LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
dget23.f
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1 *> \brief \b DGET23
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 DGET23( COMP, BALANC, JTYPE, THRESH, ISEED, NOUNIT, N,
12 * A, LDA, H, WR, WI, WR1, WI1, VL, LDVL, VR,
13 * LDVR, LRE, LDLRE, RCONDV, RCNDV1, RCDVIN,
14 * RCONDE, RCNDE1, RCDEIN, SCALE, SCALE1, RESULT,
15 * WORK, LWORK, IWORK, INFO )
16 *
17 * .. Scalar Arguments ..
18 * LOGICAL COMP
19 * CHARACTER BALANC
20 * INTEGER INFO, JTYPE, LDA, LDLRE, LDVL, LDVR, LWORK, N,
21 * \$ NOUNIT
22 * DOUBLE PRECISION THRESH
23 * ..
24 * .. Array Arguments ..
25 * INTEGER ISEED( 4 ), IWORK( * )
26 * DOUBLE PRECISION A( LDA, * ), H( LDA, * ), LRE( LDLRE, * ),
27 * \$ RCDEIN( * ), RCDVIN( * ), RCNDE1( * ),
28 * \$ RCNDV1( * ), RCONDE( * ), RCONDV( * ),
29 * \$ RESULT( 11 ), SCALE( * ), SCALE1( * ),
30 * \$ VL( LDVL, * ), VR( LDVR, * ), WI( * ),
31 * \$ WI1( * ), WORK( * ), WR( * ), WR1( * )
32 * ..
33 *
34 *
35 *> \par Purpose:
36 * =============
37 *>
38 *> \verbatim
39 *>
40 *> DGET23 checks the nonsymmetric eigenvalue problem driver SGEEVX.
41 *> If COMP = .FALSE., the first 8 of the following tests will be
42 *> performed on the input matrix A, and also test 9 if LWORK is
43 *> sufficiently large.
44 *> if COMP is .TRUE. all 11 tests will be performed.
45 *>
46 *> (1) | A * VR - VR * W | / ( n |A| ulp )
47 *>
48 *> Here VR is the matrix of unit right eigenvectors.
49 *> W is a block diagonal matrix, with a 1x1 block for each
50 *> real eigenvalue and a 2x2 block for each complex conjugate
51 *> pair. If eigenvalues j and j+1 are a complex conjugate pair,
52 *> so WR(j) = WR(j+1) = wr and WI(j) = - WI(j+1) = wi, then the
53 *> 2 x 2 block corresponding to the pair will be:
54 *>
55 *> ( wr wi )
56 *> ( -wi wr )
57 *>
58 *> Such a block multiplying an n x 2 matrix ( ur ui ) on the
59 *> right will be the same as multiplying ur + i*ui by wr + i*wi.
60 *>
61 *> (2) | A**H * VL - VL * W**H | / ( n |A| ulp )
62 *>
63 *> Here VL is the matrix of unit left eigenvectors, A**H is the
64 *> conjugate transpose of A, and W is as above.
65 *>
66 *> (3) | |VR(i)| - 1 | / ulp and largest component real
67 *>
68 *> VR(i) denotes the i-th column of VR.
69 *>
70 *> (4) | |VL(i)| - 1 | / ulp and largest component real
71 *>
72 *> VL(i) denotes the i-th column of VL.
73 *>
74 *> (5) 0 if W(full) = W(partial), 1/ulp otherwise
75 *>
76 *> W(full) denotes the eigenvalues computed when VR, VL, RCONDV
77 *> and RCONDE are also computed, and W(partial) denotes the
78 *> eigenvalues computed when only some of VR, VL, RCONDV, and
79 *> RCONDE are computed.
80 *>
81 *> (6) 0 if VR(full) = VR(partial), 1/ulp otherwise
82 *>
83 *> VR(full) denotes the right eigenvectors computed when VL, RCONDV
84 *> and RCONDE are computed, and VR(partial) denotes the result
85 *> when only some of VL and RCONDV are computed.
86 *>
87 *> (7) 0 if VL(full) = VL(partial), 1/ulp otherwise
88 *>
89 *> VL(full) denotes the left eigenvectors computed when VR, RCONDV
90 *> and RCONDE are computed, and VL(partial) denotes the result
91 *> when only some of VR and RCONDV are computed.
92 *>
93 *> (8) 0 if SCALE, ILO, IHI, ABNRM (full) =
94 *> SCALE, ILO, IHI, ABNRM (partial)
95 *> 1/ulp otherwise
96 *>
97 *> SCALE, ILO, IHI and ABNRM describe how the matrix is balanced.
98 *> (full) is when VR, VL, RCONDE and RCONDV are also computed, and
99 *> (partial) is when some are not computed.
