LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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sdrgev3.f
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1*> \brief \b SDRGEV3
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 SDRGEV3( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
12* NOUNIT, A, LDA, B, S, T, Q, LDQ, Z, QE, LDQE,
13* ALPHAR, ALPHAI, BETA, ALPHR1, ALPHI1, BETA1,
14* WORK, LWORK, RESULT, INFO )
15*
16* .. Scalar Arguments ..
17* INTEGER INFO, LDA, LDQ, LDQE, LWORK, NOUNIT, NSIZES,
18* $ NTYPES
19* REAL THRESH
20* ..
21* .. Array Arguments ..
22* LOGICAL DOTYPE( * )
23* INTEGER ISEED( 4 ), NN( * )
24* REAL A( LDA, * ), ALPHAI( * ), ALPHI1( * ),
25* $ ALPHAR( * ), ALPHR1( * ), B( LDA, * ),
26* $ BETA( * ), BETA1( * ), Q( LDQ, * ),
27* $ QE( LDQE, * ), RESULT( * ), S( LDA, * ),
28* $ T( LDA, * ), WORK( * ), Z( LDQ, * )
29* ..
30*
31*
32*> \par Purpose:
33* =============
34*>
35*> \verbatim
36*>
37*> SDRGEV3 checks the nonsymmetric generalized eigenvalue problem driver
38*> routine SGGEV3.
39*>
40*> SGGEV3 computes for a pair of n-by-n nonsymmetric matrices (A,B) the
41*> generalized eigenvalues and, optionally, the left and right
42*> eigenvectors.
43*>
44*> A generalized eigenvalue for a pair of matrices (A,B) is a scalar w
45*> or a ratio alpha/beta = w, such that A - w*B is singular. It is
46*> usually represented as the pair (alpha,beta), as there is reasonable
47*> interpretation for beta=0, and even for both being zero.
48*>
49*> A right generalized eigenvector corresponding to a generalized
50*> eigenvalue w for a pair of matrices (A,B) is a vector r such that
51*> (A - wB) * r = 0. A left generalized eigenvector is a vector l such
52*> that l**H * (A - wB) = 0, where l**H is the conjugate-transpose of l.
53*>
54*> When SDRGEV3 is called, a number of matrix "sizes" ("n's") and a
55*> number of matrix "types" are specified. For each size ("n")
56*> and each type of matrix, a pair of matrices (A, B) will be generated
57*> and used for testing. For each matrix pair, the following tests
58*> will be performed and compared with the threshold THRESH.
59*>
60*> Results from SGGEV3:
61*>
62*> (1) max over all left eigenvalue/-vector pairs (alpha/beta,l) of
63*>
64*> | VL**H * (beta A - alpha B) |/( ulp max(|beta A|, |alpha B|) )
65*>
66*> where VL**H is the conjugate-transpose of VL.
67*>
68*> (2) | |VL(i)| - 1 | / ulp and whether largest component real
69*>
70*> VL(i) denotes the i-th column of VL.
71*>
72*> (3) max over all left eigenvalue/-vector pairs (alpha/beta,r) of
73*>
74*> | (beta A - alpha B) * VR | / ( ulp max(|beta A|, |alpha B|) )
75*>
76*> (4) | |VR(i)| - 1 | / ulp and whether largest component real
77*>
78*> VR(i) denotes the i-th column of VR.
79*>
80*> (5) W(full) = W(partial)
81*> W(full) denotes the eigenvalues computed when both l and r
82*> are also computed, and W(partial) denotes the eigenvalues
83*> computed when only W, only W and r, or only W and l are
84*> computed.
85*>
86*> (6) VL(full) = VL(partial)
87*> VL(full) denotes the left eigenvectors computed when both l
88*> and r are computed, and VL(partial) denotes the result
89*> when only l is computed.
90*>
91*> (7) VR(full) = VR(partial)
92*> VR(full) denotes the right eigenvectors computed when both l
93*> and r are also computed, and VR(partial) denotes the result
94*> when only l is computed.
95*>
96*>
97*> Test Matrices
98*> ---- --------
99*>
100*> The sizes of the test matrices are specified by an array
101*> NN(1:NSIZES); the value of each element NN(j) specifies one size.
102*> The "types" are specified by a logical array DOTYPE( 1:NTYPES ); if
103*> DOTYPE(j) is .TRUE., then matrix type "j" will be generated.
104*> Currently, the list of possible types is:
105*>
106*> (1) ( 0, 0 ) (a pair of zero matrices)
107*>
108*> (2) ( I, 0 ) (an identity and a zero matrix)
109*>
110*> (3) ( 0, I ) (an identity and a zero matrix)
111*>
112*> (4) ( I, I ) (a pair of identity matrices)
113*>
114*> t t
115*> (5) ( J , J ) (a pair of transposed Jordan blocks)
116*>
117*> t ( I 0 )
118*> (6) ( X, Y ) where X = ( J 0 ) and Y = ( t )
119*> ( 0 I ) ( 0 J )
120*> and I is a k x k identity and J a (k+1)x(k+1)
121*> Jordan block; k=(N-1)/2
122*>
123*> (7) ( D, I ) where D is diag( 0, 1,..., N-1 ) (a diagonal
124*> matrix with those diagonal entries.)
