LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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ddrvpp.f
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1*> \brief \b DDRVPP
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 DDRVPP( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
12* A, AFAC, ASAV, B, BSAV, X, XACT, S, WORK,
13* RWORK, IWORK, NOUT )
14*
15* .. Scalar Arguments ..
16* LOGICAL TSTERR
17* INTEGER NMAX, NN, NOUT, NRHS
18* DOUBLE PRECISION THRESH
19* ..
20* .. Array Arguments ..
21* LOGICAL DOTYPE( * )
22* INTEGER IWORK( * ), NVAL( * )
23* DOUBLE PRECISION A( * ), AFAC( * ), ASAV( * ), B( * ),
24* \$ BSAV( * ), RWORK( * ), S( * ), WORK( * ),
25* \$ X( * ), XACT( * )
26* ..
27*
28*
29*> \par Purpose:
30* =============
31*>
32*> \verbatim
33*>
34*> DDRVPP tests the driver routines DPPSV and -SVX.
35*> \endverbatim
36*
37* Arguments:
38* ==========
39*
40*> \param[in] DOTYPE
41*> \verbatim
42*> DOTYPE is LOGICAL array, dimension (NTYPES)
43*> The matrix types to be used for testing. Matrices of type j
44*> (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
45*> .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
46*> \endverbatim
47*>
48*> \param[in] NN
49*> \verbatim
50*> NN is INTEGER
51*> The number of values of N contained in the vector NVAL.
52*> \endverbatim
53*>
54*> \param[in] NVAL
55*> \verbatim
56*> NVAL is INTEGER array, dimension (NN)
57*> The values of the matrix dimension N.
58*> \endverbatim
59*>
60*> \param[in] NRHS
61*> \verbatim
62*> NRHS is INTEGER
63*> The number of right hand side vectors to be generated for
64*> each linear system.
65*> \endverbatim
66*>
67*> \param[in] THRESH
68*> \verbatim
69*> THRESH is DOUBLE PRECISION
70*> The threshold value for the test ratios. A result is
71*> included in the output file if RESULT >= THRESH. To have
72*> every test ratio printed, use THRESH = 0.
73*> \endverbatim
74*>
75*> \param[in] TSTERR
76*> \verbatim
77*> TSTERR is LOGICAL
78*> Flag that indicates whether error exits are to be tested.
79*> \endverbatim
80*>
81*> \param[in] NMAX
82*> \verbatim
83*> NMAX is INTEGER
84*> The maximum value permitted for N, used in dimensioning the
85*> work arrays.
86*> \endverbatim
87*>
88*> \param[out] A
89*> \verbatim
90*> A is DOUBLE PRECISION array, dimension
91*> (NMAX*(NMAX+1)/2)
92*> \endverbatim
93*>
94*> \param[out] AFAC
95*> \verbatim
96*> AFAC is DOUBLE PRECISION array, dimension
97*> (NMAX*(NMAX+1)/2)
98*> \endverbatim
99*>
100*> \param[out] ASAV
101*> \verbatim
102*> ASAV is DOUBLE PRECISION array, dimension
103*> (NMAX*(NMAX+1)/2)
104*> \endverbatim
105*>
106*> \param[out] B
107*> \verbatim
108*> B is DOUBLE PRECISION array, dimension (NMAX*NRHS)
109*> \endverbatim
110*>
111*> \param[out] BSAV
112*> \verbatim
113*> BSAV is DOUBLE PRECISION array, dimension (NMAX*NRHS)
114*> \endverbatim
115*>
116*> \param[out] X
117*> \verbatim
118*> X is DOUBLE PRECISION array, dimension (NMAX*NRHS)
119*> \endverbatim
120*>
121*> \param[out] XACT
122*> \verbatim
123*> XACT is DOUBLE PRECISION array, dimension (NMAX*NRHS)
124*> \endverbatim
125*>
126*> \param[out] S
127*> \verbatim
128*> S is DOUBLE PRECISION array, dimension (NMAX)
129*> \endverbatim
130*>
131*> \param[out] WORK
132*> \verbatim
133*> WORK is DOUBLE PRECISION array, dimension
134*> (NMAX*max(3,NRHS))
135*> \endverbatim
136*>
137*> \param[out] RWORK
138*> \verbatim
139*> RWORK is DOUBLE PRECISION array, dimension (NMAX+2*NRHS)
140*> \endverbatim
141*>
142*> \param[out] IWORK
143*> \verbatim
144*> IWORK is INTEGER array, dimension (NMAX)
145*> \endverbatim
146*>
147*> \param[in] NOUT
148*> \verbatim
149*> NOUT is INTEGER
150*> The unit number for output.
