LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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zdrvvx.f
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1*> \brief \b ZDRVVX
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 ZDRVVX( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
12* NIUNIT, NOUNIT, A, LDA, H, W, W1, VL, LDVL, VR,
13* LDVR, LRE, LDLRE, RCONDV, RCNDV1, RCDVIN,
14* RCONDE, RCNDE1, RCDEIN, SCALE, SCALE1, RESULT,
15* WORK, NWORK, RWORK, INFO )
16*
17* .. Scalar Arguments ..
18* INTEGER INFO, LDA, LDLRE, LDVL, LDVR, NIUNIT, NOUNIT,
19* $ NSIZES, NTYPES, NWORK
20* DOUBLE PRECISION THRESH
21* ..
22* .. Array Arguments ..
23* LOGICAL DOTYPE( * )
24* INTEGER ISEED( 4 ), NN( * )
25* DOUBLE PRECISION RCDEIN( * ), RCDVIN( * ), RCNDE1( * ),
26* $ RCNDV1( * ), RCONDE( * ), RCONDV( * ),
27* $ RESULT( 11 ), RWORK( * ), SCALE( * ),
28* $ SCALE1( * )
29* COMPLEX*16 A( LDA, * ), H( LDA, * ), LRE( LDLRE, * ),
30* $ VL( LDVL, * ), VR( LDVR, * ), W( * ), W1( * ),
31* $ WORK( * )
32* ..
33*
34*
35*> \par Purpose:
36* =============
37*>
38*> \verbatim
39*>
40*> ZDRVVX checks the nonsymmetric eigenvalue problem expert driver
41*> ZGEEVX.
42*>
43*> ZDRVVX uses both test matrices generated randomly depending on
44*> data supplied in the calling sequence, as well as on data
45*> read from an input file and including precomputed condition
46*> numbers to which it compares the ones it computes.
47*>
48*> When ZDRVVX is called, a number of matrix "sizes" ("n's") and a
49*> number of matrix "types" are specified in the calling sequence.
50*> For each size ("n") and each type of matrix, one matrix will be
51*> generated and used to test the nonsymmetric eigenroutines. For
52*> each matrix, 9 tests will be performed:
53*>
54*> (1) | A * VR - VR * W | / ( n |A| ulp )
55*>
56*> Here VR is the matrix of unit right eigenvectors.
57*> W is a diagonal matrix with diagonal entries W(j).
58*>
59*> (2) | A**H * VL - VL * W**H | / ( n |A| ulp )
60*>
61*> Here VL is the matrix of unit left eigenvectors, A**H is the
62*> conjugate transpose of A, and W is as above.
63*>
64*> (3) | |VR(i)| - 1 | / ulp and largest component real
65*>
66*> VR(i) denotes the i-th column of VR.
67*>
68*> (4) | |VL(i)| - 1 | / ulp and largest component real
69*>
70*> VL(i) denotes the i-th column of VL.
71*>
72*> (5) W(full) = W(partial)
73*>
74*> W(full) denotes the eigenvalues computed when VR, VL, RCONDV
75*> and RCONDE are also computed, and W(partial) denotes the
76*> eigenvalues computed when only some of VR, VL, RCONDV, and
77*> RCONDE are computed.
78*>
79*> (6) VR(full) = VR(partial)
80*>
81*> VR(full) denotes the right eigenvectors computed when VL, RCONDV
82*> and RCONDE are computed, and VR(partial) denotes the result
83*> when only some of VL and RCONDV are computed.
84*>
85*> (7) VL(full) = VL(partial)
86*>
87*> VL(full) denotes the left eigenvectors computed when VR, RCONDV
88*> and RCONDE are computed, and VL(partial) denotes the result
89*> when only some of VR and RCONDV are computed.
90*>
91*> (8) 0 if SCALE, ILO, IHI, ABNRM (full) =
92*> SCALE, ILO, IHI, ABNRM (partial)
93*> 1/ulp otherwise
94*>
95*> SCALE, ILO, IHI and ABNRM describe how the matrix is balanced.
96*> (full) is when VR, VL, RCONDE and RCONDV are also computed, and
97*> (partial) is when some are not computed.
98*>
99*> (9) RCONDV(full) = RCONDV(partial)
100*>
101*> RCONDV(full) denotes the reciprocal condition numbers of the
102*> right eigenvectors computed when VR, VL and RCONDE are also
103*> computed. RCONDV(partial) denotes the reciprocal condition
104*> numbers when only some of VR, VL and RCONDE are computed.
105*>
106*> The "sizes" are specified by an array NN(1:NSIZES); the value of
107*> each element NN(j) specifies one size.
108*> The "types" are specified by a logical array DOTYPE( 1:NTYPES );
109*> if DOTYPE(j) is .TRUE., then matrix type "j" will be generated.
110*> Currently, the list of possible types is:
111*>
112*> (1) The zero matrix.
113*> (2) The identity matrix.
114*> (3) A (transposed) Jordan block, with 1's on the diagonal.
115*>
116*> (4) A diagonal matrix with evenly spaced entries
117*> 1, ..., ULP and random complex angles.
118*> (ULP = (first number larger than 1) - 1 )
119*> (5) A diagonal matrix with geometrically spaced entries
120*> 1, ..., ULP and random complex angles.
121*> (6) A diagonal matrix with "clustered" entries 1, ULP, ..., ULP
122*> and random complex angles.
