LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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slqt01.f
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1*> \brief \b SLQT01
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 SLQT01( 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* 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*> SLQT01 tests SGELQF, which computes the LQ factorization of an m-by-n
30*> matrix A, and partially tests SORGLQ which forms the n-by-n
31*> orthogonal matrix Q.
32*>
33*> SLQT01 compares L 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 REAL array, dimension (LDA,N)
54*> The m-by-n matrix A.
55*> \endverbatim
56*>
57*> \param[out] AF
58*> \verbatim
59*> AF is REAL array, dimension (LDA,N)
60*> Details of the LQ factorization of A, as returned by SGELQF.
61*> See SGELQF for further details.
62*> \endverbatim
63*>
64*> \param[out] Q
65*> \verbatim
66*> Q is REAL array, dimension (LDA,N)
67*> The n-by-n orthogonal matrix Q.
68*> \endverbatim
69*>
70*> \param[out] L
71*> \verbatim
72*> L is REAL 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 REAL array, dimension (min(M,N))
85*> The scalar factors of the elementary reflectors, as returned
86*> by SGELQF.
87*> \endverbatim
88*>
89*> \param[out] WORK
90*> \verbatim
91*> WORK is REAL 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( L - 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 single_lin
122*
123* =====================================================================
124 SUBROUTINE slqt01( 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 REAL A( LDA, * ), AF( LDA, * ), L( LDA, * ),
136 \$ q( lda, * ), result( * ), rwork( * ), tau( * ),
137 \$ work( lwork )
138* ..
139*
140* =====================================================================
141*
142* .. Parameters ..
143 REAL ZERO, ONE
144 parameter( zero = 0.0e+0, one = 1.0e+0 )
145 REAL ROGUE
146 parameter( rogue = -1.0e+10 )
147* ..
148* .. Local Scalars ..
149 INTEGER INFO, MINMN
150 REAL ANORM, EPS, RESID
151* ..
152* .. External Functions ..
153 REAL SLAMCH, SLANGE, SLANSY
154 EXTERNAL slamch, slange, slansy
155* ..
156* .. External Subroutines ..
157 EXTERNAL sgelqf, sgemm, slacpy, slaset, sorglq, ssyrk
158* ..
159* .. Intrinsic Functions ..
160 INTRINSIC 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 slacpy( 'Full', m, n, a, lda, af, lda )
176*
177* Factorize the matrix A in the array AF.
178*
179 srnamt = 'SGELQF'
180 CALL sgelqf( m, n, af, lda, tau, work, lwork, info )
181*
182* Copy details of Q
183*
184 CALL slaset( 'Full', n, n, rogue, rogue, q, lda )
185 IF( n.GT.1 )
186 \$ CALL slacpy( 'Upper', m, n-1, af( 1, 2 ), lda, q( 1, 2 ), lda )
187*
188* Generate the n-by-n matrix Q
189*
190 srnamt = 'SORGLQ'
191 CALL sorglq( n, n, minmn, q, lda, tau, work, lwork, info )
192*
193* Copy L
194*
195 CALL slaset( 'Full', m, n, zero, zero, l, lda )
196 CALL slacpy( 'Lower', m, n, af, lda, l, lda )
197*
198* Compute L - A*Q'
199*
200 CALL sgemm( 'No transpose', 'Transpose', m, n, n, -one, a, lda, q,
201 \$ lda, one, l, lda )
202*
203* Compute norm( L - Q'*A ) / ( N * norm(A) * EPS ) .
204*
205 anorm = slange( '1', m, n, a, lda, rwork )
206 resid = slange( '1', m, n, l, lda, rwork )
207 IF( anorm.GT.zero ) THEN
208 result( 1 ) = ( ( resid / real( max( 1, n ) ) ) / anorm ) / eps
209 ELSE
210 result( 1 ) = zero
211 END IF
212*
213* Compute I - Q*Q'
214*
215 CALL slaset( 'Full', n, n, zero, one, l, lda )
216 CALL ssyrk( 'Upper', 'No transpose', n, n, -one, q, lda, one, l,
217 \$ lda )
218*
219* Compute norm( I - Q*Q' ) / ( N * EPS ) .
220*
221 resid = slansy( '1', 'Upper', n, l, lda, rwork )
222*
223 result( 2 ) = ( resid / real( max( 1, n ) ) ) / eps
224*
225 RETURN
226*
227* End of SLQT01
228*
229 END
subroutine sgelqf(m, n, a, lda, tau, work, lwork, info)
SGELQF
Definition sgelqf.f:143
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 slqt01(m, n, a, af, q, l, lda, tau, work, lwork, rwork, result)
SLQT01
Definition slqt01.f:126