LAPACK  3.10.0
LAPACK: Linear Algebra PACKage
schksb2stg.f
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1 *> \brief \b SCHKSB2STG
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 SCHKSB2STG( 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 * REAL THRESH
19 * ..
20 * .. Array Arguments ..
21 * LOGICAL DOTYPE( * )
22 * INTEGER ISEED( 4 ), KK( * ), NN( * )
23 * REAL A( LDA, * ), RESULT( * ), SD( * ), SE( * ),
24 * $ D1( * ), D2( * ), D3( * ),
25 * $ U( LDU, * ), WORK( * )
26 * ..
27 *
28 *
29 *> \par Purpose:
30 * =============
31 *>
32 *> \verbatim
33 *>
34 *> SCHKSB2STG tests the reduction of a symmetric band matrix to tridiagonal
35 *> form, used with the symmetric eigenvalue problem.
36 *>
37 *> SSBTRD factors a symmetric band matrix A as U S U' , where ' means
38 *> transpose, S is symmetric tridiagonal, and U is orthogonal.
39 *> SSBTRD can use either just the lower or just the upper triangle
40 *> of A; SCHKSB2STG checks both cases.
41 *>
42 *> SSYTRD_SB2ST factors a symmetric band matrix A as U S U' ,
43 *> where ' means transpose, S is symmetric tridiagonal, and U is
44 *> orthogonal. SSYTRD_SB2ST can use either just the lower or just
45 *> the upper triangle of A; SCHKSB2STG checks both cases.
46 *>
47 *> SSTEQR factors S as Z D1 Z'.
48 *> D1 is the matrix of eigenvalues computed when Z is not computed
49 *> and from the S resulting of SSBTRD "U" (used as reference for SSYTRD_SB2ST)
50 *> D2 is the matrix of eigenvalues computed when Z is not computed
51 *> and from the S resulting of SSYTRD_SB2ST "U".
52 *> D3 is the matrix of eigenvalues computed when Z is not computed
53 *> and from the S resulting of SSYTRD_SB2ST "L".
54 *>
55 *> When SCHKSB2STG is called, a number of matrix "sizes" ("n's"), a number
56 *> of bandwidths ("k's"), and a number of matrix "types" are
57 *> specified. For each size ("n"), each bandwidth ("k") less than or
58 *> equal to "n", and each type of matrix, one matrix will be generated
59 *> and used to test the symmetric banded reduction routine. For each
60 *> matrix, a number of tests will be performed:
61 *>
62 *> (1) | A - V S V' | / ( |A| n ulp ) computed by SSBTRD with
63 *> UPLO='U'
64 *>
65 *> (2) | I - UU' | / ( n ulp )
66 *>
67 *> (3) | A - V S V' | / ( |A| n ulp ) computed by SSBTRD with
68 *> UPLO='L'
69 *>
70 *> (4) | I - UU' | / ( n ulp )
71 *>
72 *> (5) | D1 - D2 | / ( |D1| ulp ) where D1 is computed by
73 *> SSBTRD with UPLO='U' and
74 *> D2 is computed by
75 *> SSYTRD_SB2ST with UPLO='U'
76 *>
77 *> (6) | D1 - D3 | / ( |D1| ulp ) where D1 is computed by
78 *> SSBTRD with UPLO='U' and
79 *> D3 is computed by
80 *> SSYTRD_SB2ST with UPLO='L'
81 *>
82 *> The "sizes" are specified by an array NN(1:NSIZES); the value of
83 *> each element NN(j) specifies one size.
84 *> The "types" are specified by a logical array DOTYPE( 1:NTYPES );
85 *> if DOTYPE(j) is .TRUE., then matrix type "j" will be generated.
86 *> Currently, the list of possible types is:
87 *>
88 *> (1) The zero matrix.
89 *> (2) The identity matrix.
90 *>
91 *> (3) A diagonal matrix with evenly spaced entries
92 *> 1, ..., ULP and random signs.
93 *> (ULP = (first number larger than 1) - 1 )
94 *> (4) A diagonal matrix with geometrically spaced entries
95 *> 1, ..., ULP and random signs.
96 *> (5) A diagonal matrix with "clustered" entries 1, ULP, ..., ULP
97 *> and random signs.
98 *>
99 *> (6) Same as (4), but multiplied by SQRT( overflow threshold )
100 *> (7) Same as (4), but multiplied by SQRT( underflow threshold )
101 *>
102 *> (8) A matrix of the form U' D U, where U is orthogonal and
103 *> D has evenly spaced entries 1, ..., ULP with random signs
104 *> on the diagonal.
