LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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dtsqr01.f
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1*> \brief \b DTSQR01
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 DTSQR01(TSSW, M,N, MB, NB, RESULT)
12*
13* .. Scalar Arguments ..
14* INTEGER M, N, MB
15* .. Return values ..
16* DOUBLE PRECISION RESULT(6)
17*
18*
19*> \par Purpose:
20* =============
21*>
22*> \verbatim
23*>
24*> DTSQR01 tests DGEQR , DGELQ, DGEMLQ and DGEMQR.
25*> \endverbatim
26*
27* Arguments:
28* ==========
29*
30*> \param[in] TSSW
31*> \verbatim
32*> TSSW is CHARACTER
33*> 'TS' for testing tall skinny QR
34*> and anything else for testing short wide LQ
35*> \endverbatim
36*> \param[in] M
37*> \verbatim
38*> M is INTEGER
39*> Number of rows in test matrix.
40*> \endverbatim
41*>
42*> \param[in] N
43*> \verbatim
44*> N is INTEGER
45*> Number of columns in test matrix.
46*> \endverbatim
47*> \param[in] MB
48*> \verbatim
49*> MB is INTEGER
50*> Number of row in row block in test matrix.
51*> \endverbatim
52*>
53*> \param[in] NB
54*> \verbatim
55*> NB is INTEGER
56*> Number of columns in column block test matrix.
57*> \endverbatim
58*>
59*> \param[out] RESULT
60*> \verbatim
61*> RESULT is DOUBLE PRECISION array, dimension (6)
62*> Results of each of the six tests below.
63*>
64*> RESULT(1) = | A - Q R | or | A - L Q |
65*> RESULT(2) = | I - Q^H Q | or | I - Q Q^H |
66*> RESULT(3) = | Q C - Q C |
67*> RESULT(4) = | Q^H C - Q^H C |
68*> RESULT(5) = | C Q - C Q |
69*> RESULT(6) = | C Q^H - C Q^H |
70*> \endverbatim
71*
72* Authors:
73* ========
74*
75*> \author Univ. of Tennessee
76*> \author Univ. of California Berkeley
77*> \author Univ. of Colorado Denver
78*> \author NAG Ltd.
79*
80*> \ingroup double_lin
81*
82* =====================================================================
83 SUBROUTINE dtsqr01(TSSW, M, N, MB, NB, RESULT)
84 IMPLICIT NONE
85*
86* -- LAPACK test routine --
87* -- LAPACK is a software package provided by Univ. of Tennessee, --
88* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
89*
90* .. Scalar Arguments ..
91 CHARACTER TSSW
92 INTEGER M, N, MB, NB
93* .. Return values ..
94 DOUBLE PRECISION RESULT(6)
95*
96* =====================================================================
97*
98* ..
99* .. Local allocatable arrays
100 DOUBLE PRECISION, ALLOCATABLE :: AF(:,:), Q(:,:),
101 $ R(:,:), RWORK(:), WORK( : ), T(:),
102 $ CF(:,:), DF(:,:), A(:,:), C(:,:), D(:,:), LQ(:,:)
103*
104* .. Parameters ..
105 DOUBLE PRECISION ONE, ZERO
106 parameter( zero = 0.0, one = 1.0 )
107* ..
108* .. Local Scalars ..
109 LOGICAL TESTZEROS, TS
110 INTEGER INFO, J, K, L, LWORK, TSIZE, MNB
111 DOUBLE PRECISION ANORM, EPS, RESID, CNORM, DNORM
112* ..
113* .. Local Arrays ..
114 INTEGER ISEED( 4 )
115 DOUBLE PRECISION TQUERY( 5 ), WORKQUERY( 1 )
116* ..
117* .. External Functions ..
118 DOUBLE PRECISION DLAMCH, DLANGE, DLANSY
119 LOGICAL LSAME
120 INTEGER ILAENV
121 EXTERNAL dlamch, dlange, dlansy, lsame, ilaenv
122* ..
123* .. Intrinsic Functions ..
