LAPACK  3.9.0
LAPACK: Linear Algebra PACKage
dchksb2stg.f
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1 *> \brief \b DCHKSBSTG
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 DCHKSB2STG( NSIZES, NN, NWDTHS, KK, NTYPES, DOTYPE,
12 * ISEED, THRESH, NOUNIT, A, LDA, SD, SE, D1,
13 * D2, D3, U, LDU, WORK, LWORK, 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 A( LDA, * ), RESULT( * ), SD( * ), SE( * ),
24 * $ U( LDU, * ), WORK( * )
25 * ..
26 *
27 *
28 *> \par Purpose:
29 * =============
30 *>
31 *> \verbatim
32 *>
33 *> DCHKSBSTG tests the reduction of a symmetric band matrix to tridiagonal
34 *> form, used with the symmetric eigenvalue problem.
35 *>
36 *> DSBTRD factors a symmetric band matrix A as U S U' , where ' means
37 *> transpose, S is symmetric tridiagonal, and U is orthogonal.
38 *> DSBTRD can use either just the lower or just the upper triangle
39 *> of A; DCHKSBSTG checks both cases.
40 *>
41 *> DSYTRD_SB2ST factors a symmetric band matrix A as U S U' ,
42 *> where ' means transpose, S is symmetric tridiagonal, and U is
43 *> orthogonal. DSYTRD_SB2ST can use either just the lower or just
44 *> the upper triangle of A; DCHKSBSTG checks both cases.
45 *>
46 *> DSTEQR factors S as Z D1 Z'.
47 *> D1 is the matrix of eigenvalues computed when Z is not computed
48 *> and from the S resulting of DSBTRD "U" (used as reference for DSYTRD_SB2ST)
49 *> D2 is the matrix of eigenvalues computed when Z is not computed
50 *> and from the S resulting of DSYTRD_SB2ST "U".
51 *> D3 is the matrix of eigenvalues computed when Z is not computed
52 *> and from the S resulting of DSYTRD_SB2ST "L".
53 *>
54 *> When DCHKSBSTG is called, a number of matrix "sizes" ("n's"), a number
55 *> of bandwidths ("k's"), and a number of matrix "types" are
56 *> specified. For each size ("n"), each bandwidth ("k") less than or
57 *> equal to "n", and each type of matrix, one matrix will be generated
58 *> and used to test the symmetric banded reduction routine. For each
59 *> matrix, a number of tests will be performed:
60 *>
61 *> (1) | A - V S V' | / ( |A| n ulp ) computed by DSBTRD with
62 *> UPLO='U'
63 *>
64 *> (2) | I - UU' | / ( n ulp )
65 *>
66 *> (3) | A - V S V' | / ( |A| n ulp ) computed by DSBTRD with
67 *> UPLO='L'
68 *>
69 *> (4) | I - UU' | / ( n ulp )
70 *>
71 *> (5) | D1 - D2 | / ( |D1| ulp ) where D1 is computed by
72 *> DSBTRD with UPLO='U' and
73 *> D2 is computed by
74 *> DSYTRD_SB2ST with UPLO='U'
75 *>
76 *> (6) | D1 - D3 | / ( |D1| ulp ) where D1 is computed by
77 *> DSBTRD with UPLO='U' and
78 *> D3 is computed by
79 *> DSYTRD_SB2ST with UPLO='L'
80 *>
81 *> The "sizes" are specified by an array NN(1:NSIZES); the value of
82 *> each element NN(j) specifies one size.
83 *> The "types" are specified by a logical array DOTYPE( 1:NTYPES );
84 *> if DOTYPE(j) is .TRUE., then matrix type "j" will be generated.
85 *> Currently, the list of possible types is:
86 *>
87 *> (1) The zero matrix.
88 *> (2) The identity matrix.
89 *>
90 *> (3) A diagonal matrix with evenly spaced entries
91 *> 1, ..., ULP and random signs.
92 *> (ULP = (first number larger than 1) - 1 )
93 *> (4) A diagonal matrix with geometrically spaced entries
94 *> 1, ..., ULP and random signs.
95 *> (5) A diagonal matrix with "clustered" entries 1, ULP, ..., ULP
96 *> and random signs.
97 *>
98 *> (6) Same as (4), but multiplied by SQRT( overflow threshold )
99 *> (7) Same as (4), but multiplied by SQRT( underflow threshold )
100 *>
101 *> (8) A matrix of the form U' D U, where U is orthogonal and
102 *> D has evenly spaced entries 1, ..., ULP with random signs
103 *> on the diagonal.
104 *>
105 *> (9) A matrix of the form U' D U, where U is orthogonal and
106 *> D has geometrically spaced entries 1, ..., ULP with random
107 *> signs on the diagonal.
