LAPACK  3.7.0 LAPACK: Linear Algebra PACKage
zchkhb.f
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1 *> \brief \b ZCHKHB
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 ZCHKHB( NSIZES, NN, NWDTHS, KK, NTYPES, DOTYPE, ISEED,
12 * THRESH, NOUNIT, A, LDA, SD, SE, U, LDU, WORK,
13 * LWORK, RWORK, RESULT, INFO )
14 *
15 * .. Scalar Arguments ..
16 * INTEGER INFO, LDA, LDU, LWORK, NOUNIT, NSIZES, NTYPES,
17 * \$ NWDTHS
18 * DOUBLE PRECISION THRESH
19 * ..
20 * .. Array Arguments ..
21 * LOGICAL DOTYPE( * )
22 * INTEGER ISEED( 4 ), KK( * ), NN( * )
23 * DOUBLE PRECISION RESULT( * ), RWORK( * ), SD( * ), SE( * )
24 * COMPLEX*16 A( LDA, * ), U( LDU, * ), WORK( * )
25 * ..
26 *
27 *
28 *> \par Purpose:
29 * =============
30 *>
31 *> \verbatim
32 *>
33 *> ZCHKHB tests the reduction of a Hermitian band matrix to tridiagonal
34 *> from, used with the Hermitian eigenvalue problem.
35 *>
36 *> ZHBTRD factors a Hermitian band matrix A as U S U* , where * means
37 *> conjugate transpose, S is symmetric tridiagonal, and U is unitary.
38 *> ZHBTRD can use either just the lower or just the upper triangle
39 *> of A; ZCHKHB checks both cases.
40 *>
41 *> When ZCHKHB is called, a number of matrix "sizes" ("n's"), a number
42 *> of bandwidths ("k's"), and a number of matrix "types" are
43 *> specified. For each size ("n"), each bandwidth ("k") less than or
44 *> equal to "n", and each type of matrix, one matrix will be generated
45 *> and used to test the hermitian banded reduction routine. For each
46 *> matrix, a number of tests will be performed:
47 *>
48 *> (1) | A - V S V* | / ( |A| n ulp ) computed by ZHBTRD with
49 *> UPLO='U'
50 *>
51 *> (2) | I - UU* | / ( n ulp )
52 *>
53 *> (3) | A - V S V* | / ( |A| n ulp ) computed by ZHBTRD with
54 *> UPLO='L'
55 *>
56 *> (4) | I - UU* | / ( n ulp )
57 *>
58 *> The "sizes" are specified by an array NN(1:NSIZES); the value of
59 *> each element NN(j) specifies one size.
60 *> The "types" are specified by a logical array DOTYPE( 1:NTYPES );
61 *> if DOTYPE(j) is .TRUE., then matrix type "j" will be generated.
62 *> Currently, the list of possible types is:
63 *>
64 *> (1) The zero matrix.
65 *> (2) The identity matrix.
66 *>
67 *> (3) A diagonal matrix with evenly spaced entries
68 *> 1, ..., ULP and random signs.
69 *> (ULP = (first number larger than 1) - 1 )
70 *> (4) A diagonal matrix with geometrically spaced entries
71 *> 1, ..., ULP and random signs.
72 *> (5) A diagonal matrix with "clustered" entries 1, ULP, ..., ULP
73 *> and random signs.
74 *>
75 *> (6) Same as (4), but multiplied by SQRT( overflow threshold )
76 *> (7) Same as (4), but multiplied by SQRT( underflow threshold )
77 *>
78 *> (8) A matrix of the form U* D U, where U is unitary and
79 *> D has evenly spaced entries 1, ..., ULP with random signs
80 *> on the diagonal.
81 *>
82 *> (9) A matrix of the form U* D U, where U is unitary and
83 *> D has geometrically spaced entries 1, ..., ULP with random
84 *> signs on the diagonal.
85 *>
86 *> (10) A matrix of the form U* D U, where U is unitary and
87 *> D has "clustered" entries 1, ULP,..., ULP with random
88 *> signs on the diagonal.
