1*> \brief \b DQRT04
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 DQRT04(M,N,NB,RESULT)
12*
13*       .. Scalar Arguments ..
14*       INTEGER M, N, NB, LDT
15*       .. Return values ..
16*       DOUBLE PRECISION RESULT(6)
17*
18*
19*> \par Purpose:
20*  =============
21*>
22*> \verbatim
23*>
24*> DQRT04 tests DGEQRT and DGEMQRT.
25*> \endverbatim
26*
27*  Arguments:
28*  ==========
29*
30*> \param[in] M
31*> \verbatim
32*>          M is INTEGER
33*>          Number of rows in test matrix.
34*> \endverbatim
35*>
36*> \param[in] N
37*> \verbatim
38*>          N is INTEGER
39*>          Number of columns in test matrix.
40*> \endverbatim
41*>
42*> \param[in] NB
43*> \verbatim
44*>          NB is INTEGER
45*>          Block size of test matrix.  NB <= Min(M,N).
46*> \endverbatim
47*>
48*> \param[out] RESULT
49*> \verbatim
50*>          RESULT is DOUBLE PRECISION array, dimension (6)
51*>          Results of each of the six tests below.
52*>
53*>          RESULT(1) = | A - Q R |
54*>          RESULT(2) = | I - Q^H Q |
55*>          RESULT(3) = | Q C - Q C |
56*>          RESULT(4) = | Q^H C - Q^H C |
57*>          RESULT(5) = | C Q - C Q |
58*>          RESULT(6) = | C Q^H - C Q^H |
59*> \endverbatim
60*
61*  Authors:
62*  ========
63*
64*> \author Univ. of Tennessee
65*> \author Univ. of California Berkeley
66*> \author Univ. of Colorado Denver
67*> \author NAG Ltd.
68*
69*> \date April 2012
70*
71*> \ingroup double_lin
72*
73*  =====================================================================
74      SUBROUTINE DQRT04(M,N,NB,RESULT)
75      IMPLICIT NONE
76*
77*  -- LAPACK test routine (version 3.4.1) --
78*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
79*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
80*     April 2012
81*
82*     .. Scalar Arguments ..
83      INTEGER M, N, NB, LDT
84*     .. Return values ..
85      DOUBLE PRECISION RESULT(6)
86*
87*  =====================================================================
88*
89*     ..
90*     .. Local allocatable arrays
91      DOUBLE PRECISION, ALLOCATABLE :: AF(:,:), Q(:,:),
92     $  R(:,:), RWORK(:), WORK( : ), T(:,:),
93     $  CF(:,:), DF(:,:), A(:,:), C(:,:), D(:,:)
94*
95*     .. Parameters ..
96      DOUBLE PRECISION ONE, ZERO
97      PARAMETER( ZERO = 0.0, ONE = 1.0 )
98*     ..
99*     .. Local Scalars ..
100      INTEGER INFO, J, K, L, LWORK
101      DOUBLE PRECISION   ANORM, EPS, RESID, CNORM, DNORM
102*     ..
103*     .. Local Arrays ..
104      INTEGER            ISEED( 4 )
105*     ..
106*     .. External Functions ..
107      DOUBLE PRECISION DLAMCH, DLANGE, DLANSY
108      LOGICAL  LSAME
109      EXTERNAL DLAMCH, DLANGE, DLANSY, LSAME
110*     ..
111*     .. Intrinsic Functions ..
112      INTRINSIC  MAX, MIN
113*     ..
114*     .. Data statements ..
115      DATA ISEED / 1988, 1989, 1990, 1991 /
116*
117      EPS = DLAMCH( 'Epsilon' )
118      K = MIN(M,N)
119      L = MAX(M,N)
120      LWORK = MAX(2,L)*MAX(2,L)*NB
121*
122*     Dynamically allocate local arrays
123*
124      ALLOCATE ( A(M,N), AF(M,N), Q(M,M), R(M,L), RWORK(L),
125     $           WORK(LWORK), T(NB,N), C(M,N), CF(M,N),
126     $           D(N,M), DF(N,M) )
127*
128*     Put random numbers into A and copy to AF
129*
130      LDT=NB
131      DO J=1,N
132         CALL DLARNV( 2, ISEED, M, A( 1, J ) )
133      END DO
134      CALL DLACPY( 'Full', M, N, A, M, AF, M )
135*
136*     Factor the matrix A in the array AF.
