LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ dckcsd()

 subroutine dckcsd ( integer NM, integer, dimension( * ) MVAL, integer, dimension( * ) PVAL, integer, dimension( * ) QVAL, integer NMATS, integer, dimension( 4 ) ISEED, double precision THRESH, integer MMAX, double precision, dimension( * ) X, double precision, dimension( * ) XF, double precision, dimension( * ) U1, double precision, dimension( * ) U2, double precision, dimension( * ) V1T, double precision, dimension( * ) V2T, double precision, dimension( * ) THETA, integer, dimension( * ) IWORK, double precision, dimension( * ) WORK, double precision, dimension( * ) RWORK, integer NIN, integer NOUT, integer INFO )

DCKCSD

Purpose:
``` DCKCSD tests DORCSD:
the CSD for an M-by-M orthogonal matrix X partitioned as
[ X11 X12; X21 X22 ]. X11 is P-by-Q.```
Parameters
 [in] NM ``` NM is INTEGER The number of values of M contained in the vector MVAL.``` [in] MVAL ``` MVAL is INTEGER array, dimension (NM) The values of the matrix row dimension M.``` [in] PVAL ``` PVAL is INTEGER array, dimension (NM) The values of the matrix row dimension P.``` [in] QVAL ``` QVAL is INTEGER array, dimension (NM) The values of the matrix column dimension Q.``` [in] NMATS ``` NMATS is INTEGER The number of matrix types to be tested for each combination of matrix dimensions. If NMATS >= NTYPES (the maximum number of matrix types), then all the different types are generated for testing. If NMATS < NTYPES, another input line is read to get the numbers of the matrix types to be used.``` [in,out] ISEED ``` ISEED is INTEGER array, dimension (4) On entry, the seed of the random number generator. The array elements should be between 0 and 4095, otherwise they will be reduced mod 4096, and ISEED(4) must be odd. On exit, the next seed in the random number sequence after all the test matrices have been generated.``` [in] THRESH ``` THRESH is DOUBLE PRECISION The threshold value for the test ratios. A result is included in the output file if RESULT >= THRESH. To have every test ratio printed, use THRESH = 0.``` [in] MMAX ``` MMAX is INTEGER The maximum value permitted for M, used in dimensioning the work arrays.``` [out] X ` X is DOUBLE PRECISION array, dimension (MMAX*MMAX)` [out] XF ` XF is DOUBLE PRECISION array, dimension (MMAX*MMAX)` [out] U1 ` U1 is DOUBLE PRECISION array, dimension (MMAX*MMAX)` [out] U2 ` U2 is DOUBLE PRECISION array, dimension (MMAX*MMAX)` [out] V1T ` V1T is DOUBLE PRECISION array, dimension (MMAX*MMAX)` [out] V2T ` V2T is DOUBLE PRECISION array, dimension (MMAX*MMAX)` [out] THETA ` THETA is DOUBLE PRECISION array, dimension (MMAX)` [out] IWORK ` IWORK is INTEGER array, dimension (MMAX)` [out] WORK ` WORK is DOUBLE PRECISION array` [out] RWORK ` RWORK is DOUBLE PRECISION array` [in] NIN ``` NIN is INTEGER The unit number for input.``` [in] NOUT ``` NOUT is INTEGER The unit number for output.``` [out] INFO ``` INFO is INTEGER = 0 : successful exit > 0 : If DLAROR returns an error code, the absolute value of it is returned.```

Definition at line 181 of file dckcsd.f.

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 DOUBLE PRECISION THRESH
192* ..
193* .. Array Arguments ..
194 INTEGER ISEED( 4 ), IWORK( * ), MVAL( * ), PVAL( * ),
195 \$ QVAL( * )
196 DOUBLE PRECISION RWORK( * ), THETA( * )
197 DOUBLE PRECISION 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 DOUBLE PRECISION GAPDIGIT, ONE, ORTH, TEN, ZERO
209 parameter( gapdigit = 18.0d0, one = 1.0d0,
210 \$ orth = 1.0d-12,
211 \$ ten = 10.0d0, zero = 0.0d0 )
212 DOUBLE PRECISION PIOVER2
213 parameter( piover2 = 1.57079632679489661923132169163975144210d0 )
214* ..
215* .. Local Scalars ..
216 LOGICAL FIRSTT
217 CHARACTER*3 PATH
218 INTEGER I, IINFO, IM, IMAT, J, LDU1, LDU2, LDV1T,