89 *>
90 *> (11) Same as (8), but multiplied by SQRT( overflow threshold )
91 *> (12) Same as (8), but multiplied by SQRT( underflow threshold )
92 *>
93 *> (13) Hermitian matrix with random entries chosen from (-1,1).
94 *> (14) Same as (13), but multiplied by SQRT( overflow threshold )
95 *> (15) Same as (13), but multiplied by SQRT( underflow threshold )
96 *> \endverbatim
97 *
98 * Arguments:
99 * ==========
100 *
101 *> \param[in] NSIZES
102 *> \verbatim
103 *> NSIZES is INTEGER
104 *> The number of sizes of matrices to use. If it is zero,
105 *> ZCHKHB does nothing. It must be at least zero.
106 *> \endverbatim
107 *>
108 *> \param[in] NN
109 *> \verbatim
110 *> NN is INTEGER array, dimension (NSIZES)
111 *> An array containing the sizes to be used for the matrices.
112 *> Zero values will be skipped. The values must be at least
113 *> zero.
114 *> \endverbatim
115 *>
116 *> \param[in] NWDTHS
117 *> \verbatim
118 *> NWDTHS is INTEGER
119 *> The number of bandwidths to use. If it is zero,
120 *> ZCHKHB does nothing. It must be at least zero.
121 *> \endverbatim
122 *>
123 *> \param[in] KK
124 *> \verbatim
125 *> KK is INTEGER array, dimension (NWDTHS)
126 *> An array containing the bandwidths to be used for the band
127 *> matrices. The values must be at least zero.
128 *> \endverbatim
129 *>
130 *> \param[in] NTYPES
131 *> \verbatim
132 *> NTYPES is INTEGER
133 *> The number of elements in DOTYPE. If it is zero, ZCHKHB
134 *> does nothing. It must be at least zero. If it is MAXTYP+1
135 *> and NSIZES is 1, then an additional type, MAXTYP+1 is
136 *> defined, which is to use whatever matrix is in A. This
137 *> is only useful if DOTYPE(1:MAXTYP) is .FALSE. and
138 *> DOTYPE(MAXTYP+1) is .TRUE. .
139 *> \endverbatim
140 *>
141 *> \param[in] DOTYPE
142 *> \verbatim
143 *> DOTYPE is LOGICAL array, dimension (NTYPES)
144 *> If DOTYPE(j) is .TRUE., then for each size in NN a
145 *> matrix of that size and of type j will be generated.
146 *> If NTYPES is smaller than the maximum number of types
147 *> defined (PARAMETER MAXTYP), then types NTYPES+1 through
148 *> MAXTYP will not be generated. If NTYPES is larger
149 *> than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES)
150 *> will be ignored.
151 *> \endverbatim
152 *>
153 *> \param[in,out] ISEED
154 *> \verbatim
155 *> ISEED is INTEGER array, dimension (4)
156 *> On entry ISEED specifies the seed of the random number
157 *> generator. The array elements should be between 0 and 4095;
158 *> if not they will be reduced mod 4096. Also, ISEED(4) must
159 *> be odd. The random number generator uses a linear
160 *> congruential sequence limited to small integers, and so
161 *> should produce machine independent random numbers. The
162 *> values of ISEED are changed on exit, and can be used in the
163 *> next call to ZCHKHB to continue the same random number
164 *> sequence.
165 *> \endverbatim
166 *>
167 *> \param[in] THRESH
168 *> \verbatim
169 *> THRESH is DOUBLE PRECISION
170 *> A test will count as "failed" if the "error", computed as
171 *> described above, exceeds THRESH. Note that the error
172 *> is scaled to be O(1), so THRESH should be a reasonably
173 *> small multiple of 1, e.g., 10 or 100. In particular,
174 *> it should not depend on the precision (single vs. double)
175 *> or the size of the matrix. It must be at least zero.
