LAPACK  3.10.0 LAPACK: Linear Algebra PACKage
sqrt03.f
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1 *> \brief \b SQRT03
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 SQRT03( M, N, K, AF, C, CC, Q, LDA, TAU, WORK, LWORK,
12 * RWORK, RESULT )
13 *
14 * .. Scalar Arguments ..
15 * INTEGER K, LDA, LWORK, M, N
16 * ..
17 * .. Array Arguments ..
18 * REAL AF( LDA, * ), C( LDA, * ), CC( LDA, * ),
19 * \$ Q( LDA, * ), RESULT( * ), RWORK( * ), TAU( * ),
20 * \$ WORK( LWORK )
21 * ..
22 *
23 *
24 *> \par Purpose:
25 * =============
26 *>
27 *> \verbatim
28 *>
29 *> SQRT03 tests SORMQR, which computes Q*C, Q'*C, C*Q or C*Q'.
30 *>
31 *> SQRT03 compares the results of a call to SORMQR with the results of
32 *> forming Q explicitly by a call to SORGQR and then performing matrix
33 *> multiplication by a call to SGEMM.
34 *> \endverbatim
35 *
36 * Arguments:
37 * ==========
38 *
39 *> \param[in] M
40 *> \verbatim
41 *> M is INTEGER
42 *> The order of the orthogonal matrix Q. M >= 0.
43 *> \endverbatim
44 *>
45 *> \param[in] N
46 *> \verbatim
47 *> N is INTEGER
48 *> The number of rows or columns of the matrix C; C is m-by-n if
49 *> Q is applied from the left, or n-by-m if Q is applied from
50 *> the right. N >= 0.
51 *> \endverbatim
52 *>
53 *> \param[in] K
54 *> \verbatim
55 *> K is INTEGER
56 *> The number of elementary reflectors whose product defines the
57 *> orthogonal matrix Q. M >= K >= 0.
58 *> \endverbatim
59 *>
60 *> \param[in] AF
61 *> \verbatim
62 *> AF is REAL array, dimension (LDA,N)
63 *> Details of the QR factorization of an m-by-n matrix, as
64 *> returned by SGEQRF. See SGEQRF for further details.
65 *> \endverbatim
66 *>
67 *> \param[out] C
68 *> \verbatim
69 *> C is REAL array, dimension (LDA,N)
70 *> \endverbatim
71 *>
72 *> \param[out] CC
73 *> \verbatim
74 *> CC is REAL array, dimension (LDA,N)
75 *> \endverbatim
76 *>
77 *> \param[out] Q
78 *> \verbatim
79 *> Q is REAL array, dimension (LDA,M)
80 *> \endverbatim
81 *>
82 *> \param[in] LDA
83 *> \verbatim
84 *> LDA is INTEGER
85 *> The leading dimension of the arrays AF, C, CC, and Q.
86 *> \endverbatim
87 *>
88 *> \param[in] TAU
89 *> \verbatim
90 *> TAU is REAL array, dimension (min(M,N))
91 *> The scalar factors of the elementary reflectors corresponding
92 *> to the QR factorization in AF.
93 *> \endverbatim
94 *>
95 *> \param[out] WORK
96 *> \verbatim
97 *> WORK is REAL array, dimension (LWORK)
98 *> \endverbatim
99 *>
100 *> \param[in] LWORK
101 *> \verbatim
102 *> LWORK is INTEGER
103 *> The length of WORK. LWORK must be at least M, and should be
104 *> M*NB, where NB is the blocksize for this environment.
105 *> \endverbatim
106 *>
107 *> \param[out] RWORK
108 *> \verbatim
109 *> RWORK is REAL array, dimension (M)
110 *> \endverbatim
111 *>
112 *> \param[out] RESULT
113 *> \verbatim
114 *> RESULT is REAL array, dimension (4)
115 *> The test ratios compare two techniques for multiplying a
116 *> random matrix C by an m-by-m orthogonal matrix Q.
117 *> RESULT(1) = norm( Q*C - Q*C ) / ( M * norm(C) * EPS )
118 *> RESULT(2) = norm( C*Q - C*Q ) / ( M * norm(C) * EPS )
119 *> RESULT(3) = norm( Q'*C - Q'*C )/ ( M * norm(C) * EPS )
120 *> RESULT(4) = norm( C*Q' - C*Q' )/ ( M * norm(C) * 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 single_lin
132 *
133 * =====================================================================
134  SUBROUTINE sqrt03( M, N, K, AF, C, CC, Q, 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  REAL AF( LDA, * ), C( LDA, * ), CC( LDA, * ),
146  \$ q( lda, * ), result( * ), rwork( * ), tau( * ),
147  \$ work( lwork )
148 * ..