123*>
124*> (7) Same as (4), but multiplied by a constant near
125*> the overflow threshold
126*> (8) Same as (4), but multiplied by a constant near
127*> the underflow threshold
128*>
129*> (9) A matrix of the form U' T U, where U is unitary and
130*> T has evenly spaced entries 1, ..., ULP with random complex
131*> angles on the diagonal and random O(1) entries in the upper
132*> triangle.
133*>
134*> (10) A matrix of the form U' T U, where U is unitary and
135*> T has geometrically spaced entries 1, ..., ULP with random
136*> complex angles on the diagonal and random O(1) entries in
137*> the upper triangle.
138*>
139*> (11) A matrix of the form U' T U, where U is unitary and
140*> T has "clustered" entries 1, ULP,..., ULP with random
141*> complex angles on the diagonal and random O(1) entries in
142*> the upper triangle.
143*>
144*> (12) A matrix of the form U' T U, where U is unitary and
145*> T has complex eigenvalues randomly chosen from
146*> ULP < |z| < 1 and random O(1) entries in the upper
147*> triangle.
148*>
149*> (13) A matrix of the form X' T X, where X has condition
150*> SQRT( ULP ) and T has evenly spaced entries 1, ..., ULP
151*> with random complex angles on the diagonal and random O(1)
152*> entries in the upper triangle.
153*>
154*> (14) A matrix of the form X' T X, where X has condition
155*> SQRT( ULP ) and T has geometrically spaced entries
156*> 1, ..., ULP with random complex angles on the diagonal
157*> and random O(1) entries in the upper triangle.
158*>
159*> (15) A matrix of the form X' T X, where X has condition
160*> SQRT( ULP ) and T has "clustered" entries 1, ULP,..., ULP
161*> with random complex angles on the diagonal and random O(1)
162*> entries in the upper triangle.
163*>
164*> (16) A matrix of the form X' T X, where X has condition
165*> SQRT( ULP ) and T has complex eigenvalues randomly chosen
166*> from ULP < |z| < 1 and random O(1) entries in the upper
167*> triangle.
168*>
169*> (17) Same as (16), but multiplied by a constant
170*> near the overflow threshold
171*> (18) Same as (16), but multiplied by a constant
172*> near the underflow threshold
173*>
174*> (19) Nonsymmetric matrix with random entries chosen from |z| < 1
175*> If N is at least 4, all entries in first two rows and last
176*> row, and first column and last two columns are zero.
177*> (20) Same as (19), but multiplied by a constant
178*> near the overflow threshold
179*> (21) Same as (19), but multiplied by a constant
180*> near the underflow threshold
181*>
182*> In addition, an input file will be read from logical unit number
183*> NIUNIT. The file contains matrices along with precomputed
184*> eigenvalues and reciprocal condition numbers for the eigenvalues
185*> and right eigenvectors. For these matrices, in addition to tests
186*> (1) to (9) we will compute the following two tests:
187*>
188*> (10) |RCONDV - RCDVIN| / cond(RCONDV)
189*>
190*> RCONDV is the reciprocal right eigenvector condition number
191*> computed by ZGEEVX and RCDVIN (the precomputed true value)
192*> is supplied as input. cond(RCONDV) is the condition number of
193*> RCONDV, and takes errors in computing RCONDV into account, so
194*> that the resulting quantity should be O(ULP). cond(RCONDV) is
195*> essentially given by norm(A)/RCONDE.
196*>
197*> (11) |RCONDE - RCDEIN| / cond(RCONDE)
198*>
199*> RCONDE is the reciprocal eigenvalue condition number
200*> computed by ZGEEVX and RCDEIN (the precomputed true value)
201*> is supplied as input. cond(RCONDE) is the condition number
202*> of RCONDE, and takes errors in computing RCONDE into account,
203*> so that the resulting quantity should be O(ULP). cond(RCONDE)
204*> is essentially given by norm(A)/RCONDV.
205*> \endverbatim
206*
207* Arguments:
208* ==========
209*
210*> \param[in] NSIZES
211*> \verbatim
212*> NSIZES is INTEGER
213*> The number of sizes of matrices to use. NSIZES must be at
214*> least zero. If it is zero, no randomly generated matrices
215*> are tested, but any test matrices read from NIUNIT will be
216*> tested.
217*> \endverbatim
218*>
219*> \param[in] NN
220*> \verbatim
221*> NN is INTEGER array, dimension (NSIZES)
222*> An array containing the sizes to be used for the matrices.
223*> Zero values will be skipped. The values must be at least
224*> zero.
225*> \endverbatim
226*>
227*> \param[in] NTYPES
228*> \verbatim
229*> NTYPES is INTEGER
230*> The number of elements in DOTYPE. NTYPES must be at least
231*> zero. If it is zero, no randomly generated test matrices
232*> are tested, but and test matrices read from NIUNIT will be
233*> tested. If it is MAXTYP+1 and NSIZES is 1, then an
234*> additional type, MAXTYP+1 is defined, which is to use
235*> whatever matrix is in A. This is only useful if
236*> DOTYPE(1:MAXTYP) is .FALSE. and DOTYPE(MAXTYP+1) is .TRUE. .
237*> \endverbatim
238*>
239*> \param[in] DOTYPE
240*> \verbatim
241*> DOTYPE is LOGICAL array, dimension (NTYPES)
242*> If DOTYPE(j) is .TRUE., then for each size in NN a
243*> matrix of that size and of type j will be generated.