176 *> \endverbatim
177 *>
178 *> \param[in] NOUNIT
179 *> \verbatim
180 *> NOUNIT is INTEGER
181 *> The FORTRAN unit number for printing out error messages
182 *> (e.g., if a routine returns IINFO not equal to 0.)
183 *> \endverbatim
184 *>
185 *> \param[in,out] A
186 *> \verbatim
187 *> A is COMPLEX*16 array, dimension
188 *> (LDA, max(NN))
189 *> Used to hold the matrix whose eigenvalues are to be
190 *> computed.
191 *> \endverbatim
192 *>
193 *> \param[in] LDA
194 *> \verbatim
195 *> LDA is INTEGER
196 *> The leading dimension of A. It must be at least 2 (not 1!)
197 *> and at least max( KK )+1.
198 *> \endverbatim
199 *>
200 *> \param[out] SD
201 *> \verbatim
202 *> SD is DOUBLE PRECISION array, dimension (max(NN))
203 *> Used to hold the diagonal of the tridiagonal matrix computed
204 *> by ZHBTRD.
205 *> \endverbatim
206 *>
207 *> \param[out] SE
208 *> \verbatim
209 *> SE is DOUBLE PRECISION array, dimension (max(NN))
210 *> Used to hold the off-diagonal of the tridiagonal matrix
211 *> computed by ZHBTRD.
212 *> \endverbatim
213 *>
214 *> \param[out] U
215 *> \verbatim
216 *> U is COMPLEX*16 array, dimension (LDU, max(NN))
217 *> Used to hold the unitary matrix computed by ZHBTRD.
218 *> \endverbatim
219 *>
220 *> \param[in] LDU
221 *> \verbatim
222 *> LDU is INTEGER
223 *> The leading dimension of U. It must be at least 1
224 *> and at least max( NN ).
225 *> \endverbatim
226 *>
227 *> \param[out] WORK
228 *> \verbatim
229 *> WORK is COMPLEX*16 array, dimension (LWORK)
230 *> \endverbatim
231 *>
232 *> \param[in] LWORK
233 *> \verbatim
234 *> LWORK is INTEGER
235 *> The number of entries in WORK. This must be at least
236 *> max( LDA+1, max(NN)+1 )*max(NN).
237 *> \endverbatim
238 *>
239 *> \param[out] RWORK
240 *> \verbatim
241 *> RWORK is DOUBLE PRECISION array
242 *> \endverbatim
243 *>
244 *> \param[out] RESULT
245 *> \verbatim
246 *> RESULT is DOUBLE PRECISION array, dimension (4)
247 *> The values computed by the tests described above.
248 *> The values are currently limited to 1/ulp, to avoid
249 *> overflow.
250 *> \endverbatim
251 *>
252 *> \param[out] INFO
253 *> \verbatim
254 *> INFO is INTEGER
255 *> If 0, then everything ran OK.
256 *>
257 *>-----------------------------------------------------------------------
258 *>
259 *> Some Local Variables and Parameters:
260 *> ---- ----- --------- --- ----------
261 *> ZERO, ONE Real 0 and 1.
262 *> MAXTYP The number of types defined.
263 *> NTEST The number of tests performed, or which can
264 *> be performed so far, for the current matrix.
265 *> NTESTT The total number of tests performed so far.
266 *> NMAX Largest value in NN.
267 *> NMATS The number of matrices generated so far.
268 *> NERRS The number of tests which have exceeded THRESH
269 *> so far.
270 *> COND, IMODE Values to be passed to the matrix generators.
271 *> ANORM Norm of A; passed to matrix generators.
272 *>
273 *> OVFL, UNFL Overflow and underflow thresholds.
274 *> ULP, ULPINV Finest relative precision and its inverse.
275 *> RTOVFL, RTUNFL Square roots of the previous 2 values.
276 *> The following four arrays decode JTYPE:
277 *> KTYPE(j) The general type (1-10) for type "j".
278 *> KMODE(j) The MODE value to be passed to the matrix
279 *> generator for type "j".