100 *>
101 *> (9) 0 if RCONDV(full) = RCONDV(partial), 1/ulp otherwise
102 *>
103 *> RCONDV(full) denotes the reciprocal condition numbers of the
104 *> right eigenvectors computed when VR, VL and RCONDE are also
105 *> computed. RCONDV(partial) denotes the reciprocal condition
106 *> numbers when only some of VR, VL and RCONDE are computed.
107 *>
108 *> (10) |RCONDV - RCDVIN| / cond(RCONDV)
109 *>
110 *> RCONDV is the reciprocal right eigenvector condition number
111 *> computed by DGEEVX and RCDVIN (the precomputed true value)
112 *> is supplied as input. cond(RCONDV) is the condition number of
113 *> RCONDV, and takes errors in computing RCONDV into account, so
114 *> that the resulting quantity should be O(ULP). cond(RCONDV) is
115 *> essentially given by norm(A)/RCONDE.
116 *>
117 *> (11) |RCONDE - RCDEIN| / cond(RCONDE)
118 *>
119 *> RCONDE is the reciprocal eigenvalue condition number
120 *> computed by DGEEVX and RCDEIN (the precomputed true value)
121 *> is supplied as input. cond(RCONDE) is the condition number
122 *> of RCONDE, and takes errors in computing RCONDE into account,
123 *> so that the resulting quantity should be O(ULP). cond(RCONDE)
124 *> is essentially given by norm(A)/RCONDV.
125 *> \endverbatim
126 *
127 * Arguments:
128 * ==========
129 *
130 *> \param[in] COMP
131 *> \verbatim
132 *> COMP is LOGICAL
133 *> COMP describes which input tests to perform:
134 *> = .FALSE. if the computed condition numbers are not to
135 *> be tested against RCDVIN and RCDEIN
136 *> = .TRUE. if they are to be compared
137 *> \endverbatim
138 *>
139 *> \param[in] BALANC
140 *> \verbatim
141 *> BALANC is CHARACTER
142 *> Describes the balancing option to be tested.
143 *> = 'N' for no permuting or diagonal scaling
144 *> = 'P' for permuting but no diagonal scaling
145 *> = 'S' for no permuting but diagonal scaling
146 *> = 'B' for permuting and diagonal scaling
147 *> \endverbatim
148 *>
149 *> \param[in] JTYPE
150 *> \verbatim
151 *> JTYPE is INTEGER
152 *> Type of input matrix. Used to label output if error occurs.
153 *> \endverbatim
154 *>
155 *> \param[in] THRESH
156 *> \verbatim
157 *> THRESH is DOUBLE PRECISION
158 *> A test will count as "failed" if the "error", computed as
159 *> described above, exceeds THRESH. Note that the error
160 *> is scaled to be O(1), so THRESH should be a reasonably
161 *> small multiple of 1, e.g., 10 or 100. In particular,
162 *> it should not depend on the precision (single vs. double)
163 *> or the size of the matrix. It must be at least zero.
164 *> \endverbatim
165 *>
166 *> \param[in] ISEED
167 *> \verbatim
168 *> ISEED is INTEGER array, dimension (4)
169 *> If COMP = .FALSE., the random number generator seed
170 *> used to produce matrix.
171 *> If COMP = .TRUE., ISEED(1) = the number of the example.
172 *> Used to label output if error occurs.
173 *> \endverbatim
174 *>
175 *> \param[in] NOUNIT
176 *> \verbatim
177 *> NOUNIT is INTEGER
178 *> The FORTRAN unit number for printing out error messages
179 *> (e.g., if a routine returns INFO not equal to 0.)
180 *> \endverbatim
181 *>
182 *> \param[in] N
183 *> \verbatim
184 *> N is INTEGER
185 *> The dimension of A. N must be at least 0.
186 *> \endverbatim
187 *>
188 *> \param[in,out] A
189 *> \verbatim
190 *> A is DOUBLE PRECISION array, dimension (LDA,N)
191 *> Used to hold the matrix whose eigenvalues are to be
192 *> computed.
193 *> \endverbatim
194 *>
195 *> \param[in] LDA
196 *> \verbatim
197 *> LDA is INTEGER
198 *> The leading dimension of A, and H. LDA must be at
199 *> least 1 and at least N.
200 *> \endverbatim
201 *>
202 *> \param[out] H
203 *> \verbatim
204 *> H is DOUBLE PRECISION array, dimension (LDA,N)
205 *> Another copy of the test matrix A, modified by DGEEVX.
206 *> \endverbatim
207 *>
208 *> \param[out] WR
209 *> \verbatim
210 *> WR is DOUBLE PRECISION array, dimension (N)
211 *> \endverbatim
212 *>
213 *> \param[out] WI
214 *> \verbatim
215 *> WI is DOUBLE PRECISION array, dimension (N)
216 *>
217 *> The real and imaginary parts of the eigenvalues of A.