124 INTRINSIC max, min
125* .. Scalars in Common ..
126 CHARACTER*32 srnamt
127* ..
128* .. Common blocks ..
129 COMMON / srnamc / srnamt
130* ..
131* .. Data statements ..
132 DATA iseed / 1988, 1989, 1990, 1991 /
133*
134* TEST TALL SKINNY OR SHORT WIDE
135*
136 ts = lsame(tssw, 'TS')
137*
138* TEST MATRICES WITH HALF OF MATRIX BEING ZEROS
139*
140 testzeros = .false.
141*
142 eps = dlamch( 'Epsilon' )
143 k = min(m,n)
144 l = max(m,n,1)
145 mnb = max( mb, nb)
146 lwork = max(3,l)*mnb
147*
148* Dynamically allocate local arrays
149*
150 ALLOCATE ( a(m,n), af(m,n), q(l,l), r(m,l), rwork(l),
151 $ c(m,n), cf(m,n),
152 $ d(n,m), df(n,m), lq(l,n) )
153*
154* Put random numbers into A and copy to AF
155*
156 DO j=1,n
157 CALL dlarnv( 2, iseed, m, a( 1, j ) )
158 END DO
159 IF (testzeros) THEN
160 IF (m.GE.4) THEN
161 DO j=1,n
162 CALL dlarnv( 2, iseed, m/2, a( m/4, j ) )
163 END DO
164 END IF
165 END IF
166 CALL dlacpy( 'Full', m, n, a, m, af, m )
167*
168 IF (ts) THEN
169*
170* Factor the matrix A in the array AF.
171*
172 CALL dgeqr( m, n, af, m, tquery, -1, workquery, -1, info )
173 tsize = int( tquery( 1 ) )
174 lwork = int( workquery( 1 ) )
175 CALL dgemqr( 'L', 'N', m, m, k, af, m, tquery, tsize, cf, m,
176 $ workquery, -1, info)
177 lwork = max( lwork, int( workquery( 1 ) ) )
178 CALL dgemqr( 'L', 'N', m, n, k, af, m, tquery, tsize, cf, m,
179 $ workquery, -1, info)
180 lwork = max( lwork, int( workquery( 1 ) ) )
181 CALL dgemqr( 'L', 'T', m, n, k, af, m, tquery, tsize, cf, m,
182 $ workquery, -1, info)
183 lwork = max( lwork, int( workquery( 1 ) ) )
184 CALL dgemqr( 'R', 'N', n, m, k, af, m, tquery, tsize, df, n,
185 $ workquery, -1, info)
186 lwork = max( lwork, int( workquery( 1 ) ) )
187 CALL dgemqr( 'R', 'T', n, m, k, af, m, tquery, tsize, df, n,
188 $ workquery, -1, info)
189 lwork = max( lwork, int( workquery( 1 ) ) )
190 ALLOCATE ( t( tsize ) )
191 ALLOCATE ( work( lwork ) )
192 srnamt = 'DGEQR'
193 CALL dgeqr( m, n, af, m, t, tsize, work, lwork, info )
194*
195* Generate the m-by-m matrix Q
196*
197 CALL dlaset( 'Full', m, m, zero, one, q, m )
198 srnamt = 'DGEMQR'
199 CALL dgemqr( 'L', 'N', m, m, k, af, m, t, tsize, q, m,
200 $ work, lwork, info )
201*
202* Copy R
203*
204 CALL dlaset( 'Full', m, n, zero, zero, r, m )
205 CALL dlacpy( 'Upper', m, n, af, m, r, m )
206*
207* Compute |R - Q'*A| / |A| and store in RESULT(1)
208*
209 CALL dgemm( 'T', 'N', m, n, m, -one, q, m, a, m, one, r, m )
210 anorm = dlange( '1', m, n, a, m, rwork )
211 resid = dlange( '1', m, n, r, m, rwork )
212 IF( anorm.GT.zero ) THEN
213 result( 1 ) = resid / (eps*max(1,m)*anorm)
214 ELSE
215 result( 1 ) = zero
