LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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cckcsd.f
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1*> \brief \b CCKCSD
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 CCKCSD( NM, MVAL, PVAL, QVAL, NMATS, ISEED, THRESH,
12* MMAX, X, XF, U1, U2, V1T, V2T, THETA, IWORK,
13* WORK, RWORK, NIN, NOUT, INFO )
14*
15* .. Scalar Arguments ..
16* INTEGER INFO, NIN, NM, NMATS, MMAX, NOUT
17* REAL THRESH
18* ..
19* .. Array Arguments ..
20* INTEGER ISEED( 4 ), IWORK( * ), MVAL( * ), PVAL( * ),
21* $ QVAL( * )
22* REAL RWORK( * ), THETA( * )
23* COMPLEX U1( * ), U2( * ), V1T( * ), V2T( * ),
24* $ WORK( * ), X( * ), XF( * )
25* ..
26*
27*
28*> \par Purpose:
29* =============
30*>
31*> \verbatim
32*>
33*> CCKCSD tests CUNCSD:
34*> the CSD for an M-by-M unitary matrix X partitioned as
35*> [ X11 X12; X21 X22 ]. X11 is P-by-Q.
36*> \endverbatim
37*
38* Arguments:
39* ==========
40*
41*> \param[in] NM
42*> \verbatim
43*> NM is INTEGER
44*> The number of values of M contained in the vector MVAL.
45*> \endverbatim
46*>
47*> \param[in] MVAL
48*> \verbatim
49*> MVAL is INTEGER array, dimension (NM)
50*> The values of the matrix row dimension M.
51*> \endverbatim
52*>
53*> \param[in] PVAL
54*> \verbatim
55*> PVAL is INTEGER array, dimension (NM)
56*> The values of the matrix row dimension P.
57*> \endverbatim
58*>
59*> \param[in] QVAL
60*> \verbatim
61*> QVAL is INTEGER array, dimension (NM)
62*> The values of the matrix column dimension Q.
63*> \endverbatim
64*>
65*> \param[in] NMATS
66*> \verbatim
67*> NMATS is INTEGER
68*> The number of matrix types to be tested for each combination
69*> of matrix dimensions. If NMATS >= NTYPES (the maximum
70*> number of matrix types), then all the different types are
71*> generated for testing. If NMATS < NTYPES, another input line
72*> is read to get the numbers of the matrix types to be used.
73*> \endverbatim
74*>
75*> \param[in,out] ISEED
76*> \verbatim
77*> ISEED is INTEGER array, dimension (4)
78*> On entry, the seed of the random number generator. The array
79*> elements should be between 0 and 4095, otherwise they will be
80*> reduced mod 4096, and ISEED(4) must be odd.
81*> On exit, the next seed in the random number sequence after
82*> all the test matrices have been generated.
83*> \endverbatim
84*>
85*> \param[in] THRESH
86*> \verbatim
87*> THRESH is REAL
88*> The threshold value for the test ratios. A result is
89*> included in the output file if RESULT >= THRESH. To have
90*> every test ratio printed, use THRESH = 0.
91*> \endverbatim
92*>
93*> \param[in] MMAX
94*> \verbatim
95*> MMAX is INTEGER
96*> The maximum value permitted for M, used in dimensioning the
97*> work arrays.
