LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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sdrvvx.f
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1*> \brief \b SDRVVX
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 SDRVVX( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
12* NIUNIT, NOUNIT, A, LDA, H, WR, WI, WR1, WI1,
13* VL, LDVL, VR, LDVR, LRE, LDLRE, RCONDV, RCNDV1,
14* RCDVIN, RCONDE, RCNDE1, RCDEIN, SCALE, SCALE1,
15* RESULT, WORK, NWORK, IWORK, 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 ), IWORK( * ), NN( * )
25* REAL A( LDA, * ), H( LDA, * ), LRE( LDLRE, * ),
26* \$ RCDEIN( * ), RCDVIN( * ), RCNDE1( * ),
27* \$ RCNDV1( * ), RCONDE( * ), RCONDV( * ),
28* \$ RESULT( 11 ), SCALE( * ), SCALE1( * ),
29* \$ VL( LDVL, * ), VR( LDVR, * ), WI( * ),
30* \$ WI1( * ), WORK( * ), WR( * ), WR1( * )
31* ..
32*
33*
34*> \par Purpose:
35* =============
36*>
37*> \verbatim
38*>
39*> SDRVVX checks the nonsymmetric eigenvalue problem expert driver
40*> SGEEVX.
41*>
42*> SDRVVX uses both test matrices generated randomly depending on
43*> data supplied in the calling sequence, as well as on data
44*> read from an input file and including precomputed condition
45*> numbers to which it compares the ones it computes.
46*>
47*> When SDRVVX is called, a number of matrix "sizes" ("n's") and a
48*> number of matrix "types" are specified in the calling sequence.
49*> For each size ("n") and each type of matrix, one matrix will be
50*> generated and used to test the nonsymmetric eigenroutines. For
51*> each matrix, 9 tests will be performed:
52*>
53*> (1) | A * VR - VR * W | / ( n |A| ulp )
54*>
55*> Here VR is the matrix of unit right eigenvectors.
56*> W is a block diagonal matrix, with a 1x1 block for each
57*> real eigenvalue and a 2x2 block for each complex conjugate
58*> pair. If eigenvalues j and j+1 are a complex conjugate pair,
59*> so WR(j) = WR(j+1) = wr and WI(j) = - WI(j+1) = wi, then the
60*> 2 x 2 block corresponding to the pair will be:
61*>
62*> ( wr wi )
63*> ( -wi wr )
64*>
65*> Such a block multiplying an n x 2 matrix ( ur ui ) on the
66*> right will be the same as multiplying ur + i*ui by wr + i*wi.
67*>
68*> (2) | A**H * VL - VL * W**H | / ( n |A| ulp )
69*>
70*> Here VL is the matrix of unit left eigenvectors, A**H is the
71*> conjugate transpose of A, and W is as above.
72*>
73*> (3) | |VR(i)| - 1 | / ulp and largest component real
74*>
75*> VR(i) denotes the i-th column of VR.
76*>
77*> (4) | |VL(i)| - 1 | / ulp and largest component real
78*>
79*> VL(i) denotes the i-th column of VL.
80*>
81*> (5) W(full) = W(partial)
82*>
83*> W(full) denotes the eigenvalues computed when VR, VL, RCONDV
84*> and RCONDE are also computed, and W(partial) denotes the
85*> eigenvalues computed when only some of VR, VL, RCONDV, and
86*> RCONDE are computed.
87*>
88*> (6) VR(full) = VR(partial)
89*>
90*> VR(full) denotes the right eigenvectors computed when VL, RCONDV
91*> and RCONDE are computed, and VR(partial) denotes the result
92*> when only some of VL and RCONDV are computed.
93*>
94*> (7) VL(full) = VL(partial)
95*>
96*> VL(full) denotes the left eigenvectors computed when VR, RCONDV
97*> and RCONDE are computed, and VL(partial) denotes the result
98*> when only some of VR and RCONDV are computed.
99*>
100*> (8) 0 if SCALE, ILO, IHI, ABNRM (full) =
101*> SCALE, ILO, IHI, ABNRM (partial)
102*> 1/ulp otherwise
103*>
104*> SCALE, ILO, IHI and ABNRM describe how the matrix is balanced.
105*> (full) is when VR, VL, RCONDE and RCONDV are also computed, and
106*> (partial) is when some are not computed.
107*>
108*> (9) RCONDV(full) = RCONDV(partial)
109*>
110*> RCONDV(full) denotes the reciprocal condition numbers of the
111*> right eigenvectors computed when VR, VL and RCONDE are also
112*> computed. RCONDV(partial) denotes the reciprocal condition
113*> numbers when only some of VR, VL and RCONDE are computed.
114*>
115*> The "sizes" are specified by an array NN(1:NSIZES); the value of
116*> each element NN(j) specifies one size.
117*> The "types" are specified by a logical array DOTYPE( 1:NTYPES );
118*> if DOTYPE(j) is .TRUE., then matrix type "j" will be generated.
119*> Currently, the list of possible types is:
120*>
121*> (1) The zero matrix.
122*> (2) The identity matrix.
123*> (3) A (transposed) Jordan block, with 1's on the diagonal.
124*>
125*> (4) A diagonal matrix with evenly spaced entries
126*> 1, ..., ULP and random signs.
127*> (ULP = (first number larger than 1) - 1 )
128*> (5) A diagonal matrix with geometrically spaced entries
129*> 1, ..., ULP and random signs.