125*> (8) ( I, D )
126*>
127*> (9) ( big*D, small*I ) where "big" is near overflow and small=1/big
128*>
129*> (10) ( small*D, big*I )
130*>
131*> (11) ( big*I, small*D )
132*>
133*> (12) ( small*I, big*D )
134*>
135*> (13) ( big*D, big*I )
136*>
137*> (14) ( small*D, small*I )
138*>
139*> (15) ( D1, D2 ) where D1 is diag( 0, 0, 1, ..., N-3, 0 ) and
140*> D2 is diag( 0, N-3, N-4,..., 1, 0, 0 )
141*> t t
142*> (16) Q ( J , J ) Z where Q and Z are random orthogonal matrices.
143*>
144*> (17) Q ( T1, T2 ) Z where T1 and T2 are upper triangular matrices
145*> with random O(1) entries above the diagonal
146*> and diagonal entries diag(T1) =
147*> ( 0, 0, 1, ..., N-3, 0 ) and diag(T2) =
148*> ( 0, N-3, N-4,..., 1, 0, 0 )
149*>
150*> (18) Q ( T1, T2 ) Z diag(T1) = ( 0, 0, 1, 1, s, ..., s, 0 )
151*> diag(T2) = ( 0, 1, 0, 1,..., 1, 0 )
152*> s = machine precision.
153*>
154*> (19) Q ( T1, T2 ) Z diag(T1)=( 0,0,1,1, 1-d, ..., 1-(N-5)*d=s, 0 )
155*> diag(T2) = ( 0, 1, 0, 1, ..., 1, 0 )
156*>
157*> N-5
158*> (20) Q ( T1, T2 ) Z diag(T1)=( 0, 0, 1, 1, a, ..., a =s, 0 )
159*> diag(T2) = ( 0, 1, 0, 1, ..., 1, 0, 0 )
160*>
161*> (21) Q ( T1, T2 ) Z diag(T1)=( 0, 0, 1, r1, r2, ..., r(N-4), 0 )
162*> diag(T2) = ( 0, 1, 0, 1, ..., 1, 0, 0 )
163*> where r1,..., r(N-4) are random.
164*>
165*> (22) Q ( big*T1, small*T2 ) Z diag(T1) = ( 0, 0, 1, ..., N-3, 0 )
166*> diag(T2) = ( 0, 1, ..., 1, 0, 0 )
167*>
168*> (23) Q ( small*T1, big*T2 ) Z diag(T1) = ( 0, 0, 1, ..., N-3, 0 )
169*> diag(T2) = ( 0, 1, ..., 1, 0, 0 )
170*>
171*> (24) Q ( small*T1, small*T2 ) Z diag(T1) = ( 0, 0, 1, ..., N-3, 0 )
172*> diag(T2) = ( 0, 1, ..., 1, 0, 0 )
173*>
174*> (25) Q ( big*T1, big*T2 ) Z diag(T1) = ( 0, 0, 1, ..., N-3, 0 )
175*> diag(T2) = ( 0, 1, ..., 1, 0, 0 )
176*>
177*> (26) Q ( T1, T2 ) Z where T1 and T2 are random upper-triangular
178*> matrices.
179*>
180*> \endverbatim
181*
182* Arguments:
183* ==========
184*
185*> \param[in] NSIZES
186*> \verbatim
187*> NSIZES is INTEGER
188*> The number of sizes of matrices to use. If it is zero,
189*> SDRGEV3 does nothing. NSIZES >= 0.
190*> \endverbatim
191*>
192*> \param[in] NN
193*> \verbatim
194*> NN is INTEGER array, dimension (NSIZES)
195*> An array containing the sizes to be used for the matrices.
196*> Zero values will be skipped. NN >= 0.
197*> \endverbatim
198*>
199*> \param[in] NTYPES
200*> \verbatim
201*> NTYPES is INTEGER
202*> The number of elements in DOTYPE. If it is zero, SDRGEV3
203*> does nothing. It must be at least zero. If it is MAXTYP+1
204*> and NSIZES is 1, then an additional type, MAXTYP+1 is
205*> defined, which is to use whatever matrix is in A. This
206*> is only useful if DOTYPE(1:MAXTYP) is .FALSE. and
207*> DOTYPE(MAXTYP+1) is .TRUE. .
208*> \endverbatim
209*>
210*> \param[in] DOTYPE
211*> \verbatim
212*> DOTYPE is LOGICAL array, dimension (NTYPES)
213*> If DOTYPE(j) is .TRUE., then for each size in NN a
214*> matrix of that size and of type j will be generated.
215*> If NTYPES is smaller than the maximum number of types
216*> defined (PARAMETER MAXTYP), then types NTYPES+1 through
217*> MAXTYP will not be generated. If NTYPES is larger
218*> than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES)
219*> will be ignored.
220*> \endverbatim
221*>
222*> \param[in,out] ISEED
223*> \verbatim
224*> ISEED is INTEGER array, dimension (4)
225*> On entry ISEED specifies the seed of the random number
226*> generator. The array elements should be between 0 and 4095;
227*> if not they will be reduced mod 4096. Also, ISEED(4) must
228*> be odd. The random number generator uses a linear
229*> congruential sequence limited to small integers, and so
230*> should produce machine independent random numbers. The
231*> values of ISEED are changed on exit, and can be used in the
232*> next call to SDRGEV3 to continue the same random number
233*> sequence.