98*> \endverbatim
99*>
100*> \param[out] X
101*> \verbatim
102*> X is COMPLEX array, dimension (MMAX*MMAX)
103*> \endverbatim
104*>
105*> \param[out] XF
106*> \verbatim
107*> XF is COMPLEX array, dimension (MMAX*MMAX)
108*> \endverbatim
109*>
110*> \param[out] U1
111*> \verbatim
112*> U1 is COMPLEX array, dimension (MMAX*MMAX)
113*> \endverbatim
114*>
115*> \param[out] U2
116*> \verbatim
117*> U2 is COMPLEX array, dimension (MMAX*MMAX)
118*> \endverbatim
119*>
120*> \param[out] V1T
121*> \verbatim
122*> V1T is COMPLEX array, dimension (MMAX*MMAX)
123*> \endverbatim
124*>
125*> \param[out] V2T
126*> \verbatim
127*> V2T is COMPLEX array, dimension (MMAX*MMAX)
128*> \endverbatim
129*>
130*> \param[out] THETA
131*> \verbatim
132*> THETA is REAL array, dimension (MMAX)
133*> \endverbatim
134*>
135*> \param[out] IWORK
136*> \verbatim
137*> IWORK is INTEGER array, dimension (MMAX)
138*> \endverbatim
139*>
140*> \param[out] WORK
141*> \verbatim
142*> WORK is COMPLEX array
143*> \endverbatim
144*>
145*> \param[out] RWORK
146*> \verbatim
147*> RWORK is REAL array
148*> \endverbatim
149*>
150*> \param[in] NIN
151*> \verbatim
152*> NIN is INTEGER
153*> The unit number for input.
154*> \endverbatim
155*>
156*> \param[in] NOUT
157*> \verbatim
158*> NOUT is INTEGER
159*> The unit number for output.
160*> \endverbatim
161*>
162*> \param[out] INFO
163*> \verbatim
164*> INFO is INTEGER
165*> = 0 : successful exit
166*> > 0 : If CLAROR returns an error code, the absolute value
167*> of it is returned.
168*> \endverbatim
169*
170* Authors:
171* ========
172*
173*> \author Univ. of Tennessee
174*> \author Univ. of California Berkeley
175*> \author Univ. of Colorado Denver
176*> \author NAG Ltd.
177*
178*> \ingroup complex_eig
179*
180* =====================================================================
181 SUBROUTINE cckcsd( NM, MVAL, PVAL, QVAL, NMATS, ISEED, THRESH,
182 $ MMAX, X, XF, U1, U2, V1T, V2T, THETA, IWORK,
183 $ WORK, RWORK, NIN, NOUT, INFO )
184*
185* -- LAPACK test routine --
186* -- LAPACK is a software package provided by Univ. of Tennessee, --
187* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
188*
189* .. Scalar Arguments ..
190 INTEGER INFO, NIN, NM, NMATS, MMAX, NOUT
191 REAL THRESH
192* ..
193* .. Array Arguments ..
194 INTEGER ISEED( 4 ), IWORK( * ), MVAL( * ), PVAL( * ),
195 $ QVAL( * )
196 REAL RWORK( * ), THETA( * )
197 COMPLEX U1( * ), U2( * ), V1T( * ), V2T( * ),
198 $ work( * ), x( * ), xf( * )
199* ..
200*
201* =====================================================================
202*
203* .. Parameters ..
204 INTEGER NTESTS
205 PARAMETER ( NTESTS = 15 )
206 INTEGER NTYPES
207 parameter( ntypes = 4 )
208 REAL GAPDIGIT, ORTH, REALONE, REALZERO, TEN
209 parameter( gapdigit = 10.0e0, orth = 1.0e-4,
210 $ realone = 1.0e0, realzero = 0.0e0,
211 $ ten = 10.0e0 )
212 COMPLEX ONE, ZERO
213 PARAMETER ( ONE = (1.0e0,0.0e0), zero = (0.0e0,0.0e0) )
214 REAL PIOVER2
215 parameter( piover2 = 1.57079632679489661923132169163975144210e0 )
216* ..
217* .. Local Scalars ..
218 LOGICAL FIRSTT
219 CHARACTER*3 PATH
220 INTEGER I, IINFO, IM, IMAT, J, LDU1, LDU2, LDV1T,
221 $ ldv2t, ldx, lwork, m, nfail, nrun, nt, p, q, r
222* ..
223* .. Local Arrays ..
224 LOGICAL DOTYPE( NTYPES )
225 REAL RESULT( NTESTS )
226* ..
227* .. External Subroutines ..
228 EXTERNAL alahdg, alareq, alasum, ccsdts, clacsg, claror,
229 $ claset, csrot
230* ..
231* .. Intrinsic Functions ..
232 INTRINSIC abs, min
233* ..
234* .. External Functions ..