108 *>
109 *> (10) A matrix of the form U' D U, where U is orthogonal and
110 *> D has "clustered" entries 1, ULP,..., ULP with random
111 *> signs on the diagonal.
112 *>
113 *> (11) Same as (8), but multiplied by SQRT( overflow threshold )
114 *> (12) Same as (8), but multiplied by SQRT( underflow threshold )
115 *>
116 *> (13) Symmetric matrix with random entries chosen from (-1,1).
117 *> (14) Same as (13), but multiplied by SQRT( overflow threshold )
118 *> (15) Same as (13), but multiplied by SQRT( underflow threshold )
119 *> \endverbatim
120 *
121 * Arguments:
122 * ==========
123 *
124 *> \param[in] NSIZES
125 *> \verbatim
126 *> NSIZES is INTEGER
127 *> The number of sizes of matrices to use. If it is zero,
128 *> DCHKSBSTG does nothing. It must be at least zero.
129 *> \endverbatim
130 *>
131 *> \param[in] NN
132 *> \verbatim
133 *> NN is INTEGER array, dimension (NSIZES)
134 *> An array containing the sizes to be used for the matrices.
135 *> Zero values will be skipped. The values must be at least
136 *> zero.
137 *> \endverbatim
138 *>
139 *> \param[in] NWDTHS
140 *> \verbatim
141 *> NWDTHS is INTEGER
142 *> The number of bandwidths to use. If it is zero,
143 *> DCHKSBSTG does nothing. It must be at least zero.
144 *> \endverbatim
145 *>
146 *> \param[in] KK
147 *> \verbatim
148 *> KK is INTEGER array, dimension (NWDTHS)
149 *> An array containing the bandwidths to be used for the band
150 *> matrices. The values must be at least zero.
151 *> \endverbatim
152 *>
153 *> \param[in] NTYPES
154 *> \verbatim
155 *> NTYPES is INTEGER
156 *> The number of elements in DOTYPE. If it is zero, DCHKSBSTG
157 *> does nothing. It must be at least zero. If it is MAXTYP+1
158 *> and NSIZES is 1, then an additional type, MAXTYP+1 is
159 *> defined, which is to use whatever matrix is in A. This
160 *> is only useful if DOTYPE(1:MAXTYP) is .FALSE. and
161 *> DOTYPE(MAXTYP+1) is .TRUE. .
162 *> \endverbatim
163 *>
164 *> \param[in] DOTYPE
165 *> \verbatim
166 *> DOTYPE is LOGICAL array, dimension (NTYPES)
167 *> If DOTYPE(j) is .TRUE., then for each size in NN a
168 *> matrix of that size and of type j will be generated.
169 *> If NTYPES is smaller than the maximum number of types
170 *> defined (PARAMETER MAXTYP), then types NTYPES+1 through
171 *> MAXTYP will not be generated. If NTYPES is larger
172 *> than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES)
173 *> will be ignored.
174 *> \endverbatim
175 *>
176 *> \param[in,out] ISEED
177 *> \verbatim
178 *> ISEED is INTEGER array, dimension (4)
179 *> On entry ISEED specifies the seed of the random number
180 *> generator. The array elements should be between 0 and 4095;
181 *> if not they will be reduced mod 4096. Also, ISEED(4) must
182 *> be odd. The random number generator uses a linear
183 *> congruential sequence limited to small integers, and so
184 *> should produce machine independent random numbers. The
185 *> values of ISEED are changed on exit, and can be used in the
186 *> next call to DCHKSBSTG to continue the same random number
187 *> sequence.
188 *> \endverbatim
189 *>
190 *> \param[in] THRESH
191 *> \verbatim
192 *> THRESH is DOUBLE PRECISION
193 *> A test will count as "failed" if the "error", computed as
194 *> described above, exceeds THRESH. Note that the error
195 *> is scaled to be O(1), so THRESH should be a reasonably
196 *> small multiple of 1, e.g., 10 or 100. In particular,
197 *> it should not depend on the precision (single vs. double)
198 *> or the size of the matrix. It must be at least zero.
199 *> \endverbatim
200 *>
201 *> \param[in] NOUNIT
202 *> \verbatim
203 *> NOUNIT is INTEGER
204 *> The FORTRAN unit number for printing out error messages
205 *> (e.g., if a routine returns IINFO not equal to 0.)
206 *> \endverbatim
207 *>
208 *> \param[in,out] A
209 *> \verbatim
210 *> A is DOUBLE PRECISION array, dimension
211 *> (LDA, max(NN))
212 *> Used to hold the matrix whose eigenvalues are to be
213 *> computed.
214 *> \endverbatim
215 *>
216 *> \param[in] LDA
217 *> \verbatim
218 *> LDA is INTEGER
219 *> The leading dimension of A. It must be at least 2 (not 1!)