137*
138      CALL DGEQRT( M, N, NB, AF, M, T, LDT, WORK, INFO )
139*
140*     Generate the m-by-m matrix Q
141*
142      CALL DLASET( 'Full', M, M, ZERO, ONE, Q, M )
143      CALL DGEMQRT( 'R', 'N', M, M, K, NB, AF, M, T, LDT, Q, M,
144     $              WORK, INFO )
145*
146*     Copy R
147*
148      CALL DLASET( 'Full', M, N, ZERO, ZERO, R, M )
149      CALL DLACPY( 'Upper', M, N, AF, M, R, M )
150*
151*     Compute |R - Q'*A| / |A| and store in RESULT(1)
152*
153      CALL DGEMM( 'T', 'N', M, N, M, -ONE, Q, M, A, M, ONE, R, M )
154      ANORM = DLANGE( '1', M, N, A, M, RWORK )
155      RESID = DLANGE( '1', M, N, R, M, RWORK )
156      IF( ANORM.GT.ZERO ) THEN
157         RESULT( 1 ) = RESID / (EPS*MAX(1,M)*ANORM)
158      ELSE
159         RESULT( 1 ) = ZERO
160      END IF
161*
162*     Compute |I - Q'*Q| and store in RESULT(2)
163*
164      CALL DLASET( 'Full', M, M, ZERO, ONE, R, M )
165      CALL DSYRK( 'U', 'C', M, M, -ONE, Q, M, ONE, R, M )
166      RESID = DLANSY( '1', 'Upper', M, R, M, RWORK )
167      RESULT( 2 ) = RESID / (EPS*MAX(1,M))
168*
169*     Generate random m-by-n matrix C and a copy CF
170*
171      DO J=1,N
172         CALL DLARNV( 2, ISEED, M, C( 1, J ) )
173      END DO
174      CNORM = DLANGE( '1', M, N, C, M, RWORK)
175      CALL DLACPY( 'Full', M, N, C, M, CF, M )
176*
177*     Apply Q to C as Q*C
178*
179      CALL DGEMQRT( 'L', 'N', M, N, K, NB, AF, M, T, NB, CF, M,
180     $             WORK, INFO)
181*
182*     Compute |Q*C - Q*C| / |C|
183*
184      CALL DGEMM( 'N', 'N', M, N, M, -ONE, Q, M, C, M, ONE, CF, M )
185      RESID = DLANGE( '1', M, N, CF, M, RWORK )
186      IF( CNORM.GT.ZERO ) THEN
187         RESULT( 3 ) = RESID / (EPS*MAX(1,M)*CNORM)
188      ELSE
189         RESULT( 3 ) = ZERO
190      END IF
191*
192*     Copy C into CF again
193*
194      CALL DLACPY( 'Full', M, N, C, M, CF, M )
195*
196*     Apply Q to C as QT*C
197*
198      CALL DGEMQRT( 'L', 'T', M, N, K, NB, AF, M, T, NB, CF, M,
199     $             WORK, INFO)
200*
201*     Compute |QT*C - QT*C| / |C|
202*
203      CALL DGEMM( 'T', 'N', M, N, M, -ONE, Q, M, C, M, ONE, CF, M )
204      RESID = DLANGE( '1', M, N, CF, M, RWORK )
205      IF( CNORM.GT.ZERO ) THEN
206         RESULT( 4 ) = RESID / (EPS*MAX(1,M)*CNORM)
207      ELSE
208         RESULT( 4 ) = ZERO
209      END IF
210*
211*     Generate random n-by-m matrix D and a copy DF
212*
213      DO J=1,M
214         CALL DLARNV( 2, ISEED, N, D( 1, J ) )
215      END DO
216      DNORM = DLANGE( '1', N, M, D, N, RWORK)
217      CALL DLACPY( 'Full', N, M, D, N, DF, N )
218*
219*     Apply Q to D as D*Q
220*
221      CALL DGEMQRT( 'R', 'N', N, M, K, NB, AF, M, T, NB, DF, N,
222     $             WORK, INFO)
223*
224*     Compute |D*Q - D*Q| / |D|
225*
226      CALL DGEMM( 'N', 'N', N, M, M, -ONE, D, N, Q, M, ONE, DF, N )
227      RESID = DLANGE( '1', N, M, DF, N, RWORK )
228      IF( CNORM.GT.ZERO ) THEN
229         RESULT( 5 ) = RESID / (EPS*MAX(1,M)*DNORM)
230      ELSE
231         RESULT( 5 ) = ZERO
232      END IF
233*
234*     Copy D into DF again
235*
236      CALL DLACPY( 'Full', N, M, D, N, DF, N )
237*
238*     Apply Q to D as D*QT
239*
240      CALL DGEMQRT( 'R', 'T', N, M, K, NB, AF, M, T, NB, DF, N,
241     $             WORK, INFO)
242*
243*     Compute |D*QT - D*QT| / |D|
244*
245      CALL DGEMM( 'N', 'T', N, M, M, -ONE, D, N, Q, M, ONE, DF, N )
246      RESID = DLANGE( '1', N, M, DF, N, RWORK )
247      IF( CNORM.GT.ZERO ) THEN
248         RESULT( 6 ) = RESID / (EPS*MAX(1,M)*DNORM)
249      ELSE
250         RESULT( 6 ) = ZERO
251      END IF
252*
253*     Deallocate all arrays
254*
255      DEALLOCATE ( A, AF, Q, R, RWORK, WORK, T, C, D, CF, DF)
256*
257      RETURN
258      END
259
260