218 *> On exit, WR + WI*i are the eigenvalues of the matrix in A.
219 *> \endverbatim
220 *>
221 *> \param[out] WR1
222 *> \verbatim
223 *> WR1 is DOUBLE PRECISION array, dimension (N)
224 *> \endverbatim
225 *>
226 *> \param[out] WI1
227 *> \verbatim
228 *> WI1 is DOUBLE PRECISION array, dimension (N)
229 *>
230 *> Like WR, WI, these arrays contain the eigenvalues of A,
231 *> but those computed when DGEEVX only computes a partial
232 *> eigendecomposition, i.e. not the eigenvalues and left
233 *> and right eigenvectors.
234 *> \endverbatim
235 *>
236 *> \param[out] VL
237 *> \verbatim
238 *> VL is DOUBLE PRECISION array, dimension (LDVL,N)
239 *> VL holds the computed left eigenvectors.
240 *> \endverbatim
241 *>
242 *> \param[in] LDVL
243 *> \verbatim
244 *> LDVL is INTEGER
245 *> Leading dimension of VL. Must be at least max(1,N).
246 *> \endverbatim
247 *>
248 *> \param[out] VR
249 *> \verbatim
250 *> VR is DOUBLE PRECISION array, dimension (LDVR,N)
251 *> VR holds the computed right eigenvectors.
252 *> \endverbatim
253 *>
254 *> \param[in] LDVR
255 *> \verbatim
256 *> LDVR is INTEGER
257 *> Leading dimension of VR. Must be at least max(1,N).
258 *> \endverbatim
259 *>
260 *> \param[out] LRE
261 *> \verbatim
262 *> LRE is DOUBLE PRECISION array, dimension (LDLRE,N)
263 *> LRE holds the computed right or left eigenvectors.
264 *> \endverbatim
265 *>
266 *> \param[in] LDLRE
267 *> \verbatim
268 *> LDLRE is INTEGER
269 *> Leading dimension of LRE. Must be at least max(1,N).
270 *> \endverbatim
271 *>
272 *> \param[out] RCONDV
273 *> \verbatim
274 *> RCONDV is DOUBLE PRECISION array, dimension (N)
275 *> RCONDV holds the computed reciprocal condition numbers
276 *> for eigenvectors.
277 *> \endverbatim
278 *>
279 *> \param[out] RCNDV1
280 *> \verbatim
281 *> RCNDV1 is DOUBLE PRECISION array, dimension (N)
282 *> RCNDV1 holds more computed reciprocal condition numbers
283 *> for eigenvectors.
284 *> \endverbatim
285 *>
286 *> \param[in] RCDVIN
287 *> \verbatim
288 *> RCDVIN is DOUBLE PRECISION array, dimension (N)
289 *> When COMP = .TRUE. RCDVIN holds the precomputed reciprocal
290 *> condition numbers for eigenvectors to be compared with
291 *> RCONDV.
292 *> \endverbatim
293 *>
294 *> \param[out] RCONDE
295 *> \verbatim
296 *> RCONDE is DOUBLE PRECISION array, dimension (N)
297 *> RCONDE holds the computed reciprocal condition numbers
298 *> for eigenvalues.
299 *> \endverbatim
300 *>
301 *> \param[out] RCNDE1
302 *> \verbatim
303 *> RCNDE1 is DOUBLE PRECISION array, dimension (N)
304 *> RCNDE1 holds more computed reciprocal condition numbers
305 *> for eigenvalues.
306 *> \endverbatim
307 *>
308 *> \param[in] RCDEIN
309 *> \verbatim
310 *> RCDEIN is DOUBLE PRECISION array, dimension (N)
311 *> When COMP = .TRUE. RCDEIN holds the precomputed reciprocal
312 *> condition numbers for eigenvalues to be compared with
313 *> RCONDE.
314 *> \endverbatim
315 *>
316 *> \param[out] SCALE
317 *> \verbatim
318 *> SCALE is DOUBLE PRECISION array, dimension (N)
319 *> Holds information describing balancing of matrix.
320 *> \endverbatim
321 *>
322 *> \param[out] SCALE1
323 *> \verbatim
324 *> SCALE1 is DOUBLE PRECISION array, dimension (N)
325 *> Holds information describing balancing of matrix.
326 *> \endverbatim
327 *>
328 *> \param[out] RESULT
329 *> \verbatim
330 *> RESULT is DOUBLE PRECISION array, dimension (11)
331 *> The values computed by the 11 tests described above.
332 *> The values are currently limited to 1/ulp, to avoid
333 *> overflow.