130*> (6) A diagonal matrix with "clustered" entries 1, ULP, ..., ULP
131*> and random signs.
132*>
133*> (7) Same as (4), but multiplied by a constant near
134*> the overflow threshold
135*> (8) Same as (4), but multiplied by a constant near
136*> the underflow threshold
137*>
138*> (9) A matrix of the form U' T U, where U is orthogonal and
139*> T has evenly spaced entries 1, ..., ULP with random signs
140*> on the diagonal and random O(1) entries in the upper
141*> triangle.
142*>
143*> (10) A matrix of the form U' T U, where U is orthogonal and
144*> T has geometrically spaced entries 1, ..., ULP with random
145*> signs on the diagonal and random O(1) entries in the upper
146*> triangle.
147*>
148*> (11) A matrix of the form U' T U, where U is orthogonal and
149*> T has "clustered" entries 1, ULP,..., ULP with random
150*> signs on the diagonal and random O(1) entries in the upper
151*> triangle.
152*>
153*> (12) A matrix of the form U' T U, where U is orthogonal and
154*> T has real or complex conjugate paired eigenvalues randomly
155*> chosen from ( ULP, 1 ) and random O(1) entries in the upper
156*> triangle.
157*>
158*> (13) A matrix of the form X' T X, where X has condition
159*> SQRT( ULP ) and T has evenly spaced entries 1, ..., ULP
160*> with random signs on the diagonal and random O(1) entries
161*> in the upper triangle.
162*>
163*> (14) A matrix of the form X' T X, where X has condition
164*> SQRT( ULP ) and T has geometrically spaced entries
165*> 1, ..., ULP with random signs on the diagonal and random
166*> O(1) entries in the upper triangle.
167*>
168*> (15) A matrix of the form X' T X, where X has condition
169*> SQRT( ULP ) and T has "clustered" entries 1, ULP,..., ULP
170*> with random signs on the diagonal and random O(1) entries
171*> in the upper triangle.
172*>
173*> (16) A matrix of the form X' T X, where X has condition
174*> SQRT( ULP ) and T has real or complex conjugate paired
175*> eigenvalues randomly chosen from ( ULP, 1 ) and random
176*> O(1) entries in the upper triangle.
177*>
178*> (17) Same as (16), but multiplied by a constant
179*> near the overflow threshold
180*> (18) Same as (16), but multiplied by a constant
181*> near the underflow threshold
182*>
183*> (19) Nonsymmetric matrix with random entries chosen from (-1,1).
184*> If N is at least 4, all entries in first two rows and last
185*> row, and first column and last two columns are zero.
186*> (20) Same as (19), but multiplied by a constant
187*> near the overflow threshold
188*> (21) Same as (19), but multiplied by a constant
189*> near the underflow threshold
190*>
191*> In addition, an input file will be read from logical unit number
192*> NIUNIT. The file contains matrices along with precomputed
193*> eigenvalues and reciprocal condition numbers for the eigenvalues
194*> and right eigenvectors. For these matrices, in addition to tests
195*> (1) to (9) we will compute the following two tests:
196*>
197*> (10) |RCONDV - RCDVIN| / cond(RCONDV)
198*>
199*> RCONDV is the reciprocal right eigenvector condition number
200*> computed by SGEEVX and RCDVIN (the precomputed true value)
201*> is supplied as input. cond(RCONDV) is the condition number of
202*> RCONDV, and takes errors in computing RCONDV into account, so
203*> that the resulting quantity should be O(ULP). cond(RCONDV) is
204*> essentially given by norm(A)/RCONDE.
205*>
206*> (11) |RCONDE - RCDEIN| / cond(RCONDE)
207*>
208*> RCONDE is the reciprocal eigenvalue condition number
209*> computed by SGEEVX and RCDEIN (the precomputed true value)
210*> is supplied as input. cond(RCONDE) is the condition number
211*> of RCONDE, and takes errors in computing RCONDE into account,
212*> so that the resulting quantity should be O(ULP). cond(RCONDE)
213*> is essentially given by norm(A)/RCONDV.
214*> \endverbatim
215*
216* Arguments:
217* ==========
218*
219*> \param[in] NSIZES
220*> \verbatim
221*> NSIZES is INTEGER
222*> The number of sizes of matrices to use. NSIZES must be at
223*> least zero. If it is zero, no randomly generated matrices
224*> are tested, but any test matrices read from NIUNIT will be
225*> tested.
226*> \endverbatim
227*>
228*> \param[in] NN
229*> \verbatim
230*> NN is INTEGER array, dimension (NSIZES)
231*> An array containing the sizes to be used for the matrices.
232*> Zero values will be skipped. The values must be at least
233*> zero.
234*> \endverbatim
235*>
236*> \param[in] NTYPES
237*> \verbatim
238*> NTYPES is INTEGER
239*> The number of elements in DOTYPE. NTYPES must be at least
240*> zero. If it is zero, no randomly generated test matrices
241*> are tested, but and test matrices read from NIUNIT will be
242*> tested. If it is MAXTYP+1 and NSIZES is 1, then an
243*> additional type, MAXTYP+1 is defined, which is to use
244*> whatever matrix is in A. This is only useful if
245*> DOTYPE(1:MAXTYP) is .FALSE. and DOTYPE(MAXTYP+1) is .TRUE. .
