1*> \brief \b DQLT03
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 DQLT03( 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*       DOUBLE PRECISION   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*> DQLT03 tests DORMQL, which computes Q*C, Q'*C, C*Q or C*Q'.
30*>
31*> DQLT03 compares the results of a call to DORMQL with the results of
32*> forming Q explicitly by a call to DORGQL and then performing matrix
33*> multiplication by a call to DGEMM.
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 DOUBLE PRECISION array, dimension (LDA,N)
63*>          Details of the QL factorization of an m-by-n matrix, as
64*>          returned by DGEQLF. See SGEQLF for further details.
65*> \endverbatim
66*>
67*> \param[out] C
68*> \verbatim
69*>          C is DOUBLE PRECISION array, dimension (LDA,N)
70*> \endverbatim
71*>
72*> \param[out] CC
73*> \verbatim
74*>          CC is DOUBLE PRECISION array, dimension (LDA,N)
75*> \endverbatim
76*>
77*> \param[out] Q
78*> \verbatim
79*>          Q is DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (min(M,N))
91*>          The scalar factors of the elementary reflectors corresponding
92*>          to the QL factorization in AF.
93*> \endverbatim
94*>
95*> \param[out] WORK
96*> \verbatim
97*>          WORK is DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (M)
110*> \endverbatim
111*>
112*> \param[out] RESULT
113*> \verbatim
114*>          RESULT is DOUBLE PRECISION 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 double_lin
132*
133*  =====================================================================
134      SUBROUTINE DQLT03( 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      DOUBLE PRECISION   AF( LDA, * ), C( LDA, * ), CC( LDA, * ),
146     $                   Q( LDA, * ), RESULT( * ), RWORK( * ), TAU( * ),
147     $                   WORK( LWORK )
148*     ..
149*
150*  =====================================================================
151*
152*     .. Parameters ..
153      DOUBLE PRECISION   ZERO, ONE
154      PARAMETER          ( ZERO = 0.0D0, ONE = 1.0D0 )
155      DOUBLE PRECISION   ROGUE
156      PARAMETER          ( ROGUE = -1.0D+10 )
157*     ..
158*     .. Local Scalars ..
159      CHARACTER          SIDE, TRANS
160      INTEGER            INFO, ISIDE, ITRANS, J, MC, MINMN, NC
161      DOUBLE PRECISION   CNORM, EPS, RESID
162*     ..
163*     .. External Functions ..
164      LOGICAL            LSAME
165      DOUBLE PRECISION   DLAMCH, DLANGE
166      EXTERNAL           LSAME, DLAMCH, DLANGE
167*     ..
168*     .. External Subroutines ..
169      EXTERNAL           DGEMM, DLACPY, DLARNV, DLASET, DORGQL, DORMQL
170*     ..
171*     .. Local Arrays ..
172      INTEGER            ISEED( 4 )
173*     ..
174*     .. Intrinsic Functions ..
175      INTRINSIC          DBLE, MAX, MIN
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 = DLAMCH( 'Epsilon' )
189      MINMN = MIN( M, N )
190*
191*     Quick return if possible
192*
193      IF( MINMN.EQ.0 ) THEN
194         RESULT( 1 ) = ZERO
195         RESULT( 2 ) = ZERO
196         RESULT( 3 ) = ZERO
197         RESULT( 4 ) = ZERO
198         RETURN
199      END IF
200*
201*     Copy the last k columns of the factorization to the array Q
202*
203      CALL DLASET( 'Full', M, M, ROGUE, ROGUE, Q, LDA )
204      IF( K.GT.0 .AND. M.GT.K )
205     $   CALL DLACPY( 'Full', M-K, K, AF( 1, N-K+1 ), LDA,
206     $                Q( 1, M-K+1 ), LDA )
207      IF( K.GT.1 )
208     $   CALL DLACPY( 'Upper', K-1, K-1, AF( M-K+1, N-K+2 ), LDA,
209     $                Q( M-K+1, M-K+2 ), LDA )
210*
211*     Generate the m-by-m matrix Q
212*
213      SRNAMT = 'DORGQL'
214      CALL DORGQL( M, M, K, Q, LDA, TAU( MINMN-K+1 ), WORK, LWORK,
215     $             INFO )
216*
217      DO 30 ISIDE = 1, 2
218         IF( ISIDE.EQ.1 ) THEN
219            SIDE = 'L'
220            MC = M
221            NC = N
222         ELSE
223            SIDE = 'R'
224            MC = N
225            NC = M
226         END IF
227*
228*        Generate MC by NC matrix C
229*
230         DO 10 J = 1, NC
231            CALL DLARNV( 2, ISEED, MC, C( 1, J ) )
232   10    CONTINUE
233         CNORM = DLANGE( '1', MC, NC, C, LDA, RWORK )
234         IF( CNORM.EQ.0.0D0 )
235     $      CNORM = ONE
236*
237         DO 20 ITRANS = 1, 2
238            IF( ITRANS.EQ.1 ) THEN
239               TRANS = 'N'
240            ELSE
241               TRANS = 'T'
242            END IF
243*
244*           Copy C
245*
246            CALL DLACPY( 'Full', MC, NC, C, LDA, CC, LDA )
247*
248*           Apply Q or Q' to C
249*
250            SRNAMT = 'DORMQL'
251            IF( K.GT.0 )
252     $         CALL DORMQL( SIDE, TRANS, MC, NC, K, AF( 1, N-K+1 ), LDA,
253     $                      TAU( MINMN-K+1 ), CC, LDA, WORK, LWORK,
254     $                      INFO )
255*
256*           Form explicit product and subtract
257*
258            IF( LSAME( SIDE, 'L' ) ) THEN
259               CALL DGEMM( TRANS, 'No transpose', MC, NC, MC, -ONE, Q,
260     $                     LDA, C, LDA, ONE, CC, LDA )
261            ELSE
262               CALL DGEMM( 'No transpose', TRANS, MC, NC, NC, -ONE, C,
263     $                     LDA, Q, LDA, ONE, CC, LDA )
264            END IF
265*
266*           Compute error in the difference
267*
268            RESID = DLANGE( '1', MC, NC, CC, LDA, RWORK )
269            RESULT( ( ISIDE-1 )*2+ITRANS ) = RESID /
270     $         ( DBLE( MAX( 1, M ) )*CNORM*EPS )
271*
272   20    CONTINUE
273   30 CONTINUE
274*
275      RETURN
276*
277*     End of DQLT03
278*
279      END
280