334 *> \endverbatim
335 *>
336 *> \param[out] WORK
337 *> \verbatim
338 *> WORK is DOUBLE PRECISION array, dimension (LWORK)
339 *> \endverbatim
340 *>
341 *> \param[in] LWORK
342 *> \verbatim
343 *> LWORK is INTEGER
344 *> The number of entries in WORK. This must be at least
345 *> 3*N, and 6*N+N**2 if tests 9, 10 or 11 are to be performed.
346 *> \endverbatim
347 *>
348 *> \param[out] IWORK
349 *> \verbatim
350 *> IWORK is INTEGER array, dimension (2*N)
351 *> \endverbatim
352 *>
353 *> \param[out] INFO
354 *> \verbatim
355 *> INFO is INTEGER
356 *> If 0, successful exit.
357 *> If <0, input parameter -INFO had an incorrect value.
358 *> If >0, DGEEVX returned an error code, the absolute
359 *> value of which is returned.
360 *> \endverbatim
361 *
362 * Authors:
363 * ========
364 *
365 *> \author Univ. of Tennessee
366 *> \author Univ. of California Berkeley
367 *> \author Univ. of Colorado Denver
368 *> \author NAG Ltd.
369 *
370 *> \date November 2011
371 *
372 *> \ingroup double_eig
373 *
374 * =====================================================================
375  SUBROUTINE dget23( COMP, BALANC, JTYPE, THRESH, ISEED, NOUNIT, N,
376  \$ a, lda, h, wr, wi, wr1, wi1, vl, ldvl, vr,
377  \$ ldvr, lre, ldlre, rcondv, rcndv1, rcdvin,
378  \$ rconde, rcnde1, rcdein, scale, scale1, result,
379  \$ work, lwork, iwork, info )
380 *
381 * -- LAPACK test routine (version 3.4.0) --
382 * -- LAPACK is a software package provided by Univ. of Tennessee, --
383 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
384 * November 2011
385 *
386 * .. Scalar Arguments ..
387  LOGICAL COMP
388  CHARACTER BALANC
389  INTEGER INFO, JTYPE, LDA, LDLRE, LDVL, LDVR, LWORK, N,
390  \$ nounit
391  DOUBLE PRECISION THRESH
392 * ..
393 * .. Array Arguments ..
394  INTEGER ISEED( 4 ), IWORK( * )
395  DOUBLE PRECISION A( lda, * ), H( lda, * ), LRE( ldlre, * ),
396  \$ rcdein( * ), rcdvin( * ), rcnde1( * ),
397  \$ rcndv1( * ), rconde( * ), rcondv( * ),
398  \$ result( 11 ), scale( * ), scale1( * ),
399  \$ vl( ldvl, * ), vr( ldvr, * ), wi( * ),
400  \$ wi1( * ), work( * ), wr( * ), wr1( * )
401 * ..
402 *
403 * =====================================================================
404 *
405 *
406 * .. Parameters ..
407  DOUBLE PRECISION ZERO, ONE, TWO
408  parameter ( zero = 0.0d0, one = 1.0d0, two = 2.0d0 )
409  DOUBLE PRECISION EPSIN
410  parameter ( epsin = 5.9605d-8 )
411 * ..
412 * .. Local Scalars ..
413  LOGICAL BALOK, NOBAL
414  CHARACTER SENSE
415  INTEGER I, IHI, IHI1, IINFO, ILO, ILO1, ISENS, ISENSM,
416  \$ j, jj, kmin
417  DOUBLE PRECISION ABNRM, ABNRM1, EPS, SMLNUM, TNRM, TOL, TOLIN,
418  \$ ulp, ulpinv, v, vimin, vmax, vmx, vrmin, vrmx,
419  \$ vtst
420 * ..
421 * .. Local Arrays ..
422  CHARACTER SENS( 2 )
423  DOUBLE PRECISION DUM( 1 ), RES( 2 )
424 * ..
425 * .. External Functions ..
426  LOGICAL LSAME
427  DOUBLE PRECISION DLAMCH, DLAPY2, DNRM2
428  EXTERNAL lsame, dlamch, dlapy2, dnrm2
429 * ..
430 * .. External Subroutines ..
431  EXTERNAL dgeevx, dget22, dlacpy, xerbla
432 * ..
433 * .. Intrinsic Functions ..
434  INTRINSIC abs, dble, max, min
435 * ..
436 * .. Data statements ..
437  DATA sens / 'N', 'V' /
438 * ..
439 * .. Executable Statements ..
440 *
441 * Check for errors
442 *
443  nobal = lsame( balanc, 'N' )
444  balok = nobal .OR. lsame( balanc, 'P' ) .OR.
