( 'Full', m, n, rogue, rogue, q, lda )
184 CALL slacpy( 'Upper', k, n-1, af( 1, 2 ), lda, q( 1, 2 ), lda )
185*
186* Generate the first n columns of the matrix Q
187*
188 srnamt = 'SORGLQ'
189 CALL sorglq( m, n, k, q, lda, tau, work, lwork, info )
190*
191* Copy L(1:k,1:m)
192*
193 CALL slaset( 'Full', k, m, zero, zero, l, lda )
194 CALL slacpy( 'Lower', k, m, af, lda, l, lda )
195*
196* Compute L(1:k,1:m) - A(1:k,1:n) * Q(1:m,1:n)'
197*
198 CALL sgemm( 'No transpose', 'Transpose', k, m, n, -one, a, lda, q,
199 \$ lda, one, l, lda )
200*
201* Compute norm( L - A*Q' ) / ( N * norm(A) * EPS ) .
202*
203 anorm = slange( '1', k, n, a, lda, rwork )
204 resid = slange( '1', k, m, l, lda, rwork )
205 IF( anorm.GT.zero ) THEN
206 result( 1 ) = ( ( resid / real( max( 1, n ) ) ) / anorm ) / eps
207 ELSE
208 result( 1 ) = zero
209 END IF
210*
211* Compute I - Q*Q'
212*
213 CALL slaset( 'Full', m, m, zero, one, l, lda )
214 CALL ssyrk( 'Upper', 'No transpose', m, n, -one, q, lda, one, l,
215 \$ lda )
216*
217* Compute norm( I - Q*Q' ) / ( N * EPS ) .
218*
219 resid = slansy( '1', 'Upper', m, l, lda, rwork )
220*
221 result( 2 ) = ( resid / real( max( 1, n ) ) ) / eps
222*
223 RETURN
224*
225* End of SLQT02
226*
227 END
subroutine sgemm(transa, transb, m, n, k, alpha, a, lda, b, ldb, beta, c, ldc)
SGEMM
Definition sgemm.f:188
subroutine ssyrk(uplo, trans, n, k, alpha, a, lda, beta, c, ldc)
SSYRK
Definition ssyrk.f:169
subroutine slacpy(uplo, m, n, a, lda, b, ldb)
SLACPY copies all or part of one two-dimensional array to another.
Definition slacpy.f:103
subroutine slaset(uplo, m, n, alpha, beta, a, lda)
SLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition slaset.f:110
subroutine sorglq(m, n, k, a, lda, tau, work, lwork, info)
SORGLQ
Definition sorglq.f:127
subroutine slqt02(m, n, k, a, af, q, l, lda, tau, work, lwork, rwork, result)
SLQT02
Definition slqt02.f:135