216 END IF
217*
218* Compute |I - Q'*Q| and store in RESULT(2)
219*
220 CALL dlaset( 'Full', m, m, zero, one, r, m )
221 CALL dsyrk( 'U', 'C', m, m, -one, q, m, one, r, m )
222 resid = dlansy( '1', 'Upper', m, r, m, rwork )
223 result( 2 ) = resid / (eps*max(1,m))
224*
225* Generate random m-by-n matrix C and a copy CF
226*
227 DO j=1,n
228 CALL dlarnv( 2, iseed, m, c( 1, j ) )
229 END DO
230 cnorm = dlange( '1', m, n, c, m, rwork)
231 CALL dlacpy( 'Full', m, n, c, m, cf, m )
232*
233* Apply Q to C as Q*C
234*
235 srnamt = 'DGEMQR'
236 CALL dgemqr( 'L', 'N', m, n, k, af, m, t, tsize, cf, m,
237 $ work, lwork, info)
238*
239* Compute |Q*C - Q*C| / |C|
240*
241 CALL dgemm( 'N', 'N', m, n, m, -one, q, m, c, m, one, cf, m )
242 resid = dlange( '1', m, n, cf, m, rwork )
243 IF( cnorm.GT.zero ) THEN
244 result( 3 ) = resid / (eps*max(1,m)*cnorm)
245 ELSE
246 result( 3 ) = zero
247 END IF
248*
249* Copy C into CF again
250*
251 CALL dlacpy( 'Full', m, n, c, m, cf, m )
252*
253* Apply Q to C as QT*C
254*
255 srnamt = 'DGEMQR'
256 CALL dgemqr( 'L', 'T', m, n, k, af, m, t, tsize, cf, m,
257 $ work, lwork, info)
258*
259* Compute |QT*C - QT*C| / |C|
260*
261 CALL dgemm( 'T', 'N', m, n, m, -one, q, m, c, m, one, cf, m )
262 resid = dlange( '1', m, n, cf, m, rwork )
263 IF( cnorm.GT.zero ) THEN
264 result( 4 ) = resid / (eps*max(1,m)*cnorm)
265 ELSE
266 result( 4 ) = zero
267 END IF
268*
269* Generate random n-by-m matrix D and a copy DF
270*
271 DO j=1,m
272 CALL dlarnv( 2, iseed, n, d( 1, j ) )
273 END DO
274 dnorm = dlange( '1', n, m, d, n, rwork)
275 CALL dlacpy( 'Full', n, m, d, n, df, n )
276*
277* Apply Q to D as D*Q
278*
279 srnamt = 'DGEMQR'
280 CALL dgemqr( 'R', 'N', n, m, k, af, m, t, tsize, df, n,
281 $ work, lwork, info)
282*
283* Compute |D*Q - D*Q| / |D|
284*
285 CALL dgemm( 'N', 'N', n, m, m, -one, d, n, q, m, one, df, n )
286 resid = dlange( '1', n, m, df, n, rwork )
287 IF( dnorm.GT.zero ) THEN
288 result( 5 ) = resid / (eps*max(1,m)*dnorm)
289 ELSE
290 result( 5 ) = zero
291 END IF
292*
293* Copy D into DF again
294*
295 CALL dlacpy( 'Full', n, m, d, n, df, n )
296*
297* Apply Q to D as D*QT
298*
299 CALL dgemqr( 'R', 'T', n, m, k, af, m, t, tsize, df, n,
300 $ work, lwork, info)
301*
302* Compute |D*QT - D*QT| / |D|
303*
304 CALL dgemm( 'N', 'T', n, m, m, -one, d, n, q, m, one, df, n )
305 resid = dlange( '1', n, m, df, n, rwork )
306 IF( cnorm.GT.zero ) THEN
307 result( 6 ) = resid / (eps*max(1,m)*dnorm)
308 ELSE
309 result( 6 ) = zero
310 END IF
311*
312* Short and wide
313*
314 ELSE
315 CALL dgelq( m, n, af, m, tquery, -1, workquery, -1, info )
316 tsize = int( tquery( 1 ) )