105 *>
106 *> (9) A matrix of the form U' D U, where U is orthogonal and
107 *> D has geometrically spaced entries 1, ..., ULP with random
108 *> signs on the diagonal.
109 *>
110 *> (10) A matrix of the form U' D U, where U is orthogonal and
111 *> D has "clustered" entries 1, ULP,..., ULP with random
112 *> signs on the diagonal.
113 *>
114 *> (11) Same as (8), but multiplied by SQRT( overflow threshold )
115 *> (12) Same as (8), but multiplied by SQRT( underflow threshold )
116 *>
117 *> (13) Symmetric matrix with random entries chosen from (-1,1).
118 *> (14) Same as (13), but multiplied by SQRT( overflow threshold )
119 *> (15) Same as (13), but multiplied by SQRT( underflow threshold )
120 *> \endverbatim
121 *
122 * Arguments:
123 * ==========
124 *
125 *> \param[in] NSIZES
126 *> \verbatim
127 *> NSIZES is INTEGER
128 *> The number of sizes of matrices to use. If it is zero,
129 *> SCHKSB2STG does nothing. It must be at least zero.
130 *> \endverbatim
131 *>
132 *> \param[in] NN
133 *> \verbatim
134 *> NN is INTEGER array, dimension (NSIZES)
135 *> An array containing the sizes to be used for the matrices.
136 *> Zero values will be skipped. The values must be at least
137 *> zero.
138 *> \endverbatim
139 *>
140 *> \param[in] NWDTHS
141 *> \verbatim
142 *> NWDTHS is INTEGER
143 *> The number of bandwidths to use. If it is zero,
144 *> SCHKSB2STG does nothing. It must be at least zero.
145 *> \endverbatim
146 *>
147 *> \param[in] KK
148 *> \verbatim
149 *> KK is INTEGER array, dimension (NWDTHS)
150 *> An array containing the bandwidths to be used for the band
151 *> matrices. The values must be at least zero.
152 *> \endverbatim
153 *>
154 *> \param[in] NTYPES
155 *> \verbatim
156 *> NTYPES is INTEGER
157 *> The number of elements in DOTYPE. If it is zero, SCHKSB2STG
158 *> does nothing. It must be at least zero. If it is MAXTYP+1
159 *> and NSIZES is 1, then an additional type, MAXTYP+1 is
160 *> defined, which is to use whatever matrix is in A. This
161 *> is only useful if DOTYPE(1:MAXTYP) is .FALSE. and
162 *> DOTYPE(MAXTYP+1) is .TRUE. .
163 *> \endverbatim
164 *>
165 *> \param[in] DOTYPE
166 *> \verbatim
167 *> DOTYPE is LOGICAL array, dimension (NTYPES)
168 *> If DOTYPE(j) is .TRUE., then for each size in NN a
169 *> matrix of that size and of type j will be generated.
170 *> If NTYPES is smaller than the maximum number of types
171 *> defined (PARAMETER MAXTYP), then types NTYPES+1 through
172 *> MAXTYP will not be generated. If NTYPES is larger
173 *> than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES)
174 *> will be ignored.
175 *> \endverbatim
176 *>
177 *> \param[in,out] ISEED
178 *> \verbatim
179 *> ISEED is INTEGER array, dimension (4)
180 *> On entry ISEED specifies the seed of the random number
181 *> generator. The array elements should be between 0 and 4095;
182 *> if not they will be reduced mod 4096. Also, ISEED(4) must
183 *> be odd. The random number generator uses a linear
184 *> congruential sequence limited to small integers, and so
185 *> should produce machine independent random numbers. The
186 *> values of ISEED are changed on exit, and can be used in the
187 *> next call to SCHKSB2STG to continue the same random number
188 *> sequence.
189 *> \endverbatim
190 *>
191 *> \param[in] THRESH
192 *> \verbatim
193 *> THRESH is REAL
194 *> A test will count as "failed" if the "error", computed as
195 *> described above, exceeds THRESH. Note that the error
196 *> is scaled to be O(1), so THRESH should be a reasonably
197 *> small multiple of 1, e.g., 10 or 100. In particular,
198 *> it should not depend on the precision (single vs. double)
199 *> or the size of the matrix. It must be at least zero.