234*> \endverbatim
235*>
236*> \param[in] THRESH
237*> \verbatim
238*> THRESH is REAL
239*> A test will count as "failed" if the "error", computed as
240*> described above, exceeds THRESH. Note that the error is
241*> scaled to be O(1), so THRESH should be a reasonably small
242*> multiple of 1, e.g., 10 or 100. In particular, it should
243*> not depend on the precision (single vs. double) or the size
244*> of the matrix. It must be at least zero.
245*> \endverbatim
246*>
247*> \param[in] NOUNIT
248*> \verbatim
249*> NOUNIT is INTEGER
250*> The FORTRAN unit number for printing out error messages
251*> (e.g., if a routine returns IERR not equal to 0.)
252*> \endverbatim
253*>
254*> \param[in,out] A
255*> \verbatim
256*> A is REAL array,
257*> dimension(LDA, max(NN))
258*> Used to hold the original A matrix. Used as input only
259*> if NTYPES=MAXTYP+1, DOTYPE(1:MAXTYP)=.FALSE., and
260*> DOTYPE(MAXTYP+1)=.TRUE.
261*> \endverbatim
262*>
263*> \param[in] LDA
264*> \verbatim
265*> LDA is INTEGER
266*> The leading dimension of A, B, S, and T.
267*> It must be at least 1 and at least max( NN ).
268*> \endverbatim
269*>
270*> \param[in,out] B
271*> \verbatim
272*> B is REAL array,
273*> dimension(LDA, max(NN))
274*> Used to hold the original B matrix. Used as input only
275*> if NTYPES=MAXTYP+1, DOTYPE(1:MAXTYP)=.FALSE., and
276*> DOTYPE(MAXTYP+1)=.TRUE.
277*> \endverbatim
278*>
279*> \param[out] S
280*> \verbatim
281*> S is REAL array,
282*> dimension (LDA, max(NN))
283*> The Schur form matrix computed from A by SGGEV3. On exit, S
284*> contains the Schur form matrix corresponding to the matrix
285*> in A.
286*> \endverbatim
287*>
288*> \param[out] T
289*> \verbatim
290*> T is REAL array,
291*> dimension (LDA, max(NN))
292*> The upper triangular matrix computed from B by SGGEV3.
293*> \endverbatim
294*>
295*> \param[out] Q
296*> \verbatim
297*> Q is REAL array,
298*> dimension (LDQ, max(NN))
299*> The (left) eigenvectors matrix computed by SGGEV3.
300*> \endverbatim
301*>
302*> \param[in] LDQ
303*> \verbatim
304*> LDQ is INTEGER
305*> The leading dimension of Q and Z. It must
306*> be at least 1 and at least max( NN ).
307*> \endverbatim
308*>
309*> \param[out] Z
310*> \verbatim
311*> Z is REAL array, dimension( LDQ, max(NN) )
312*> The (right) orthogonal matrix computed by SGGEV3.
313*> \endverbatim
314*>
315*> \param[out] QE
316*> \verbatim
317*> QE is REAL array, dimension( LDQ, max(NN) )
318*> QE holds the computed right or left eigenvectors.
319*> \endverbatim
320*>
321*> \param[in] LDQE
322*> \verbatim
323*> LDQE is INTEGER
324*> The leading dimension of QE. LDQE >= max(1,max(NN)).
325*> \endverbatim
326*>
327*> \param[out] ALPHAR
328*> \verbatim
329*> ALPHAR is REAL array, dimension (max(NN))
330*> \endverbatim
331*>
332*> \param[out] ALPHAI
333*> \verbatim
334*> ALPHAI is REAL array, dimension (max(NN))
335*> \endverbatim
336*>
337*> \param[out] BETA
338*> \verbatim
339*> BETA is REAL array, dimension (max(NN))
340*> \verbatim
341*> The generalized eigenvalues of (A,B) computed by SGGEV3.
342*> ( ALPHAR(k)+ALPHAI(k)*i ) / BETA(k) is the k-th
343*> generalized eigenvalue of A and B.
344*> \endverbatim
345*>
346*> \param[out] ALPHR1
347*> \verbatim
348*> ALPHR1 is REAL array, dimension (max(NN))
349*> \endverbatim
350*>
351*> \param[out] ALPHI1
352*> \verbatim
353*> ALPHI1 is REAL array, dimension (max(NN))
354*> \endverbatim
355*>
356*> \param[out] BETA1
357*> \verbatim
358*> BETA1 is REAL array, dimension (max(NN))
359*>
360*> Like ALPHAR, ALPHAI, BETA, these arrays contain the
361*> eigenvalues of A and B, but those computed when SGGEV3 only
362*> computes a partial eigendecomposition, i.e. not the
363*> eigenvalues and left and right eigenvectors.
364*> \endverbatim
365*>
366*> \param[out] WORK
367*> \verbatim
368*> WORK is REAL array, dimension (LWORK)
369*> \endverbatim
370*>
371*> \param[in] LWORK
372*> \verbatim
373*> LWORK is INTEGER
374*> The number of entries in WORK. LWORK >= MAX( 8*N, N*(N+1) ).
375*> \endverbatim
376*>
377*> \param[out] RESULT
378*> \verbatim
379*> RESULT is REAL array, dimension (2)
380*> The values computed by the tests described above.
381*> The values are currently limited to 1/ulp, to avoid overflow.
382*> \endverbatim
383*>
384*> \param[out] INFO
385*> \verbatim
386*> INFO is INTEGER
387*> = 0: successful exit
388*> < 0: if INFO = -i, the i-th argument had an illegal value.