244*> If NTYPES is smaller than the maximum number of types
245*> defined (PARAMETER MAXTYP), then types NTYPES+1 through
246*> MAXTYP will not be generated. If NTYPES is larger
247*> than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES)
248*> will be ignored.
249*> \endverbatim
250*>
251*> \param[in,out] ISEED
252*> \verbatim
253*> ISEED is INTEGER array, dimension (4)
254*> On entry ISEED specifies the seed of the random number
255*> generator. The array elements should be between 0 and 4095;
256*> if not they will be reduced mod 4096. Also, ISEED(4) must
257*> be odd. The random number generator uses a linear
258*> congruential sequence limited to small integers, and so
259*> should produce machine independent random numbers. The
260*> values of ISEED are changed on exit, and can be used in the
261*> next call to ZDRVVX to continue the same random number
262*> sequence.
263*> \endverbatim
264*>
265*> \param[in] THRESH
266*> \verbatim
267*> THRESH is DOUBLE PRECISION
268*> A test will count as "failed" if the "error", computed as
269*> described above, exceeds THRESH. Note that the error
270*> is scaled to be O(1), so THRESH should be a reasonably
271*> small multiple of 1, e.g., 10 or 100. In particular,
272*> it should not depend on the precision (single vs. double)
273*> or the size of the matrix. It must be at least zero.
274*> \endverbatim
275*>
276*> \param[in] NIUNIT
277*> \verbatim
278*> NIUNIT is INTEGER
279*> The FORTRAN unit number for reading in the data file of
280*> problems to solve.
281*> \endverbatim
282*>
283*> \param[in] NOUNIT
284*> \verbatim
285*> NOUNIT is INTEGER
286*> The FORTRAN unit number for printing out error messages
287*> (e.g., if a routine returns INFO not equal to 0.)
288*> \endverbatim
289*>
290*> \param[out] A
291*> \verbatim
292*> A is COMPLEX*16 array, dimension (LDA, max(NN,12))
293*> Used to hold the matrix whose eigenvalues are to be
294*> computed. On exit, A contains the last matrix actually used.
295*> \endverbatim
296*>
297*> \param[in] LDA
298*> \verbatim
299*> LDA is INTEGER
300*> The leading dimension of A, and H. LDA must be at
301*> least 1 and at least max( NN, 12 ). (12 is the
302*> dimension of the largest matrix on the precomputed
303*> input file.)
304*> \endverbatim
305*>
306*> \param[out] H
307*> \verbatim
308*> H is COMPLEX*16 array, dimension (LDA, max(NN,12))
309*> Another copy of the test matrix A, modified by ZGEEVX.
310*> \endverbatim
311*>
312*> \param[out] W
313*> \verbatim
314*> W is COMPLEX*16 array, dimension (max(NN,12))
315*> Contains the eigenvalues of A.
316*> \endverbatim
317*>
318*> \param[out] W1
319*> \verbatim
320*> W1 is COMPLEX*16 array, dimension (max(NN,12))
321*> Like W, this array contains the eigenvalues of A,
322*> but those computed when ZGEEVX only computes a partial
323*> eigendecomposition, i.e. not the eigenvalues and left
324*> and right eigenvectors.
325*> \endverbatim
326*>
327*> \param[out] VL
328*> \verbatim
329*> VL is COMPLEX*16 array, dimension (LDVL, max(NN,12))
330*> VL holds the computed left eigenvectors.
331*> \endverbatim
332*>
333*> \param[in] LDVL
334*> \verbatim
335*> LDVL is INTEGER
336*> Leading dimension of VL. Must be at least max(1,max(NN,12)).
337*> \endverbatim
338*>
339*> \param[out] VR
340*> \verbatim
341*> VR is COMPLEX*16 array, dimension (LDVR, max(NN,12))
342*> VR holds the computed right eigenvectors.
343*> \endverbatim
344*>
345*> \param[in] LDVR
346*> \verbatim
347*> LDVR is INTEGER
348*> Leading dimension of VR. Must be at least max(1,max(NN,12)).
349*> \endverbatim
350*>
351*> \param[out] LRE
352*> \verbatim
353*> LRE is COMPLEX*16 array, dimension (LDLRE, max(NN,12))
354*> LRE holds the computed right or left eigenvectors.
355*> \endverbatim
356*>
357*> \param[in] LDLRE
358*> \verbatim
359*> LDLRE is INTEGER
360*> Leading dimension of LRE. Must be at least max(1,max(NN,12))
361*> \endverbatim
362*>
363*> \param[out] RCONDV
364*> \verbatim
365*> RCONDV is DOUBLE PRECISION array, dimension (N)
366*> RCONDV holds the computed reciprocal condition numbers
367*> for eigenvectors.
368*> \endverbatim
369*>
370*> \param[out] RCNDV1
371*> \verbatim
372*> RCNDV1 is DOUBLE PRECISION array, dimension (N)
373*> RCNDV1 holds more computed reciprocal condition numbers
374*> for eigenvectors.
375*> \endverbatim
376*>
377*> \param[in] RCDVIN
378*> \verbatim
379*> RCDVIN is DOUBLE PRECISION array, dimension (N)
380*> When COMP = .TRUE. RCDVIN holds the precomputed reciprocal
381*> condition numbers for eigenvectors to be compared with
382*> RCONDV.