151*> \endverbatim
152*
153* Authors:
154* ========
155*
156*> \author Univ. of Tennessee
157*> \author Univ. of California Berkeley
158*> \author Univ. of Colorado Denver
159*> \author NAG Ltd.
160*
161*> \ingroup double_lin
162*
163* =====================================================================
164 SUBROUTINE ddrvpp( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
165 \$ A, AFAC, ASAV, B, BSAV, X, XACT, S, WORK,
166 \$ RWORK, IWORK, NOUT )
167*
168* -- LAPACK test routine --
169* -- LAPACK is a software package provided by Univ. of Tennessee, --
170* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
171*
172* .. Scalar Arguments ..
173 LOGICAL TSTERR
174 INTEGER NMAX, NN, NOUT, NRHS
175 DOUBLE PRECISION THRESH
176* ..
177* .. Array Arguments ..
178 LOGICAL DOTYPE( * )
179 INTEGER IWORK( * ), NVAL( * )
180 DOUBLE PRECISION A( * ), AFAC( * ), ASAV( * ), B( * ),
181 \$ bsav( * ), rwork( * ), s( * ), work( * ),
182 \$ x( * ), xact( * )
183* ..
184*
185* =====================================================================
186*
187* .. Parameters ..
188 DOUBLE PRECISION ONE, ZERO
189 PARAMETER ( ONE = 1.0d+0, zero = 0.0d+0 )
190 INTEGER NTYPES
191 parameter( ntypes = 9 )
192 INTEGER NTESTS
193 parameter( ntests = 6 )
194* ..
195* .. Local Scalars ..
196 LOGICAL EQUIL, NOFACT, PREFAC, ZEROT
197 CHARACTER DIST, EQUED, FACT, PACKIT, TYPE, UPLO, XTYPE
198 CHARACTER*3 PATH
199 INTEGER I, IEQUED, IFACT, IMAT, IN, INFO, IOFF, IUPLO,
200 \$ izero, k, k1, kl, ku, lda, mode, n, nerrs,
201 \$ nfact, nfail, nimat, npp, nrun, nt
202 DOUBLE PRECISION AINVNM, AMAX, ANORM, CNDNUM, RCOND, RCONDC,
203 \$ ROLDC, SCOND
204* ..
205* .. Local Arrays ..
206 CHARACTER EQUEDS( 2 ), FACTS( 3 ), PACKS( 2 ), UPLOS( 2 )
207 INTEGER ISEED( 4 ), ISEEDY( 4 )
208 DOUBLE PRECISION RESULT( NTESTS )
209* ..
210* .. External Functions ..
211 LOGICAL LSAME
212 DOUBLE PRECISION DGET06, DLANSP
213 EXTERNAL lsame, dget06, dlansp
214* ..
215* .. External Subroutines ..
216 EXTERNAL aladhd, alaerh, alasvm, dcopy, derrvx, dget04,
219 \$ dpptrf, dpptri
220* ..
221* .. Scalars in Common ..
222 LOGICAL LERR, OK
223 CHARACTER*32 SRNAMT
224 INTEGER INFOT, NUNIT
225* ..
226* .. Common blocks ..
227 COMMON / infoc / infot, nunit, ok, lerr
228 COMMON / srnamc / srnamt
229* ..
230* .. Intrinsic Functions ..
231 INTRINSIC max
232* ..
233* .. Data statements ..