246*> \endverbatim
247*>
248*> \param[in] DOTYPE
249*> \verbatim
250*> DOTYPE is LOGICAL array, dimension (NTYPES)
251*> If DOTYPE(j) is .TRUE., then for each size in NN a
252*> matrix of that size and of type j will be generated.
253*> If NTYPES is smaller than the maximum number of types
254*> defined (PARAMETER MAXTYP), then types NTYPES+1 through
255*> MAXTYP will not be generated. If NTYPES is larger
256*> than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES)
257*> will be ignored.
258*> \endverbatim
259*>
260*> \param[in,out] ISEED
261*> \verbatim
262*> ISEED is INTEGER array, dimension (4)
263*> On entry ISEED specifies the seed of the random number
264*> generator. The array elements should be between 0 and 4095;
265*> if not they will be reduced mod 4096. Also, ISEED(4) must
266*> be odd. The random number generator uses a linear
267*> congruential sequence limited to small integers, and so
268*> should produce machine independent random numbers. The
269*> values of ISEED are changed on exit, and can be used in the
270*> next call to SDRVVX to continue the same random number
271*> sequence.
272*> \endverbatim
273*>
274*> \param[in] THRESH
275*> \verbatim
276*> THRESH is REAL
277*> A test will count as "failed" if the "error", computed as
278*> described above, exceeds THRESH. Note that the error
279*> is scaled to be O(1), so THRESH should be a reasonably
280*> small multiple of 1, e.g., 10 or 100. In particular,
281*> it should not depend on the precision (single vs. double)
282*> or the size of the matrix. It must be at least zero.
283*> \endverbatim
284*>
285*> \param[in] NIUNIT
286*> \verbatim
287*> NIUNIT is INTEGER
288*> The FORTRAN unit number for reading in the data file of
289*> problems to solve.
290*> \endverbatim
291*>
292*> \param[in] NOUNIT
293*> \verbatim
294*> NOUNIT is INTEGER
295*> The FORTRAN unit number for printing out error messages
296*> (e.g., if a routine returns INFO not equal to 0.)
297*> \endverbatim
298*>
299*> \param[out] A
300*> \verbatim
301*> A is REAL array, dimension
302*> (LDA, max(NN,12))
303*> Used to hold the matrix whose eigenvalues are to be
304*> computed. On exit, A contains the last matrix actually used.
305*> \endverbatim
306*>
307*> \param[in] LDA
308*> \verbatim
309*> LDA is INTEGER
310*> The leading dimension of the arrays A and H.
311*> LDA >= max(NN,12), since 12 is the dimension of the largest
312*> matrix in the precomputed input file.
313*> \endverbatim
314*>
315*> \param[out] H
316*> \verbatim
317*> H is REAL array, dimension
318*> (LDA, max(NN,12))
319*> Another copy of the test matrix A, modified by SGEEVX.
320*> \endverbatim
321*>
322*> \param[out] WR
323*> \verbatim
324*> WR is REAL array, dimension (max(NN))
325*> \endverbatim
326*>
327*> \param[out] WI
328*> \verbatim
329*> WI is REAL array, dimension (max(NN))
330*> The real and imaginary parts of the eigenvalues of A.
331*> On exit, WR + WI*i are the eigenvalues of the matrix in A.
332*> \endverbatim
333*>
334*> \param[out] WR1
335*> \verbatim
336*> WR1 is REAL array, dimension (max(NN,12))
337*> \endverbatim
338*>
339*> \param[out] WI1
340*> \verbatim
341*> WI1 is REAL array, dimension (max(NN,12))
342*>
343*> Like WR, WI, these arrays contain the eigenvalues of A,
344*> but those computed when SGEEVX only computes a partial
345*> eigendecomposition, i.e. not the eigenvalues and left
346*> and right eigenvectors.
347*> \endverbatim
348*>
349*> \param[out] VL
350*> \verbatim
351*> VL is REAL array, dimension
352*> (LDVL, max(NN,12))
353*> VL holds the computed left eigenvectors.
354*> \endverbatim
355*>
356*> \param[in] LDVL
357*> \verbatim
358*> LDVL is INTEGER
359*> Leading dimension of VL. Must be at least max(1,max(NN,12)).
360*> \endverbatim
361*>
362*> \param[out] VR
363*> \verbatim
364*> VR is REAL array, dimension
365*> (LDVR, max(NN,12))
366*> VR holds the computed right eigenvectors.
367*> \endverbatim
368*>
369*> \param[in] LDVR
370*> \verbatim
371*> LDVR is INTEGER
372*> Leading dimension of VR. Must be at least max(1,max(NN,12)).
373*> \endverbatim
374*>
375*> \param[out] LRE
376*> \verbatim
377*> LRE is REAL array, dimension
378*> (LDLRE, max(NN,12))
379*> LRE holds the computed right or left eigenvectors.
380*> \endverbatim
381*>
382*> \param[in] LDLRE
383*> \verbatim
384*> LDLRE is INTEGER
385*> Leading dimension of LRE. Must be at least max(1,max(NN,12))
386*> \endverbatim
387*>
388*> \param[out] RCONDV
389*> \verbatim
390*> RCONDV is REAL array, dimension (N)
391*> RCONDV holds the computed reciprocal condition numbers
392*> for eigenvectors.
393*> \endverbatim
394*>
395*> \param[out] RCNDV1
396*> \verbatim
397*> RCNDV1 is REAL array, dimension (N)
398*> RCNDV1 holds more computed reciprocal condition numbers
399*> for eigenvectors.