149 *
150 * =====================================================================
151 *
152 * .. Parameters ..
153  REAL ONE
154  parameter( one = 1.0e0 )
155  REAL ROGUE
156  parameter( rogue = -1.0e+10 )
157 * ..
158 * .. Local Scalars ..
159  CHARACTER SIDE, TRANS
160  INTEGER INFO, ISIDE, ITRANS, J, MC, NC
161  REAL CNORM, EPS, RESID
162 * ..
163 * .. External Functions ..
164  LOGICAL LSAME
165  REAL SLAMCH, SLANGE
166  EXTERNAL lsame, slamch, slange
167 * ..
168 * .. External Subroutines ..
169  EXTERNAL sgemm, slacpy, slarnv, slaset, sorgqr, sormqr
170 * ..
171 * .. Local Arrays ..
172  INTEGER ISEED( 4 )
173 * ..
174 * .. Intrinsic Functions ..
175  INTRINSIC max, real
176 * ..
177 * .. Scalars in Common ..
178  CHARACTER*32 SRNAMT
179 * ..
180 * .. Common blocks ..
181  COMMON / srnamc / srnamt
182 * ..
183 * .. Data statements ..
184  DATA iseed / 1988, 1989, 1990, 1991 /
185 * ..
186 * .. Executable Statements ..
187 *
188  eps = slamch( 'Epsilon' )
189 *
190 * Copy the first k columns of the factorization to the array Q
191 *
192  CALL slaset( 'Full', m, m, rogue, rogue, q, lda )
193  CALL slacpy( 'Lower', m-1, k, af( 2, 1 ), lda, q( 2, 1 ), lda )
194 *
195 * Generate the m-by-m matrix Q
196 *
197  srnamt = 'SORGQR'
198  CALL sorgqr( m, m, k, q, lda, tau, work, lwork, info )
199 *
200  DO 30 iside = 1, 2
201  IF( iside.EQ.1 ) THEN
202  side = 'L'
203  mc = m
204  nc = n
205  ELSE
206  side = 'R'
207  mc = n
208  nc = m
209  END IF
210 *
211 * Generate MC by NC matrix C
212 *
213  DO 10 j = 1, nc
214  CALL slarnv( 2, iseed, mc, c( 1, j ) )
215  10 CONTINUE
216  cnorm = slange( '1', mc, nc, c, lda, rwork )
217  IF( cnorm.EQ.0.0 )
218  \$ cnorm = one
219 *
220  DO 20 itrans = 1, 2
221  IF( itrans.EQ.1 ) THEN
222  trans = 'N'
223  ELSE
224  trans = 'T'
225  END IF
226 *
227 * Copy C
228 *
229  CALL slacpy( 'Full', mc, nc, c, lda, cc, lda )
230 *
231 * Apply Q or Q' to C
232 *
233  srnamt = 'SORMQR'
234  CALL sormqr( side, trans, mc, nc, k, af, lda, tau, cc, lda,
235  \$ work, lwork, info )
236 *
237 * Form explicit product and subtract
238 *
239  IF( lsame( side, 'L' ) ) THEN
240  CALL sgemm( trans, 'No transpose', mc, nc, mc, -one, q,
241  \$ lda, c, lda, one, cc, lda )
242  ELSE
243  CALL sgemm( 'No transpose', trans, mc, nc, nc, -one, c,
244  \$ lda, q, lda, one, cc, lda )
245  END IF
246 *
247 * Compute error in the difference
248 *
249  resid = slange( '1', mc, nc, cc, lda, rwork )
250  result( ( iside-1 )*2+itrans ) = resid /
251  \$ ( real( max( 1, m ) )*cnorm*eps )
252 *
253  20 CONTINUE
254  30 CONTINUE
255 *
256  RETURN
257 *
258 * End of SQRT03
259 *
260  END
subroutine slarnv(IDIST, ISEED, N, X)
SLARNV returns a vector of random numbers from a uniform or normal distribution.
Definition: slarnv.f:97
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 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 sorgqr(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
SORGQR
Definition: sorgqr.f:128
subroutine sormqr(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
SORMQR
Definition: sormqr.f:168
subroutine sgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
SGEMM
Definition: sgemm.f:187
subroutine sqrt03(M, N, K, AF, C, CC, Q, LDA, TAU, WORK, LWORK, RWORK, RESULT)
SQRT03
Definition: sqrt03.f:136