389*> > 0: A routine returned an error code. INFO is the
390*> absolute value of the INFO value returned.
391*> \endverbatim
392*
393* Authors:
394* ========
395*
396*> \author Univ. of Tennessee
397*> \author Univ. of California Berkeley
398*> \author Univ. of Colorado Denver
399*> \author NAG Ltd.
400*
401*> \ingroup single_eig
402*
403* =====================================================================
404 SUBROUTINE sdrgev3( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
405 $ NOUNIT, A, LDA, B, S, T, Q, LDQ, Z, QE, LDQE,
406 $ ALPHAR, ALPHAI, BETA, ALPHR1, ALPHI1, BETA1,
407 $ WORK, LWORK, RESULT, INFO )
408*
409* -- LAPACK test routine --
410* -- LAPACK is a software package provided by Univ. of Tennessee, --
411* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
412*
413* .. Scalar Arguments ..
414 INTEGER INFO, LDA, LDQ, LDQE, LWORK, NOUNIT, NSIZES,
415 $ NTYPES
416 REAL THRESH
417* ..
418* .. Array Arguments ..
419 LOGICAL DOTYPE( * )
420 INTEGER ISEED( 4 ), NN( * )
421 REAL A( LDA, * ), ALPHAI( * ), ALPHI1( * ),
422 $ alphar( * ), alphr1( * ), b( lda, * ),
423 $ beta( * ), beta1( * ), q( ldq, * ),
424 $ qe( ldqe, * ), result( * ), s( lda, * ),
425 $ t( lda, * ), work( * ), z( ldq, * )
426* ..
427*
428* =====================================================================
429*
430* .. Parameters ..
431 REAL ZERO, ONE
432 PARAMETER ( ZERO = 0.0e+0, one = 1.0e+0 )
433 INTEGER MAXTYP
434 parameter( maxtyp = 26 )
435* ..
436* .. Local Scalars ..
437 LOGICAL BADNN
438 INTEGER I, IADD, IERR, IN, J, JC, JR, JSIZE, JTYPE,
439 $ MAXWRK, MINWRK, MTYPES, N, N1, NERRS, NMATS,
440 $ nmax, ntestt
441 REAL SAFMAX, SAFMIN, ULP, ULPINV
442* ..
443* .. Local Arrays ..
444 INTEGER IASIGN( MAXTYP ), IBSIGN( MAXTYP ),
445 $ IOLDSD( 4 ), KADD( 6 ), KAMAGN( MAXTYP ),
446 $ KATYPE( MAXTYP ), KAZERO( MAXTYP ),
447 $ kbmagn( maxtyp ), kbtype( maxtyp ),
448 $ kbzero( maxtyp ), kclass( maxtyp ),
449 $ ktrian( maxtyp ), kz1( 6 ), kz2( 6 )
450 REAL RMAGN( 0: 3 )
451* ..
452* .. External Functions ..
453 INTEGER ILAENV
454 REAL SLAMCH, SLARND
455 EXTERNAL ILAENV, SLAMCH, SLARND
456* ..
457* .. External Subroutines ..
458 EXTERNAL alasvm, sget52, sggev3, slabad, slacpy, slarfg,
460* ..
461* .. Intrinsic Functions ..
462 INTRINSIC abs, max, min, real, sign
463* ..
464* .. Data statements ..
465 DATA kclass / 15*1, 10*2, 1*3 /
466 DATA kz1 / 0, 1, 2, 1, 3, 3 /
467 DATA kz2 / 0, 0, 1, 2, 1, 1 /
468 DATA kadd / 0, 0, 0, 0, 3, 2 /
469 DATA katype / 0, 1, 0, 1, 2, 3, 4, 1, 4, 4, 1, 1, 4,
470 $ 4, 4, 2, 4, 5, 8, 7, 9, 4*4, 0 /
471 DATA kbtype / 0, 0, 1, 1, 2, -3, 1, 4, 1, 1, 4, 4,
472 $ 1, 1, -4, 2, -4, 8*8, 0 /
473 DATA kazero / 6*1, 2, 1, 2*2, 2*1, 2*2, 3, 1, 3,
474 $ 4*5, 4*3, 1 /
475 DATA kbzero / 6*1, 1, 2, 2*1, 2*2, 2*1, 4, 1, 4,
476 $ 4*6, 4*4, 1 /
477 DATA kamagn / 8*1, 2, 3, 2, 3, 2, 3, 7*1, 2, 3, 3,
478 $ 2, 1 /
479 DATA kbmagn / 8*1, 3, 2, 3, 2, 2, 3, 7*1, 3, 2, 3,
480 $ 2, 1 /
481 DATA ktrian / 16*0, 10*1 /
482 DATA iasign / 6*0, 2, 0, 2*2, 2*0, 3*2, 0, 2, 3*0,
483 $ 5*2, 0 /
484 DATA ibsign / 7*0, 2, 2*0, 2*2, 2*0, 2, 0, 2, 9*0 /
485* ..
486* .. Executable Statements ..
487*
488* Check for errors
489*
490 info = 0
491*
492 badnn = .false.
493 nmax = 1
494 DO 10 j = 1, nsizes
495 nmax = max( nmax, nn( j ) )
496 IF( nn( j ).LT.0 )
497 $ badnn = .true.