280 *> KMAGN(j) The order of magnitude ( O(1),
281 *> O(overflow^(1/2) ), O(underflow^(1/2) )
282 *> \endverbatim
283 *
284 * Authors:
285 * ========
286 *
287 *> \author Univ. of Tennessee
288 *> \author Univ. of California Berkeley
289 *> \author Univ. of Colorado Denver
290 *> \author NAG Ltd.
291 *
292 *> \date December 2016
293 *
294 *> \ingroup complex16_eig
295 *
296 * =====================================================================
297  SUBROUTINE zchkhb( NSIZES, NN, NWDTHS, KK, NTYPES, DOTYPE, ISEED,
298  \$ thresh, nounit, a, lda, sd, se, u, ldu, work,
299  \$ lwork, rwork, result, info )
300 *
301 * -- LAPACK test routine (version 3.7.0) --
302 * -- LAPACK is a software package provided by Univ. of Tennessee, --
303 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
304 * December 2016
305 *
306 * .. Scalar Arguments ..
307  INTEGER INFO, LDA, LDU, LWORK, NOUNIT, NSIZES, NTYPES,
308  \$ nwdths
309  DOUBLE PRECISION THRESH
310 * ..
311 * .. Array Arguments ..
312  LOGICAL DOTYPE( * )
313  INTEGER ISEED( 4 ), KK( * ), NN( * )
314  DOUBLE PRECISION RESULT( * ), RWORK( * ), SD( * ), SE( * )
315  COMPLEX*16 A( lda, * ), U( ldu, * ), WORK( * )
316 * ..
317 *
318 * =====================================================================
319 *
320 * .. Parameters ..
321  COMPLEX*16 CZERO, CONE
322  parameter ( czero = ( 0.0d+0, 0.0d+0 ),
323  \$ cone = ( 1.0d+0, 0.0d+0 ) )
324  DOUBLE PRECISION ZERO, ONE, TWO, TEN
325  parameter ( zero = 0.0d+0, one = 1.0d+0, two = 2.0d+0,
326  \$ ten = 10.0d+0 )
327  DOUBLE PRECISION HALF
328  parameter ( half = one / two )
329  INTEGER MAXTYP
330  parameter ( maxtyp = 15 )
331 * ..
332 * .. Local Scalars ..
334  INTEGER I, IINFO, IMODE, ITYPE, J, JC, JCOL, JR, JSIZE,
335  \$ jtype, jwidth, k, kmax, mtypes, n, nerrs,
336  \$ nmats, nmax, ntest, ntestt
337  DOUBLE PRECISION ANINV, ANORM, COND, OVFL, RTOVFL, RTUNFL,
338  \$ temp1, ulp, ulpinv, unfl
339 * ..
340 * .. Local Arrays ..
341  INTEGER IDUMMA( 1 ), IOLDSD( 4 ), KMAGN( maxtyp ),
342  \$ kmode( maxtyp ), ktype( maxtyp )
343 * ..
344 * .. External Functions ..
345  DOUBLE PRECISION DLAMCH
346  EXTERNAL dlamch
347 * ..
348 * .. External Subroutines ..
349  EXTERNAL dlasum, xerbla, zhbt21, zhbtrd, zlacpy, zlaset,
350  \$ zlatmr, zlatms
351 * ..
352 * .. Intrinsic Functions ..
353  INTRINSIC abs, dble, dconjg, max, min, sqrt
354 * ..
355 * .. Data statements ..
356  DATA ktype / 1, 2, 5*4, 5*5, 3*8 /
357  DATA kmagn / 2*1, 1, 1, 1, 2, 3, 1, 1, 1, 2, 3, 1,
358  \$ 2, 3 /
359  DATA kmode / 2*0, 4, 3, 1, 4, 4, 4, 3, 1, 4, 4, 0,
360  \$ 0, 0 /
361 * ..
362 * .. Executable Statements ..