317 lwork = int( workquery( 1 ) )
318 CALL dgemlq( 'R', 'N', n, n, k, af, m, tquery, tsize, q, n,
319 $ workquery, -1, info )
320 lwork = max( lwork, int( workquery( 1 ) ) )
321 CALL dgemlq( 'L', 'N', n, m, k, af, m, tquery, tsize, df, n,
322 $ workquery, -1, info)
323 lwork = max( lwork, int( workquery( 1 ) ) )
324 CALL dgemlq( 'L', 'T', n, m, k, af, m, tquery, tsize, df, n,
325 $ workquery, -1, info)
326 lwork = max( lwork, int( workquery( 1 ) ) )
327 CALL dgemlq( 'R', 'N', m, n, k, af, m, tquery, tsize, cf, m,
328 $ workquery, -1, info)
329 lwork = max( lwork, int( workquery( 1 ) ) )
330 CALL dgemlq( 'R', 'T', m, n, k, af, m, tquery, tsize, cf, m,
331 $ workquery, -1, info)
332 lwork = max( lwork, int( workquery( 1 ) ) )
333 ALLOCATE ( t( tsize ) )
334 ALLOCATE ( work( lwork ) )
335 srnamt = 'DGELQ'
336 CALL dgelq( m, n, af, m, t, tsize, work, lwork, info )
337*
338*
339* Generate the n-by-n matrix Q
340*
341 CALL dlaset( 'Full', n, n, zero, one, q, n )
342 srnamt = 'DGEMLQ'
343 CALL dgemlq( 'R', 'N', n, n, k, af, m, t, tsize, q, n,
344 $ work, lwork, info )
345*
346* Copy R
347*
348 CALL dlaset( 'Full', m, n, zero, zero, lq, l )
349 CALL dlacpy( 'Lower', m, n, af, m, lq, l )
350*
351* Compute |L - A*Q'| / |A| and store in RESULT(1)
352*
353 CALL dgemm( 'N', 'T', m, n, n, -one, a, m, q, n, one, lq, l )
354 anorm = dlange( '1', m, n, a, m, rwork )
355 resid = dlange( '1', m, n, lq, l, rwork )
356 IF( anorm.GT.zero ) THEN
357 result( 1 ) = resid / (eps*max(1,n)*anorm)
358 ELSE
359 result( 1 ) = zero
360 END IF
361*
362* Compute |I - Q'*Q| and store in RESULT(2)
363*
364 CALL dlaset( 'Full', n, n, zero, one, lq, l )
365 CALL dsyrk( 'U', 'C', n, n, -one, q, n, one, lq, l )
366 resid = dlansy( '1', 'Upper', n, lq, l, rwork )
367 result( 2 ) = resid / (eps*max(1,n))
368*
369* Generate random m-by-n matrix C and a copy CF
370*
371 DO j=1,m
372 CALL dlarnv( 2, iseed, n, d( 1, j ) )
373 END DO
374 dnorm = dlange( '1', n, m, d, n, rwork)
375 CALL dlacpy( 'Full', n, m, d, n, df, n )
376*
377* Apply Q to C as Q*C
378*
379 CALL dgemlq( 'L', 'N', n, m, k, af, m, t, tsize, df, n,
380 $ work, lwork, info)
381*
382* Compute |Q*D - Q*D| / |D|
383*
384 CALL dgemm( 'N', 'N', n, m, n, -one, q, n, d, n, one, df, n )
385 resid = dlange( '1', n, m, df, n, rwork )
386 IF( dnorm.GT.zero ) THEN
387 result( 3 ) = resid / (eps*max(1,n)*dnorm)
388 ELSE
389 result( 3 ) = zero
390 END IF
391*
392* Copy D into DF again
393*
394 CALL dlacpy( 'Full', n, m, d, n, df, n )
395*
396* Apply Q to D as QT*D
397*
398 CALL dgemlq( 'L', 'T', n, m, k, af, m, t, tsize, df, n,
399 $ work, lwork, info)
400*
401* Compute |QT*D - QT*D| / |D|