400*> \endverbatim
401*>
402*> \param[out] RCDVIN
403*> \verbatim
404*> RCDVIN is REAL array, dimension (N)
405*> When COMP = .TRUE. RCDVIN holds the precomputed reciprocal
406*> condition numbers for eigenvectors to be compared with
407*> RCONDV.
408*> \endverbatim
409*>
410*> \param[out] RCONDE
411*> \verbatim
412*> RCONDE is REAL array, dimension (N)
413*> RCONDE holds the computed reciprocal condition numbers
414*> for eigenvalues.
415*> \endverbatim
416*>
417*> \param[out] RCNDE1
418*> \verbatim
419*> RCNDE1 is REAL array, dimension (N)
420*> RCNDE1 holds more computed reciprocal condition numbers
421*> for eigenvalues.
422*> \endverbatim
423*>
424*> \param[out] RCDEIN
425*> \verbatim
426*> RCDEIN is REAL array, dimension (N)
427*> When COMP = .TRUE. RCDEIN holds the precomputed reciprocal
428*> condition numbers for eigenvalues to be compared with
429*> RCONDE.
430*> \endverbatim
431*>
432*> \param[out] SCALE
433*> \verbatim
434*> SCALE is REAL array, dimension (N)
435*> Holds information describing balancing of matrix.
436*> \endverbatim
437*>
438*> \param[out] SCALE1
439*> \verbatim
440*> SCALE1 is REAL array, dimension (N)
441*> Holds information describing balancing of matrix.
442*> \endverbatim
443*>
444*> \param[out] RESULT
445*> \verbatim
446*> RESULT is REAL array, dimension (11)
447*> The values computed by the seven tests described above.
448*> The values are currently limited to 1/ulp, to avoid overflow.
449*> \endverbatim
450*>
451*> \param[out] WORK
452*> \verbatim
453*> WORK is REAL array, dimension (NWORK)
454*> \endverbatim
455*>
456*> \param[in] NWORK
457*> \verbatim
458*> NWORK is INTEGER
459*> The number of entries in WORK. This must be at least
460*> max(6*12+2*12**2,6*NN(j)+2*NN(j)**2) =
461*> max( 360 ,6*NN(j)+2*NN(j)**2) for all j.
462*> \endverbatim
463*>
464*> \param[out] IWORK
465*> \verbatim
466*> IWORK is INTEGER array, dimension (2*max(NN,12))
467*> \endverbatim
468*>
469*> \param[out] INFO
470*> \verbatim
471*> INFO is INTEGER
472*> If 0, then successful exit.
473*> If <0, then input parameter -INFO is incorrect.
474*> If >0, SLATMR, SLATMS, SLATME or SGET23 returned an error
475*> code, and INFO is its absolute value.
476*>
477*>-----------------------------------------------------------------------
478*>
479*> Some Local Variables and Parameters:
480*> ---- ----- --------- --- ----------
481*>
482*> ZERO, ONE Real 0 and 1.
483*> MAXTYP The number of types defined.
484*> NMAX Largest value in NN or 12.
485*> NERRS The number of tests which have exceeded THRESH
486*> COND, CONDS,
487*> IMODE Values to be passed to the matrix generators.
488*> ANORM Norm of A; passed to matrix generators.
489*>
490*> OVFL, UNFL Overflow and underflow thresholds.
491*> ULP, ULPINV Finest relative precision and its inverse.
492*> RTULP, RTULPI Square roots of the previous 4 values.
493*>
494*> The following four arrays decode JTYPE:
495*> KTYPE(j) The general type (1-10) for type "j".
496*> KMODE(j) The MODE value to be passed to the matrix
497*> generator for type "j".
498*> KMAGN(j) The order of magnitude ( O(1),
499*> O(overflow^(1/2) ), O(underflow^(1/2) )
500*> KCONDS(j) Selectw whether CONDS is to be 1 or
501*> 1/sqrt(ulp). (0 means irrelevant.)
502*> \endverbatim
503*
504* Authors:
505* ========
506*
507*> \author Univ. of Tennessee
508*> \author Univ. of California Berkeley
509*> \author Univ. of Colorado Denver
510*> \author NAG Ltd.
511*
512*> \ingroup single_eig
513*
514* =====================================================================
515 SUBROUTINE sdrvvx( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
516 \$ NIUNIT, NOUNIT, A, LDA, H, WR, WI, WR1, WI1,
517 \$ VL, LDVL, VR, LDVR, LRE, LDLRE, RCONDV, RCNDV1,
518 \$ RCDVIN, RCONDE, RCNDE1, RCDEIN, SCALE, SCALE1,
519 \$ RESULT, WORK, NWORK, IWORK, INFO )
520*
521* -- LAPACK test routine --
522* -- LAPACK is a software package provided by Univ. of Tennessee, --
523* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
524*
525* .. Scalar Arguments ..
526 INTEGER INFO, LDA, LDLRE, LDVL, LDVR, NIUNIT, NOUNIT,
527 \$ NSIZES, NTYPES, NWORK
528 REAL THRESH
529* ..
530* .. Array Arguments ..