445  \$ lsame( balanc, 'S' ) .OR. lsame( balanc, 'B' )
446  info = 0
447  IF( .NOT.balok ) THEN
448  info = -2
449  ELSE IF( thresh.LT.zero ) THEN
450  info = -4
451  ELSE IF( nounit.LE.0 ) THEN
452  info = -6
453  ELSE IF( n.LT.0 ) THEN
454  info = -7
455  ELSE IF( lda.LT.1 .OR. lda.LT.n ) THEN
456  info = -9
457  ELSE IF( ldvl.LT.1 .OR. ldvl.LT.n ) THEN
458  info = -16
459  ELSE IF( ldvr.LT.1 .OR. ldvr.LT.n ) THEN
460  info = -18
461  ELSE IF( ldlre.LT.1 .OR. ldlre.LT.n ) THEN
462  info = -20
463  ELSE IF( lwork.LT.3*n .OR. ( comp .AND. lwork.LT.6*n+n*n ) ) THEN
464  info = -31
465  END IF
466 *
467  IF( info.NE.0 ) THEN
468  CALL xerbla( 'DGET23', -info )
469  RETURN
470  END IF
471 *
472 * Quick return if nothing to do
473 *
474  DO 10 i = 1, 11
475  result( i ) = -one
476  10 CONTINUE
477 *
478  IF( n.EQ.0 )
479  \$ RETURN
480 *
481 * More Important constants
482 *
483  ulp = dlamch( 'Precision' )
484  smlnum = dlamch( 'S' )
485  ulpinv = one / ulp
486 *
487 * Compute eigenvalues and eigenvectors, and test them
488 *
489  IF( lwork.GE.6*n+n*n ) THEN
490  sense = 'B'
491  isensm = 2
492  ELSE
493  sense = 'E'
494  isensm = 1
495  END IF
496  CALL dlacpy( 'F', n, n, a, lda, h, lda )
497  CALL dgeevx( balanc, 'V', 'V', sense, n, h, lda, wr, wi, vl, ldvl,
498  \$ vr, ldvr, ilo, ihi, scale, abnrm, rconde, rcondv,
499  \$ work, lwork, iwork, iinfo )
500  IF( iinfo.NE.0 ) THEN
501  result( 1 ) = ulpinv
502  IF( jtype.NE.22 ) THEN
503  WRITE( nounit, fmt = 9998 )'DGEEVX1', iinfo, n, jtype,
504  \$ balanc, iseed
505  ELSE
506  WRITE( nounit, fmt = 9999 )'DGEEVX1', iinfo, n, iseed( 1 )
507  END IF
508  info = abs( iinfo )
509  RETURN
510  END IF
511 *
512 * Do Test (1)
513 *
514  CALL dget22( 'N', 'N', 'N', n, a, lda, vr, ldvr, wr, wi, work,
515  \$ res )
516  result( 1 ) = res( 1 )
517 *
518 * Do Test (2)
519 *
520  CALL dget22( 'T', 'N', 'T', n, a, lda, vl, ldvl, wr, wi, work,
521  \$ res )
522  result( 2 ) = res( 1 )
523 *
524 * Do Test (3)
525 *
526  DO 30 j = 1, n
527  tnrm = one
528  IF( wi( j ).EQ.zero ) THEN
529  tnrm = dnrm2( n, vr( 1, j ), 1 )
530  ELSE IF( wi( j ).GT.zero ) THEN
531  tnrm = dlapy2( dnrm2( n, vr( 1, j ), 1 ),
532  \$ dnrm2( n, vr( 1, j+1 ), 1 ) )
533  END IF
534  result( 3 ) = max( result( 3 ),
535  \$ min( ulpinv, abs( tnrm-one ) / ulp ) )
536  IF( wi( j ).GT.zero ) THEN
537  vmx = zero
538  vrmx = zero
539  DO 20 jj = 1, n
540  vtst = dlapy2( vr( jj, j ), vr( jj, j+1 ) )