383*> \endverbatim
384*>
385*> \param[out] RCONDE
386*> \verbatim
387*> RCONDE is DOUBLE PRECISION array, dimension (N)
388*> RCONDE holds the computed reciprocal condition numbers
389*> for eigenvalues.
390*> \endverbatim
391*>
392*> \param[out] RCNDE1
393*> \verbatim
394*> RCNDE1 is DOUBLE PRECISION array, dimension (N)
395*> RCNDE1 holds more computed reciprocal condition numbers
396*> for eigenvalues.
397*> \endverbatim
398*>
399*> \param[in] RCDEIN
400*> \verbatim
401*> RCDEIN is DOUBLE PRECISION array, dimension (N)
402*> When COMP = .TRUE. RCDEIN holds the precomputed reciprocal
403*> condition numbers for eigenvalues to be compared with
404*> RCONDE.
405*> \endverbatim
406*>
407*> \param[out] SCALE
408*> \verbatim
409*> SCALE is DOUBLE PRECISION array, dimension (N)
410*> Holds information describing balancing of matrix.
411*> \endverbatim
412*>
413*> \param[out] SCALE1
414*> \verbatim
415*> SCALE1 is DOUBLE PRECISION array, dimension (N)
416*> Holds information describing balancing of matrix.
417*> \endverbatim
418*>
419*> \param[out] WORK
420*> \verbatim
421*> WORK is COMPLEX*16 array, dimension (NWORK)
422*> \endverbatim
423*>
424*> \param[out] RESULT
425*> \verbatim
426*> RESULT is DOUBLE PRECISION array, dimension (11)
427*> The values computed by the seven tests described above.
428*> The values are currently limited to 1/ulp, to avoid
429*> overflow.
430*> \endverbatim
431*>
432*> \param[in] NWORK
433*> \verbatim
434*> NWORK is INTEGER
435*> The number of entries in WORK. This must be at least
436*> max(6*12+2*12**2,6*NN(j)+2*NN(j)**2) =
437*> max( 360 ,6*NN(j)+2*NN(j)**2) for all j.
438*> \endverbatim
439*>
440*> \param[out] RWORK
441*> \verbatim
442*> RWORK is DOUBLE PRECISION array, dimension (2*max(NN,12))
443*> \endverbatim
444*>
445*> \param[out] INFO
446*> \verbatim
447*> INFO is INTEGER
448*> If 0, then successful exit.
449*> If <0, then input parameter -INFO is incorrect.
450*> If >0, ZLATMR, CLATMS, CLATME or ZGET23 returned an error
451*> code, and INFO is its absolute value.
452*>
453*>-----------------------------------------------------------------------
454*>
455*> Some Local Variables and Parameters:
456*> ---- ----- --------- --- ----------
457*>
458*> ZERO, ONE Real 0 and 1.
459*> MAXTYP The number of types defined.
460*> NMAX Largest value in NN or 12.
461*> NERRS The number of tests which have exceeded THRESH
462*> COND, CONDS,
463*> IMODE Values to be passed to the matrix generators.
464*> ANORM Norm of A; passed to matrix generators.
465*>
466*> OVFL, UNFL Overflow and underflow thresholds.
467*> ULP, ULPINV Finest relative precision and its inverse.
468*> RTULP, RTULPI Square roots of the previous 4 values.
469*>
470*> The following four arrays decode JTYPE:
471*> KTYPE(j) The general type (1-10) for type "j".
472*> KMODE(j) The MODE value to be passed to the matrix
473*> generator for type "j".
474*> KMAGN(j) The order of magnitude ( O(1),
475*> O(overflow^(1/2) ), O(underflow^(1/2) )
476*> KCONDS(j) Selectw whether CONDS is to be 1 or
477*> 1/sqrt(ulp). (0 means irrelevant.)
478*> \endverbatim
479*
480* Authors:
481* ========
482*
483*> \author Univ. of Tennessee
484*> \author Univ. of California Berkeley
485*> \author Univ. of Colorado Denver
486*> \author NAG Ltd.
487*
488*> \ingroup complex16_eig
489*
490* =====================================================================
491 SUBROUTINE zdrvvx( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
492 $ NIUNIT, NOUNIT, A, LDA, H, W, W1, VL, LDVL, VR,
493 $ LDVR, LRE, LDLRE, RCONDV, RCNDV1, RCDVIN,
494 $ RCONDE, RCNDE1, RCDEIN, SCALE, SCALE1, RESULT,
495 $ WORK, NWORK, RWORK, INFO )
496*
497* -- LAPACK test routine --
498* -- LAPACK is a software package provided by Univ. of Tennessee, --
499* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
500*
501* .. Scalar Arguments ..
502 INTEGER INFO, LDA, LDLRE, LDVL, LDVR, NIUNIT, NOUNIT,
503 $ NSIZES, NTYPES, NWORK
504 DOUBLE PRECISION THRESH
505* ..
506* .. Array Arguments ..
507 LOGICAL DOTYPE( * )
508 INTEGER ISEED( 4 ), NN( * )
509 DOUBLE PRECISION RCDEIN( * ), RCDVIN( * ), RCNDE1( * ),
510 $ RCNDV1( * ), RCONDE( * ), RCONDV( * ),
511 $ result( 11 ), rwork( * ), scale( * ),
512 $ scale1( * )
513 COMPLEX*16 A( LDA, * ), H( LDA, * ), LRE( LDLRE, * ),
514 $ VL( LDVL, * ), VR( LDVR, * ), W( * ), W1( * ),
515 $ WORK( * )
516* ..