200 *> \endverbatim
201 *>
202 *> \param[in] NOUNIT
203 *> \verbatim
204 *> NOUNIT is INTEGER
205 *> The FORTRAN unit number for printing out error messages
206 *> (e.g., if a routine returns IINFO not equal to 0.)
207 *> \endverbatim
208 *>
209 *> \param[in,out] A
210 *> \verbatim
211 *> A is REAL array, dimension
212 *> (LDA, max(NN))
213 *> Used to hold the matrix whose eigenvalues are to be
214 *> computed.
215 *> \endverbatim
216 *>
217 *> \param[in] LDA
218 *> \verbatim
219 *> LDA is INTEGER
220 *> The leading dimension of A. It must be at least 2 (not 1!)
221 *> and at least max( KK )+1.
222 *> \endverbatim
223 *>
224 *> \param[out] SD
225 *> \verbatim
226 *> SD is REAL array, dimension (max(NN))
227 *> Used to hold the diagonal of the tridiagonal matrix computed
228 *> by SSBTRD.
229 *> \endverbatim
230 *>
231 *> \param[out] SE
232 *> \verbatim
233 *> SE is REAL array, dimension (max(NN))
234 *> Used to hold the off-diagonal of the tridiagonal matrix
235 *> computed by SSBTRD.
236 *> \endverbatim
237 *>
238 *> \param[out] D1
239 *> \verbatim
240 *> D1 is REAL array, dimension (max(NN))
241 *> \endverbatim
242 *>
243 *> \param[out] D2
244 *> \verbatim
245 *> D2 is REAL array, dimension (max(NN))
246 *> \endverbatim
247 *>
248 *> \param[out] D3
249 *> \verbatim
250 *> D3 is REAL array, dimension (max(NN))
251 *> \endverbatim
252 *>
253 *> \param[out] U
254 *> \verbatim
255 *> U is REAL array, dimension (LDU, max(NN))
256 *> Used to hold the orthogonal matrix computed by SSBTRD.
257 *> \endverbatim
258 *>
259 *> \param[in] LDU
260 *> \verbatim
261 *> LDU is INTEGER
262 *> The leading dimension of U. It must be at least 1
263 *> and at least max( NN ).
264 *> \endverbatim
265 *>
266 *> \param[out] WORK
267 *> \verbatim
268 *> WORK is REAL array, dimension (LWORK)
269 *> \endverbatim
270 *>
271 *> \param[in] LWORK
272 *> \verbatim
273 *> LWORK is INTEGER
274 *> The number of entries in WORK. This must be at least
275 *> max( LDA+1, max(NN)+1 )*max(NN).
276 *> \endverbatim
277 *>
278 *> \param[out] RESULT
279 *> \verbatim
280 *> RESULT is REAL array, dimension (4)
281 *> The values computed by the tests described above.
282 *> The values are currently limited to 1/ulp, to avoid
283 *> overflow.
284 *> \endverbatim
285 *>
286 *> \param[out] INFO
287 *> \verbatim
288 *> INFO is INTEGER
289 *> If 0, then everything ran OK.
290 *>
291 *>-----------------------------------------------------------------------
292 *>
293 *> Some Local Variables and Parameters:
294 *> ---- ----- --------- --- ----------
295 *> ZERO, ONE Real 0 and 1.
296 *> MAXTYP The number of types defined.
297 *> NTEST The number of tests performed, or which can
298 *> be performed so far, for the current matrix.
299 *> NTESTT The total number of tests performed so far.
300 *> NMAX Largest value in NN.
301 *> NMATS The number of matrices generated so far.
302 *> NERRS The number of tests which have exceeded THRESH
303 *> so far.
304 *> COND, IMODE Values to be passed to the matrix generators.
305 *> ANORM Norm of A; passed to matrix generators.
306 *>
307 *> OVFL, UNFL Overflow and underflow thresholds.
308 *> ULP, ULPINV Finest relative precision and its inverse.
309 *> RTOVFL, RTUNFL Square roots of the previous 2 values.
310 *> The following four arrays decode JTYPE:
311 *> KTYPE(j) The general type (1-10) for type "j".
312 *> KMODE(j) The MODE value to be passed to the matrix
313 *> generator for type "j".
314 *> KMAGN(j) The order of magnitude ( O(1),
315 *> O(overflow^(1/2) ), O(underflow^(1/2) )
316 *> \endverbatim
317 *
318 * Authors:
319 * ========
320 *
321 *> \author Univ. of Tennessee
322 *> \author Univ. of California Berkeley
323 *> \author Univ. of Colorado Denver
324 *> \author NAG Ltd.
