1*> \brief \b ZQRT05
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 ZQRT05(M,N,L,NB,RESULT)
12*
13*       .. Scalar Arguments ..
14*       INTEGER LWORK, M, N, L, NB, LDT
15*       .. Return values ..
16*       DOUBLE PRECISION RESULT(6)
17*
18*
19*> \par Purpose:
20*  =============
21*>
22*> \verbatim
23*>
24*> ZQRT05 tests ZTPQRT and ZTPMQRT.
25*> \endverbatim
26*
27*  Arguments:
28*  ==========
29*
30*> \param[in] M
31*> \verbatim
32*>          M is INTEGER
33*>          Number of rows in lower part of the 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] L
43*> \verbatim
44*>          L is INTEGER
45*>          The number of rows of the upper trapezoidal part the
46*>          lower test matrix.  0 <= L <= M.
47*> \endverbatim
48*>
49*> \param[in] NB
50*> \verbatim
51*>          NB is INTEGER
52*>          Block size of test matrix.  NB <= N.
53*> \endverbatim
54*>
55*> \param[out] RESULT
56*> \verbatim
57*>          RESULT is DOUBLE PRECISION array, dimension (6)
58*>          Results of each of the six tests below.
59*>
60*>          RESULT(1) = | A - Q R |
61*>          RESULT(2) = | I - Q^H Q |
62*>          RESULT(3) = | Q C - Q C |
63*>          RESULT(4) = | Q^H C - Q^H C |
64*>          RESULT(5) = | C Q - C Q |
65*>          RESULT(6) = | C Q^H - C Q^H |
66*> \endverbatim
67*
68*  Authors:
69*  ========
70*
71*> \author Univ. of Tennessee
72*> \author Univ. of California Berkeley
73*> \author Univ. of Colorado Denver
74*> \author NAG Ltd.
75*
76*> \date April 2012
77*
78*> \ingroup complex16_lin
79*
80*  =====================================================================
81      SUBROUTINE ZQRT05(M,N,L,NB,RESULT)
82      IMPLICIT NONE
83*
84*  -- LAPACK test routine (version 3.4.1) --
85*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
86*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
87*     April 2012
88*
89*     .. Scalar Arguments ..
90      INTEGER LWORK, M, N, L, NB, LDT
91*     .. Return values ..
92      DOUBLE PRECISION RESULT(6)
93*
94*  =====================================================================
95*
96*     ..
97*     .. Local allocatable arrays
98      COMPLEX*16, ALLOCATABLE :: AF(:,:), Q(:,:),
99     $  R(:,:), RWORK(:), WORK( : ), T(:,:),
100     $  CF(:,:), DF(:,:), A(:,:), C(:,:), D(:,:)
101*
102*     .. Parameters ..
103      DOUBLE PRECISION ZERO
104      COMPLEX*16 ONE, CZERO
105      PARAMETER( ZERO = 0.0, ONE = (1.0,0.0), CZERO=(0.0,0.0) )
106*     ..
107*     .. Local Scalars ..
108      INTEGER INFO, J, K, M2, NP1
109      DOUBLE PRECISION ANORM, EPS, RESID, CNORM, DNORM
110*     ..
111*     .. Local Arrays ..
112      INTEGER            ISEED( 4 )
113*     ..
114*     .. External Functions ..
115      DOUBLE PRECISION DLAMCH
116      DOUBLE PRECISION ZLANGE, ZLANSY
117      LOGICAL  LSAME
118      EXTERNAL DLAMCH, ZLANGE, ZLANSY, LSAME
119*     ..
120*     .. Data statements ..
121      DATA ISEED / 1988, 1989, 1990, 1991 /
122*
123      EPS = DLAMCH( 'Epsilon' )
124      K = N
125      M2 = M+N
126      IF( M.GT.0 ) THEN
127         NP1 = N+1
128      ELSE
129         NP1 = 1
130      END IF
131      LWORK = M2*M2*NB
132*
133*     Dynamically allocate all arrays
134*
135      ALLOCATE(A(M2,N),AF(M2,N),Q(M2,M2),R(M2,M2),RWORK(M2),
136     $           WORK(LWORK),T(NB,N),C(M2,N),CF(M2,N),
137     $           D(N,M2),DF(N,M2) )
138*
139*     Put random stuff into A
140*
141      LDT=NB
142      CALL ZLASET( 'Full', M2, N, CZERO, CZERO, A, M2 )
143      CALL ZLASET( 'Full', NB, N, CZERO, CZERO, T, NB )
144      DO J=1,N
145         CALL ZLARNV( 2, ISEED, J, A( 1, J ) )
146      END DO
147      IF( M.GT.0 ) THEN
148         DO J=1,N
149            CALL ZLARNV( 2, ISEED, M-L, A( MIN(N+M,N+1), J ) )
150         END DO
151      END IF
152      IF( L.GT.0 ) THEN
153         DO J=1,N
154            CALL ZLARNV( 2, ISEED, MIN(J,L), A( MIN(N+M,N+M-L+1), J ) )
155         END DO
156      END IF
157*
158*     Copy the matrix A to the array AF.
159*
160      CALL ZLACPY( 'Full', M2, N, A, M2, AF, M2 )
161*
162*     Factor the matrix A in the array AF.