517*
518* =====================================================================
519*
520* .. Parameters ..
521 COMPLEX*16 CZERO
522 PARAMETER ( CZERO = ( 0.0d+0, 0.0d+0 ) )
523 COMPLEX*16 CONE
524 PARAMETER ( CONE = ( 1.0d+0, 0.0d+0 ) )
525 DOUBLE PRECISION ZERO, ONE
526 parameter( zero = 0.0d+0, one = 1.0d+0 )
527 INTEGER MAXTYP
528 parameter( maxtyp = 21 )
529* ..
530* .. Local Scalars ..
531 LOGICAL BADNN
532 CHARACTER BALANC
533 CHARACTER*3 PATH
534 INTEGER I, IBAL, IINFO, IMODE, ISRT, ITYPE, IWK, J,
535 $ jcol, jsize, jtype, mtypes, n, nerrs, nfail,
536 $ nmax, nnwork, ntest, ntestf, ntestt
537 DOUBLE PRECISION ANORM, COND, CONDS, OVFL, RTULP, RTULPI, ULP,
538 $ ulpinv, unfl, wi, wr
539* ..
540* .. Local Arrays ..
541 CHARACTER BAL( 4 )
542 INTEGER IDUMMA( 1 ), IOLDSD( 4 ), KCONDS( MAXTYP ),
543 $ KMAGN( MAXTYP ), KMODE( MAXTYP ),
544 $ KTYPE( MAXTYP )
545* ..
546* .. External Functions ..
547 DOUBLE PRECISION DLAMCH
548 EXTERNAL DLAMCH
549* ..
550* .. External Subroutines ..
551 EXTERNAL dlabad, dlasum, xerbla, zget23, zlaset, zlatme,
552 $ zlatmr, zlatms
553* ..
554* .. Intrinsic Functions ..
555 INTRINSIC abs, dcmplx, max, min, sqrt
556* ..
557* .. Data statements ..
558 DATA ktype / 1, 2, 3, 5*4, 4*6, 6*6, 3*9 /
559 DATA kmagn / 3*1, 1, 1, 1, 2, 3, 4*1, 1, 1, 1, 1, 2,
560 $ 3, 1, 2, 3 /
561 DATA kmode / 3*0, 4, 3, 1, 4, 4, 4, 3, 1, 5, 4, 3,
562 $ 1, 5, 5, 5, 4, 3, 1 /
563 DATA kconds / 3*0, 5*0, 4*1, 6*2, 3*0 /
564 DATA bal / 'N', 'P', 'S', 'B' /
565* ..
566* .. Executable Statements ..
567*
568 path( 1: 1 ) = 'Zomplex precision'
569 path( 2: 3 ) = 'VX'
570*
571* Check for errors
572*
573 ntestt = 0
574 ntestf = 0
575 info = 0
576*
577* Important constants
578*
579 badnn = .false.
580*
581* 7 is the largest dimension in the input file of precomputed
582* problems
583*
584 nmax = 7
585 DO 10 j = 1, nsizes
586 nmax = max( nmax, nn( j ) )
587 IF( nn( j ).LT.0 )
588 $ badnn = .true.
589 10 CONTINUE
590*
591* Check for errors
592*
593 IF( nsizes.LT.0 ) THEN
594 info = -1
595 ELSE IF( badnn ) THEN
596 info = -2
597 ELSE IF( ntypes.LT.0 ) THEN
598 info = -3
599 ELSE IF( thresh.LT.zero ) THEN
600 info = -6
601 ELSE IF( lda.LT.1 .OR. lda.LT.nmax ) THEN
602 info = -10
603 ELSE IF( ldvl.LT.1 .OR. ldvl.LT.nmax ) THEN
604 info = -15
605 ELSE IF( ldvr.LT.1 .OR. ldvr.LT.nmax ) THEN
606 info = -17
607 ELSE IF( ldlre.LT.1 .OR. ldlre.LT.nmax ) THEN
608 info = -19
609 ELSE IF( 6*nmax+2*nmax**2.GT.nwork ) THEN
610 info = -30
611 END IF
612*
613 IF( info.NE.0 ) THEN
614 CALL xerbla( 'ZDRVVX', -info )
615 RETURN
616 END IF
617*
618* If nothing to do check on NIUNIT
619*
620 IF( nsizes.EQ.0 .OR. ntypes.EQ.0 )
621 $ GO TO 160
622*
623* More Important constants
624*
625 unfl = dlamch( 'Safe minimum' )
626 ovfl = one / unfl
627 CALL dlabad( unfl, ovfl )
628 ulp = dlamch( 'Precision' )
629 ulpinv = one / ulp
630 rtulp = sqrt( ulp )
631 rtulpi = one / rtulp
632*
633* Loop over sizes, types
634*
635 nerrs = 0
636*
637 DO 150 jsize = 1, nsizes
638 n = nn( jsize )
639 IF( nsizes.NE.1 ) THEN
640 mtypes = min( maxtyp, ntypes )
641 ELSE
642 mtypes = min( maxtyp+1, ntypes )
643 END IF
644*
645 DO 140 jtype = 1, mtypes
646 IF( .NOT.dotype( jtype ) )
647 $ GO TO 140
648*
649* Save ISEED in case of an error.