325 *
326 *> \ingroup single_eig
327 *
328 * =====================================================================
329  SUBROUTINE schksb2stg( NSIZES, NN, NWDTHS, KK, NTYPES, DOTYPE,
330  $ ISEED, THRESH, NOUNIT, A, LDA, SD, SE, D1,
331  $ D2, D3, U, LDU, WORK, LWORK, RESULT, INFO )
332 *
333 * -- LAPACK test routine --
334 * -- LAPACK is a software package provided by Univ. of Tennessee, --
335 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
336 *
337 * .. Scalar Arguments ..
338  INTEGER INFO, LDA, LDU, LWORK, NOUNIT, NSIZES, NTYPES,
339  $ NWDTHS
340  REAL THRESH
341 * ..
342 * .. Array Arguments ..
343  LOGICAL DOTYPE( * )
344  INTEGER ISEED( 4 ), KK( * ), NN( * )
345  REAL A( LDA, * ), RESULT( * ), SD( * ), SE( * ),
346  $ d1( * ), d2( * ), d3( * ),
347  $ u( ldu, * ), work( * )
348 * ..
349 *
350 * =====================================================================
351 *
352 * .. Parameters ..
353  REAL ZERO, ONE, TWO, TEN
354  PARAMETER ( ZERO = 0.0e0, one = 1.0e0, two = 2.0e0,
355  $ ten = 10.0e0 )
356  REAL HALF
357  PARAMETER ( HALF = one / two )
358  INTEGER MAXTYP
359  parameter( maxtyp = 15 )
360 * ..
361 * .. Local Scalars ..
362  LOGICAL BADNN, BADNNB
363  INTEGER I, IINFO, IMODE, ITYPE, J, JC, JCOL, JR, JSIZE,
364  $ jtype, jwidth, k, kmax, lh, lw, mtypes, n,
365  $ nerrs, nmats, nmax, ntest, ntestt
366  REAL ANINV, ANORM, COND, OVFL, RTOVFL, RTUNFL,
367  $ TEMP1, TEMP2, TEMP3, TEMP4, ULP, ULPINV, UNFL
368 * ..
369 * .. Local Arrays ..
370  INTEGER IDUMMA( 1 ), IOLDSD( 4 ), KMAGN( MAXTYP ),
371  $ KMODE( MAXTYP ), KTYPE( MAXTYP )
372 * ..
373 * .. External Functions ..
374  REAL SLAMCH
375  EXTERNAL SLAMCH
376 * ..
377 * .. External Subroutines ..
378  EXTERNAL slacpy, slaset, slasum, slatmr, slatms, ssbt21,
380 * ..
381 * .. Intrinsic Functions ..
382  INTRINSIC abs, real, max, min, sqrt
383 * ..
384 * .. Data statements ..
385  DATA ktype / 1, 2, 5*4, 5*5, 3*8 /
386  DATA kmagn / 2*1, 1, 1, 1, 2, 3, 1, 1, 1, 2, 3, 1,
387  $ 2, 3 /
388  DATA kmode / 2*0, 4, 3, 1, 4, 4, 4, 3, 1, 4, 4, 0,
389  $ 0, 0 /
390 * ..
391 * .. Executable Statements ..
392 *
393 * Check for errors
394 *
395  ntestt = 0
396  info = 0
397 *
398 * Important constants
399 *
400  badnn = .false.
401  nmax = 1
402  DO 10 j = 1, nsizes
403  nmax = max( nmax, nn( j ) )
404  IF( nn( j ).LT.0 )
405  $ badnn = .true.
406  10 CONTINUE
407 *
408  badnnb = .false.
409  kmax = 0
410  DO 20 j = 1, nsizes
411  kmax = max( kmax, kk( j ) )
412  IF( kk( j ).LT.0 )
413  $ badnnb = .true.