498 10 CONTINUE
499*
500 IF( nsizes.LT.0 ) THEN
501 info = -1
502 ELSE IF( badnn ) THEN
503 info = -2
504 ELSE IF( ntypes.LT.0 ) THEN
505 info = -3
506 ELSE IF( thresh.LT.zero ) THEN
507 info = -6
508 ELSE IF( lda.LE.1 .OR. lda.LT.nmax ) THEN
509 info = -9
510 ELSE IF( ldq.LE.1 .OR. ldq.LT.nmax ) THEN
511 info = -14
512 ELSE IF( ldqe.LE.1 .OR. ldqe.LT.nmax ) THEN
513 info = -17
514 END IF
515*
516* Compute workspace
517* (Note: Comments in the code beginning "Workspace:" describe the
518* minimal amount of workspace needed at that point in the code,
519* as well as the preferred amount for good performance.
520* NB refers to the optimal block size for the immediately
521* following subroutine, as returned by ILAENV.
522*
523 minwrk = 1
524 IF( info.EQ.0 .AND. lwork.GE.1 ) THEN
525 minwrk = max( 1, 8*nmax, nmax*( nmax+1 ) )
526 maxwrk = 7*nmax + nmax*ilaenv( 1, 'SGEQRF', ' ', nmax, 1, nmax,
527 $ 0 )
528 maxwrk = max( maxwrk, nmax*( nmax+1 ) )
529 work( 1 ) = maxwrk
530 END IF
531*
532 IF( lwork.LT.minwrk )
533 $ info = -25
534*
535 IF( info.NE.0 ) THEN
536 CALL xerbla( 'SDRGEV3', -info )
537 RETURN
538 END IF
539*
540* Quick return if possible
541*
542 IF( nsizes.EQ.0 .OR. ntypes.EQ.0 )
543 $ RETURN
544*
545 safmin = slamch( 'Safe minimum' )
546 ulp = slamch( 'Epsilon' )*slamch( 'Base' )
547 safmin = safmin / ulp
548 safmax = one / safmin
549 CALL slabad( safmin, safmax )
550 ulpinv = one / ulp
551*
552* The values RMAGN(2:3) depend on N, see below.
553*
554 rmagn( 0 ) = zero
555 rmagn( 1 ) = one
556*
557* Loop over sizes, types
558*
559 ntestt = 0
560 nerrs = 0
561 nmats = 0
562*
563 DO 220 jsize = 1, nsizes
564 n = nn( jsize )
565 n1 = max( 1, n )
566 rmagn( 2 ) = safmax*ulp / real( n1 )
567 rmagn( 3 ) = safmin*ulpinv*n1
568*
569 IF( nsizes.NE.1 ) THEN
570 mtypes = min( maxtyp, ntypes )
571 ELSE
572 mtypes = min( maxtyp+1, ntypes )
573 END IF
574*
575 DO 210 jtype = 1, mtypes
576 IF( .NOT.dotype( jtype ) )
577 $ GO TO 210
578 nmats = nmats + 1
579*
580* Save ISEED in case of an error.
581*
582 DO 20 j = 1, 4
583 ioldsd( j ) = iseed( j )
584 20 CONTINUE
585*
586* Generate test matrices A and B
587*
588* Description of control parameters:
589*
590* KCLASS: =1 means w/o rotation, =2 means w/ rotation,
591* =3 means random.
592* KATYPE: the "type" to be passed to SLATM4 for computing A.
593* KAZERO: the pattern of zeros on the diagonal for A:
594* =1: ( xxx ), =2: (0, xxx ) =3: ( 0, 0, xxx, 0 ),
595* =4: ( 0, xxx, 0, 0 ), =5: ( 0, 0, 1, xxx, 0 ),
596* =6: ( 0, 1, 0, xxx, 0 ). (xxx means a string of
597* non-zero entries.)
598* KAMAGN: the magnitude of the matrix: =0: zero, =1: O(1),
599* =2: large, =3: small.
600* IASIGN: 1 if the diagonal elements of A are to be
601* multiplied by a random magnitude 1 number, =2 if
602* randomly chosen diagonal blocks are to be rotated
603* to form 2x2 blocks.
604* KBTYPE, KBZERO, KBMAGN, IBSIGN: the same, but for B.
605* KTRIAN: =0: don't fill in the upper triangle, =1: do.
606* KZ1, KZ2, KADD: used to implement KAZERO and KBZERO.
607* RMAGN: used to implement KAMAGN and KBMAGN.
608*
609 IF( mtypes.GT.maxtyp )
610 $ GO TO 100
611 ierr = 0
612 IF( kclass( jtype ).LT.3 ) THEN
613*
614* Generate A (w/o rotation)
615*
616 IF( abs( katype( jtype ) ).EQ.3 ) THEN
617 in = 2*( ( n-1 ) / 2 ) + 1
618 IF( in.NE.n )
619 $ CALL slaset( 'Full', n, n, zero, zero, a, lda )
620 ELSE
621 in = n
622 END IF
623 CALL slatm4( katype( jtype ), in, kz1( kazero( jtype ) ),
624 $ kz2( kazero( jtype ) ), iasign( jtype ),
625 $ rmagn( kamagn( jtype ) ), ulp,
626 $ rmagn( ktrian( jtype )*kamagn( jtype ) ), 2,
627 $ iseed, a, lda )
628 iadd = kadd( kazero( jtype ) )
629 IF( iadd.GT.0 .AND. iadd.LE.n )
630 $ a( iadd, iadd ) = one
631*
632* Generate B (w/o rotation)
633*
634 IF( abs( kbtype( jtype ) ).EQ.3 ) THEN
635 in = 2*( ( n-1 ) / 2 ) + 1
636 IF( in.NE.n )
637 $ CALL slaset( 'Full', n, n, zero, zero, b, lda )
638 ELSE
639 in = n
640 END IF
641 CALL slatm4( kbtype( jtype ), in, kz1( kbzero( jtype ) ),
642 $ kz2( kbzero( jtype ) ), ibsign( jtype ),
643 $ rmagn( kbmagn( jtype ) ), one,
644 $ rmagn( ktrian( jtype )*kbmagn( jtype ) ), 2,
645 $ iseed, b, lda )
646 iadd = kadd( kbzero( jtype ) )
647 IF( iadd.NE.0 .AND. iadd.LE.n )
648 $ b( iadd, iadd ) = one
649*
650 IF( kclass( jtype ).EQ.2 .AND. n.GT.0 ) THEN
651*
652* Include rotations
653*
654* Generate Q, Z as Householder transformations times
655* a diagonal matrix.