235 REAL SLARAN, SLARND
236 EXTERNAL SLARAN, SLARND
237* ..
238* .. Executable Statements ..
239*
240* Initialize constants and the random number seed.
241*
242 path( 1: 3 ) = 'CSD'
243 info = 0
244 nrun = 0
245 nfail = 0
246 firstt = .true.
247 CALL alareq( path, nmats, dotype, ntypes, nin, nout )
248 ldx = mmax
249 ldu1 = mmax
250 ldu2 = mmax
251 ldv1t = mmax
252 ldv2t = mmax
253 lwork = mmax*mmax
254*
255* Do for each value of M in MVAL.
256*
257 DO 30 im = 1, nm
258 m = mval( im )
259 p = pval( im )
260 q = qval( im )
261*
262 DO 20 imat = 1, ntypes
263*
264* Do the tests only if DOTYPE( IMAT ) is true.
265*
266 IF( .NOT.dotype( imat ) )
267 $ GO TO 20
268*
269* Generate X
270*
271 IF( imat.EQ.1 ) THEN
272 CALL claror( 'L', 'I', m, m, x, ldx, iseed, work, iinfo )
273 IF( m .NE. 0 .AND. iinfo .NE. 0 ) THEN
274 WRITE( nout, fmt = 9999 ) m, iinfo
275 info = abs( iinfo )
276 GO TO 20
277 END IF
278 ELSE IF( imat.EQ.2 ) THEN
279 r = min( p, m-p, q, m-q )
280 DO i = 1, r
281 theta(i) = piover2 * slarnd( 1, iseed )
282 END DO
283 CALL clacsg( m, p, q, theta, iseed, x, ldx, work )
284 DO i = 1, m
285 DO j = 1, m
286 x(i+(j-1)*ldx) = x(i+(j-1)*ldx) +
287 $ orth*slarnd(2,iseed)
288 END DO
289 END DO
290 ELSE IF( imat.EQ.3 ) THEN
291 r = min( p, m-p, q, m-q )
292 DO i = 1, r+1
293 theta(i) = ten**(-slarnd(1,iseed)*gapdigit)
294 END DO
295 DO i = 2, r+1
296 theta(i) = theta(i-1) + theta(i)
297 END DO
298 DO i = 1, r
299 theta(i) = piover2 * theta(i) / theta(r+1)
300 END DO
301 CALL clacsg( m, p, q, theta, iseed, x, ldx, work )
302 ELSE
303 CALL claset( 'F', m, m, zero, one, x, ldx )
304 DO i = 1, m
305 j = int( slaran( iseed ) * m ) + 1
306 IF( j .NE. i ) THEN
307 CALL csrot( m, x(1+(i-1)*ldx), 1, x(1+(j-1)*ldx),
308 $ 1, realzero, realone )
309 END IF
310 END DO
311 END IF
312*
313 nt = 15
314*
315 CALL ccsdts( m, p, q, x, xf, ldx, u1, ldu1, u2, ldu2, v1t,
316 $ ldv1t, v2t, ldv2t, theta, iwork, work, lwork,
317 $ rwork, result )
318*
319* Print information about the tests that did not
320* pass the threshold.
321*
322 DO 10 i = 1, nt
323 IF( result( i ).GE.thresh ) THEN
324 IF( nfail.EQ.0 .AND. firstt ) THEN
325 firstt = .false.
326 CALL alahdg( nout, path )
327 END IF
328 WRITE( nout, fmt = 9998 )m, p, q, imat, i,
329 $ result( i )
330 nfail = nfail + 1
331 END IF
332 10 CONTINUE
333 nrun = nrun + nt
334 20 CONTINUE
335 30 CONTINUE
336*
337* Print a summary of the results.