650*
651 DO 20 j = 1, 4
652 ioldsd( j ) = iseed( j )
653 20 CONTINUE
654*
655* Compute "A"
656*
657* Control parameters:
658*
659* KMAGN KCONDS KMODE KTYPE
660* =1 O(1) 1 clustered 1 zero
661* =2 large large clustered 2 identity
662* =3 small exponential Jordan
663* =4 arithmetic diagonal, (w/ eigenvalues)
664* =5 random log symmetric, w/ eigenvalues
665* =6 random general, w/ eigenvalues
666* =7 random diagonal
667* =8 random symmetric
668* =9 random general
669* =10 random triangular
670*
671 IF( mtypes.GT.maxtyp )
672 $ GO TO 90
673*
674 itype = ktype( jtype )
675 imode = kmode( jtype )
676*
677* Compute norm
678*
679 GO TO ( 30, 40, 50 )kmagn( jtype )
680*
681 30 CONTINUE
682 anorm = one
683 GO TO 60
684*
685 40 CONTINUE
686 anorm = ovfl*ulp
687 GO TO 60
688*
689 50 CONTINUE
690 anorm = unfl*ulpinv
691 GO TO 60
692*
693 60 CONTINUE
694*
695 CALL zlaset( 'Full', lda, n, czero, czero, a, lda )
696 iinfo = 0
697 cond = ulpinv
698*
699* Special Matrices -- Identity & Jordan block
700*
701* Zero
702*
703 IF( itype.EQ.1 ) THEN
704 iinfo = 0
705*
706 ELSE IF( itype.EQ.2 ) THEN
707*
708* Identity
709*
710 DO 70 jcol = 1, n
711 a( jcol, jcol ) = anorm
712 70 CONTINUE
713*
714 ELSE IF( itype.EQ.3 ) THEN
715*
716* Jordan Block
717*
718 DO 80 jcol = 1, n
719 a( jcol, jcol ) = anorm
720 IF( jcol.GT.1 )
721 $ a( jcol, jcol-1 ) = one
722 80 CONTINUE
723*
724 ELSE IF( itype.EQ.4 ) THEN
725*
726* Diagonal Matrix, [Eigen]values Specified
727*
728 CALL zlatms( n, n, 'S', iseed, 'H', rwork, imode, cond,
729 $ anorm, 0, 0, 'N', a, lda, work( n+1 ),
730 $ iinfo )
731*
732 ELSE IF( itype.EQ.5 ) THEN
733*
734* Symmetric, eigenvalues specified
735*
736 CALL zlatms( n, n, 'S', iseed, 'H', rwork, imode, cond,
737 $ anorm, n, n, 'N', a, lda, work( n+1 ),
738 $ iinfo )
739*
740 ELSE IF( itype.EQ.6 ) THEN
741*
742* General, eigenvalues specified
743*
744 IF( kconds( jtype ).EQ.1 ) THEN
745 conds = one
746 ELSE IF( kconds( jtype ).EQ.2 ) THEN
747 conds = rtulpi
748 ELSE
749 conds = zero
750 END IF
751*
752 CALL zlatme( n, 'D', iseed, work, imode, cond, cone,
753 $ 'T', 'T', 'T', rwork, 4, conds, n, n, anorm,
754 $ a, lda, work( 2*n+1 ), iinfo )
755*
756 ELSE IF( itype.EQ.7 ) THEN
757*
758* Diagonal, random eigenvalues
759*
760 CALL zlatmr( n, n, 'D', iseed, 'S', work, 6, one, cone,
761 $ 'T', 'N', work( n+1 ), 1, one,
762 $ work( 2*n+1 ), 1, one, 'N', idumma, 0, 0,
763 $ zero, anorm, 'NO', a, lda, idumma, iinfo )
764*
765 ELSE IF( itype.EQ.8 ) THEN
766*
767* Symmetric, random eigenvalues
768*
769 CALL zlatmr( n, n, 'D', iseed, 'H', work, 6, one, cone,
770 $ 'T', 'N', work( n+1 ), 1, one,
771 $ work( 2*n+1 ), 1, one, 'N', idumma, n, n,
772 $ zero, anorm, 'NO', a, lda, idumma, iinfo )
773*
774 ELSE IF( itype.EQ.9 ) THEN
775*
776* General, random eigenvalues
777*
778 CALL zlatmr( n, n, 'D', iseed, 'N', work, 6, one, cone,
779 $ 'T', 'N', work( n+1 ), 1, one,
780 $ work( 2*n+1 ), 1, one, 'N', idumma, n, n,
781 $ zero, anorm, 'NO', a, lda, idumma, iinfo )
782 IF( n.GE.4 ) THEN
783 CALL zlaset( 'Full', 2, n, czero, czero, a, lda )
784 CALL zlaset( 'Full', n-3, 1, czero, czero, a( 3, 1 ),
785 $ lda )
786 CALL zlaset( 'Full', n-3, 2, czero, czero,
787 $ a( 3, n-1 ), lda )
788 CALL zlaset( 'Full', 1, n, czero, czero, a( n, 1 ),
789 $ lda )
790 END IF
791*
792 ELSE IF( itype.EQ.10 ) THEN
793*
794* Triangular, random eigenvalues
795*
796 CALL zlatmr( n, n, 'D', iseed, 'N', work, 6, one, cone,
797 $ 'T', 'N', work( n+1 ), 1, one,
798 $ work( 2*n+1 ), 1, one, 'N', idumma, n, 0,
799 $ zero, anorm, 'NO', a, lda, idumma, iinfo )
800*