656*
657 DO 40 jc = 1, n - 1
658 DO 30 jr = jc, n
659 q( jr, jc ) = slarnd( 3, iseed )
660 z( jr, jc ) = slarnd( 3, iseed )
661 30 CONTINUE
662 CALL slarfg( n+1-jc, q( jc, jc ), q( jc+1, jc ), 1,
663 $ work( jc ) )
664 work( 2*n+jc ) = sign( one, q( jc, jc ) )
665 q( jc, jc ) = one
666 CALL slarfg( n+1-jc, z( jc, jc ), z( jc+1, jc ), 1,
667 $ work( n+jc ) )
668 work( 3*n+jc ) = sign( one, z( jc, jc ) )
669 z( jc, jc ) = one
670 40 CONTINUE
671 q( n, n ) = one
672 work( n ) = zero
673 work( 3*n ) = sign( one, slarnd( 2, iseed ) )
674 z( n, n ) = one
675 work( 2*n ) = zero
676 work( 4*n ) = sign( one, slarnd( 2, iseed ) )
677*
678* Apply the diagonal matrices
679*
680 DO 60 jc = 1, n
681 DO 50 jr = 1, n
682 a( jr, jc ) = work( 2*n+jr )*work( 3*n+jc )*
683 $ a( jr, jc )
684 b( jr, jc ) = work( 2*n+jr )*work( 3*n+jc )*
685 $ b( jr, jc )
686 50 CONTINUE
687 60 CONTINUE
688 CALL sorm2r( 'L', 'N', n, n, n-1, q, ldq, work, a,
689 $ lda, work( 2*n+1 ), ierr )
690 IF( ierr.NE.0 )
691 $ GO TO 90
692 CALL sorm2r( 'R', 'T', n, n, n-1, z, ldq, work( n+1 ),
693 $ a, lda, work( 2*n+1 ), ierr )
694 IF( ierr.NE.0 )
695 $ GO TO 90
696 CALL sorm2r( 'L', 'N', n, n, n-1, q, ldq, work, b,
697 $ lda, work( 2*n+1 ), ierr )
698 IF( ierr.NE.0 )
699 $ GO TO 90
700 CALL sorm2r( 'R', 'T', n, n, n-1, z, ldq, work( n+1 ),
701 $ b, lda, work( 2*n+1 ), ierr )
702 IF( ierr.NE.0 )
703 $ GO TO 90
704 END IF
705 ELSE
706*
707* Random matrices
708*
709 DO 80 jc = 1, n
710 DO 70 jr = 1, n
711 a( jr, jc ) = rmagn( kamagn( jtype ) )*
712 $ slarnd( 2, iseed )
713 b( jr, jc ) = rmagn( kbmagn( jtype ) )*
714 $ slarnd( 2, iseed )
715 70 CONTINUE
716 80 CONTINUE
717 END IF
718*
719 90 CONTINUE
720*
721 IF( ierr.NE.0 ) THEN
722 WRITE( nounit, fmt = 9999 )'Generator', ierr, n, jtype,
723 $ ioldsd
724 info = abs( ierr )
725 RETURN
726 END IF
727*
728 100 CONTINUE
729*
730 DO 110 i = 1, 7
731 result( i ) = -one
732 110 CONTINUE
733*
734* Call XLAENV to set the parameters used in SLAQZ0
735*
736 CALL xlaenv( 12, 10 )
737 CALL xlaenv( 13, 12 )
738 CALL xlaenv( 14, 13 )
739 CALL xlaenv( 15, 2 )
740 CALL xlaenv( 17, 10 )
741*
742* Call SGGEV3 to compute eigenvalues and eigenvectors.