363 *
364 * Check for errors
365 *
366  ntestt = 0
367  info = 0
368 *
369 * Important constants
370 *
372  nmax = 1
373  DO 10 j = 1, nsizes
374  nmax = max( nmax, nn( j ) )
375  IF( nn( j ).LT.0 )
377  10 CONTINUE
378 *
380  kmax = 0
381  DO 20 j = 1, nsizes
382  kmax = max( kmax, kk( j ) )
383  IF( kk( j ).LT.0 )
385  20 CONTINUE
386  kmax = min( nmax-1, kmax )
387 *
388 * Check for errors
389 *
390  IF( nsizes.LT.0 ) THEN
391  info = -1
392  ELSE IF( badnn ) THEN
393  info = -2
394  ELSE IF( nwdths.LT.0 ) THEN
395  info = -3
396  ELSE IF( badnnb ) THEN
397  info = -4
398  ELSE IF( ntypes.LT.0 ) THEN
399  info = -5
400  ELSE IF( lda.LT.kmax+1 ) THEN
401  info = -11
402  ELSE IF( ldu.LT.nmax ) THEN
403  info = -15
404  ELSE IF( ( max( lda, nmax )+1 )*nmax.GT.lwork ) THEN
405  info = -17
406  END IF
407 *
408  IF( info.NE.0 ) THEN
409  CALL xerbla( 'ZCHKHB', -info )
410  RETURN
411  END IF
412 *
413 * Quick return if possible
414 *
415  IF( nsizes.EQ.0 .OR. ntypes.EQ.0 .OR. nwdths.EQ.0 )
416  \$ RETURN
417 *
418 * More Important constants
419 *
420  unfl = dlamch( 'Safe minimum' )
421  ovfl = one / unfl
422  ulp = dlamch( 'Epsilon' )*dlamch( 'Base' )
423  ulpinv = one / ulp
424  rtunfl = sqrt( unfl )
425  rtovfl = sqrt( ovfl )
426 *
427 * Loop over sizes, types
428 *
429  nerrs = 0
430  nmats = 0
431 *
432  DO 190 jsize = 1, nsizes
433  n = nn( jsize )
434  aninv = one / dble( max( 1, n ) )
435 *
436  DO 180 jwidth = 1, nwdths
437  k = kk( jwidth )
438  IF( k.GT.n )
439  \$ GO TO 180
440  k = max( 0, min( n-1, k ) )
441 *
442  IF( nsizes.NE.1 ) THEN
443  mtypes = min( maxtyp, ntypes )
444  ELSE
445  mtypes = min( maxtyp+1, ntypes )
446  END IF
447 *
448  DO 170 jtype = 1, mtypes
449  IF( .NOT.dotype( jtype ) )
450  \$ GO TO 170
451  nmats = nmats + 1
452  ntest = 0
453 *
454  DO 30 j = 1, 4
455  ioldsd( j ) = iseed( j )
456  30 CONTINUE
457 *
458 * Compute "A".
459 * Store as "Upper"; later, we will copy to other format.