414  20 CONTINUE
415  kmax = min( nmax-1, kmax )
416 *
417 * Check for errors
418 *
419  IF( nsizes.LT.0 ) THEN
420  info = -1
421  ELSE IF( badnn ) THEN
422  info = -2
423  ELSE IF( nwdths.LT.0 ) THEN
424  info = -3
425  ELSE IF( badnnb ) THEN
426  info = -4
427  ELSE IF( ntypes.LT.0 ) THEN
428  info = -5
429  ELSE IF( lda.LT.kmax+1 ) THEN
430  info = -11
431  ELSE IF( ldu.LT.nmax ) THEN
432  info = -15
433  ELSE IF( ( max( lda, nmax )+1 )*nmax.GT.lwork ) THEN
434  info = -17
435  END IF
436 *
437  IF( info.NE.0 ) THEN
438  CALL xerbla( 'SCHKSB2STG', -info )
439  RETURN
440  END IF
441 *
442 * Quick return if possible
443 *
444  IF( nsizes.EQ.0 .OR. ntypes.EQ.0 .OR. nwdths.EQ.0 )
445  $ RETURN
446 *
447 * More Important constants
448 *
449  unfl = slamch( 'Safe minimum' )
450  ovfl = one / unfl
451  ulp = slamch( 'Epsilon' )*slamch( 'Base' )
452  ulpinv = one / ulp
453  rtunfl = sqrt( unfl )
454  rtovfl = sqrt( ovfl )
455 *
456 * Loop over sizes, types
457 *
458  nerrs = 0
459  nmats = 0
460 *
461  DO 190 jsize = 1, nsizes
462  n = nn( jsize )
463  aninv = one / real( max( 1, n ) )
464 *
465  DO 180 jwidth = 1, nwdths
466  k = kk( jwidth )
467  IF( k.GT.n )
468  $ GO TO 180
469  k = max( 0, min( n-1, k ) )
470 *
471  IF( nsizes.NE.1 ) THEN
472  mtypes = min( maxtyp, ntypes )
473  ELSE
474  mtypes = min( maxtyp+1, ntypes )
475  END IF
476 *
477  DO 170 jtype = 1, mtypes
478  IF( .NOT.dotype( jtype ) )
479  $ GO TO 170
480  nmats = nmats + 1
481  ntest = 0
482 *
483  DO 30 j = 1, 4
484  ioldsd( j ) = iseed( j )
485  30 CONTINUE
486 *
487 * Compute "A".
488 * Store as "Upper"; later, we will copy to other format.
489 *
490 * Control parameters:
491 *
492 * KMAGN KMODE KTYPE
493 * =1 O(1) clustered 1 zero
494 * =2 large clustered 2 identity
495 * =3 small exponential (none)
496 * =4 arithmetic diagonal, (w/ eigenvalues)
497 * =5 random log symmetric, w/ eigenvalues
498 * =6 random (none)
499 * =7 random diagonal
500 * =8 random symmetric
501 * =9 positive definite
502 * =10 diagonally dominant tridiagonal
503 *
504  IF( mtypes.GT.maxtyp )
505  $ GO TO 100
506 *
507  itype = ktype( jtype )
508  imode = kmode( jtype )
509 *
510 * Compute norm
511 *
512  GO TO ( 40, 50, 60 )kmagn( jtype )
513 *
514  40 CONTINUE
515  anorm = one
516  GO TO 70
517 *
518  50 CONTINUE
519  anorm = ( rtovfl*ulp )*aninv
520  GO TO 70
521 *
522  60 CONTINUE
523  anorm = rtunfl*n*ulpinv
524  GO TO 70
525 *
526  70 CONTINUE
527 *
528  CALL slaset( 'Full', lda, n, zero, zero, a, lda )
529  iinfo = 0
530  IF( jtype.LE.15 ) THEN
531  cond = ulpinv
532  ELSE
533  cond = ulpinv*aninv / ten
534  END IF
535 *
536 * Special Matrices -- Identity & Jordan block
537 *
538 * Zero
539 *
540  IF( itype.EQ.1 ) THEN
541  iinfo = 0
542 *
543  ELSE IF( itype.EQ.2 ) THEN
544 *
545 * Identity
546 *
547  DO 80 jcol = 1, n
548  a( k+1, jcol ) = anorm
549  80 CONTINUE
550 *
551  ELSE IF( itype.EQ.4 ) THEN
552 *
553 * Diagonal Matrix, [Eigen]values Specified
554 *
555  CALL slatms( n, n, 'S', iseed, 'S', work, imode, cond,
556  $ anorm, 0, 0, 'Q', a( k+1, 1 ), lda,
557  $ work( n+1 ), iinfo )
558 *
559  ELSE IF( itype.EQ.5 ) THEN
560 *
561 * Symmetric, eigenvalues specified
562 *
563  CALL slatms( n, n, 'S', iseed, 'S', work, imode, cond,
564  $ anorm, k, k, 'Q', a, lda, work( n+1 ),
565  $ iinfo )
566 *
567  ELSE IF( itype.EQ.7 ) THEN
568 *
569 * Diagonal, random eigenvalues
570 *
571  CALL slatmr( n, n, 'S', iseed, 'S', work, 6, one, one,
572  $ 'T', 'N', work( n+1 ), 1, one,
573  $ work( 2*n+1 ), 1, one, 'N', idumma, 0, 0,
574  $ zero, anorm, 'Q', a( k+1, 1 ), lda,
575  $ idumma, iinfo )
576 *
577  ELSE IF( itype.EQ.8 ) THEN
578 *
579 * Symmetric, random eigenvalues
580 *
581  CALL slatmr( n, n, 'S', iseed, 'S', work, 6, one, one,
582  $ 'T', 'N', work( n+1 ), 1, one,
583  $ work( 2*n+1 ), 1, one, 'N', idumma, k, k,
584  $ zero, anorm, 'Q', a, lda, idumma, iinfo )
585 *
586  ELSE IF( itype.EQ.9 ) THEN
587 *
588 * Positive definite, eigenvalues specified.