220 *> and at least max( KK )+1.
221 *> \endverbatim
222 *>
223 *> \param[out] SD
224 *> \verbatim
225 *> SD is DOUBLE PRECISION array, dimension (max(NN))
226 *> Used to hold the diagonal of the tridiagonal matrix computed
227 *> by DSBTRD.
228 *> \endverbatim
229 *>
230 *> \param[out] SE
231 *> \verbatim
232 *> SE is DOUBLE PRECISION array, dimension (max(NN))
233 *> Used to hold the off-diagonal of the tridiagonal matrix
234 *> computed by DSBTRD.
235 *> \endverbatim
236 *>
237 *> \param[out] U
238 *> \verbatim
239 *> U is DOUBLE PRECISION array, dimension (LDU, max(NN))
240 *> Used to hold the orthogonal matrix computed by DSBTRD.
241 *> \endverbatim
242 *>
243 *> \param[in] LDU
244 *> \verbatim
245 *> LDU is INTEGER
246 *> The leading dimension of U. It must be at least 1
247 *> and at least max( NN ).
248 *> \endverbatim
249 *>
250 *> \param[out] WORK
251 *> \verbatim
252 *> WORK is DOUBLE PRECISION array, dimension (LWORK)
253 *> \endverbatim
254 *>
255 *> \param[in] LWORK
256 *> \verbatim
257 *> LWORK is INTEGER
258 *> The number of entries in WORK. This must be at least
259 *> max( LDA+1, max(NN)+1 )*max(NN).
260 *> \endverbatim
261 *>
262 *> \param[out] RESULT
263 *> \verbatim
264 *> RESULT is DOUBLE PRECISION array, dimension (4)
265 *> The values computed by the tests described above.
266 *> The values are currently limited to 1/ulp, to avoid
267 *> overflow.
268 *> \endverbatim
269 *>
270 *> \param[out] INFO
271 *> \verbatim
272 *> INFO is INTEGER
273 *> If 0, then everything ran OK.
274 *>
275 *>-----------------------------------------------------------------------
276 *>
277 *> Some Local Variables and Parameters:
278 *> ---- ----- --------- --- ----------
279 *> ZERO, ONE Real 0 and 1.
280 *> MAXTYP The number of types defined.
281 *> NTEST The number of tests performed, or which can
282 *> be performed so far, for the current matrix.
283 *> NTESTT The total number of tests performed so far.
284 *> NMAX Largest value in NN.
285 *> NMATS The number of matrices generated so far.
286 *> NERRS The number of tests which have exceeded THRESH
287 *> so far.
288 *> COND, IMODE Values to be passed to the matrix generators.
289 *> ANORM Norm of A; passed to matrix generators.
290 *>
291 *> OVFL, UNFL Overflow and underflow thresholds.
292 *> ULP, ULPINV Finest relative precision and its inverse.
293 *> RTOVFL, RTUNFL Square roots of the previous 2 values.
294 *> The following four arrays decode JTYPE:
295 *> KTYPE(j) The general type (1-10) for type "j".
296 *> KMODE(j) The MODE value to be passed to the matrix
297 *> generator for type "j".
298 *> KMAGN(j) The order of magnitude ( O(1),
299 *> O(overflow^(1/2) ), O(underflow^(1/2) )
300 *> \endverbatim
301 *
302 * Authors:
303 * ========
304 *
305 *> \author Univ. of Tennessee
306 *> \author Univ. of California Berkeley
307 *> \author Univ. of Colorado Denver
308 *> \author NAG Ltd.
309 *
310 *> \date June 2017
311 *
312 *> \ingroup double_eig
313 *
314 * =====================================================================
315  SUBROUTINE dchksb2stg( NSIZES, NN, NWDTHS, KK, NTYPES, DOTYPE,
316  $ ISEED, THRESH, NOUNIT, A, LDA, SD, SE, D1,
317  $ D2, D3, U, LDU, WORK, LWORK, RESULT, INFO )
318 *
319 * -- LAPACK test routine (version 3.7.1) --
320 * -- LAPACK is a software package provided by Univ. of Tennessee, --
321 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
322 * June 2017
323 *
324 * .. Scalar Arguments ..
325  INTEGER INFO, LDA, LDU, LWORK, NOUNIT, NSIZES, NTYPES,
326  $ NWDTHS
327  DOUBLE PRECISION THRESH
328 * ..
329 * .. Array Arguments ..
330  LOGICAL DOTYPE( * )
331  INTEGER ISEED( 4 ), KK( * ), NN( * )
332  DOUBLE PRECISION A( LDA, * ), RESULT( * ), SD( * ), SE( * ),
333  $ d1( * ), d2( * ), d3( * ),
334  $ u( ldu, * ), work( * )
335 * ..