460 *
461 * Control parameters:
462 *
463 * KMAGN KMODE KTYPE
464 * =1 O(1) clustered 1 zero
465 * =2 large clustered 2 identity
466 * =3 small exponential (none)
467 * =4 arithmetic diagonal, (w/ eigenvalues)
468 * =5 random log hermitian, w/ eigenvalues
469 * =6 random (none)
470 * =7 random diagonal
471 * =8 random hermitian
472 * =9 positive definite
473 * =10 diagonally dominant tridiagonal
474 *
475  IF( mtypes.GT.maxtyp )
476  \$ GO TO 100
477 *
478  itype = ktype( jtype )
479  imode = kmode( jtype )
480 *
481 * Compute norm
482 *
483  GO TO ( 40, 50, 60 )kmagn( jtype )
484 *
485  40 CONTINUE
486  anorm = one
487  GO TO 70
488 *
489  50 CONTINUE
490  anorm = ( rtovfl*ulp )*aninv
491  GO TO 70
492 *
493  60 CONTINUE
494  anorm = rtunfl*n*ulpinv
495  GO TO 70
496 *
497  70 CONTINUE
498 *
499  CALL zlaset( 'Full', lda, n, czero, czero, a, lda )
500  iinfo = 0
501  IF( jtype.LE.15 ) THEN
502  cond = ulpinv
503  ELSE
504  cond = ulpinv*aninv / ten
505  END IF
506 *
507 * Special Matrices -- Identity & Jordan block
508 *
509 * Zero
510 *
511  IF( itype.EQ.1 ) THEN
512  iinfo = 0
513 *
514  ELSE IF( itype.EQ.2 ) THEN
515 *
516 * Identity
517 *
518  DO 80 jcol = 1, n
519  a( k+1, jcol ) = anorm
520  80 CONTINUE
521 *
522  ELSE IF( itype.EQ.4 ) THEN
523 *
524 * Diagonal Matrix, [Eigen]values Specified
525 *
526  CALL zlatms( n, n, 'S', iseed, 'H', rwork, imode,
527  \$ cond, anorm, 0, 0, 'Q', a( k+1, 1 ), lda,
528  \$ work, iinfo )
529 *
530  ELSE IF( itype.EQ.5 ) THEN
531 *
532 * Hermitian, eigenvalues specified
533 *
534  CALL zlatms( n, n, 'S', iseed, 'H', rwork, imode,
535  \$ cond, anorm, k, k, 'Q', a, lda, work,
536  \$ iinfo )
537 *
538  ELSE IF( itype.EQ.7 ) THEN
539 *
540 * Diagonal, random eigenvalues
541 *
542  CALL zlatmr( n, n, 'S', iseed, 'H', work, 6, one,
543  \$ cone, 'T', 'N', work( n+1 ), 1, one,
544  \$ work( 2*n+1 ), 1, one, 'N', idumma, 0, 0,
545  \$ zero, anorm, 'Q', a( k+1, 1 ), lda,
546  \$ idumma, iinfo )
547 *
548  ELSE IF( itype.EQ.8 ) THEN
549 *
550 * Hermitian, random eigenvalues
551 *
552  CALL zlatmr( n, n, 'S', iseed, 'H', work, 6, one,
553  \$ cone, 'T', 'N', work( n+1 ), 1, one,
554  \$ work( 2*n+1 ), 1, one, 'N', idumma, k, k,
555  \$ zero, anorm, 'Q', a, lda, idumma, iinfo )
556 *
557  ELSE IF( itype.EQ.9 ) THEN
558 *
559 * Positive definite, eigenvalues specified.
560 *
561  CALL zlatms( n, n, 'S', iseed, 'P', rwork, imode,
562  \$ cond, anorm, k, k, 'Q', a, lda,
563  \$ work( n+1 ), iinfo )
564 *
565  ELSE IF( itype.EQ.10 ) THEN
566 *
567 * Positive definite tridiagonal, eigenvalues specified.
568 *
569  IF( n.GT.1 )
570  \$ k = max( 1, k )
571  CALL zlatms( n, n, 'S', iseed, 'P', rwork, imode,
572  \$ cond, anorm, 1, 1, 'Q', a( k, 1 ), lda,
573  \$ work, iinfo )
574  DO 90 i = 2, n
575  temp1 = abs( a( k, i ) ) /
576  \$ sqrt( abs( a( k+1, i-1 )*a( k+1, i ) ) )
577  IF( temp1.GT.half ) THEN
578  a( k, i ) = half*sqrt( abs( a( k+1,
579  \$ i-1 )*a( k+1, i ) ) )
580  END IF
581  90 CONTINUE
582 *
583  ELSE
584 *
585  iinfo = 1
586  END IF
587 *
588  IF( iinfo.NE.0 ) THEN
589  WRITE( nounit, fmt = 9999 )'Generator', iinfo, n,
590  \$ jtype, ioldsd
591  info = abs( iinfo )
592  RETURN
593  END IF
594 *
595  100 CONTINUE
596 *
597 * Call ZHBTRD to compute S and U from upper triangle.