219 \$ LDV2T, LDX, LWORK, M, NFAIL, NRUN, NT, P, Q, R
220* ..
221* .. Local Arrays ..
222 LOGICAL DOTYPE( NTYPES )
223 DOUBLE PRECISION RESULT( NTESTS )
224* ..
225* .. External Subroutines ..
226 EXTERNAL alahdg, alareq, alasum, dcsdts, dlacsg, dlaror,
227 \$ dlaset, drot
228* ..
229* .. Intrinsic Functions ..
230 INTRINSIC abs, min
231* ..
232* .. External Functions ..
233 DOUBLE PRECISION DLARAN, DLARND
234 EXTERNAL dlaran, dlarnd
235* ..
236* .. Executable Statements ..
237*
238* Initialize constants and the random number seed.
239*
240 path( 1: 3 ) = 'CSD'
241 info = 0
242 nrun = 0
243 nfail = 0
244 firstt = .true.
245 CALL alareq( path, nmats, dotype, ntypes, nin, nout )
246 ldx = mmax
247 ldu1 = mmax
248 ldu2 = mmax
249 ldv1t = mmax
250 ldv2t = mmax
251 lwork = mmax*mmax
252*
253* Do for each value of M in MVAL.
254*
255 DO 30 im = 1, nm
256 m = mval( im )
257 p = pval( im )
258 q = qval( im )
259*
260 DO 20 imat = 1, ntypes
261*
262* Do the tests only if DOTYPE( IMAT ) is true.
263*
264 IF( .NOT.dotype( imat ) )
265 \$ GO TO 20
266*
267* Generate X
268*
269 IF( imat.EQ.1 ) THEN
270 CALL dlaror( 'L', 'I', m, m, x, ldx, iseed, work, iinfo )
271 IF( m .NE. 0 .AND. iinfo .NE. 0 ) THEN
272 WRITE( nout, fmt = 9999 ) m, iinfo
273 info = abs( iinfo )
274 GO TO 20
275 END IF
276 ELSE IF( imat.EQ.2 ) THEN
277 r = min( p, m-p, q, m-q )
278 DO i = 1, r
279 theta(i) = piover2 * dlarnd( 1, iseed )
280 END DO
281 CALL dlacsg( m, p, q, theta, iseed, x, ldx, work )
282 DO i = 1, m
283 DO j = 1, m
284 x(i+(j-1)*ldx) = x(i+(j-1)*ldx) +
285 \$ orth*dlarnd(2,iseed)
286 END DO
287 END DO
288 ELSE IF( imat.EQ.3 ) THEN
289 r = min( p, m-p, q, m-q )
290 DO i = 1, r+1
291 theta(i) = ten**(-dlarnd(1,iseed)*gapdigit)
292 END DO
293 DO i = 2, r+1
294 theta(i) = theta(i-1) + theta(i)
295 END DO
296 DO i = 1, r
297 theta(i) = piover2 * theta(i) / theta(r+1)
298 END DO
299 CALL dlacsg( m, p, q, theta, iseed, x, ldx, work )
300 ELSE
301 CALL dlaset( 'F', m, m, zero, one, x, ldx )
302 DO i = 1, m
303 j = int( dlaran( iseed ) * m ) + 1
304 IF( j .NE. i ) THEN
305 CALL drot( m, x(1+(i-1)*ldx), 1, x(1+(j-1)*ldx), 1,
306 \$ zero, one )
307 END IF
308 END DO
309 END IF
310*
311 nt = 15
312*
313 CALL dcsdts( m, p, q, x, xf, ldx, u1, ldu1, u2, ldu2, v1t,
314 \$ ldv1t, v2t, ldv2t, theta, iwork, work, lwork,
315 \$ rwork, result )
316*
317* Print information about the tests that did not
318* pass the threshold.
319*
320 DO 10 i = 1, nt
321 IF( result( i ).GE.thresh ) THEN
322 IF( nfail.EQ.0 .AND. firstt ) THEN
323 firstt = .false.
324 CALL alahdg( nout, path )
325 END IF
326 WRITE( nout, fmt = 9998 )m, p, q, imat, i,
327 \$ result( i )
328 nfail = nfail + 1
329 END IF
330 10 CONTINUE
331 nrun = nrun + nt
332 20 CONTINUE
333 30 CONTINUE
334*
335* Print a summary of the results.
336*
337 CALL alasum( path, nout, nfail, nrun, 0 )
338*
339 9999 FORMAT( ' DLAROR in DCKCSD: M = ', i5, ', INFO = ', i15 )
340 9998 FORMAT( ' M=', i4, ' P=', i4, ', Q=', i4, ', type ', i2,
341 \$ ', test ', i2, ', ratio=', g13.6 )
342 RETURN
343*
344* End of DCKCSD
345*
subroutine dlacsg(M, P, Q, THETA, ISEED, X, LDX, WORK)
Definition: dckcsd.f:351
double precision function dlaran(ISEED)
DLARAN
Definition: dlaran.f:67
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
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 drot(N, DX, INCX, DY, INCY, C, S)
DROT
Definition: drot.f:92
subroutine dcsdts(M, P, Q, X, XF, LDX, U1, LDU1, U2, LDU2, V1T, LDV1T, V2T, LDV2T, THETA, IWORK, WORK, LWORK, RWORK, RESULT)
DCSDTS
Definition: dcsdts.f:229
double precision function dlarnd(IDIST, ISEED)
DLARND
Definition: dlarnd.f:73
subroutine dlaror(SIDE, INIT, M, N, A, LDA, ISEED, X, INFO)
DLAROR
Definition: dlaror.f:146
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