1*> \brief \b SLQT05
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 SLQT05(M,N,L,NB,RESULT)
12*
13*       .. Scalar Arguments ..
14*       INTEGER LWORK, M, N, L, NB, LDT
15*       .. Return values ..
16*       REAL RESULT(6)
17*
18*
19*> \par Purpose:
20*  =============
21*>
22*> \verbatim
23*> SQRT05 tests STPLQT and STPMLQT.
24*> \endverbatim
25*
26*  Arguments:
27*  ==========
28*
29*> \param[in] M
30*> \verbatim
31*>          M is INTEGER
32*>          Number of rows in lower part of the test matrix.
33*> \endverbatim
34*>
35*> \param[in] N
36*> \verbatim
37*>          N is INTEGER
38*>          Number of columns in test matrix.
39*> \endverbatim
40*>
41*> \param[in] L
42*> \verbatim
43*>          L is INTEGER
44*>          The number of rows of the upper trapezoidal part the
45*>          lower test matrix.  0 <= L <= M.
46*> \endverbatim
47*>
48*> \param[in] NB
49*> \verbatim
50*>          NB is INTEGER
51*>          Block size of test matrix.  NB <= N.
52*> \endverbatim
53*>
54*> \param[out] RESULT
55*> \verbatim
56*>          RESULT is REAL array, dimension (6)
57*>          Results of each of the six tests below.
58*>
59*>          RESULT(1) = | A - Q R |
60*>          RESULT(2) = | I - Q^H Q |
61*>          RESULT(3) = | Q C - Q C |
62*>          RESULT(4) = | Q^H C - Q^H C |
63*>          RESULT(5) = | C Q - C Q |
64*>          RESULT(6) = | C Q^H - C Q^H |
65*> \endverbatim
66*
67*  Authors:
68*  ========
69*
70*> \author Univ. of Tennessee
71*> \author Univ. of California Berkeley
72*> \author Univ. of Colorado Denver
73*> \author NAG Ltd.
74*
75*> \ingroup double_lin
76*
77*  =====================================================================
78      SUBROUTINE SLQT05(M,N,L,NB,RESULT)
79      IMPLICIT NONE
80*
81*  -- LAPACK test routine --
82*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
83*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
84*
85*     .. Scalar Arguments ..
86      INTEGER  LWORK, M, N, L, NB, LDT
87*     .. Return values ..
88      REAL     RESULT(6)
89*
90*  =====================================================================
91*
92*     ..
93*     .. Local allocatable arrays
94      REAL, ALLOCATABLE :: AF(:,:), Q(:,:),
95     $  R(:,:), RWORK(:), WORK( : ), T(:,:),
96     $  CF(:,:), DF(:,:), A(:,:), C(:,:), D(:,:)
97*
98*     .. Parameters ..
99      REAL ONE, ZERO
100      PARAMETER( ZERO = 0.0, ONE = 1.0 )
101*     ..
102*     .. Local Scalars ..
103      INTEGER     INFO, J, K, N2, NP1,i
104      REAL        ANORM, EPS, RESID, CNORM, DNORM
105*     ..
106*     .. Local Arrays ..
107      INTEGER            ISEED( 4 )
108*     ..
109*     .. External Functions ..
110      REAL        SLAMCH, SLANGE, SLANSY
111      LOGICAL     LSAME
112      EXTERNAL    SLAMCH, SLANGE, SLANSY, LSAME
113*     ..
114*     .. Data statements ..
115      DATA ISEED / 1988, 1989, 1990, 1991 /
116*
117      EPS = SLAMCH( 'Epsilon' )
118      K = M
119      N2 = M+N
120      IF( N.GT.0 ) THEN
121         NP1 = M+1
122      ELSE
123         NP1 = 1
124      END IF
125      LWORK = N2*N2*NB
126*
127*     Dynamically allocate all arrays
128*
129      ALLOCATE(A(M,N2),AF(M,N2),Q(N2,N2),R(N2,N2),RWORK(N2),
130     $           WORK(LWORK),T(NB,M),C(N2,M),CF(N2,M),
131     $           D(M,N2),DF(M,N2) )
132*
133*     Put random stuff into A
134*
135      LDT=NB
136      CALL SLASET( 'Full', M, N2, ZERO, ZERO, A, M )
137      CALL SLASET( 'Full', NB, M, ZERO, ZERO, T, NB )
138      DO J=1,M
139         CALL SLARNV( 2, ISEED, M-J+1, A( J, J ) )
140      END DO
141      IF( N.GT.0 ) THEN
142         DO J=1,N-L
143            CALL SLARNV( 2, ISEED, M, A( 1, MIN(N+M,M+1) + J - 1 ) )
144         END DO
145      END IF
146      IF( L.GT.0 ) THEN
147         DO J=1,L
148            CALL SLARNV( 2, ISEED, M-J+1, A( J, MIN(N+M,N+M-L+1)
149     $          + J - 1 ) )
150         END DO
151      END IF
152*
153*     Copy the matrix A to the array AF.
154*
155      CALL SLACPY( 'Full', M, N2, A, M, AF, M )
156*
157*     Factor the matrix A in the array AF.