336 *
337 * =====================================================================
338 *
339 * .. Parameters ..
340  DOUBLE PRECISION ZERO, ONE, TWO, TEN
341  PARAMETER ( ZERO = 0.0d0, one = 1.0d0, two = 2.0d0,
342  $ ten = 10.0d0 )
343  DOUBLE PRECISION HALF
344  PARAMETER ( HALF = one / two )
345  INTEGER MAXTYP
346  parameter( maxtyp = 15 )
347 * ..
348 * .. Local Scalars ..
349  LOGICAL BADNN, BADNNB
350  INTEGER I, IINFO, IMODE, ITYPE, J, JC, JCOL, JR, JSIZE,
351  $ jtype, jwidth, k, kmax, lh, lw, mtypes, n,
352  $ nerrs, nmats, nmax, ntest, ntestt
353  DOUBLE PRECISION ANINV, ANORM, COND, OVFL, RTOVFL, RTUNFL,
354  $ TEMP1, TEMP2, TEMP3, TEMP4, ULP, ULPINV, UNFL
355 * ..
356 * .. Local Arrays ..
357  INTEGER IDUMMA( 1 ), IOLDSD( 4 ), KMAGN( MAXTYP ),
358  $ KMODE( MAXTYP ), KTYPE( MAXTYP )
359 * ..
360 * .. External Functions ..
361  DOUBLE PRECISION DLAMCH
362  EXTERNAL DLAMCH
363 * ..
364 * .. External Subroutines ..
365  EXTERNAL dlacpy, dlaset, dlasum, dlatmr, dlatms, dsbt21,
366  $ dsbtrd, xerbla, dsytrd_sb2st, dsteqr
367 * ..
368 * .. Intrinsic Functions ..
369  INTRINSIC abs, dble, max, min, sqrt
370 * ..
371 * .. Data statements ..
372  DATA ktype / 1, 2, 5*4, 5*5, 3*8 /
373  DATA kmagn / 2*1, 1, 1, 1, 2, 3, 1, 1, 1, 2, 3, 1,
374  $ 2, 3 /
375  DATA kmode / 2*0, 4, 3, 1, 4, 4, 4, 3, 1, 4, 4, 0,
376  $ 0, 0 /
377 * ..
378 * .. Executable Statements ..
379 *
380 * Check for errors
381 *
382  ntestt = 0
383  info = 0
384 *
385 * Important constants
386 *
387  badnn = .false.
388  nmax = 1
389  DO 10 j = 1, nsizes
390  nmax = max( nmax, nn( j ) )
391  IF( nn( j ).LT.0 )
392  $ badnn = .true.
393  10 CONTINUE
394 *
395  badnnb = .false.
396  kmax = 0
397  DO 20 j = 1, nsizes
398  kmax = max( kmax, kk( j ) )
399  IF( kk( j ).LT.0 )
400  $ badnnb = .true.
401  20 CONTINUE
402  kmax = min( nmax-1, kmax )
403 *
404 * Check for errors
405 *
406  IF( nsizes.LT.0 ) THEN
407  info = -1
408  ELSE IF( badnn ) THEN
409  info = -2
410  ELSE IF( nwdths.LT.0 ) THEN
411  info = -3
412  ELSE IF( badnnb ) THEN
413  info = -4
414  ELSE IF( ntypes.LT.0 ) THEN
415  info = -5
416  ELSE IF( lda.LT.kmax+1 ) THEN
417  info = -11
418  ELSE IF( ldu.LT.nmax ) THEN
419  info = -15
420  ELSE IF( ( max( lda, nmax )+1 )*nmax.GT.lwork ) THEN
421  info = -17
422  END IF
423 *
424  IF( info.NE.0 ) THEN
425  CALL xerbla( 'DCHKSBSTG', -info )
426  RETURN
427  END IF
428 *
429 * Quick return if possible
430 *
431  IF( nsizes.EQ.0 .OR. ntypes.EQ.0 .OR. nwdths.EQ.0 )
432  $ RETURN
433 *
434 * More Important constants
435 *
436  unfl = dlamch( 'Safe minimum' )
437  ovfl = one / unfl
438  ulp = dlamch( 'Epsilon' )*dlamch( 'Base' )
439  ulpinv = one / ulp
440  rtunfl = sqrt( unfl )
441  rtovfl = sqrt( ovfl )
442 *
443 * Loop over sizes, types
444 *
445  nerrs = 0
446  nmats = 0
447 *
448  DO 190 jsize = 1, nsizes
449  n = nn( jsize )
450  aninv = one / dble( max( 1, n ) )
451 *
452  DO 180 jwidth = 1, nwdths
453  k = kk( jwidth )
454  IF( k.GT.n )
455  $ GO TO 180
456  k = max( 0, min( n-1, k ) )
457 *
458  IF( nsizes.NE.1 ) THEN
459  mtypes = min( maxtyp, ntypes )
460  ELSE
461  mtypes = min( maxtyp+1, ntypes )
462  END IF
463 *
464  DO 170 jtype = 1, mtypes
465  IF( .NOT.dotype( jtype ) )
466  $ GO TO 170
467  nmats = nmats + 1
468  ntest = 0
469 *
470  DO 30 j = 1, 4
471  ioldsd( j ) = iseed( j )
472  30 CONTINUE
473 *
474 * Compute "A".
