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

 subroutine zckcsd ( integer NM, integer, dimension( * ) MVAL, integer, dimension( * ) PVAL, integer, dimension( * ) QVAL, integer NMATS, integer, dimension( 4 ) ISEED, double precision THRESH, integer MMAX, complex*16, dimension( * ) X, complex*16, dimension( * ) XF, complex*16, dimension( * ) U1, complex*16, dimension( * ) U2, complex*16, dimension( * ) V1T, complex*16, dimension( * ) V2T, double precision, dimension( * ) THETA, integer, dimension( * ) IWORK, complex*16, dimension( * ) WORK, double precision, dimension( * ) RWORK, integer NIN, integer NOUT, integer INFO )

ZCKCSD

Purpose:
``` ZCKCSD tests ZUNCSD:
the CSD for an M-by-M unitary 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 COMPLEX*16 array, dimension (MMAX*MMAX)` [out] XF ` XF is COMPLEX*16 array, dimension (MMAX*MMAX)` [out] U1 ` U1 is COMPLEX*16 array, dimension (MMAX*MMAX)` [out] U2 ` U2 is COMPLEX*16 array, dimension (MMAX*MMAX)` [out] V1T ` V1T is COMPLEX*16 array, dimension (MMAX*MMAX)` [out] V2T ` V2T is COMPLEX*16 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 COMPLEX*16 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 ZLAROR returns an error code, the absolute value of it is returned.```

Definition at line 181 of file zckcsd.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 COMPLEX*16 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, ORTH, REALONE, REALZERO, TEN
209 parameter( gapdigit = 18.0d0, orth = 1.0d-12,
210 \$ realone = 1.0d0, realzero = 0.0d0,
211 \$ ten = 10.0d0 )
212 COMPLEX*16 ONE, ZERO
213 parameter( one = (1.0d0,0.0d0), zero = (0.0d0,0.0d0) )
214 DOUBLE PRECISION PIOVER2
215 parameter( piover2 = 1.57079632679489661923132169163975144210d0 )
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 DOUBLE PRECISION RESULT( NTESTS )
226* ..
227* .. External Subroutines ..
228 EXTERNAL alahdg, alareq, alasum, zcsdts, zlacsg, zlaror,
229 \$ zlaset, zdrot
230* ..
231* .. Intrinsic Functions ..
232 INTRINSIC abs, min
233* ..
234* .. External Functions ..
235 DOUBLE PRECISION DLARAN, DLARND
236 EXTERNAL dlaran, dlarnd
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 zlaror( '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 * dlarnd( 1, iseed )
282 END DO
283 CALL zlacsg( 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*dlarnd(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**(-dlarnd(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 zlacsg( m, p, q, theta, iseed, x, ldx, work )
302 ELSE
303 CALL zlaset( 'F', m, m, zero, one, x, ldx )
304 DO i = 1, m
305 j = int( dlaran( iseed ) * m ) + 1
306 IF( j .NE. i ) THEN
307 CALL zdrot( 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 zcsdts( 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( ' ZLAROR in ZCKCSD: 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 ZCKCSD
347*
double precision function dlaran(ISEED)
DLARAN
Definition: dlaran.f:67
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 zdrot(N, ZX, INCX, ZY, INCY, C, S)
ZDROT
Definition: zdrot.f:98
subroutine zcsdts(M, P, Q, X, XF, LDX, U1, LDU1, U2, LDU2, V1T, LDV1T, V2T, LDV2T, THETA, IWORK, WORK, LWORK, RWORK, RESULT)
ZCSDTS
Definition: zcsdts.f:229
subroutine zlaror(SIDE, INIT, M, N, A, LDA, ISEED, X, INFO)
ZLAROR
Definition: zlaror.f:158
subroutine zlaset(UPLO, M, N, ALPHA, BETA, A, LDA)
ZLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition: zlaset.f:106
double precision function dlarnd(IDIST, ISEED)
DLARND
Definition: dlarnd.f:73
subroutine zlacsg(M, P, Q, THETA, ISEED, X, LDX, WORK)
Definition: zckcsd.f:353
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