234 DATA iseedy / 1988, 1989, 1990, 1991 /
235 DATA uplos / 'U', 'L' / , facts / 'F', 'N', 'E' / ,
236 \$ packs / 'C', 'R' / , equeds / 'N', 'Y' /
237* ..
238* .. Executable Statements ..
239*
240* Initialize constants and the random number seed.
241*
242 path( 1: 1 ) = 'Double precision'
243 path( 2: 3 ) = 'PP'
244 nrun = 0
245 nfail = 0
246 nerrs = 0
247 DO 10 i = 1, 4
248 iseed( i ) = iseedy( i )
249 10 CONTINUE
250*
251* Test the error exits
252*
253 IF( tsterr )
254 \$ CALL derrvx( path, nout )
255 infot = 0
256*
257* Do for each value of N in NVAL
258*
259 DO 140 in = 1, nn
260 n = nval( in )
261 lda = max( n, 1 )
262 npp = n*( n+1 ) / 2
263 xtype = 'N'
264 nimat = ntypes
265 IF( n.LE.0 )
266 \$ nimat = 1
267*
268 DO 130 imat = 1, nimat
269*
270* Do the tests only if DOTYPE( IMAT ) is true.
271*
272 IF( .NOT.dotype( imat ) )
273 \$ GO TO 130
274*
275* Skip types 3, 4, or 5 if the matrix size is too small.
276*
277 zerot = imat.GE.3 .AND. imat.LE.5
278 IF( zerot .AND. n.LT.imat-2 )
279 \$ GO TO 130
280*
281* Do first for UPLO = 'U', then for UPLO = 'L'
282*
283 DO 120 iuplo = 1, 2
284 uplo = uplos( iuplo )
285 packit = packs( iuplo )
286*
287* Set up parameters with DLATB4 and generate a test matrix
288* with DLATMS.
289*
290 CALL dlatb4( path, imat, n, n, TYPE, kl, ku, anorm, mode,
291 \$ cndnum, dist )
292 rcondc = one / cndnum
293*
294 srnamt = 'DLATMS'
295 CALL dlatms( n, n, dist, iseed, TYPE, rwork, mode,
296 \$ cndnum, anorm, kl, ku, packit, a, lda, work,
297 \$ info )
298*
299* Check error code from DLATMS.
300*
301 IF( info.NE.0 ) THEN
302 CALL alaerh( path, 'DLATMS', info, 0, uplo, n, n, -1,
303 \$ -1, -1, imat, nfail, nerrs, nout )
304 GO TO 120
305 END IF
306*
307* For types 3-5, zero one row and column of the matrix to
308* test that INFO is returned correctly.
309*
310 IF( zerot ) THEN
311 IF( imat.EQ.3 ) THEN
312 izero = 1
313 ELSE IF( imat.EQ.4 ) THEN
314 izero = n
315 ELSE
316 izero = n / 2 + 1
317 END IF
318*
319* Set row and column IZERO of A to 0.
320*
321 IF( iuplo.EQ.1 ) THEN
322 ioff = ( izero-1 )*izero / 2
323 DO 20 i = 1, izero - 1
324 a( ioff+i ) = zero
325 20 CONTINUE
326 ioff = ioff + izero
327 DO 30 i = izero, n
328 a( ioff ) = zero
329 ioff = ioff + i
330 30 CONTINUE
331 ELSE
332 ioff = izero
333 DO 40 i = 1, izero - 1
334 a( ioff ) = zero
335 ioff = ioff + n - i
336 40 CONTINUE
337 ioff = ioff - izero
338 DO 50 i = izero, n
339 a( ioff+i ) = zero
340 50 CONTINUE
341 END IF
342 ELSE
343 izero = 0
344 END IF
345*
346* Save a copy of the matrix A in ASAV.