743*
744 CALL slacpy( ' ', n, n, a, lda, s, lda )
745 CALL slacpy( ' ', n, n, b, lda, t, lda )
746 CALL sggev3( 'V', 'V', n, s, lda, t, lda, alphar, alphai,
747 $ beta, q, ldq, z, ldq, work, lwork, ierr )
748 IF( ierr.NE.0 .AND. ierr.NE.n+1 ) THEN
749 result( 1 ) = ulpinv
750 WRITE( nounit, fmt = 9999 )'SGGEV31', ierr, n, jtype,
751 $ ioldsd
752 info = abs( ierr )
753 GO TO 190
754 END IF
755*
756* Do the tests (1) and (2)
757*
758 CALL sget52( .true., n, a, lda, b, lda, q, ldq, alphar,
759 $ alphai, beta, work, result( 1 ) )
760 IF( result( 2 ).GT.thresh ) THEN
761 WRITE( nounit, fmt = 9998 )'Left', 'SGGEV31',
762 $ result( 2 ), n, jtype, ioldsd
763 END IF
764*
765* Do the tests (3) and (4)
766*
767 CALL sget52( .false., n, a, lda, b, lda, z, ldq, alphar,
768 $ alphai, beta, work, result( 3 ) )
769 IF( result( 4 ).GT.thresh ) THEN
770 WRITE( nounit, fmt = 9998 )'Right', 'SGGEV31',
771 $ result( 4 ), n, jtype, ioldsd
772 END IF
773*
774* Do the test (5)
775*
776 CALL slacpy( ' ', n, n, a, lda, s, lda )
777 CALL slacpy( ' ', n, n, b, lda, t, lda )
778 CALL sggev3( 'N', 'N', n, s, lda, t, lda, alphr1, alphi1,
779 $ beta1, q, ldq, z, ldq, work, lwork, ierr )
780 IF( ierr.NE.0 .AND. ierr.NE.n+1 ) THEN
781 result( 1 ) = ulpinv
782 WRITE( nounit, fmt = 9999 )'SGGEV32', ierr, n, jtype,
783 $ ioldsd
784 info = abs( ierr )
785 GO TO 190
786 END IF
787*
788 DO 120 j = 1, n
789 IF( alphar( j ).NE.alphr1( j ) .OR.
790 $ beta( j ).NE. beta1( j ) ) THEN
791 result( 5 ) = ulpinv
792 END IF
793 120 CONTINUE
794*
795* Do the test (6): Compute eigenvalues and left eigenvectors,
796* and test them
797*
798 CALL slacpy( ' ', n, n, a, lda, s, lda )
799 CALL slacpy( ' ', n, n, b, lda, t, lda )
800 CALL sggev3( 'V', 'N', n, s, lda, t, lda, alphr1, alphi1,
801 $ beta1, qe, ldqe, z, ldq, work, lwork, ierr )
802 IF( ierr.NE.0 .AND. ierr.NE.n+1 ) THEN
803 result( 1 ) = ulpinv
804 WRITE( nounit, fmt = 9999 )'SGGEV33', ierr, n, jtype,
805 $ ioldsd
806 info = abs( ierr )
807 GO TO 190
808 END IF
809*
810 DO 130 j = 1, n
811 IF( alphar( j ).NE.alphr1( j ) .OR. alphai( j ).NE.
812 $ alphi1( j ) .OR. beta( j ).NE.beta1( j ) )
813 $ result( 6 ) = ulpinv
814 130 CONTINUE
815*
816 DO 150 j = 1, n
817 DO 140 jc = 1, n
818 IF( q( j, jc ).NE.qe( j, jc ) )
819 $ result( 6 ) = ulpinv
820 140 CONTINUE
821 150 CONTINUE
822*
823* DO the test (7): Compute eigenvalues and right eigenvectors,
824* and test them
825*
826 CALL slacpy( ' ', n, n, a, lda, s, lda )
827 CALL slacpy( ' ', n, n, b, lda, t, lda )
828 CALL sggev3( 'N', 'V', n, s, lda, t, lda, alphr1, alphi1,
829 $ beta1, q, ldq, qe, ldqe, work, lwork, ierr )
830 IF( ierr.NE.0 .AND. ierr.NE.n+1 ) THEN
831 result( 1 ) = ulpinv
832 WRITE( nounit, fmt = 9999 )'SGGEV34', ierr, n, jtype,
833 $ ioldsd
834 info = abs( ierr )
835 GO TO 190
836 END IF
837*
838 DO 160 j = 1, n
839 IF( alphar( j ).NE.alphr1( j ) .OR. alphai( j ).NE.
840 $ alphi1( j ) .OR. beta( j ).NE.beta1( j ) )
841 $ result( 7 ) = ulpinv
842 160 CONTINUE
843*
844 DO 180 j = 1, n
845 DO 170 jc = 1, n
846 IF( z( j, jc ).NE.qe( j, jc ) )
847 $ result( 7 ) = ulpinv
848 170 CONTINUE
849 180 CONTINUE
850*
851* End of Loop -- Check for RESULT(j) > THRESH
852*
853 190 CONTINUE
854*
855 ntestt = ntestt + 7
856*
857* Print out tests which fail.
858*
859 DO 200 jr = 1, 7
860 IF( result( jr ).GE.thresh ) THEN
861*
862* If this is the first test to fail,
863* print a header to the data file.