402*
403 CALL dgemm( 'T', 'N', n, m, n, -one, q, n, d, n, one, df, n )
404 resid = dlange( '1', n, m, df, n, rwork )
405 IF( dnorm.GT.zero ) THEN
406 result( 4 ) = resid / (eps*max(1,n)*dnorm)
407 ELSE
408 result( 4 ) = zero
409 END IF
410*
411* Generate random n-by-m matrix D and a copy DF
412*
413 DO j=1,n
414 CALL dlarnv( 2, iseed, m, c( 1, j ) )
415 END DO
416 cnorm = dlange( '1', m, n, c, m, rwork)
417 CALL dlacpy( 'Full', m, n, c, m, cf, m )
418*
419* Apply Q to C as C*Q
420*
421 CALL dgemlq( 'R', 'N', m, n, k, af, m, t, tsize, cf, m,
422 $ work, lwork, info)
423*
424* Compute |C*Q - C*Q| / |C|
425*
426 CALL dgemm( 'N', 'N', m, n, n, -one, c, m, q, n, one, cf, m )
427 resid = dlange( '1', n, m, df, n, rwork )
428 IF( cnorm.GT.zero ) THEN
429 result( 5 ) = resid / (eps*max(1,n)*cnorm)
430 ELSE
431 result( 5 ) = zero
432 END IF
433*
434* Copy C into CF again
435*
436 CALL dlacpy( 'Full', m, n, c, m, cf, m )
437*
438* Apply Q to D as D*QT
439*
440 CALL dgemlq( 'R', 'T', m, n, k, af, m, t, tsize, cf, m,
441 $ work, lwork, info)
442*
443* Compute |C*QT - C*QT| / |C|
444*
445 CALL dgemm( 'N', 'T', m, n, n, -one, c, m, q, n, one, cf, m )
446 resid = dlange( '1', m, n, cf, m, rwork )
447 IF( cnorm.GT.zero ) THEN
448 result( 6 ) = resid / (eps*max(1,n)*cnorm)
449 ELSE
450 result( 6 ) = zero
451 END IF
452*
453 END IF
454*
455* Deallocate all arrays
456*
457 DEALLOCATE ( a, af, q, r, rwork, work, t, c, d, cf, df)
458*
459 RETURN
460 END
dtsqr01
subroutine dtsqr01(tssw, m, n, mb, nb, result)
DTSQR01
Definition dtsqr01.f:84
dgelq
subroutine dgelq(m, n, a, lda, t, tsize, work, lwork, info)
DGELQ
Definition dgelq.f:174
dgemlq
subroutine dgemlq(side, trans, m, n, k, a, lda, t, tsize, c, ldc, work, lwork, info)
DGEMLQ
Definition dgemlq.f:173
dgemm
subroutine dgemm(transa, transb, m, n, k, alpha, a, lda, b, ldb, beta, c, ldc)
DGEMM
Definition dgemm.f:188
dgemqr
subroutine dgemqr(side, trans, m, n, k, a, lda, t, tsize, c, ldc, work, lwork, info)
DGEMQR
Definition dgemqr.f:174
dgeqr
subroutine dgeqr(m, n, a, lda, t, tsize, work, lwork, info)
DGEQR
Definition dgeqr.f:176
dsyrk
subroutine dsyrk(uplo, trans, n, k, alpha, a, lda, beta, c, ldc)
DSYRK
Definition dsyrk.f:169
dlacpy
subroutine dlacpy(uplo, m, n, a, lda, b, ldb)
DLACPY copies all or part of one two-dimensional array to another.
Definition dlacpy.f:103
dlarnv
subroutine dlarnv(idist, iseed, n, x)
DLARNV returns a vector of random numbers from a uniform or normal distribution.
Definition dlarnv.f:97
dlaset
subroutine dlaset(uplo, m, n, alpha, beta, a, lda)
DLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition dlaset.f:110