1*> \brief \b CDRVVX
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 CDRVVX( 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*       REAL               THRESH
21*       ..
22*       .. Array Arguments ..
23*       LOGICAL            DOTYPE( * )
24*       INTEGER            ISEED( 4 ), NN( * )
25*       REAL               RCDEIN( * ), RCDVIN( * ), RCNDE1( * ),
26*      $                   RCNDV1( * ), RCONDE( * ), RCONDV( * ),
27*      $                   RESULT( 11 ), RWORK( * ), SCALE( * ),
28*      $                   SCALE1( * )
29*       COMPLEX            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*>    CDRVVX  checks the nonsymmetric eigenvalue problem expert driver
41*>    CGEEVX.
42*>
43*>    CDRVVX 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 CDRVVX 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 CGEEVX 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 CGEEVX 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 CDRVVX to continue the same random number
262*>          sequence.
263*> \endverbatim
264*>
265*> \param[in] THRESH
266*> \verbatim
267*>          THRESH is REAL
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 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 array, dimension (LDA, max(NN,12))
309*>          Another copy of the test matrix A, modified by CGEEVX.
310*> \endverbatim
311*>
312*> \param[out] W
313*> \verbatim
314*>          W is COMPLEX array, dimension (max(NN,12))
315*>          Contains the eigenvalues of A.
316*> \endverbatim
317*>
318*> \param[out] W1
319*> \verbatim
320*>          W1 is COMPLEX array, dimension (max(NN,12))
321*>          Like W, this array contains the eigenvalues of A,
322*>          but those computed when CGEEVX 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 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 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 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 REAL 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 REAL 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 REAL 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 REAL 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 REAL 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 REAL 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 REAL array, dimension (N)
410*>          Holds information describing balancing of matrix.
411*> \endverbatim
412*>
413*> \param[out] SCALE1
414*> \verbatim
415*>          SCALE1 is REAL array, dimension (N)
416*>          Holds information describing balancing of matrix.
417*> \endverbatim
418*>
419*> \param[out] RESULT
420*> \verbatim
421*>          RESULT is REAL array, dimension (11)
422*>          The values computed by the seven tests described above.
423*>          The values are currently limited to 1/ulp, to avoid
424*>          overflow.
425*> \endverbatim
426*>
427*> \param[out] WORK
428*> \verbatim
429*>          WORK is COMPLEX array, dimension (NWORK)
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 REAL 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, CLATMR, CLATMS, CLATME or CGET23 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 complex_eig
489*
490*  =====================================================================
491      SUBROUTINE CDRVVX( 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      REAL               THRESH
505*     ..
506*     .. Array Arguments ..
507      LOGICAL            DOTYPE( * )
508      INTEGER            ISEED( 4 ), NN( * )
509      REAL               RCDEIN( * ), RCDVIN( * ), RCNDE1( * ),
510     $                   RCNDV1( * ), RCONDE( * ), RCONDV( * ),
511     $                   RESULT( 11 ), RWORK( * ), SCALE( * ),
512     $                   SCALE1( * )
513      COMPLEX            A( LDA, * ), H( LDA, * ), LRE( LDLRE, * ),
514     $                   VL( LDVL, * ), VR( LDVR, * ), W( * ), W1( * ),
515     $                   WORK( * )
516*     ..
517*
518*  =====================================================================
519*
520*     .. Parameters ..
521      COMPLEX            CZERO
522      PARAMETER          ( CZERO = ( 0.0E+0, 0.0E+0 ) )
523      COMPLEX            CONE
524      PARAMETER          ( CONE = ( 1.0E+0, 0.0E+0 ) )
525      REAL               ZERO, ONE
526      PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+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,
536     $                   NFAIL, NMAX, NNWORK, NTEST, NTESTF, NTESTT
537      REAL               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      REAL               SLAMCH
548      EXTERNAL           SLAMCH
549*     ..
550*     .. External Subroutines ..
551      EXTERNAL           CGET23, CLATME, CLATMR, CLATMS, CLASET, SLABAD,
552     $                   SLASUM, XERBLA
553*     ..
554*     .. Intrinsic Functions ..
555      INTRINSIC          ABS, CMPLX, 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 ) = 'Complex 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( 'CDRVVX', -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 = SLAMCH( 'Safe minimum' )
626      OVFL = ONE / UNFL
627      CALL SLABAD( UNFL, OVFL )
628      ULP = SLAMCH( '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 CLASET( '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 CLATMS( 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 CLATMS( 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 CLATME( 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 CLATMR( 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 CLATMR( 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 CLATMR( 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 CLASET( 'Full', 2, N, CZERO, CZERO, A, LDA )
784                  CALL CLASET( 'Full', N-3, 1, CZERO, CZERO, A( 3, 1 ),
785     $                         LDA )
786                  CALL CLASET( 'Full', N-3, 2, CZERO, CZERO,
787     $                         A( 3, N-1 ), LDA )
788                  CALL CLASET( '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 CLATMR( 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 CGET23( .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 ) = CMPLX( WR, WI )
900  190 CONTINUE
901      CALL CGET23( .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 SLASUM( PATH, NOUNIT, NERRS, NTESTT )
943*
944 9999 FORMAT( / 1X, A3, ' -- Complex Eigenvalue-Eigenvector ',
945     $      'Decomposition Expert Driver',
946     $      / ' Matrix types (see CDRVVX 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( ' CDRVVX: ', A, ' returned INFO=', I6, '.', / 9X, 'N=',
989     $      I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5, ')' )
990*
991      RETURN
992*
993*     End of CDRVVX
994*
995      END
996