864*
865 IF( nerrs.EQ.0 ) THEN
866 WRITE( nounit, fmt = 9997 )'SGV'
867*
868* Matrix types
869*
870 WRITE( nounit, fmt = 9996 )
871 WRITE( nounit, fmt = 9995 )
872 WRITE( nounit, fmt = 9994 )'Orthogonal'
873*
874* Tests performed
875*
876 WRITE( nounit, fmt = 9993 )
877*
878 END IF
879 nerrs = nerrs + 1
880 IF( result( jr ).LT.10000.0 ) THEN
881 WRITE( nounit, fmt = 9992 )n, jtype, ioldsd, jr,
882 $ result( jr )
883 ELSE
884 WRITE( nounit, fmt = 9991 )n, jtype, ioldsd, jr,
885 $ result( jr )
886 END IF
887 END IF
888 200 CONTINUE
889*
890 210 CONTINUE
891 220 CONTINUE
892*
893* Summary
894*
895 CALL alasvm( 'SGV', nounit, nerrs, ntestt, 0 )
896*
897 work( 1 ) = maxwrk
898*
899 RETURN
900*
901 9999 FORMAT( ' SDRGEV3: ', a, ' returned INFO=', i6, '.', / 3x, 'N=',
902 $ i6, ', JTYPE=', i6, ', ISEED=(', 4( i4, ',' ), i5, ')' )
903*
904 9998 FORMAT( ' SDRGEV3: ', a, ' Eigenvectors from ', a,
905 $ ' incorrectly normalized.', / ' Bits of error=', 0p, g10.3,
906 $ ',', 3x, 'N=', i4, ', JTYPE=', i3, ', ISEED=(',
907 $ 4( i4, ',' ), i5, ')' )
908*
909 9997 FORMAT( / 1x, a3, ' -- Real Generalized eigenvalue problem driver'
910 $ )
911*
912 9996 FORMAT( ' Matrix types (see SDRGEV3 for details): ' )
913*
914 9995 FORMAT( ' Special Matrices:', 23x,
915 $ '(J''=transposed Jordan block)',
916 $ / ' 1=(0,0) 2=(I,0) 3=(0,I) 4=(I,I) 5=(J'',J'') ',
917 $ '6=(diag(J'',I), diag(I,J''))', / ' Diagonal Matrices: ( ',
918 $ 'D=diag(0,1,2,...) )', / ' 7=(D,I) 9=(large*D, small*I',
919 $ ') 11=(large*I, small*D) 13=(large*D, large*I)', /
920 $ ' 8=(I,D) 10=(small*D, large*I) 12=(small*I, large*D) ',
921 $ ' 14=(small*D, small*I)', / ' 15=(D, reversed D)' )
922 9994 FORMAT( ' Matrices Rotated by Random ', a, ' Matrices U, V:',
923 $ / ' 16=Transposed Jordan Blocks 19=geometric ',
924 $ 'alpha, beta=0,1', / ' 17=arithm. alpha&beta ',
925 $ ' 20=arithmetic alpha, beta=0,1', / ' 18=clustered ',
926 $ 'alpha, beta=0,1 21=random alpha, beta=0,1',
927 $ / ' Large & Small Matrices:', / ' 22=(large, small) ',
928 $ '23=(small,large) 24=(small,small) 25=(large,large)',
929 $ / ' 26=random O(1) matrices.' )
930*
931 9993 FORMAT( / ' Tests performed: ',
932 $ / ' 1 = max | ( b A - a B )''*l | / const.,',
933 $ / ' 2 = | |VR(i)| - 1 | / ulp,',
934 $ / ' 3 = max | ( b A - a B )*r | / const.',
935 $ / ' 4 = | |VL(i)| - 1 | / ulp,',
936 $ / ' 5 = 0 if W same no matter if r or l computed,',
937 $ / ' 6 = 0 if l same no matter if l computed,',
938 $ / ' 7 = 0 if r same no matter if r computed,', / 1x )
939 9992 FORMAT( ' Matrix order=', i5, ', type=', i2, ', seed=',
940 $ 4( i4, ',' ), ' result ', i2, ' is', 0p, f8.2 )
941 9991 FORMAT( ' Matrix order=', i5, ', type=', i2, ', seed=',
942 $ 4( i4, ',' ), ' result ', i2, ' is', 1p, e10.3 )
943*
944* End of SDRGEV3
945*
946 END
subroutine slabad(SMALL, LARGE)
SLABAD
Definition: slabad.f:74
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 slacpy(UPLO, M, N, A, LDA, B, LDB)
SLACPY copies all or part of one two-dimensional array to another.
Definition: slacpy.f:103
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine alasvm(TYPE, NOUT, NFAIL, NRUN, NERRS)
ALASVM
Definition: alasvm.f:73
subroutine xlaenv(ISPEC, NVALUE)
XLAENV
Definition: xlaenv.f:81
subroutine sggev3(JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHAR, ALPHAI, BETA, VL, LDVL, VR, LDVR, WORK, LWORK, INFO)
SGGEV3 computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices (...
Definition: sggev3.f:226
subroutine slarfg(N, ALPHA, X, INCX, TAU)
SLARFG generates an elementary reflector (Householder matrix).
Definition: slarfg.f:106
subroutine sorm2r(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, INFO)
SORM2R multiplies a general matrix by the orthogonal matrix from a QR factorization determined by sge...
Definition: sorm2r.f:159
subroutine sdrgev3(NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH, NOUNIT, A, LDA, B, S, T, Q, LDQ, Z, QE, LDQE, ALPHAR, ALPHAI, BETA, ALPHR1, ALPHI1, BETA1, WORK, LWORK, RESULT, INFO)
SDRGEV3
Definition: sdrgev3.f:408
subroutine sget52(LEFT, N, A, LDA, B, LDB, E, LDE, ALPHAR, ALPHAI, BETA, WORK, RESULT)
SGET52
Definition: sget52.f:199
subroutine slatm4(ITYPE, N, NZ1, NZ2, ISIGN, AMAGN, RCOND, TRIANG, IDIST, ISEED, A, LDA)
SLATM4
Definition: slatm4.f:175