347*
348 CALL dcopy( npp, a, 1, asav, 1 )
349*
350 DO 110 iequed = 1, 2
351 equed = equeds( iequed )
352 IF( iequed.EQ.1 ) THEN
353 nfact = 3
354 ELSE
355 nfact = 1
356 END IF
357*
358 DO 100 ifact = 1, nfact
359 fact = facts( ifact )
360 prefac = lsame( fact, 'F' )
361 nofact = lsame( fact, 'N' )
362 equil = lsame( fact, 'E' )
363*
364 IF( zerot ) THEN
365 IF( prefac )
366 \$ GO TO 100
367 rcondc = zero
368*
369 ELSE IF( .NOT.lsame( fact, 'N' ) ) THEN
370*
371* Compute the condition number for comparison with
372* the value returned by DPPSVX (FACT = 'N' reuses
373* the condition number from the previous iteration
374* with FACT = 'F').
375*
376 CALL dcopy( npp, asav, 1, afac, 1 )
377 IF( equil .OR. iequed.GT.1 ) THEN
378*
379* Compute row and column scale factors to
380* equilibrate the matrix A.
381*
382 CALL dppequ( uplo, n, afac, s, scond, amax,
383 \$ info )
384 IF( info.EQ.0 .AND. n.GT.0 ) THEN
385 IF( iequed.GT.1 )
386 \$ scond = zero
387*
388* Equilibrate the matrix.
389*
390 CALL dlaqsp( uplo, n, afac, s, scond,
391 \$ amax, equed )
392 END IF
393 END IF
394*
395* Save the condition number of the
396* non-equilibrated system for use in DGET04.
397*
398 IF( equil )
399 \$ roldc = rcondc
400*
401* Compute the 1-norm of A.
402*
403 anorm = dlansp( '1', uplo, n, afac, rwork )
404*
405* Factor the matrix A.
406*
407 CALL dpptrf( uplo, n, afac, info )
408*
409* Form the inverse of A.
410*
411 CALL dcopy( npp, afac, 1, a, 1 )
412 CALL dpptri( uplo, n, a, info )
413*
414* Compute the 1-norm condition number of A.
415*
416 ainvnm = dlansp( '1', uplo, n, a, rwork )
417 IF( anorm.LE.zero .OR. ainvnm.LE.zero ) THEN
418 rcondc = one
419 ELSE
420 rcondc = ( one / anorm ) / ainvnm
421 END IF
422 END IF
423*
424* Restore the matrix A.
425*
426 CALL dcopy( npp, asav, 1, a, 1 )
427*
428* Form an exact solution and set the right hand side.
429*
430 srnamt = 'DLARHS'
431 CALL dlarhs( path, xtype, uplo, ' ', n, n, kl, ku,
432 \$ nrhs, a, lda, xact, lda, b, lda,
433 \$ iseed, info )
434 xtype = 'C'
435 CALL dlacpy( 'Full', n, nrhs, b, lda, bsav, lda )
436*
437 IF( nofact ) THEN
438*
439* --- Test DPPSV ---
440*
441* Compute the L*L' or U'*U factorization of the
442* matrix and solve the system.
443*
444 CALL dcopy( npp, a, 1, afac, 1 )
445 CALL dlacpy( 'Full', n, nrhs, b, lda, x, lda )
446*
447 srnamt = 'DPPSV '
448 CALL dppsv( uplo, n, nrhs, afac, x, lda, info )
449*
450* Check error code from DPPSV .
451*
452 IF( info.NE.izero ) THEN
453 CALL alaerh( path, 'DPPSV ', info, izero,
454 \$ uplo, n, n, -1, -1, nrhs, imat,
455 \$ nfail, nerrs, nout )
456 GO TO 70
457 ELSE IF( info.NE.0 ) THEN
458 GO TO 70
459 END IF
460*
461* Reconstruct matrix from factors and compute
462* residual.
463*
464 CALL dppt01( uplo, n, a, afac, rwork,
465 \$ result( 1 ) )
466*
467* Compute residual of the computed solution.
468*
469 CALL dlacpy( 'Full', n, nrhs, b, lda, work,
470 \$ lda )
471 CALL dppt02( uplo, n, nrhs, a, x, lda, work,
472 \$ lda, rwork, result( 2 ) )
473*
474* Check solution from generated exact solution.