531 LOGICAL DOTYPE( * )
532 INTEGER ISEED( 4 ), IWORK( * ), NN( * )
533 REAL A( LDA, * ), H( LDA, * ), LRE( LDLRE, * ),
534 \$ RCDEIN( * ), RCDVIN( * ), RCNDE1( * ),
535 \$ rcndv1( * ), rconde( * ), rcondv( * ),
536 \$ result( 11 ), scale( * ), scale1( * ),
537 \$ vl( ldvl, * ), vr( ldvr, * ), wi( * ),
538 \$ wi1( * ), work( * ), wr( * ), wr1( * )
539* ..
540*
541* =====================================================================
542*
543* .. Parameters ..
544 REAL ZERO, ONE
545 PARAMETER ( ZERO = 0.0e0, one = 1.0e0 )
546 INTEGER MAXTYP
547 PARAMETER ( MAXTYP = 21 )
548* ..
549* .. Local Scalars ..
551 CHARACTER BALANC
552 CHARACTER*3 PATH
553 INTEGER I, IBAL, IINFO, IMODE, ITYPE, IWK, J, JCOL,
554 \$ jsize, jtype, mtypes, n, nerrs, nfail,
555 \$ nmax, nnwork, ntest, ntestf, ntestt
556 REAL ANORM, COND, CONDS, OVFL, RTULP, RTULPI, ULP,
557 \$ ulpinv, unfl
558* ..
559* .. Local Arrays ..
560 CHARACTER ADUMMA( 1 ), BAL( 4 )
561 INTEGER IDUMMA( 1 ), IOLDSD( 4 ), KCONDS( MAXTYP ),
562 \$ KMAGN( MAXTYP ), KMODE( MAXTYP ),
563 \$ KTYPE( MAXTYP )
564* ..
565* .. External Functions ..
566 REAL SLAMCH
567 EXTERNAL SLAMCH
568* ..
569* .. External Subroutines ..
570 EXTERNAL sget23, slabad, slasum, slatme, slatmr, slatms,
571 \$ slaset, xerbla
572* ..
573* .. Intrinsic Functions ..
574 INTRINSIC abs, max, min, sqrt
575* ..
576* .. Data statements ..
577 DATA ktype / 1, 2, 3, 5*4, 4*6, 6*6, 3*9 /
578 DATA kmagn / 3*1, 1, 1, 1, 2, 3, 4*1, 1, 1, 1, 1, 2,
579 \$ 3, 1, 2, 3 /
580 DATA kmode / 3*0, 4, 3, 1, 4, 4, 4, 3, 1, 5, 4, 3,
581 \$ 1, 5, 5, 5, 4, 3, 1 /
582 DATA kconds / 3*0, 5*0, 4*1, 6*2, 3*0 /
583 DATA bal / 'N', 'P', 'S', 'B' /
584* ..
585* .. Executable Statements ..
586*
587 path( 1: 1 ) = 'Single precision'
588 path( 2: 3 ) = 'VX'
589*
590* Check for errors
591*
592 ntestt = 0
593 ntestf = 0
594 info = 0
595*
596* Important constants
597*
599*
600* 12 is the largest dimension in the input file of precomputed
601* problems
602*
603 nmax = 12
604 DO 10 j = 1, nsizes
605 nmax = max( nmax, nn( j ) )
606 IF( nn( j ).LT.0 )
608 10 CONTINUE
609*
610* Check for errors
611*
612 IF( nsizes.LT.0 ) THEN
613 info = -1
614 ELSE IF( badnn ) THEN
615 info = -2
616 ELSE IF( ntypes.LT.0 ) THEN
617 info = -3
618 ELSE IF( thresh.LT.zero ) THEN
619 info = -6
620 ELSE IF( lda.LT.1 .OR. lda.LT.nmax ) THEN
621 info = -10
622 ELSE IF( ldvl.LT.1 .OR. ldvl.LT.nmax ) THEN
623 info = -17
624 ELSE IF( ldvr.LT.1 .OR. ldvr.LT.nmax ) THEN
625 info = -19
626 ELSE IF( ldlre.LT.1 .OR. ldlre.LT.nmax ) THEN
627 info = -21
628 ELSE IF( 6*nmax+2*nmax**2.GT.nwork ) THEN
629 info = -32
630 END IF
631*
632 IF( info.NE.0 ) THEN
633 CALL xerbla( 'SDRVVX', -info )
634 RETURN
635 END IF
636*
637* If nothing to do check on NIUNIT
638*
639 IF( nsizes.EQ.0 .OR. ntypes.EQ.0 )
640 \$ GO TO 160
641*
642* More Important constants
643*
644 unfl = slamch( 'Safe minimum' )
645 ovfl = one / unfl
646 CALL slabad( unfl, ovfl )
647 ulp = slamch( 'Precision' )
648 ulpinv = one / ulp
649 rtulp = sqrt( ulp )
650 rtulpi = one / rtulp
651*
652* Loop over sizes, types
653*
654 nerrs = 0
655*
656 DO 150 jsize = 1, nsizes
657 n = nn( jsize )
658 IF( nsizes.NE.1 ) THEN
659 mtypes = min( maxtyp, ntypes )
660 ELSE
661 mtypes = min( maxtyp+1, ntypes )
662 END IF
663*
664 DO 140 jtype = 1, mtypes
665 IF( .NOT.dotype( jtype ) )
666 \$ GO TO 140
667*
668* Save ISEED in case of an error.