338*
339 CALL alasum( path, nout, nfail, nrun, 0 )
340*
341 9999 FORMAT( ' CLAROR in CCKCSD: M = ', i5, ', INFO = ', i15 )
342 9998 FORMAT( ' M=', i4, ' P=', i4, ', Q=', i4, ', type ', i2,
343 $ ', test ', i2, ', ratio=', g13.6 )
344 RETURN
345*
346* End of CCKCSD
347*
348 END
349*
350*
351*
352 SUBROUTINE clacsg( M, P, Q, THETA, ISEED, X, LDX, WORK )
353 IMPLICIT NONE
354*
355 INTEGER LDX, M, P, Q
356 INTEGER ISEED( 4 )
357 REAL THETA( * )
358 COMPLEX WORK( * ), X( LDX, * )
359*
360 COMPLEX ONE, ZERO
361 PARAMETER ( ONE = (1.0e0,0.0e0), zero = (0.0e0,0.0e0) )
362*
363 INTEGER I, INFO, R
364*
365 r = min( p, m-p, q, m-q )
366*
367 CALL claset( 'Full', m, m, zero, zero, x, ldx )
368*
369 DO i = 1, min(p,q)-r
370 x(i,i) = one
371 END DO
372 DO i = 1, r
373 x(min(p,q)-r+i,min(p,q)-r+i) = cmplx( cos(theta(i)), 0.0e0 )
374 END DO
375 DO i = 1, min(p,m-q)-r
376 x(p-i+1,m-i+1) = -one
377 END DO
378 DO i = 1, r
379 x(p-(min(p,m-q)-r)+1-i,m-(min(p,m-q)-r)+1-i) =
380 $ cmplx( -sin(theta(r-i+1)), 0.0e0 )
381 END DO
382 DO i = 1, min(m-p,q)-r
383 x(m-i+1,q-i+1) = one
384 END DO
385 DO i = 1, r
386 x(m-(min(m-p,q)-r)+1-i,q-(min(m-p,q)-r)+1-i) =
387 $ cmplx( sin(theta(r-i+1)), 0.0e0 )
388 END DO
389 DO i = 1, min(m-p,m-q)-r
390 x(p+i,q+i) = one
391 END DO
392 DO i = 1, r
393 x(p+(min(m-p,m-q)-r)+i,q+(min(m-p,m-q)-r)+i) =
394 $ cmplx( cos(theta(i)), 0.0e0 )
395 END DO
396 CALL claror( 'Left', 'No init', p, m, x, ldx, iseed, work, info )
397 CALL claror( 'Left', 'No init', m-p, m, x(p+1,1), ldx,
398 $ iseed, work, info )
399 CALL claror( 'Right', 'No init', m, q, x, ldx, iseed,
400 $ work, info )
401 CALL claror( 'Right', 'No init', m, m-q,
402 $ x(1,q+1), ldx, iseed, work, info )
403*
404 END
405
subroutine clacsg(M, P, Q, THETA, ISEED, X, LDX, WORK)
Definition: cckcsd.f:353
subroutine alareq(PATH, NMATS, DOTYPE, NTYPES, NIN, NOUT)
ALAREQ
Definition: alareq.f:90
subroutine alahdg(IOUNIT, PATH)
ALAHDG
Definition: alahdg.f:62
subroutine alasum(TYPE, NOUT, NFAIL, NRUN, NERRS)
ALASUM
Definition: alasum.f:73
subroutine csrot(N, CX, INCX, CY, INCY, C, S)
CSROT
Definition: csrot.f:98
subroutine cckcsd(NM, MVAL, PVAL, QVAL, NMATS, ISEED, THRESH, MMAX, X, XF, U1, U2, V1T, V2T, THETA, IWORK, WORK, RWORK, NIN, NOUT, INFO)
CCKCSD
Definition: cckcsd.f:184
subroutine ccsdts(M, P, Q, X, XF, LDX, U1, LDU1, U2, LDU2, V1T, LDV1T, V2T, LDV2T, THETA, IWORK, WORK, LWORK, RWORK, RESULT)
CCSDTS
Definition: ccsdts.f:229
subroutine claror(SIDE, INIT, M, N, A, LDA, ISEED, X, INFO)
CLAROR
Definition: claror.f:158
subroutine claset(UPLO, M, N, ALPHA, BETA, A, LDA)
CLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition: claset.f:106