475 * Store as "Upper"; later, we will copy to other format.
476 *
477 * Control parameters:
478 *
479 * KMAGN KMODE KTYPE
480 * =1 O(1) clustered 1 zero
481 * =2 large clustered 2 identity
482 * =3 small exponential (none)
483 * =4 arithmetic diagonal, (w/ eigenvalues)
484 * =5 random log symmetric, w/ eigenvalues
485 * =6 random (none)
486 * =7 random diagonal
487 * =8 random symmetric
488 * =9 positive definite
489 * =10 diagonally dominant tridiagonal
490 *
491  IF( mtypes.GT.maxtyp )
492  $ GO TO 100
493 *
494  itype = ktype( jtype )
495  imode = kmode( jtype )
496 *
497 * Compute norm
498 *
499  GO TO ( 40, 50, 60 )kmagn( jtype )
500 *
501  40 CONTINUE
502  anorm = one
503  GO TO 70
504 *
505  50 CONTINUE
506  anorm = ( rtovfl*ulp )*aninv
507  GO TO 70
508 *
509  60 CONTINUE
510  anorm = rtunfl*n*ulpinv
511  GO TO 70
512 *
513  70 CONTINUE
514 *
515  CALL dlaset( 'Full', lda, n, zero, zero, a, lda )
516  iinfo = 0
517  IF( jtype.LE.15 ) THEN
518  cond = ulpinv
519  ELSE
520  cond = ulpinv*aninv / ten
521  END IF
522 *
523 * Special Matrices -- Identity & Jordan block
524 *
525 * Zero
526 *
527  IF( itype.EQ.1 ) THEN
528  iinfo = 0
529 *
530  ELSE IF( itype.EQ.2 ) THEN
531 *
532 * Identity
533 *
534  DO 80 jcol = 1, n
535  a( k+1, jcol ) = anorm
536  80 CONTINUE
537 *
538  ELSE IF( itype.EQ.4 ) THEN
539 *
540 * Diagonal Matrix, [Eigen]values Specified
541 *
542  CALL dlatms( n, n, 'S', iseed, 'S', work, imode, cond,
543  $ anorm, 0, 0, 'Q', a( k+1, 1 ), lda,
544  $ work( n+1 ), iinfo )
545 *
546  ELSE IF( itype.EQ.5 ) THEN
547 *
548 * Symmetric, eigenvalues specified
549 *
550  CALL dlatms( n, n, 'S', iseed, 'S', work, imode, cond,
551  $ anorm, k, k, 'Q', a, lda, work( n+1 ),
552  $ iinfo )
553 *
554  ELSE IF( itype.EQ.7 ) THEN
555 *
556 * Diagonal, random eigenvalues
557 *
558  CALL dlatmr( n, n, 'S', iseed, 'S', work, 6, one, one,
559  $ 'T', 'N', work( n+1 ), 1, one,
560  $ work( 2*n+1 ), 1, one, 'N', idumma, 0, 0,
561  $ zero, anorm, 'Q', a( k+1, 1 ), lda,
562  $ idumma, iinfo )
563 *
564  ELSE IF( itype.EQ.8 ) THEN
565 *
566 * Symmetric, random eigenvalues
567 *
568  CALL dlatmr( n, n, 'S', iseed, 'S', work, 6, one, one,
569  $ 'T', 'N', work( n+1 ), 1, one,
570  $ work( 2*n+1 ), 1, one, 'N', idumma, k, k,
571  $ zero, anorm, 'Q', a, lda, idumma, iinfo )
572 *
573  ELSE IF( itype.EQ.9 ) THEN
574 *
575 * Positive definite, eigenvalues specified.
576 *
577  CALL dlatms( n, n, 'S', iseed, 'P', work, imode, cond,
578  $ anorm, k, k, 'Q', a, lda, work( n+1 ),
579  $ iinfo )
580 *
581  ELSE IF( itype.EQ.10 ) THEN
582 *
583 * Positive definite tridiagonal, eigenvalues specified.