669*
670 DO 20 j = 1, 4
671 ioldsd( j ) = iseed( j )
672 20 CONTINUE
673*
674* Compute "A"
675*
676* Control parameters:
677*
678* KMAGN KCONDS KMODE KTYPE
679* =1 O(1) 1 clustered 1 zero
680* =2 large large clustered 2 identity
681* =3 small exponential Jordan
682* =4 arithmetic diagonal, (w/ eigenvalues)
683* =5 random log symmetric, w/ eigenvalues
684* =6 random general, w/ eigenvalues
685* =7 random diagonal
686* =8 random symmetric
687* =9 random general
688* =10 random triangular
689*
690 IF( mtypes.GT.maxtyp )
691 \$ GO TO 90
692*
693 itype = ktype( jtype )
694 imode = kmode( jtype )
695*
696* Compute norm
697*
698 GO TO ( 30, 40, 50 )kmagn( jtype )
699*
700 30 CONTINUE
701 anorm = one
702 GO TO 60
703*
704 40 CONTINUE
705 anorm = ovfl*ulp
706 GO TO 60
707*
708 50 CONTINUE
709 anorm = unfl*ulpinv
710 GO TO 60
711*
712 60 CONTINUE
713*
714 CALL slaset( 'Full', lda, n, zero, zero, a, lda )
715 iinfo = 0
716 cond = ulpinv
717*
718* Special Matrices -- Identity & Jordan block
719*
720* Zero
721*
722 IF( itype.EQ.1 ) THEN
723 iinfo = 0
724*
725 ELSE IF( itype.EQ.2 ) THEN
726*
727* Identity
728*
729 DO 70 jcol = 1, n
730 a( jcol, jcol ) = anorm
731 70 CONTINUE
732*
733 ELSE IF( itype.EQ.3 ) THEN
734*
735* Jordan Block
736*
737 DO 80 jcol = 1, n
738 a( jcol, jcol ) = anorm
739 IF( jcol.GT.1 )
740 \$ a( jcol, jcol-1 ) = one
741 80 CONTINUE
742*
743 ELSE IF( itype.EQ.4 ) THEN
744*
745* Diagonal Matrix, [Eigen]values Specified
746*
747 CALL slatms( n, n, 'S', iseed, 'S', work, imode, cond,
748 \$ anorm, 0, 0, 'N', a, lda, work( n+1 ),
749 \$ iinfo )
750*
751 ELSE IF( itype.EQ.5 ) THEN
752*
753* Symmetric, eigenvalues specified
754*
755 CALL slatms( n, n, 'S', iseed, 'S', work, imode, cond,
756 \$ anorm, n, n, 'N', a, lda, work( n+1 ),
757 \$ iinfo )
758*
759 ELSE IF( itype.EQ.6 ) THEN
760*
761* General, eigenvalues specified
762*
763 IF( kconds( jtype ).EQ.1 ) THEN
764 conds = one
765 ELSE IF( kconds( jtype ).EQ.2 ) THEN
766 conds = rtulpi
767 ELSE
768 conds = zero
769 END IF
770*
771 adumma( 1 ) = ' '
772 CALL slatme( n, 'S', iseed, work, imode, cond, one,
773 \$ adumma, 'T', 'T', 'T', work( n+1 ), 4,
774 \$ conds, n, n, anorm, a, lda, work( 2*n+1 ),
775 \$ iinfo )
776*
777 ELSE IF( itype.EQ.7 ) THEN
778*
779* Diagonal, random eigenvalues
780*
781 CALL slatmr( n, n, 'S', iseed, 'S', work, 6, one, one,
782 \$ 'T', 'N', work( n+1 ), 1, one,
783 \$ work( 2*n+1 ), 1, one, 'N', idumma, 0, 0,
784 \$ zero, anorm, 'NO', a, lda, iwork, iinfo )
785*
786 ELSE IF( itype.EQ.8 ) THEN
787*
788* Symmetric, random eigenvalues
789*
790 CALL slatmr( n, n, 'S', iseed, 'S', work, 6, one, one,
791 \$ 'T', 'N', work( n+1 ), 1, one,
792 \$ work( 2*n+1 ), 1, one, 'N', idumma, n, n,
793 \$ zero, anorm, 'NO', a, lda, iwork, iinfo )
794*
795 ELSE IF( itype.EQ.9 ) THEN
796*
797* General, random eigenvalues
798*
799 CALL slatmr( n, n, 'S', iseed, 'N', work, 6, one, one,
800 \$ 'T', 'N', work( n+1 ), 1, one,
801 \$ work( 2*n+1 ), 1, one, 'N', idumma, n, n,
802 \$ zero, anorm, 'NO', a, lda, iwork, iinfo )
803 IF( n.GE.4 ) THEN
804 CALL slaset( 'Full', 2, n, zero, zero, a, lda )
805 CALL slaset( 'Full', n-3, 1, zero, zero, a( 3, 1 ),
806 \$ lda )
807 CALL slaset( 'Full', n-3, 2, zero, zero, a( 3, n-1 ),
808 \$ lda )
809 CALL slaset( 'Full', 1, n, zero, zero, a( n, 1 ),
810 \$ lda )
811 END IF
812*
813 ELSE IF( itype.EQ.10 ) THEN
814*
815* Triangular, random eigenvalues
816*
817 CALL slatmr( n, n, 'S', iseed, 'N', work, 6, one, one,
818 \$ 'T', 'N', work( n+1 ), 1, one,
819 \$ work( 2*n+1 ), 1, one, 'N', idumma, n, 0,