163*
164      CALL ZTPQRT( M,N,L,NB,AF,M2,AF(NP1,1),M2,T,LDT,WORK,INFO)
165*
166*     Generate the (M+N)-by-(M+N) matrix Q by applying H to I
167*
168      CALL ZLASET( 'Full', M2, M2, CZERO, ONE, Q, M2 )
169      CALL ZGEMQRT( 'R', 'N', M2, M2, K, NB, AF, M2, T, LDT, Q, M2,
170     $              WORK, INFO )
171*
172*     Copy R
173*
174      CALL ZLASET( 'Full', M2, N, CZERO, CZERO, R, M2 )
175      CALL ZLACPY( 'Upper', M2, N, AF, M2, R, M2 )
176*
177*     Compute |R - Q'*A| / |A| and store in RESULT(1)
178*
179      CALL ZGEMM( 'C', 'N', M2, N, M2, -ONE, Q, M2, A, M2, ONE, R, M2 )
180      ANORM = ZLANGE( '1', M2, N, A, M2, RWORK )
181      RESID = ZLANGE( '1', M2, N, R, M2, RWORK )
182      IF( ANORM.GT.ZERO ) THEN
183         RESULT( 1 ) = RESID / (EPS*ANORM*MAX(1,M2))
184      ELSE
185         RESULT( 1 ) = ZERO
186      END IF
187*
188*     Compute |I - Q'*Q| and store in RESULT(2)
189*
190      CALL ZLASET( 'Full', M2, M2, CZERO, ONE, R, M2 )
191      CALL ZHERK( 'U', 'C', M2, M2, DREAL(-ONE), Q, M2, DREAL(ONE),
192     $            R, M2 )
193      RESID = ZLANSY( '1', 'Upper', M2, R, M2, RWORK )
194      RESULT( 2 ) = RESID / (EPS*MAX(1,M2))
195*
196*     Generate random m-by-n matrix C and a copy CF
197*
198      DO J=1,N
199         CALL ZLARNV( 2, ISEED, M2, C( 1, J ) )
200      END DO
201      CNORM = ZLANGE( '1', M2, N, C, M2, RWORK)
202      CALL ZLACPY( 'Full', M2, N, C, M2, CF, M2 )
203*
204*     Apply Q to C as Q*C
205*
206      CALL ZTPMQRT( 'L','N', M,N,K,L,NB,AF(NP1,1),M2,T,LDT,CF,M2,
207     $               CF(NP1,1),M2,WORK,INFO)
208*
209*     Compute |Q*C - Q*C| / |C|
210*
211      CALL ZGEMM( 'N', 'N', M2, N, M2, -ONE, Q, M2, C, M2, ONE, CF, M2 )
212      RESID = ZLANGE( '1', M2, N, CF, M2, RWORK )
213      IF( CNORM.GT.ZERO ) THEN
214         RESULT( 3 ) = RESID / (EPS*MAX(1,M2)*CNORM)
215      ELSE
216         RESULT( 3 ) = ZERO
217      END IF
218*
219*     Copy C into CF again
220*
221      CALL ZLACPY( 'Full', M2, N, C, M2, CF, M2 )
222*
223*     Apply Q to C as QT*C
224*
225      CALL ZTPMQRT( 'L','C',M,N,K,L,NB,AF(NP1,1),M2,T,LDT,CF,M2,
226     $              CF(NP1,1),M2,WORK,INFO)
227*
228*     Compute |QT*C - QT*C| / |C|
229*
230      CALL ZGEMM('C','N',M2,N,M2,-ONE,Q,M2,C,M2,ONE,CF,M2)
231      RESID = ZLANGE( '1', M2, N, CF, M2, RWORK )
232      IF( CNORM.GT.ZERO ) THEN
233         RESULT( 4 ) = RESID / (EPS*MAX(1,M2)*CNORM)
234      ELSE
235         RESULT( 4 ) = ZERO
236      END IF
237*
238*     Generate random n-by-m matrix D and a copy DF
239*
240      DO J=1,M2
241         CALL ZLARNV( 2, ISEED, N, D( 1, J ) )
242      END DO
243      DNORM = ZLANGE( '1', N, M2, D, N, RWORK)
244      CALL ZLACPY( 'Full', N, M2, D, N, DF, N )
245*
246*     Apply Q to D as D*Q
247*
248      CALL ZTPMQRT('R','N',N,M,N,L,NB,AF(NP1,1),M2,T,LDT,DF,N,
249     $             DF(1,NP1),N,WORK,INFO)
250*
251*     Compute |D*Q - D*Q| / |D|
252*
253      CALL ZGEMM('N','N',N,M2,M2,-ONE,D,N,Q,M2,ONE,DF,N)
254      RESID = ZLANGE('1',N, M2,DF,N,RWORK )
255      IF( CNORM.GT.ZERO ) THEN
256         RESULT( 5 ) = RESID / (EPS*MAX(1,M2)*DNORM)
257      ELSE
258         RESULT( 5 ) = ZERO
259      END IF
260*
261*     Copy D into DF again
262*
263      CALL ZLACPY('Full',N,M2,D,N,DF,N )
264*
265*     Apply Q to D as D*QT
266*
267      CALL ZTPMQRT('R','C',N,M,N,L,NB,AF(NP1,1),M2,T,LDT,DF,N,
268     $             DF(1,NP1),N,WORK,INFO)
269
270*
271*     Compute |D*QT - D*QT| / |D|
272*
273      CALL ZGEMM( 'N', 'C', N, M2, M2, -ONE, D, N, Q, M2, ONE, DF, N )
274      RESID = ZLANGE( '1', N, M2, DF, N, RWORK )
275      IF( CNORM.GT.ZERO ) THEN
276         RESULT( 6 ) = RESID / (EPS*MAX(1,M2)*DNORM)
277      ELSE
278         RESULT( 6 ) = ZERO
279      END IF
280*
281*     Deallocate all arrays
282*
283      DEALLOCATE ( A, AF, Q, R, RWORK, WORK, T, C, D, CF, DF)
284      RETURN
285      END
286
287