598 *
599  CALL zlacpy( ' ', k+1, n, a, lda, work, lda )
600 *
601  ntest = 1
602  CALL zhbtrd( 'V', 'U', n, k, work, lda, sd, se, u, ldu,
603  \$ work( lda*n+1 ), iinfo )
604 *
605  IF( iinfo.NE.0 ) THEN
606  WRITE( nounit, fmt = 9999 )'ZHBTRD(U)', iinfo, n,
607  \$ jtype, ioldsd
608  info = abs( iinfo )
609  IF( iinfo.LT.0 ) THEN
610  RETURN
611  ELSE
612  result( 1 ) = ulpinv
613  GO TO 150
614  END IF
615  END IF
616 *
617 * Do tests 1 and 2
618 *
619  CALL zhbt21( 'Upper', n, k, 1, a, lda, sd, se, u, ldu,
620  \$ work, rwork, result( 1 ) )
621 *
622 * Convert A from Upper-Triangle-Only storage to
623 * Lower-Triangle-Only storage.
624 *
625  DO 120 jc = 1, n
626  DO 110 jr = 0, min( k, n-jc )
627  a( jr+1, jc ) = dconjg( a( k+1-jr, jc+jr ) )
628  110 CONTINUE
629  120 CONTINUE
630  DO 140 jc = n + 1 - k, n
631  DO 130 jr = min( k, n-jc ) + 1, k
632  a( jr+1, jc ) = zero
633  130 CONTINUE
634  140 CONTINUE
635 *
636 * Call ZHBTRD to compute S and U from lower triangle
637 *
638  CALL zlacpy( ' ', k+1, n, a, lda, work, lda )
639 *
640  ntest = 3
641  CALL zhbtrd( 'V', 'L', n, k, work, lda, sd, se, u, ldu,
642  \$ work( lda*n+1 ), iinfo )
643 *
644  IF( iinfo.NE.0 ) THEN
645  WRITE( nounit, fmt = 9999 )'ZHBTRD(L)', iinfo, n,
646  \$ jtype, ioldsd
647  info = abs( iinfo )
648  IF( iinfo.LT.0 ) THEN
649  RETURN
650  ELSE
651  result( 3 ) = ulpinv
652  GO TO 150
653  END IF
654  END IF
655  ntest = 4
656 *
657 * Do tests 3 and 4
658 *
659  CALL zhbt21( 'Lower', n, k, 1, a, lda, sd, se, u, ldu,
660  \$ work, rwork, result( 3 ) )
661 *
662 * End of Loop -- Check for RESULT(j) > THRESH
663 *
664  150 CONTINUE
665  ntestt = ntestt + ntest
666 *
667 * Print out tests which fail.
668 *
669  DO 160 jr = 1, ntest
670  IF( result( jr ).GE.thresh ) THEN
671 *
672 * If this is the first test to fail,
673 * print a header to the data file.