541  IF( vtst.GT.vmx )
542  \$ vmx = vtst
543  IF( vr( jj, j+1 ).EQ.zero .AND. abs( vr( jj, j ) ).GT.
544  \$ vrmx )vrmx = abs( vr( jj, j ) )
545  20 CONTINUE
546  IF( vrmx / vmx.LT.one-two*ulp )
547  \$ result( 3 ) = ulpinv
548  END IF
549  30 CONTINUE
550 *
551 * Do Test (4)
552 *
553  DO 50 j = 1, n
554  tnrm = one
555  IF( wi( j ).EQ.zero ) THEN
556  tnrm = dnrm2( n, vl( 1, j ), 1 )
557  ELSE IF( wi( j ).GT.zero ) THEN
558  tnrm = dlapy2( dnrm2( n, vl( 1, j ), 1 ),
559  \$ dnrm2( n, vl( 1, j+1 ), 1 ) )
560  END IF
561  result( 4 ) = max( result( 4 ),
562  \$ min( ulpinv, abs( tnrm-one ) / ulp ) )
563  IF( wi( j ).GT.zero ) THEN
564  vmx = zero
565  vrmx = zero
566  DO 40 jj = 1, n
567  vtst = dlapy2( vl( jj, j ), vl( jj, j+1 ) )
568  IF( vtst.GT.vmx )
569  \$ vmx = vtst
570  IF( vl( jj, j+1 ).EQ.zero .AND. abs( vl( jj, j ) ).GT.
571  \$ vrmx )vrmx = abs( vl( jj, j ) )
572  40 CONTINUE
573  IF( vrmx / vmx.LT.one-two*ulp )
574  \$ result( 4 ) = ulpinv
575  END IF
576  50 CONTINUE
577 *
578 * Test for all options of computing condition numbers
579 *
580  DO 200 isens = 1, isensm
581 *
582  sense = sens( isens )
583 *
584 * Compute eigenvalues only, and test them
585 *
586  CALL dlacpy( 'F', n, n, a, lda, h, lda )
587  CALL dgeevx( balanc, 'N', 'N', sense, n, h, lda, wr1, wi1, dum,
588  \$ 1, dum, 1, ilo1, ihi1, scale1, abnrm1, rcnde1,
589  \$ rcndv1, work, lwork, iwork, iinfo )
590  IF( iinfo.NE.0 ) THEN
591  result( 1 ) = ulpinv
592  IF( jtype.NE.22 ) THEN
593  WRITE( nounit, fmt = 9998 )'DGEEVX2', iinfo, n, jtype,
594  \$ balanc, iseed
595  ELSE
596  WRITE( nounit, fmt = 9999 )'DGEEVX2', iinfo, n,
597  \$ iseed( 1 )
598  END IF
599  info = abs( iinfo )
600  GO TO 190
601  END IF
602 *
603 * Do Test (5)
604 *
605  DO 60 j = 1, n
606  IF( wr( j ).NE.wr1( j ) .OR. wi( j ).NE.wi1( j ) )
607  \$ result( 5 ) = ulpinv
608  60 CONTINUE
609 *
610 * Do Test (8)
611 *
612  IF( .NOT.nobal ) THEN
613  DO 70 j = 1, n
614  IF( scale( j ).NE.scale1( j ) )
615  \$ result( 8 ) = ulpinv
616  70 CONTINUE
617  IF( ilo.NE.ilo1 )
618  \$ result( 8 ) = ulpinv
619  IF( ihi.NE.ihi1 )
620  \$ result( 8 ) = ulpinv
621  IF( abnrm.NE.abnrm1 )
622  \$ result( 8 ) = ulpinv
623  END IF
624 *
625 * Do Test (9)
626 *
627  IF( isens.EQ.2 .AND. n.GT.1 ) THEN
628  DO 80 j = 1, n
629  IF( rcondv( j ).NE.rcndv1( j ) )
630  \$ result( 9 ) = ulpinv
631  80 CONTINUE
632  END IF
633 *
634 * Compute eigenvalues and right eigenvectors, and test them
635 *
636  CALL dlacpy( 'F', n, n, a, lda, h, lda )
637  CALL dgeevx( balanc, 'N', 'V', sense, n, h, lda, wr1, wi1, dum,
638  \$ 1, lre, ldlre, ilo1, ihi1, scale1, abnrm1, rcnde1,
639  \$ rcndv1, work, lwork, iwork, iinfo )
640  IF( iinfo.NE.0 ) THEN
641  result( 1 ) = ulpinv
642  IF( jtype.NE.22 ) THEN
643  WRITE( nounit, fmt = 9998 )'DGEEVX3', iinfo, n, jtype,
644  \$ balanc, iseed
645  ELSE
646  WRITE( nounit, fmt = 9999 )'DGEEVX3', iinfo, n,
647  \$ iseed( 1 )
648  END IF
649  info = abs( iinfo )
650  GO TO 190
651  END IF
652 *
653 * Do Test (5) again
654 *
655  DO 90 j = 1, n
656  IF( wr( j ).NE.wr1( j ) .OR. wi( j ).NE.wi1( j ) )
657  \$ result( 5 ) = ulpinv
658  90 CONTINUE
659 *
660 * Do Test (6)
661 *