820 \$ zero, anorm, 'NO', a, lda, iwork, iinfo )
821*
822 ELSE
823*
824 iinfo = 1
825 END IF
826*
827 IF( iinfo.NE.0 ) THEN
828 WRITE( nounit, fmt = 9992 )'Generator', iinfo, n, jtype,
829 \$ ioldsd
830 info = abs( iinfo )
831 RETURN
832 END IF
833*
834 90 CONTINUE
835*
836* Test for minimal and generous workspace
837*
838 DO 130 iwk = 1, 3
839 IF( iwk.EQ.1 ) THEN
840 nnwork = 3*n
841 ELSE IF( iwk.EQ.2 ) THEN
842 nnwork = 6*n + n**2
843 ELSE
844 nnwork = 6*n + 2*n**2
845 END IF
846 nnwork = max( nnwork, 1 )
847*
848* Test for all balancing options
849*
850 DO 120 ibal = 1, 4
851 balanc = bal( ibal )
852*
853* Perform tests
854*
855 CALL sget23( .false., balanc, jtype, thresh, ioldsd,
856 \$ nounit, n, a, lda, h, wr, wi, wr1, wi1,
857 \$ vl, ldvl, vr, ldvr, lre, ldlre, rcondv,
858 \$ rcndv1, rcdvin, rconde, rcnde1, rcdein,
859 \$ scale, scale1, result, work, nnwork,
860 \$ iwork, info )
861*
862* Check for RESULT(j) > THRESH
863*
864 ntest = 0
865 nfail = 0
866 DO 100 j = 1, 9
867 IF( result( j ).GE.zero )
868 \$ ntest = ntest + 1
869 IF( result( j ).GE.thresh )
870 \$ nfail = nfail + 1
871 100 CONTINUE
872*
873 IF( nfail.GT.0 )
874 \$ ntestf = ntestf + 1
875 IF( ntestf.EQ.1 ) THEN
876 WRITE( nounit, fmt = 9999 )path
877 WRITE( nounit, fmt = 9998 )
878 WRITE( nounit, fmt = 9997 )
879 WRITE( nounit, fmt = 9996 )
880 WRITE( nounit, fmt = 9995 )thresh
881 ntestf = 2
882 END IF
883*
884 DO 110 j = 1, 9
885 IF( result( j ).GE.thresh ) THEN
886 WRITE( nounit, fmt = 9994 )balanc, n, iwk,
887 \$ ioldsd, jtype, j, result( j )
888 END IF
889 110 CONTINUE
890*
891 nerrs = nerrs + nfail
892 ntestt = ntestt + ntest
893*
894 120 CONTINUE
895 130 CONTINUE
896 140 CONTINUE
897 150 CONTINUE
898*
899 160 CONTINUE
900*
901* Read in data from file to check accuracy of condition estimation.
902* Assume input eigenvalues are sorted lexicographically (increasing
903* by real part, then decreasing by imaginary part)
904*
905 jtype = 0
906 170 CONTINUE
907 READ( niunit, fmt = *, END = 220 )n
908*
909* Read input data until N=0
910*
911 IF( n.EQ.0 )
912 \$ GO TO 220
913 jtype = jtype + 1
914 iseed( 1 ) = jtype
915 DO 180 i = 1, n
916 READ( niunit, fmt = * )( a( i, j ), j = 1, n )
917 180 CONTINUE
918 DO 190 i = 1, n
919 READ( niunit, fmt = * )wr1( i ), wi1( i ), rcdein( i ),
920 \$ rcdvin( i )
921 190 CONTINUE
922 CALL sget23( .true., 'N', 22, thresh, iseed, nounit, n, a, lda, h,
923 \$ wr, wi, wr1, wi1, vl, ldvl, vr, ldvr, lre, ldlre,
924 \$ rcondv, rcndv1, rcdvin, rconde, rcnde1, rcdein,
925 \$ scale, scale1, result, work, 6*n+2*n**2, iwork,
926 \$ info )
927*
928* Check for RESULT(j) > THRESH
929*
930 ntest = 0
931 nfail = 0
932 DO 200 j = 1, 11
933 IF( result( j ).GE.zero )
934 \$ ntest = ntest + 1
935 IF( result( j ).GE.thresh )
936 \$ nfail = nfail + 1
937 200 CONTINUE
938*
939 IF( nfail.GT.0 )
940 \$ ntestf = ntestf + 1
941 IF( ntestf.EQ.1 ) THEN
942 WRITE( nounit, fmt = 9999 )path
943 WRITE( nounit, fmt = 9998 )
944 WRITE( nounit, fmt = 9997 )
945 WRITE( nounit, fmt = 9996 )
946 WRITE( nounit, fmt = 9995 )thresh
947 ntestf = 2
948 END IF
949*
950 DO 210 j = 1, 11
951 IF( result( j ).GE.thresh ) THEN
952 WRITE( nounit, fmt = 9993 )n, jtype, j, result( j )
953 END IF
954 210 CONTINUE
955*
956 nerrs = nerrs + nfail
957 ntestt = ntestt + ntest
958 GO TO 170
959 220 CONTINUE
960*
961* Summary
962*
963 CALL slasum( path, nounit, nerrs, ntestt )
964*
965 9999 FORMAT( / 1x, a3, ' -- Real Eigenvalue-Eigenvector Decomposition',
966 \$ ' Expert Driver', /
967 \$ ' Matrix types (see SDRVVX for details): ' )
968*
969 9998 FORMAT( / ' Special Matrices:', / ' 1=Zero matrix. ',