674 *
675  IF( nerrs.EQ.0 ) THEN
676  WRITE( nounit, fmt = 9998 )'ZHB'
677  WRITE( nounit, fmt = 9997 )
678  WRITE( nounit, fmt = 9996 )
679  WRITE( nounit, fmt = 9995 )'Hermitian'
680  WRITE( nounit, fmt = 9994 )'unitary', '*',
681  \$ 'conjugate transpose', ( '*', j = 1, 4 )
682  END IF
683  nerrs = nerrs + 1
684  WRITE( nounit, fmt = 9993 )n, k, ioldsd, jtype,
685  \$ jr, result( jr )
686  END IF
687  160 CONTINUE
688 *
689  170 CONTINUE
690  180 CONTINUE
691  190 CONTINUE
692 *
693 * Summary
694 *
695  CALL dlasum( 'ZHB', nounit, nerrs, ntestt )
696  RETURN
697 *
698  9999 FORMAT( ' ZCHKHB: ', a, ' returned INFO=', i6, '.', / 9x, 'N=',
699  \$ i6, ', JTYPE=', i6, ', ISEED=(', 3( i5, ',' ), i5, ')' )
700  9998 FORMAT( / 1x, a3,
701  \$ ' -- Complex Hermitian Banded Tridiagonal Reduction Routines'
702  \$ )
703  9997 FORMAT( ' Matrix types (see DCHK23 for details): ' )
704 *
705  9996 FORMAT( / ' Special Matrices:',
706  \$ / ' 1=Zero matrix. ',
707  \$ ' 5=Diagonal: clustered entries.',
708  \$ / ' 2=Identity matrix. ',
709  \$ ' 6=Diagonal: large, evenly spaced.',
710  \$ / ' 3=Diagonal: evenly spaced entries. ',
711  \$ ' 7=Diagonal: small, evenly spaced.',
712  \$ / ' 4=Diagonal: geometr. spaced entries.' )
713  9995 FORMAT( ' Dense ', a, ' Banded Matrices:',
714  \$ / ' 8=Evenly spaced eigenvals. ',
715  \$ ' 12=Small, evenly spaced eigenvals.',
716  \$ / ' 9=Geometrically spaced eigenvals. ',
717  \$ ' 13=Matrix with random O(1) entries.',
718  \$ / ' 10=Clustered eigenvalues. ',
719  \$ ' 14=Matrix with large random entries.',
720  \$ / ' 11=Large, evenly spaced eigenvals. ',
721  \$ ' 15=Matrix with small random entries.' )
722 *
723  9994 FORMAT( / ' Tests performed: (S is Tridiag, U is ', a, ',',
724  \$ / 20x, a, ' means ', a, '.', / ' UPLO=''U'':',
725  \$ / ' 1= | A - U S U', a1, ' | / ( |A| n ulp ) ',
726  \$ ' 2= | I - U U', a1, ' | / ( n ulp )', / ' UPLO=''L'':',
727  \$ / ' 3= | A - U S U', a1, ' | / ( |A| n ulp ) ',
728  \$ ' 4= | I - U U', a1, ' | / ( n ulp )' )
729  9993 FORMAT( ' N=', i5, ', K=', i4, ', seed=', 4( i4, ',' ), ' type ',
730  \$ i2, ', test(', i2, ')=', g10.3 )
731 *
732 * End of ZCHKHB
733 *
734  END
subroutine zlatmr(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, RSIGN, GRADE, DL, MODEL, CONDL, DR, MODER, CONDR, PIVTNG, IPIVOT, KL, KU, SPARSE, ANORM, PACK, A, LDA, IWORK, INFO)
ZLATMR
Definition: zlatmr.f:492
subroutine zlacpy(UPLO, M, N, A, LDA, B, LDB)
ZLACPY copies all or part of one two-dimensional array to another.
Definition: zlacpy.f:105
subroutine zhbtrd(VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ, WORK, INFO)
ZHBTRD
Definition: zhbtrd.f:165
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine zlaset(UPLO, M, N, ALPHA, BETA, A, LDA)
ZLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values...
Definition: zlaset.f:108
subroutine dlasum(TYPE, IOUNIT, IE, NRUN)
DLASUM
Definition: dlasum.f:45
subroutine zhbt21(UPLO, N, KA, KS, A, LDA, D, E, U, LDU, WORK, RWORK, RESULT)
ZHBT21
Definition: zhbt21.f:152
subroutine zlatms(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, KL, KU, PACK, A, LDA, WORK, INFO)
ZLATMS
Definition: zlatms.f:334
subroutine zchkhb(NSIZES, NN, NWDTHS, KK, NTYPES, DOTYPE, ISEED, THRESH, NOUNIT, A, LDA, SD, SE, U, LDU, WORK, LWORK, RWORK, RESULT, INFO)
ZCHKHB
Definition: zchkhb.f:300