589 *
590  CALL slatms( n, n, 'S', iseed, 'P', work, imode, cond,
591  $ anorm, k, k, 'Q', a, lda, work( n+1 ),
592  $ iinfo )
593 *
594  ELSE IF( itype.EQ.10 ) THEN
595 *
596 * Positive definite tridiagonal, eigenvalues specified.
597 *
598  IF( n.GT.1 )
599  $ k = max( 1, k )
600  CALL slatms( n, n, 'S', iseed, 'P', work, imode, cond,
601  $ anorm, 1, 1, 'Q', a( k, 1 ), lda,
602  $ work( n+1 ), iinfo )
603  DO 90 i = 2, n
604  temp1 = abs( a( k, i ) ) /
605  $ sqrt( abs( a( k+1, i-1 )*a( k+1, i ) ) )
606  IF( temp1.GT.half ) THEN
607  a( k, i ) = half*sqrt( abs( a( k+1,
608  $ i-1 )*a( k+1, i ) ) )
609  END IF
610  90 CONTINUE
611 *
612  ELSE
613 *
614  iinfo = 1
615  END IF
616 *
617  IF( iinfo.NE.0 ) THEN
618  WRITE( nounit, fmt = 9999 )'Generator', iinfo, n,
619  $ jtype, ioldsd
620  info = abs( iinfo )
621  RETURN
622  END IF
623 *
624  100 CONTINUE
625 *
626 * Call SSBTRD to compute S and U from upper triangle.
627 *
628  CALL slacpy( ' ', k+1, n, a, lda, work, lda )
629 *
630  ntest = 1
631  CALL ssbtrd( 'V', 'U', n, k, work, lda, sd, se, u, ldu,
632  $ work( lda*n+1 ), iinfo )
633 *
634  IF( iinfo.NE.0 ) THEN
635  WRITE( nounit, fmt = 9999 )'SSBTRD(U)', iinfo, n,
636  $ jtype, ioldsd
637  info = abs( iinfo )
638  IF( iinfo.LT.0 ) THEN
639  RETURN
640  ELSE
641  result( 1 ) = ulpinv
642  GO TO 150
643  END IF
644  END IF
645 *
646 * Do tests 1 and 2
647 *
648  CALL ssbt21( 'Upper', n, k, 1, a, lda, sd, se, u, ldu,
649  $ work, result( 1 ) )
650 *
651 * Before converting A into lower for SSBTRD, run SSYTRD_SB2ST
652 * otherwise matrix A will be converted to lower and then need
653 * to be converted back to upper in order to run the upper case
654 * ofSSYTRD_SB2ST
655 *
656 * Compute D1 the eigenvalues resulting from the tridiagonal
657 * form using the SSBTRD and used as reference to compare
658 * with the SSYTRD_SB2ST routine
659 *
660 * Compute D1 from the SSBTRD and used as reference for the
661 * SSYTRD_SB2ST
662 *
663  CALL scopy( n, sd, 1, d1, 1 )
664  IF( n.GT.0 )
665  $ CALL scopy( n-1, se, 1, work, 1 )
666 *
667  CALL ssteqr( 'N', n, d1, work, work( n+1 ), ldu,
668  $ work( n+1 ), iinfo )
669  IF( iinfo.NE.0 ) THEN
670  WRITE( nounit, fmt = 9999 )'SSTEQR(N)', iinfo, n,
671  $ jtype, ioldsd
672  info = abs( iinfo )
673  IF( iinfo.LT.0 ) THEN
674  RETURN
675  ELSE
676  result( 5 ) = ulpinv
677  GO TO 150
678  END IF
679  END IF
680 *
681 * SSYTRD_SB2ST Upper case is used to compute D2.