662  DO 110 j = 1, n
663  DO 100 jj = 1, n
664  IF( vr( j, jj ).NE.lre( j, jj ) )
665  \$ result( 6 ) = ulpinv
666  100 CONTINUE
667  110 CONTINUE
668 *
669 * Do Test (8) again
670 *
671  IF( .NOT.nobal ) THEN
672  DO 120 j = 1, n
673  IF( scale( j ).NE.scale1( j ) )
674  \$ result( 8 ) = ulpinv
675  120 CONTINUE
676  IF( ilo.NE.ilo1 )
677  \$ result( 8 ) = ulpinv
678  IF( ihi.NE.ihi1 )
679  \$ result( 8 ) = ulpinv
680  IF( abnrm.NE.abnrm1 )
681  \$ result( 8 ) = ulpinv
682  END IF
683 *
684 * Do Test (9) again
685 *
686  IF( isens.EQ.2 .AND. n.GT.1 ) THEN
687  DO 130 j = 1, n
688  IF( rcondv( j ).NE.rcndv1( j ) )
689  \$ result( 9 ) = ulpinv
690  130 CONTINUE
691  END IF
692 *
693 * Compute eigenvalues and left eigenvectors, and test them
694 *
695  CALL dlacpy( 'F', n, n, a, lda, h, lda )
696  CALL dgeevx( balanc, 'V', 'N', sense, n, h, lda, wr1, wi1, lre,
697  \$ ldlre, dum, 1, ilo1, ihi1, scale1, abnrm1, rcnde1,
698  \$ rcndv1, work, lwork, iwork, iinfo )
699  IF( iinfo.NE.0 ) THEN
700  result( 1 ) = ulpinv
701  IF( jtype.NE.22 ) THEN
702  WRITE( nounit, fmt = 9998 )'DGEEVX4', iinfo, n, jtype,
703  \$ balanc, iseed
704  ELSE
705  WRITE( nounit, fmt = 9999 )'DGEEVX4', iinfo, n,
706  \$ iseed( 1 )
707  END IF
708  info = abs( iinfo )
709  GO TO 190
710  END IF
711 *
712 * Do Test (5) again
713 *
714  DO 140 j = 1, n
715  IF( wr( j ).NE.wr1( j ) .OR. wi( j ).NE.wi1( j ) )
716  \$ result( 5 ) = ulpinv
717  140 CONTINUE
718 *
719 * Do Test (7)
720 *
721  DO 160 j = 1, n
722  DO 150 jj = 1, n
723  IF( vl( j, jj ).NE.lre( j, jj ) )
724  \$ result( 7 ) = ulpinv
725  150 CONTINUE
726  160 CONTINUE
727 *
728 * Do Test (8) again
729 *
730  IF( .NOT.nobal ) THEN
731  DO 170 j = 1, n
732  IF( scale( j ).NE.scale1( j ) )
733  \$ result( 8 ) = ulpinv
734  170 CONTINUE
735  IF( ilo.NE.ilo1 )
736  \$ result( 8 ) = ulpinv
737  IF( ihi.NE.ihi1 )
738  \$ result( 8 ) = ulpinv
739  IF( abnrm.NE.abnrm1 )
740  \$ result( 8 ) = ulpinv
741  END IF
742 *
743 * Do Test (9) again
744 *
745  IF( isens.EQ.2 .AND. n.GT.1 ) THEN
746  DO 180 j = 1, n
747  IF( rcondv( j ).NE.rcndv1( j ) )
748  \$ result( 9 ) = ulpinv
749  180 CONTINUE
750  END IF
751 *
752  190 CONTINUE
753 *
754  200 CONTINUE
755 *
756 * If COMP, compare condition numbers to precomputed ones
757 *
758  IF( comp ) THEN
759  CALL dlacpy( 'F', n, n, a, lda, h, lda )
760  CALL dgeevx( 'N', 'V', 'V', 'B', n, h, lda, wr, wi, vl, ldvl,
761  \$ vr, ldvr, ilo, ihi, scale, abnrm, rconde, rcondv,
762  \$ work, lwork, iwork, iinfo )
763  IF( iinfo.NE.0 ) THEN
764  result( 1 ) = ulpinv
765  WRITE( nounit, fmt = 9999 )'DGEEVX5', iinfo, n, iseed( 1 )
766  info = abs( iinfo )
767  GO TO 250
768  END IF
769 *
770 * Sort eigenvalues and condition numbers lexicographically
771 * to compare with inputs
772 *
773  DO 220 i = 1, n - 1
774  kmin = i
775  vrmin = wr( i )
776  vimin = wi( i )
777  DO 210 j = i + 1, n
778  IF( wr( j ).LT.vrmin ) THEN
779  kmin = j
780  vrmin = wr( j )
781  vimin = wi( j )
782  END IF
783  210 CONTINUE
784  wr( kmin ) = wr( i )
785  wi( kmin ) = wi( i )
786  wr( i ) = vrmin
787  wi( i ) = vimin
788  vrmin = rconde( kmin )
789  rconde( kmin ) = rconde( i )