584 *
585  IF( n.GT.1 )
586  $ k = max( 1, k )
587  CALL dlatms( n, n, 'S', iseed, 'P', work, imode, cond,
588  $ anorm, 1, 1, 'Q', a( k, 1 ), lda,
589  $ work( n+1 ), iinfo )
590  DO 90 i = 2, n
591  temp1 = abs( a( k, i ) ) /
592  $ sqrt( abs( a( k+1, i-1 )*a( k+1, i ) ) )
593  IF( temp1.GT.half ) THEN
594  a( k, i ) = half*sqrt( abs( a( k+1,
595  $ i-1 )*a( k+1, i ) ) )
596  END IF
597  90 CONTINUE
598 *
599  ELSE
600 *
601  iinfo = 1
602  END IF
603 *
604  IF( iinfo.NE.0 ) THEN
605  WRITE( nounit, fmt = 9999 )'Generator', iinfo, n,
606  $ jtype, ioldsd
607  info = abs( iinfo )
608  RETURN
609  END IF
610 *
611  100 CONTINUE
612 *
613 * Call DSBTRD to compute S and U from upper triangle.
614 *
615  CALL dlacpy( ' ', k+1, n, a, lda, work, lda )
616 *
617  ntest = 1
618  CALL dsbtrd( 'V', 'U', n, k, work, lda, sd, se, u, ldu,
619  $ work( lda*n+1 ), iinfo )
620 *
621  IF( iinfo.NE.0 ) THEN
622  WRITE( nounit, fmt = 9999 )'DSBTRD(U)', iinfo, n,
623  $ jtype, ioldsd
624  info = abs( iinfo )
625  IF( iinfo.LT.0 ) THEN
626  RETURN
627  ELSE
628  result( 1 ) = ulpinv
629  GO TO 150
630  END IF
631  END IF
632 *
633 * Do tests 1 and 2
634 *
635  CALL dsbt21( 'Upper', n, k, 1, a, lda, sd, se, u, ldu,
636  $ work, result( 1 ) )
637 *
638 * Before converting A into lower for DSBTRD, run DSYTRD_SB2ST
639 * otherwise matrix A will be converted to lower and then need
640 * to be converted back to upper in order to run the upper case
641 * ofDSYTRD_SB2ST
642 *
643 * Compute D1 the eigenvalues resulting from the tridiagonal
644 * form using the DSBTRD and used as reference to compare
645 * with the DSYTRD_SB2ST routine
646 *
647 * Compute D1 from the DSBTRD and used as reference for the
648 * DSYTRD_SB2ST
649 *
650  CALL dcopy( n, sd, 1, d1, 1 )
651  IF( n.GT.0 )
652  $ CALL dcopy( n-1, se, 1, work, 1 )
653 *
654  CALL dsteqr( 'N', n, d1, work, work( n+1 ), ldu,
655  $ work( n+1 ), iinfo )
656  IF( iinfo.NE.0 ) THEN
657  WRITE( nounit, fmt = 9999 )'DSTEQR(N)', iinfo, n,
658  $ jtype, ioldsd
659  info = abs( iinfo )
660  IF( iinfo.LT.0 ) THEN
661  RETURN
662  ELSE
663  result( 5 ) = ulpinv
664  GO TO 150
665  END IF
666  END IF
667 *
668 * DSYTRD_SB2ST Upper case is used to compute D2.
669 * Note to set SD and SE to zero to be sure not reusing
670 * the one from above. Compare it with D1 computed
671 * using the DSBTRD.
672 *
673  CALL dlaset( 'Full', n, 1, zero, zero, sd, 1 )
674  CALL dlaset( 'Full', n, 1, zero, zero, se, 1 )
675  CALL dlacpy( ' ', k+1, n, a, lda, u, ldu )
676  lh = max(1, 4*n)
677  lw = lwork - lh
678  CALL dsytrd_sb2st( 'N', 'N', "U", n, k, u, ldu, sd, se,
679  $ work, lh, work( lh+1 ), lw, iinfo )
680 *
681 * Compute D2 from the DSYTRD_SB2ST Upper case
682 *
683  CALL dcopy( n, sd, 1, d2, 1 )
684  IF( n.GT.0 )
685  $ CALL dcopy( n-1, se, 1, work, 1 )
686 *
687  CALL dsteqr( 'N', n, d2, work, work( n+1 ), ldu,
688  $ work( n+1 ), iinfo )
689  IF( iinfo.NE.0 ) THEN
690  WRITE( nounit, fmt = 9999 )'DSTEQR(N)', iinfo, n,
691  $ jtype, ioldsd
692  info = abs( iinfo )
693  IF( iinfo.LT.0 ) THEN
694  RETURN
695  ELSE
696  result( 5 ) = ulpinv
697  GO TO 150
698  END IF
699  END IF
700 *
701 * Convert A from Upper-Triangle-Only storage to
702 * Lower-Triangle-Only storage.