158*
159      CALL STPLQT( M,N,L,NB,AF,M,AF(1,NP1),M,T,LDT,WORK,INFO)
160*
161*     Generate the (M+N)-by-(M+N) matrix Q by applying H to I
162*
163      CALL SLASET( 'Full', N2, N2, ZERO, ONE, Q, N2 )
164      CALL SGEMLQT( 'L', 'N', N2, N2, K, NB, AF, M, T, LDT, Q, N2,
165     $              WORK, INFO )
166*
167*     Copy L
168*
169      CALL SLASET( 'Full', N2, N2, ZERO, ZERO, R, N2 )
170      CALL SLACPY( 'Lower', M, N2, AF, M, R, N2 )
171*
172*     Compute |L - A*Q*T| / |A| and store in RESULT(1)
173*
174      CALL SGEMM( 'N', 'T', M, N2, N2, -ONE,  A, M, Q, N2, ONE, R, N2)
175      ANORM = SLANGE( '1', M, N2, A, M, RWORK )
176      RESID = SLANGE( '1', M, N2, R, N2, RWORK )
177      IF( ANORM.GT.ZERO ) THEN
178         RESULT( 1 ) = RESID / (EPS*ANORM*MAX(1,N2))
179      ELSE
180         RESULT( 1 ) = ZERO
181      END IF
182*
183*     Compute |I - Q*Q'| and store in RESULT(2)
184*
185      CALL SLASET( 'Full', N2, N2, ZERO, ONE, R, N2 )
186      CALL SSYRK( 'U', 'N', N2, N2, -ONE, Q, N2, ONE, R, N2 )
187      RESID = SLANSY( '1', 'Upper', N2, R, N2, RWORK )
188      RESULT( 2 ) = RESID / (EPS*MAX(1,N2))
189*
190*     Generate random m-by-n matrix C and a copy CF
191*
192      CALL SLASET( 'Full', N2, M, ZERO, ONE, C, N2 )
193      DO J=1,M
194         CALL SLARNV( 2, ISEED, N2, C( 1, J ) )
195      END DO
196      CNORM = SLANGE( '1', N2, M, C, N2, RWORK)
197      CALL SLACPY( 'Full', N2, M, C, N2, CF, N2 )
198*
199*     Apply Q to C as Q*C
200*
201      CALL STPMLQT( 'L','N', N,M,K,L,NB,AF(1, NP1),M,T,LDT,CF,N2,
202     $               CF(NP1,1),N2,WORK,INFO)
203*
204*     Compute |Q*C - Q*C| / |C|
205*
206      CALL SGEMM( 'N', 'N', N2, M, N2, -ONE, Q, N2, C, N2, ONE, CF, N2 )
207      RESID = SLANGE( '1', N2, M, CF, N2, RWORK )
208      IF( CNORM.GT.ZERO ) THEN
209         RESULT( 3 ) = RESID / (EPS*MAX(1,N2)*CNORM)
210      ELSE
211         RESULT( 3 ) = ZERO
212      END IF
213
214*
215*     Copy C into CF again
216*
217      CALL SLACPY( 'Full', N2, M, C, N2, CF, N2 )
218*
219*     Apply Q to C as QT*C
220*
221      CALL STPMLQT( 'L','T',N,M,K,L,NB,AF(1,NP1),M,T,LDT,CF,N2,
222     $              CF(NP1,1),N2,WORK,INFO)
223*
224*     Compute |QT*C - QT*C| / |C|
225*
226      CALL SGEMM('T','N',N2,M,N2,-ONE,Q,N2,C,N2,ONE,CF,N2)
227      RESID = SLANGE( '1', N2, M, CF, N2, RWORK )
228
229      IF( CNORM.GT.ZERO ) THEN
230         RESULT( 4 ) = RESID / (EPS*MAX(1,N2)*CNORM)
231      ELSE
232         RESULT( 4 ) = ZERO
233      END IF
234*
235*     Generate random m-by-n matrix D and a copy DF
236*
237      DO J=1,N2
238         CALL SLARNV( 2, ISEED, M, D( 1, J ) )
239      END DO
240      DNORM = SLANGE( '1', M, N2, D, M, RWORK)
241      CALL SLACPY( 'Full', M, N2, D, M, DF, M )
242*
243*     Apply Q to D as D*Q
244*
245      CALL STPMLQT('R','N',M,N,K,L,NB,AF(1,NP1),M,T,LDT,DF,M,
246     $             DF(1,NP1),M,WORK,INFO)
247*
248*     Compute |D*Q - D*Q| / |D|
249*
250      CALL SGEMM('N','N',M,N2,N2,-ONE,D,M,Q,N2,ONE,DF,M)
251      RESID = SLANGE('1',M, N2,DF,M,RWORK )
252      IF( CNORM.GT.ZERO ) THEN
253         RESULT( 5 ) = RESID / (EPS*MAX(1,N2)*DNORM)
254      ELSE
255         RESULT( 5 ) = ZERO
256      END IF
257*
258*     Copy D into DF again
259*
260      CALL SLACPY('Full',M,N2,D,M,DF,M )
261*
262*     Apply Q to D as D*QT
263*
264      CALL STPMLQT('R','T',M,N,K,L,NB,AF(1,NP1),M,T,LDT,DF,M,
265     $             DF(1,NP1),M,WORK,INFO)
266
267*
268*     Compute |D*QT - D*QT| / |D|
269*
270      CALL SGEMM( 'N', 'T', M, N2, N2, -ONE, D, M, Q, N2, ONE, DF, M )
271      RESID = SLANGE( '1', M, N2, DF, M, RWORK )
272      IF( CNORM.GT.ZERO ) THEN
273         RESULT( 6 ) = RESID / (EPS*MAX(1,N2)*DNORM)
274      ELSE
275         RESULT( 6 ) = ZERO
276      END IF
277*
278*     Deallocate all arrays
279*
280      DEALLOCATE ( A, AF, Q, R, RWORK, WORK, T, C, D, CF, DF)
281      RETURN
282      END
283