475*
476 CALL dget04( n, nrhs, x, lda, xact, lda, rcondc,
477 \$ result( 3 ) )
478 nt = 3
479*
480* Print information about the tests that did not
481* pass the threshold.
482*
483 DO 60 k = 1, nt
484 IF( result( k ).GE.thresh ) THEN
485 IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
486 \$ CALL aladhd( nout, path )
487 WRITE( nout, fmt = 9999 )'DPPSV ', uplo,
488 \$ n, imat, k, result( k )
489 nfail = nfail + 1
490 END IF
491 60 CONTINUE
492 nrun = nrun + nt
493 70 CONTINUE
494 END IF
495*
496* --- Test DPPSVX ---
497*
498 IF( .NOT.prefac .AND. npp.GT.0 )
499 \$ CALL dlaset( 'Full', npp, 1, zero, zero, afac,
500 \$ npp )
501 CALL dlaset( 'Full', n, nrhs, zero, zero, x, lda )
502 IF( iequed.GT.1 .AND. n.GT.0 ) THEN
503*
504* Equilibrate the matrix if FACT='F' and
505* EQUED='Y'.
506*
507 CALL dlaqsp( uplo, n, a, s, scond, amax, equed )
508 END IF
509*
510* Solve the system and compute the condition number
511* and error bounds using DPPSVX.
512*
513 srnamt = 'DPPSVX'
514 CALL dppsvx( fact, uplo, n, nrhs, a, afac, equed,
515 \$ s, b, lda, x, lda, rcond, rwork,
516 \$ rwork( nrhs+1 ), work, iwork, info )
517*
518* Check the error code from DPPSVX.
519*
520 IF( info.NE.izero ) THEN
521 CALL alaerh( path, 'DPPSVX', info, izero,
522 \$ fact // uplo, n, n, -1, -1, nrhs,
523 \$ imat, nfail, nerrs, nout )
524 GO TO 90
525 END IF
526*
527 IF( info.EQ.0 ) THEN
528 IF( .NOT.prefac ) THEN
529*
530* Reconstruct matrix from factors and compute
531* residual.
532*
533 CALL dppt01( uplo, n, a, afac,
534 \$ rwork( 2*nrhs+1 ), result( 1 ) )
535 k1 = 1
536 ELSE
537 k1 = 2
538 END IF
539*
540* Compute residual of the computed solution.
541*
542 CALL dlacpy( 'Full', n, nrhs, bsav, lda, work,
543 \$ lda )
544 CALL dppt02( uplo, n, nrhs, asav, x, lda, work,
545 \$ lda, rwork( 2*nrhs+1 ),
546 \$ result( 2 ) )
547*
548* Check solution from generated exact solution.
549*
550 IF( nofact .OR. ( prefac .AND. lsame( equed,
551 \$ 'N' ) ) ) THEN
552 CALL dget04( n, nrhs, x, lda, xact, lda,
553 \$ rcondc, result( 3 ) )
554 ELSE
555 CALL dget04( n, nrhs, x, lda, xact, lda,
556 \$ roldc, result( 3 ) )
557 END IF
558*
559* Check the error bounds from iterative
560* refinement.
561*
562 CALL dppt05( uplo, n, nrhs, asav, b, lda, x,
563 \$ lda, xact, lda, rwork,
564 \$ rwork( nrhs+1 ), result( 4 ) )
565 ELSE
566 k1 = 6
567 END IF
568*
569* Compare RCOND from DPPSVX with the computed value
570* in RCONDC.
571*
572 result( 6 ) = dget06( rcond, rcondc )
573*
574* Print information about the tests that did not pass
575* the threshold.
576*
577 DO 80 k = k1, 6
578 IF( result( k ).GE.thresh ) THEN
579 IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
580 \$ CALL aladhd( nout, path )
581 IF( prefac ) THEN
582 WRITE( nout, fmt = 9997 )'DPPSVX', fact,
583 \$ uplo, n, equed, imat, k, result( k )
584 ELSE
585 WRITE( nout, fmt = 9998 )'DPPSVX', fact,
586 \$ uplo, n, imat, k, result( k )
587 END IF
588 nfail = nfail + 1
589 END IF
590 80 CONTINUE
591 nrun = nrun + 7 - k1
592 90 CONTINUE
593 100 CONTINUE
594 110 CONTINUE
595 120 CONTINUE
596 130 CONTINUE
597 140 CONTINUE
598*
599* Print a summary of the results.