682 * Note to set SD and SE to zero to be sure not reusing
683 * the one from above. Compare it with D1 computed
684 * using the SSBTRD.
685 *
686  CALL slaset( 'Full', n, 1, zero, zero, sd, n )
687  CALL slaset( 'Full', n, 1, zero, zero, se, n )
688  CALL slacpy( ' ', k+1, n, a, lda, u, ldu )
689  lh = max(1, 4*n)
690  lw = lwork - lh
691  CALL ssytrd_sb2st( 'N', 'N', "U", n, k, u, ldu, sd, se,
692  $ work, lh, work( lh+1 ), lw, iinfo )
693 *
694 * Compute D2 from the SSYTRD_SB2ST Upper case
695 *
696  CALL scopy( n, sd, 1, d2, 1 )
697  IF( n.GT.0 )
698  $ CALL scopy( n-1, se, 1, work, 1 )
699 *
700  CALL ssteqr( 'N', n, d2, work, work( n+1 ), ldu,
701  $ work( n+1 ), iinfo )
702  IF( iinfo.NE.0 ) THEN
703  WRITE( nounit, fmt = 9999 )'SSTEQR(N)', iinfo, n,
704  $ jtype, ioldsd
705  info = abs( iinfo )
706  IF( iinfo.LT.0 ) THEN
707  RETURN
708  ELSE
709  result( 5 ) = ulpinv
710  GO TO 150
711  END IF
712  END IF
713 *
714 * Convert A from Upper-Triangle-Only storage to
715 * Lower-Triangle-Only storage.
716 *
717  DO 120 jc = 1, n
718  DO 110 jr = 0, min( k, n-jc )
719  a( jr+1, jc ) = a( k+1-jr, jc+jr )
720  110 CONTINUE
721  120 CONTINUE
722  DO 140 jc = n + 1 - k, n
723  DO 130 jr = min( k, n-jc ) + 1, k
724  a( jr+1, jc ) = zero
725  130 CONTINUE
726  140 CONTINUE
727 *
728 * Call SSBTRD to compute S and U from lower triangle
729 *
730  CALL slacpy( ' ', k+1, n, a, lda, work, lda )
731 *
732  ntest = 3
733  CALL ssbtrd( 'V', 'L', n, k, work, lda, sd, se, u, ldu,
734  $ work( lda*n+1 ), iinfo )
735 *
736  IF( iinfo.NE.0 ) THEN
737  WRITE( nounit, fmt = 9999 )'SSBTRD(L)', iinfo, n,
738  $ jtype, ioldsd
739  info = abs( iinfo )
740  IF( iinfo.LT.0 ) THEN
741  RETURN
742  ELSE
743  result( 3 ) = ulpinv
744  GO TO 150
745  END IF
746  END IF
747  ntest = 4
748 *
749 * Do tests 3 and 4
750 *
751  CALL ssbt21( 'Lower', n, k, 1, a, lda, sd, se, u, ldu,
752  $ work, result( 3 ) )
753 *
754 * SSYTRD_SB2ST Lower case is used to compute D3.
755 * Note to set SD and SE to zero to be sure not reusing
756 * the one from above. Compare it with D1 computed
757 * using the SSBTRD.