790  rconde( i ) = vrmin
791  vrmin = rcondv( kmin )
792  rcondv( kmin ) = rcondv( i )
793  rcondv( i ) = vrmin
794  220 CONTINUE
795 *
796 * Compare condition numbers for eigenvectors
797 * taking their condition numbers into account
798 *
799  result( 10 ) = zero
800  eps = max( epsin, ulp )
801  v = max( dble( n )*eps*abnrm, smlnum )
802  IF( abnrm.EQ.zero )
803  \$ v = one
804  DO 230 i = 1, n
805  IF( v.GT.rcondv( i )*rconde( i ) ) THEN
806  tol = rcondv( i )
807  ELSE
808  tol = v / rconde( i )
809  END IF
810  IF( v.GT.rcdvin( i )*rcdein( i ) ) THEN
811  tolin = rcdvin( i )
812  ELSE
813  tolin = v / rcdein( i )
814  END IF
815  tol = max( tol, smlnum / eps )
816  tolin = max( tolin, smlnum / eps )
817  IF( eps*( rcdvin( i )-tolin ).GT.rcondv( i )+tol ) THEN
818  vmax = one / eps
819  ELSE IF( rcdvin( i )-tolin.GT.rcondv( i )+tol ) THEN
820  vmax = ( rcdvin( i )-tolin ) / ( rcondv( i )+tol )
821  ELSE IF( rcdvin( i )+tolin.LT.eps*( rcondv( i )-tol ) ) THEN
822  vmax = one / eps
823  ELSE IF( rcdvin( i )+tolin.LT.rcondv( i )-tol ) THEN
824  vmax = ( rcondv( i )-tol ) / ( rcdvin( i )+tolin )
825  ELSE
826  vmax = one
827  END IF
828  result( 10 ) = max( result( 10 ), vmax )
829  230 CONTINUE
830 *
831 * Compare condition numbers for eigenvalues
832 * taking their condition numbers into account
833 *
834  result( 11 ) = zero
835  DO 240 i = 1, n
836  IF( v.GT.rcondv( i ) ) THEN
837  tol = one
838  ELSE
839  tol = v / rcondv( i )
840  END IF
841  IF( v.GT.rcdvin( i ) ) THEN
842  tolin = one
843  ELSE
844  tolin = v / rcdvin( i )
845  END IF
846  tol = max( tol, smlnum / eps )
847  tolin = max( tolin, smlnum / eps )
848  IF( eps*( rcdein( i )-tolin ).GT.rconde( i )+tol ) THEN
849  vmax = one / eps
850  ELSE IF( rcdein( i )-tolin.GT.rconde( i )+tol ) THEN
851  vmax = ( rcdein( i )-tolin ) / ( rconde( i )+tol )
852  ELSE IF( rcdein( i )+tolin.LT.eps*( rconde( i )-tol ) ) THEN
853  vmax = one / eps
854  ELSE IF( rcdein( i )+tolin.LT.rconde( i )-tol ) THEN
855  vmax = ( rconde( i )-tol ) / ( rcdein( i )+tolin )
856  ELSE
857  vmax = one
858  END IF
859  result( 11 ) = max( result( 11 ), vmax )
860  240 CONTINUE
861  250 CONTINUE
862 *
863  END IF
864 *
865  9999 FORMAT( ' DGET23: ', a, ' returned INFO=', i6, '.', / 9x, 'N=',
866  \$ i6, ', INPUT EXAMPLE NUMBER = ', i4 )
867  9998 FORMAT( ' DGET23: ', a, ' returned INFO=', i6, '.', / 9x, 'N=',
868  \$ i6, ', JTYPE=', i6, ', BALANC = ', a, ', ISEED=(',
869  \$ 3( i5, ',' ), i5, ')' )
870 *
871  RETURN
872 *
873 * End of DGET23
874 *
875  END
subroutine dgeevx(BALANC, JOBVL, JOBVR, SENSE, N, A, LDA, WR, WI, VL, LDVL, VR, LDVR, ILO, IHI, SCALE, ABNRM, RCONDE, RCONDV, WORK, LWORK, IWORK, INFO)
DGEEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices ...
Definition: dgeevx.f:307
subroutine dget22(TRANSA, TRANSE, TRANSW, N, A, LDA, E, LDE, WR, WI, WORK, RESULT)
DGET22
Definition: dget22.f:169
subroutine dlacpy(UPLO, M, N, A, LDA, B, LDB)
DLACPY copies all or part of one two-dimensional array to another.
Definition: dlacpy.f:105
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine dget23(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)
DGET23
Definition: dget23.f:380