703 *
704  DO 120 jc = 1, n
705  DO 110 jr = 0, min( k, n-jc )
706  a( jr+1, jc ) = a( k+1-jr, jc+jr )
707  110 CONTINUE
708  120 CONTINUE
709  DO 140 jc = n + 1 - k, n
710  DO 130 jr = min( k, n-jc ) + 1, k
711  a( jr+1, jc ) = zero
712  130 CONTINUE
713  140 CONTINUE
714 *
715 * Call DSBTRD to compute S and U from lower triangle
716 *
717  CALL dlacpy( ' ', k+1, n, a, lda, work, lda )
718 *
719  ntest = 3
720  CALL dsbtrd( 'V', 'L', n, k, work, lda, sd, se, u, ldu,
721  $ work( lda*n+1 ), iinfo )
722 *
723  IF( iinfo.NE.0 ) THEN
724  WRITE( nounit, fmt = 9999 )'DSBTRD(L)', iinfo, n,
725  $ jtype, ioldsd
726  info = abs( iinfo )
727  IF( iinfo.LT.0 ) THEN
728  RETURN
729  ELSE
730  result( 3 ) = ulpinv
731  GO TO 150
732  END IF
733  END IF
734  ntest = 4
735 *
736 * Do tests 3 and 4
737 *
738  CALL dsbt21( 'Lower', n, k, 1, a, lda, sd, se, u, ldu,
739  $ work, result( 3 ) )
740 *
741 * DSYTRD_SB2ST Lower case is used to compute D3.
742 * Note to set SD and SE to zero to be sure not reusing
743 * the one from above. Compare it with D1 computed
744 * using the DSBTRD.
745 *
746  CALL dlaset( 'Full', n, 1, zero, zero, sd, 1 )
747  CALL dlaset( 'Full', n, 1, zero, zero, se, 1 )
748  CALL dlacpy( ' ', k+1, n, a, lda, u, ldu )
749  lh = max(1, 4*n)
750  lw = lwork - lh
751  CALL dsytrd_sb2st( 'N', 'N', "L", n, k, u, ldu, sd, se,
752  $ work, lh, work( lh+1 ), lw, iinfo )
753 *
754 * Compute D3 from the 2-stage Upper case
755 *
756  CALL dcopy( n, sd, 1, d3, 1 )
757  IF( n.GT.0 )
758  $ CALL dcopy( n-1, se, 1, work, 1 )
759 *
760  CALL dsteqr( 'N', n, d3, work, work( n+1 ), ldu,
761  $ work( n+1 ), iinfo )
762  IF( iinfo.NE.0 ) THEN
763  WRITE( nounit, fmt = 9999 )'DSTEQR(N)', iinfo, n,
764  $ jtype, ioldsd
765  info = abs( iinfo )
766  IF( iinfo.LT.0 ) THEN
767  RETURN
768  ELSE
769  result( 6 ) = ulpinv
770  GO TO 150
771  END IF
772  END IF
773 *
774 *
775 * Do Tests 3 and 4 which are similar to 11 and 12 but with the
776 * D1 computed using the standard 1-stage reduction as reference
777 *
778  ntest = 6
779  temp1 = zero
780  temp2 = zero
781  temp3 = zero
782  temp4 = zero
783 *
784  DO 151 j = 1, n
785  temp1 = max( temp1, abs( d1( j ) ), abs( d2( j ) ) )
786  temp2 = max( temp2, abs( d1( j )-d2( j ) ) )
787  temp3 = max( temp3, abs( d1( j ) ), abs( d3( j ) ) )
788  temp4 = max( temp4, abs( d1( j )-d3( j ) ) )
789  151 CONTINUE
790 *
791  result(5) = temp2 / max( unfl, ulp*max( temp1, temp2 ) )
792  result(6) = temp4 / max( unfl, ulp*max( temp3, temp4 ) )
793 *
794 * End of Loop -- Check for RESULT(j) > THRESH
795 *
796  150 CONTINUE
797  ntestt = ntestt + ntest
798 *
799 * Print out tests which fail.
800 *
801  DO 160 jr = 1, ntest
802  IF( result( jr ).GE.thresh ) THEN
803 *
804 * If this is the first test to fail,
805 * print a header to the data file.