801 ELSE
802*
803 iinfo = 1
804 END IF
805*
806 IF( iinfo.NE.0 ) THEN
807 WRITE( nounit, fmt = 9992 )'Generator', iinfo, n, jtype,
808 $ ioldsd
809 info = abs( iinfo )
810 RETURN
811 END IF
812*
813 90 CONTINUE
814*
815* Test for minimal and generous workspace
816*
817 DO 130 iwk = 1, 3
818 IF( iwk.EQ.1 ) THEN
819 nnwork = 2*n
820 ELSE IF( iwk.EQ.2 ) THEN
821 nnwork = 2*n + n**2
822 ELSE
823 nnwork = 6*n + 2*n**2
824 END IF
825 nnwork = max( nnwork, 1 )
826*
827* Test for all balancing options
828*
829 DO 120 ibal = 1, 4
830 balanc = bal( ibal )
831*
832* Perform tests
833*
834 CALL zget23( .false., 0, balanc, jtype, thresh,
835 $ ioldsd, nounit, n, a, lda, h, w, w1, vl,
836 $ ldvl, vr, ldvr, lre, ldlre, rcondv,
837 $ rcndv1, rcdvin, rconde, rcnde1, rcdein,
838 $ scale, scale1, result, work, nnwork,
839 $ rwork, info )
840*
841* Check for RESULT(j) > THRESH
842*
843 ntest = 0
844 nfail = 0
845 DO 100 j = 1, 9
846 IF( result( j ).GE.zero )
847 $ ntest = ntest + 1
848 IF( result( j ).GE.thresh )
849 $ nfail = nfail + 1
850 100 CONTINUE
851*
852 IF( nfail.GT.0 )
853 $ ntestf = ntestf + 1
854 IF( ntestf.EQ.1 ) THEN
855 WRITE( nounit, fmt = 9999 )path
856 WRITE( nounit, fmt = 9998 )
857 WRITE( nounit, fmt = 9997 )
858 WRITE( nounit, fmt = 9996 )
859 WRITE( nounit, fmt = 9995 )thresh
860 ntestf = 2
861 END IF
862*
863 DO 110 j = 1, 9
864 IF( result( j ).GE.thresh ) THEN
865 WRITE( nounit, fmt = 9994 )balanc, n, iwk,
866 $ ioldsd, jtype, j, result( j )
867 END IF
868 110 CONTINUE
869*
870 nerrs = nerrs + nfail
871 ntestt = ntestt + ntest
872*
873 120 CONTINUE
874 130 CONTINUE
875 140 CONTINUE
876 150 CONTINUE
877*
878 160 CONTINUE
879*
880* Read in data from file to check accuracy of condition estimation.
881* Assume input eigenvalues are sorted lexicographically (increasing
882* by real part, then decreasing by imaginary part)
883*
884 jtype = 0
885 170 CONTINUE
886 READ( niunit, fmt = *, END = 220 )N, isrt
887*
888* Read input data until N=0
889*
890 IF( n.EQ.0 )
891 $ GO TO 220
892 jtype = jtype + 1
893 iseed( 1 ) = jtype
894 DO 180 i = 1, n
895 READ( niunit, fmt = * )( a( i, j ), j = 1, n )
896 180 CONTINUE
897 DO 190 i = 1, n
898 READ( niunit, fmt = * )wr, wi, rcdein( i ), rcdvin( i )
899 w1( i ) = dcmplx( wr, wi )
900 190 CONTINUE
901 CALL zget23( .true., isrt, 'N', 22, thresh, iseed, nounit, n, a,
902 $ lda, h, w, w1, vl, ldvl, vr, ldvr, lre, ldlre,
903 $ rcondv, rcndv1, rcdvin, rconde, rcnde1, rcdein,
904 $ scale, scale1, result, work, 6*n+2*n**2, rwork,
905 $ info )
906*
907* Check for RESULT(j) > THRESH
908*
909 ntest = 0
910 nfail = 0
911 DO 200 j = 1, 11
912 IF( result( j ).GE.zero )
913 $ ntest = ntest + 1
914 IF( result( j ).GE.thresh )
915 $ nfail = nfail + 1
916 200 CONTINUE
917*
918 IF( nfail.GT.0 )
919 $ ntestf = ntestf + 1
920 IF( ntestf.EQ.1 ) THEN
921 WRITE( nounit, fmt = 9999 )path
922 WRITE( nounit, fmt = 9998 )
923 WRITE( nounit, fmt = 9997 )
924 WRITE( nounit, fmt = 9996 )
925 WRITE( nounit, fmt = 9995 )thresh
926 ntestf = 2
927 END IF
928*
929 DO 210 j = 1, 11
930 IF( result( j ).GE.thresh ) THEN
931 WRITE( nounit, fmt = 9993 )n, jtype, j, result( j )
932 END IF
933 210 CONTINUE
934*
935 nerrs = nerrs + nfail
936 ntestt = ntestt + ntest
937 GO TO 170
938 220 CONTINUE
939*
940* Summary
941*
942 CALL dlasum( path, nounit, nerrs, ntestt )
943*
944 9999 FORMAT( / 1x, a3, ' -- Complex Eigenvalue-Eigenvector ',
945 $ 'Decomposition Expert Driver',
946 $ / ' Matrix types (see ZDRVVX for details): ' )
947*
948 9998 FORMAT( / ' Special Matrices:', / ' 1=Zero matrix. ',
