LAPACK  3.9.0 LAPACK: Linear Algebra PACKage
sqlt01.f
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1 *> \brief \b SQLT01
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 SQLT01( 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 *> SQLT01 tests SGEQLF, which computes the QL factorization of an m-by-n
30 *> matrix A, and partially tests SORGQL which forms the m-by-m
31 *> orthogonal matrix Q.
32 *>
33 *> SQLT01 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 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 QL factorization of A, as returned by SGEQLF.
61 *> See SGEQLF for further details.
62 *> \endverbatim
63 *>
64 *> \param[out] Q
65 *> \verbatim
66 *> Q is REAL array, dimension (LDA,M)
67 *> The m-by-m 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 R.
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 SGEQLF.
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 (M)
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 - 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 *> \date December 2016
122 *
123 *> \ingroup single_lin
124 *
125 * =====================================================================
126  SUBROUTINE sqlt01( M, N, A, AF, Q, L, LDA, TAU, WORK, LWORK,
127  \$ RWORK, RESULT )
128 *
129 * -- LAPACK test routine (version 3.7.0) --
130 * -- LAPACK is a software package provided by Univ. of Tennessee, --
131 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
132 * December 2016
133 *
134 * .. Scalar Arguments ..
135  INTEGER LDA, LWORK, M, N
136 * ..
137 * .. Array Arguments ..
138  REAL A( LDA, * ), AF( LDA, * ), L( LDA, * ),
139  \$ q( lda, * ), result( * ), rwork( * ), tau( * ),
140  \$ work( lwork )
141 * ..
142 *
143 * =====================================================================
144 *
145 * .. Parameters ..
146  REAL ZERO, ONE
147  parameter( zero = 0.0e+0, one = 1.0e+0 )
148  REAL ROGUE
149  parameter( rogue = -1.0e+10 )
150 * ..
151 * .. Local Scalars ..
152  INTEGER INFO, MINMN
153  REAL ANORM, EPS, RESID
154 * ..
155 * .. External Functions ..
156  REAL SLAMCH, SLANGE, SLANSY
157  EXTERNAL slamch, slange, slansy
158 * ..
159 * .. External Subroutines ..
160  EXTERNAL sgemm, sgeqlf, slacpy, slaset, sorgql, ssyrk
161 * ..
162 * .. Intrinsic Functions ..
163  INTRINSIC max, min, real
164 * ..
165 * .. Scalars in Common ..
166  CHARACTER*32 SRNAMT
167 * ..
168 * .. Common blocks ..
169  COMMON / srnamc / srnamt
170 * ..
171 * .. Executable Statements ..
172 *
173  minmn = min( m, n )
174  eps = slamch( 'Epsilon' )
175 *
176 * Copy the matrix A to the array AF.
177 *
178  CALL slacpy( 'Full', m, n, a, lda, af, lda )
179 *
180 * Factorize the matrix A in the array AF.
181 *
182  srnamt = 'SGEQLF'
183  CALL sgeqlf( m, n, af, lda, tau, work, lwork, info )
184 *
185 * Copy details of Q
186 *
187  CALL slaset( 'Full', m, m, rogue, rogue, q, lda )
188  IF( m.GE.n ) THEN
189  IF( n.LT.m .AND. n.GT.0 )
190  \$ CALL slacpy( 'Full', m-n, n, af, lda, q( 1, m-n+1 ), lda )
191  IF( n.GT.1 )
192  \$ CALL slacpy( 'Upper', n-1, n-1, af( m-n+1, 2 ), lda,
193  \$ q( m-n+1, m-n+2 ), lda )
194  ELSE
195  IF( m.GT.1 )
196  \$ CALL slacpy( 'Upper', m-1, m-1, af( 1, n-m+2 ), lda,
197  \$ q( 1, 2 ), lda )
198  END IF
199 *
200 * Generate the m-by-m matrix Q
201 *
202  srnamt = 'SORGQL'
203  CALL sorgql( m, m, minmn, q, lda, tau, work, lwork, info )
204 *
205 * Copy L
206 *
207  CALL slaset( 'Full', m, n, zero, zero, l, lda )
208  IF( m.GE.n ) THEN
209  IF( n.GT.0 )
210  \$ CALL slacpy( 'Lower', n, n, af( m-n+1, 1 ), lda,
211  \$ l( m-n+1, 1 ), lda )
212  ELSE
213  IF( n.GT.m .AND. m.GT.0 )
214  \$ CALL slacpy( 'Full', m, n-m, af, lda, l, lda )
215  IF( m.GT.0 )
216  \$ CALL slacpy( 'Lower', m, m, af( 1, n-m+1 ), lda,
217  \$ l( 1, n-m+1 ), lda )
218  END IF
219 *
220 * Compute L - Q'*A
221 *
222  CALL sgemm( 'Transpose', 'No transpose', m, n, m, -one, q, lda, a,
223  \$ lda, one, l, lda )
224 *
225 * Compute norm( L - Q'*A ) / ( M * norm(A) * EPS ) .
226 *
227  anorm = slange( '1', m, n, a, lda, rwork )
228  resid = slange( '1', m, n, l, lda, rwork )
229  IF( anorm.GT.zero ) THEN
230  result( 1 ) = ( ( resid / real( max( 1, m ) ) ) / anorm ) / eps
231  ELSE
232  result( 1 ) = zero
233  END IF
234 *
235 * Compute I - Q'*Q
236 *
237  CALL slaset( 'Full', m, m, zero, one, l, lda )
238  CALL ssyrk( 'Upper', 'Transpose', m, m, -one, q, lda, one, l,
239  \$ lda )
240 *
241 * Compute norm( I - Q'*Q ) / ( M * EPS ) .
242 *
243  resid = slansy( '1', 'Upper', m, l, lda, rwork )
244 *
245  result( 2 ) = ( resid / real( max( 1, m ) ) ) / eps
246 *
247  RETURN
248 *
249 * End of SQLT01
250 *
251  END
sorgql
subroutine sorgql(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
SORGQL
Definition: sorgql.f:130
sgemm
subroutine sgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
SGEMM
Definition: sgemm.f:189
slacpy
subroutine slacpy(UPLO, M, N, A, LDA, B, LDB)
SLACPY copies all or part of one two-dimensional array to another.
Definition: slacpy.f:105
sgeqlf
subroutine sgeqlf(M, N, A, LDA, TAU, WORK, LWORK, INFO)
SGEQLF
Definition: sgeqlf.f:140
sqlt01
subroutine sqlt01(M, N, A, AF, Q, L, LDA, TAU, WORK, LWORK, RWORK, RESULT)
SQLT01
Definition: sqlt01.f:128
slaset
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:112
ssyrk
subroutine ssyrk(UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC)
SSYRK
Definition: ssyrk.f:171