806 *
807  IF( nerrs.EQ.0 ) THEN
808  WRITE( nounit, fmt = 9998 )'DSB'
809  WRITE( nounit, fmt = 9997 )
810  WRITE( nounit, fmt = 9996 )
811  WRITE( nounit, fmt = 9995 )'Symmetric'
812  WRITE( nounit, fmt = 9994 )'orthogonal', '''',
813  $ 'transpose', ( '''', j = 1, 6 )
814  END IF
815  nerrs = nerrs + 1
816  WRITE( nounit, fmt = 9993 )n, k, ioldsd, jtype,
817  $ jr, result( jr )
818  END IF
819  160 CONTINUE
820 *
821  170 CONTINUE
822  180 CONTINUE
823  190 CONTINUE
824 *
825 * Summary
826 *
827  CALL dlasum( 'DSB', nounit, nerrs, ntestt )
828  RETURN
829 *
830  9999 FORMAT( ' DCHKSBSTG: ', a, ' returned INFO=', i6, '.', / 9x, 'N=',
831  $ i6, ', JTYPE=', i6, ', ISEED=(', 3( i5, ',' ), i5, ')' )
832 *
833  9998 FORMAT( / 1x, a3,
834  $ ' -- Real Symmetric Banded Tridiagonal Reduction Routines' )
835  9997 FORMAT( ' Matrix types (see DCHKSBSTG for details): ' )
836 *
837  9996 FORMAT( / ' Special Matrices:',
838  $ / ' 1=Zero matrix. ',
839  $ ' 5=Diagonal: clustered entries.',
840  $ / ' 2=Identity matrix. ',
841  $ ' 6=Diagonal: large, evenly spaced.',
842  $ / ' 3=Diagonal: evenly spaced entries. ',
843  $ ' 7=Diagonal: small, evenly spaced.',
844  $ / ' 4=Diagonal: geometr. spaced entries.' )
845  9995 FORMAT( ' Dense ', a, ' Banded Matrices:',
846  $ / ' 8=Evenly spaced eigenvals. ',
847  $ ' 12=Small, evenly spaced eigenvals.',
848  $ / ' 9=Geometrically spaced eigenvals. ',
849  $ ' 13=Matrix with random O(1) entries.',
850  $ / ' 10=Clustered eigenvalues. ',
851  $ ' 14=Matrix with large random entries.',
852  $ / ' 11=Large, evenly spaced eigenvals. ',
853  $ ' 15=Matrix with small random entries.' )
854 *
855  9994 FORMAT( / ' Tests performed: (S is Tridiag, U is ', a, ',',
856  $ / 20x, a, ' means ', a, '.', / ' UPLO=''U'':',
857  $ / ' 1= | A - U S U', a1, ' | / ( |A| n ulp ) ',
858  $ ' 2= | I - U U', a1, ' | / ( n ulp )', / ' UPLO=''L'':',
859  $ / ' 3= | A - U S U', a1, ' | / ( |A| n ulp ) ',
860  $ ' 4= | I - U U', a1, ' | / ( n ulp )' / ' Eig check:',
861  $ /' 5= | D1 - D2', '', ' | / ( |D1| ulp ) ',
862  $ ' 6= | D1 - D3', '', ' | / ( |D1| ulp ) ' )
863  9993 FORMAT( ' N=', i5, ', K=', i4, ', seed=', 4( i4, ',' ), ' type ',
864  $ i2, ', test(', i2, ')=', g10.3 )
865 *
866 * End of DCHKSBSTG
867 *
868  END
dlatms
subroutine dlatms(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, KL, KU, PACK, A, LDA, WORK, INFO)
DLATMS
Definition: dlatms.f:323
dsytrd_sb2st
subroutine dsytrd_sb2st(STAGE1, VECT, UPLO, N, KD, AB, LDAB, D, E, HOUS, LHOUS, WORK, LWORK, INFO)
DSYTRD_SB2ST reduces a real symmetric band matrix A to real symmetric tridiagonal form T
Definition: dsytrd_sb2st.F:232
dlasum
subroutine dlasum(TYPE, IOUNIT, IE, NRUN)
DLASUM
Definition: dlasum.f:45
dchksb2stg
subroutine dchksb2stg(NSIZES, NN, NWDTHS, KK, NTYPES, DOTYPE, ISEED, THRESH, NOUNIT, A, LDA, SD, SE, D1, D2, D3, U, LDU, WORK, LWORK, RESULT, INFO)
DCHKSBSTG
Definition: dchksb2stg.f:318
dlatmr
subroutine dlatmr(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)
DLATMR
Definition: dlatmr.f:473
dcopy
subroutine dcopy(N, DX, INCX, DY, INCY)
DCOPY
Definition: dcopy.f:84
dsteqr
subroutine dsteqr(COMPZ, N, D, E, Z, LDZ, WORK, INFO)
DSTEQR
Definition: dsteqr.f:133
dsbtrd
subroutine dsbtrd(VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ, WORK, INFO)
DSBTRD
Definition: dsbtrd.f:165
xerbla
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
dsbt21
subroutine dsbt21(UPLO, N, KA, KS, A, LDA, D, E, U, LDU, WORK, RESULT)
DSBT21
Definition: dsbt21.f:149
dlaset
subroutine dlaset(UPLO, M, N, ALPHA, BETA, A, LDA)
DLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition: dlaset.f:112
dlacpy
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