970 \$ ' ', ' 5=Diagonal: geometr. spaced entries.',
971 \$ / ' 2=Identity matrix. ', ' 6=Diagona',
972 \$ 'l: clustered entries.', / ' 3=Transposed Jordan block. ',
973 \$ ' ', ' 7=Diagonal: large, evenly spaced.', / ' ',
974 \$ '4=Diagonal: evenly spaced entries. ', ' 8=Diagonal: s',
975 \$ 'mall, evenly spaced.' )
976 9997 FORMAT( ' Dense, Non-Symmetric Matrices:', / ' 9=Well-cond., ev',
977 \$ 'enly spaced eigenvals.', ' 14=Ill-cond., geomet. spaced e',
978 \$ 'igenals.', / ' 10=Well-cond., geom. spaced eigenvals. ',
979 \$ ' 15=Ill-conditioned, clustered e.vals.', / ' 11=Well-cond',
980 \$ 'itioned, clustered e.vals. ', ' 16=Ill-cond., random comp',
981 \$ 'lex ', / ' 12=Well-cond., random complex ', ' ',
982 \$ ' 17=Ill-cond., large rand. complx ', / ' 13=Ill-condi',
983 \$ 'tioned, evenly spaced. ', ' 18=Ill-cond., small rand.',
984 \$ ' complx ' )
985 9996 FORMAT( ' 19=Matrix with random O(1) entries. ', ' 21=Matrix ',
986 \$ 'with small random entries.', / ' 20=Matrix with large ran',
987 \$ 'dom entries. ', ' 22=Matrix read from input file', / )
988 9995 FORMAT( ' Tests performed with test threshold =', f8.2,
989 \$ / / ' 1 = | A VR - VR W | / ( n |A| ulp ) ',
990 \$ / ' 2 = | transpose(A) VL - VL W | / ( n |A| ulp ) ',
991 \$ / ' 3 = | |VR(i)| - 1 | / ulp ',
992 \$ / ' 4 = | |VL(i)| - 1 | / ulp ',
993 \$ / ' 5 = 0 if W same no matter if VR or VL computed,',
994 \$ ' 1/ulp otherwise', /
995 \$ ' 6 = 0 if VR same no matter what else computed,',
996 \$ ' 1/ulp otherwise', /
997 \$ ' 7 = 0 if VL same no matter what else computed,',
998 \$ ' 1/ulp otherwise', /
999 \$ ' 8 = 0 if RCONDV same no matter what else computed,',
1000 \$ ' 1/ulp otherwise', /
1001 \$ ' 9 = 0 if SCALE, ILO, IHI, ABNRM same no matter what else',
1002 \$ ' computed, 1/ulp otherwise',
1003 \$ / ' 10 = | RCONDV - RCONDV(precomputed) | / cond(RCONDV),',
1004 \$ / ' 11 = | RCONDE - RCONDE(precomputed) | / cond(RCONDE),' )
1005 9994 FORMAT( ' BALANC=''', a1, ''',N=', i4, ',IWK=', i1, ', seed=',
1006 \$ 4( i4, ',' ), ' type ', i2, ', test(', i2, ')=', g10.3 )
1007 9993 FORMAT( ' N=', i5, ', input example =', i3, ', test(', i2, ')=',
1008 \$ g10.3 )
1009 9992 FORMAT( ' SDRVVX: ', a, ' returned INFO=', i6, '.', / 9x, 'N=',
1010 \$ i6, ', JTYPE=', i6, ', ISEED=(', 3( i5, ',' ), i5, ')' )
1011*
1012 RETURN
1013*
1014* End of SDRVVX
1015*
1016 END
subroutine slaset(UPLO, M, N, ALPHA, BETA, A, LDA)
SLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition: slaset.f:110
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine slatms(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, KL, KU, PACK, A, LDA, WORK, INFO)
SLATMS
Definition: slatms.f:321
subroutine slatme(N, DIST, ISEED, D, MODE, COND, DMAX, EI, RSIGN, UPPER, SIM, DS, MODES, CONDS, KL, KU, ANORM, A, LDA, WORK, INFO)
SLATME
Definition: slatme.f:332
subroutine slatmr(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)
SLATMR
Definition: slatmr.f:471
subroutine sdrvvx(NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH, NIUNIT, NOUNIT, A, LDA, H, WR, WI, WR1, WI1, VL, LDVL, VR, LDVR, LRE, LDLRE, RCONDV, RCNDV1, RCDVIN, RCONDE, RCNDE1, RCDEIN, SCALE, SCALE1, RESULT, WORK, NWORK, IWORK, INFO)
SDRVVX
Definition: sdrvvx.f:520
subroutine sget23(COMP, BALANC, JTYPE, THRESH, ISEED, NOUNIT, N, A, LDA, H, WR, WI, WR1, WI1, VL, LDVL, VR, LDVR, LRE, LDLRE, RCONDV, RCNDV1, RCDVIN, RCONDE, RCNDE1, RCDEIN, SCALE, SCALE1, RESULT, WORK, LWORK, IWORK, INFO)
SGET23
Definition: sget23.f:378
subroutine slasum(TYPE, IOUNIT, IE, NRUN)
SLASUM
Definition: slasum.f:41