949 $ ' ', ' 5=Diagonal: geometr. spaced entries.',
950 $ / ' 2=Identity matrix. ', ' 6=Diagona',
951 $ 'l: clustered entries.', / ' 3=Transposed Jordan block. ',
952 $ ' ', ' 7=Diagonal: large, evenly spaced.', / ' ',
953 $ '4=Diagonal: evenly spaced entries. ', ' 8=Diagonal: s',
954 $ 'mall, evenly spaced.' )
955 9997 FORMAT( ' Dense, Non-Symmetric Matrices:', / ' 9=Well-cond., ev',
956 $ 'enly spaced eigenvals.', ' 14=Ill-cond., geomet. spaced e',
957 $ 'igenals.', / ' 10=Well-cond., geom. spaced eigenvals. ',
958 $ ' 15=Ill-conditioned, clustered e.vals.', / ' 11=Well-cond',
959 $ 'itioned, clustered e.vals. ', ' 16=Ill-cond., random comp',
960 $ 'lex ', / ' 12=Well-cond., random complex ', ' ',
961 $ ' 17=Ill-cond., large rand. complx ', / ' 13=Ill-condi',
962 $ 'tioned, evenly spaced. ', ' 18=Ill-cond., small rand.',
963 $ ' complx ' )
964 9996 FORMAT( ' 19=Matrix with random O(1) entries. ', ' 21=Matrix ',
965 $ 'with small random entries.', / ' 20=Matrix with large ran',
966 $ 'dom entries. ', ' 22=Matrix read from input file', / )
967 9995 FORMAT( ' Tests performed with test threshold =', f8.2,
968 $ / / ' 1 = | A VR - VR W | / ( n |A| ulp ) ',
969 $ / ' 2 = | transpose(A) VL - VL W | / ( n |A| ulp ) ',
970 $ / ' 3 = | |VR(i)| - 1 | / ulp ',
971 $ / ' 4 = | |VL(i)| - 1 | / ulp ',
972 $ / ' 5 = 0 if W same no matter if VR or VL computed,',
973 $ ' 1/ulp otherwise', /
974 $ ' 6 = 0 if VR same no matter what else computed,',
975 $ ' 1/ulp otherwise', /
976 $ ' 7 = 0 if VL same no matter what else computed,',
977 $ ' 1/ulp otherwise', /
978 $ ' 8 = 0 if RCONDV same no matter what else computed,',
979 $ ' 1/ulp otherwise', /
980 $ ' 9 = 0 if SCALE, ILO, IHI, ABNRM same no matter what else',
981 $ ' computed, 1/ulp otherwise',
982 $ / ' 10 = | RCONDV - RCONDV(precomputed) | / cond(RCONDV),',
983 $ / ' 11 = | RCONDE - RCONDE(precomputed) | / cond(RCONDE),' )
984 9994 FORMAT( ' BALANC=''', a1, ''',N=', i4, ',IWK=', i1, ', seed=',
985 $ 4( i4, ',' ), ' type ', i2, ', test(', i2, ')=', g10.3 )
986 9993 FORMAT( ' N=', i5, ', input example =', i3, ', test(', i2, ')=',
987 $ g10.3 )
988 9992 FORMAT( ' ZDRVVX: ', a, ' returned INFO=', i6, '.', / 9x, 'N=',
989 $ i6, ', JTYPE=', i6, ', ISEED=(', 3( i5, ',' ), i5, ')' )
990*
991 RETURN
992*
993* End of ZDRVVX
994*
995 END
subroutine dlabad(SMALL, LARGE)
DLABAD
Definition: dlabad.f:74
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine zdrvvx(NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH, NIUNIT, NOUNIT, A, LDA, H, W, W1, VL, LDVL, VR, LDVR, LRE, LDLRE, RCONDV, RCNDV1, RCDVIN, RCONDE, RCNDE1, RCDEIN, SCALE, SCALE1, RESULT, WORK, NWORK, RWORK, INFO)
ZDRVVX
Definition: zdrvvx.f:496
subroutine zget23(COMP, ISRT, BALANC, JTYPE, THRESH, ISEED, NOUNIT, N, A, LDA, H, W, W1, VL, LDVL, VR, LDVR, LRE, LDLRE, RCONDV, RCNDV1, RCDVIN, RCONDE, RCNDE1, RCDEIN, SCALE, SCALE1, RESULT, WORK, LWORK, RWORK, INFO)
ZGET23
Definition: zget23.f:368
subroutine zlatms(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, KL, KU, PACK, A, LDA, WORK, INFO)
ZLATMS
Definition: zlatms.f:332
subroutine zlatmr(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, RSIGN, GRADE, DL, MODEL, CONDL, DR, MODER, CONDR, PIVTNG, IPIVOT, KL, KU, SPARSE, ANORM, PACK, A, LDA, IWORK, INFO)
ZLATMR
Definition: zlatmr.f:490
subroutine zlatme(N, DIST, ISEED, D, MODE, COND, DMAX, RSIGN, UPPER, SIM, DS, MODES, CONDS, KL, KU, ANORM, A, LDA, WORK, INFO)
ZLATME
Definition: zlatme.f:301
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
subroutine dlasum(TYPE, IOUNIT, IE, NRUN)
DLASUM
Definition: dlasum.f:43