600*
601 CALL alasvm( path, nout, nfail, nrun, nerrs )
602*
603 9999 FORMAT( 1x, a, ', UPLO=''', a1, ''', N =', i5, ', type ', i1,
604 \$ ', test(', i1, ')=', g12.5 )
605 9998 FORMAT( 1x, a, ', FACT=''', a1, ''', UPLO=''', a1, ''', N=', i5,
606 \$ ', type ', i1, ', test(', i1, ')=', g12.5 )
607 9997 FORMAT( 1x, a, ', FACT=''', a1, ''', UPLO=''', a1, ''', N=', i5,
608 \$ ', EQUED=''', a1, ''', type ', i1, ', test(', i1, ')=',
609 \$ g12.5 )
610 RETURN
611*
612* End of DDRVPP
613*
614 END
subroutine alasvm(type, nout, nfail, nrun, nerrs)
ALASVM
Definition alasvm.f:73
subroutine dlarhs(path, xtype, uplo, trans, m, n, kl, ku, nrhs, a, lda, x, ldx, b, ldb, iseed, info)
DLARHS
Definition dlarhs.f:205
subroutine alaerh(path, subnam, info, infoe, opts, m, n, kl, ku, n5, imat, nfail, nerrs, nout)
ALAERH
Definition alaerh.f:147
subroutine ddrvpp(dotype, nn, nval, nrhs, thresh, tsterr, nmax, a, afac, asav, b, bsav, x, xact, s, work, rwork, iwork, nout)
DDRVPP
Definition ddrvpp.f:167
subroutine derrvx(path, nunit)
DERRVX
Definition derrvx.f:55
subroutine dget04(n, nrhs, x, ldx, xact, ldxact, rcond, resid)
DGET04
Definition dget04.f:102
subroutine dlatb4(path, imat, m, n, type, kl, ku, anorm, mode, cndnum, dist)
DLATB4
Definition dlatb4.f:120
subroutine dlatms(m, n, dist, iseed, sym, d, mode, cond, dmax, kl, ku, pack, a, lda, work, info)
DLATMS
Definition dlatms.f:321
subroutine dppt01(uplo, n, a, afac, rwork, resid)
DPPT01
Definition dppt01.f:93
subroutine dppt02(uplo, n, nrhs, a, x, ldx, b, ldb, rwork, resid)
DPPT02
Definition dppt02.f:122
subroutine dppt05(uplo, n, nrhs, ap, b, ldb, x, ldx, xact, ldxact, ferr, berr, reslts)
DPPT05
Definition dppt05.f:156
subroutine dcopy(n, dx, incx, dy, incy)
DCOPY
Definition dcopy.f:82
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
subroutine dlaqsp(uplo, n, ap, s, scond, amax, equed)
DLAQSP scales a symmetric/Hermitian matrix in packed storage, using scaling factors computed by sppeq...
Definition dlaqsp.f:125
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 dppequ(uplo, n, ap, s, scond, amax, info)
DPPEQU
Definition dppequ.f:116
subroutine dppsv(uplo, n, nrhs, ap, b, ldb, info)
DPPSV computes the solution to system of linear equations A * X = B for OTHER matrices
Definition dppsv.f:144
subroutine dppsvx(fact, uplo, n, nrhs, ap, afp, equed, s, b, ldb, x, ldx, rcond, ferr, berr, work, iwork, info)
DPPSVX computes the solution to system of linear equations A * X = B for OTHER matrices
Definition dppsvx.f:311
subroutine dpptrf(uplo, n, ap, info)
DPPTRF
Definition dpptrf.f:119
subroutine dpptri(uplo, n, ap, info)
DPPTRI
Definition dpptri.f:93