758 *
759  CALL slaset( 'Full', n, 1, zero, zero, sd, n )
760  CALL slaset( 'Full', n, 1, zero, zero, se, n )
761  CALL slacpy( ' ', k+1, n, a, lda, u, ldu )
762  lh = max(1, 4*n)
763  lw = lwork - lh
764  CALL ssytrd_sb2st( 'N', 'N', "L", n, k, u, ldu, sd, se,
765  $ work, lh, work( lh+1 ), lw, iinfo )
766 *
767 * Compute D3 from the 2-stage Upper case
768 *
769  CALL scopy( n, sd, 1, d3, 1 )
770  IF( n.GT.0 )
771  $ CALL scopy( n-1, se, 1, work, 1 )
772 *
773  CALL ssteqr( 'N', n, d3, work, work( n+1 ), ldu,
774  $ work( n+1 ), iinfo )
775  IF( iinfo.NE.0 ) THEN
776  WRITE( nounit, fmt = 9999 )'SSTEQR(N)', iinfo, n,
777  $ jtype, ioldsd
778  info = abs( iinfo )
779  IF( iinfo.LT.0 ) THEN
780  RETURN
781  ELSE
782  result( 6 ) = ulpinv
783  GO TO 150
784  END IF
785  END IF
786 *
787 *
788 * Do Tests 3 and 4 which are similar to 11 and 12 but with the
789 * D1 computed using the standard 1-stage reduction as reference
790 *
791  ntest = 6
792  temp1 = zero
793  temp2 = zero
794  temp3 = zero
795  temp4 = zero
796 *
797  DO 151 j = 1, n
798  temp1 = max( temp1, abs( d1( j ) ), abs( d2( j ) ) )
799  temp2 = max( temp2, abs( d1( j )-d2( j ) ) )
800  temp3 = max( temp3, abs( d1( j ) ), abs( d3( j ) ) )
801  temp4 = max( temp4, abs( d1( j )-d3( j ) ) )
802  151 CONTINUE
803 *
804  result(5) = temp2 / max( unfl, ulp*max( temp1, temp2 ) )
805  result(6) = temp4 / max( unfl, ulp*max( temp3, temp4 ) )
806 *
807 * End of Loop -- Check for RESULT(j) > THRESH
808 *
809  150 CONTINUE
810  ntestt = ntestt + ntest
811 *
812 * Print out tests which fail.
813 *
814  DO 160 jr = 1, ntest
815  IF( result( jr ).GE.thresh ) THEN
816 *
817 * If this is the first test to fail,
818 * print a header to the data file.
819 *
820  IF( nerrs.EQ.0 ) THEN
821  WRITE( nounit, fmt = 9998 )'SSB'
822  WRITE( nounit, fmt = 9997 )
823  WRITE( nounit, fmt = 9996 )
824  WRITE( nounit, fmt = 9995 )'Symmetric'
825  WRITE( nounit, fmt = 9994 )'orthogonal', '''',
826  $ 'transpose', ( '''', j = 1, 6 )
827  END IF
828  nerrs = nerrs + 1
829  WRITE( nounit, fmt = 9993 )n, k, ioldsd, jtype,
830  $ jr, result( jr )
831  END IF
832  160 CONTINUE
833 *
834  170 CONTINUE
835  180 CONTINUE
836  190 CONTINUE
837 *
838 * Summary
839 *
840  CALL slasum( 'SSB', nounit, nerrs, ntestt )
841  RETURN
842 *
843  9999 FORMAT( ' SCHKSB2STG: ', a, ' returned INFO=', i6, '.', / 9x, 'N=',
844  $ i6, ', JTYPE=', i6, ', ISEED=(', 3( i5, ',' ), i5, ')' )
845 *
846  9998 FORMAT( / 1x, a3,
847  $ ' -- Real Symmetric Banded Tridiagonal Reduction Routines' )
848  9997 FORMAT( ' Matrix types (see SCHKSB2STG for details): ' )
849 *
850  9996 FORMAT( / ' Special Matrices:',
851  $ / ' 1=Zero matrix. ',
852  $ ' 5=Diagonal: clustered entries.',
853  $ / ' 2=Identity matrix. ',
854  $ ' 6=Diagonal: large, evenly spaced.',
855  $ / ' 3=Diagonal: evenly spaced entries. ',
856  $ ' 7=Diagonal: small, evenly spaced.',
857  $ / ' 4=Diagonal: geometr. spaced entries.' )
858  9995 FORMAT( ' Dense ', a, ' Banded Matrices:',
859  $ / ' 8=Evenly spaced eigenvals. ',
860  $ ' 12=Small, evenly spaced eigenvals.',
861  $ / ' 9=Geometrically spaced eigenvals. ',
862  $ ' 13=Matrix with random O(1) entries.',
863  $ / ' 10=Clustered eigenvalues. ',
864  $ ' 14=Matrix with large random entries.',
865  $ / ' 11=Large, evenly spaced eigenvals. ',
866  $ ' 15=Matrix with small random entries.' )
867 *
868  9994 FORMAT( / ' Tests performed: (S is Tridiag, U is ', a, ',',
869  $ / 20x, a, ' means ', a, '.', / ' UPLO=''U'':',
870  $ / ' 1= | A - U S U', a1, ' | / ( |A| n ulp ) ',
871  $ ' 2= | I - U U', a1, ' | / ( n ulp )', / ' UPLO=''L'':',
872  $ / ' 3= | A - U S U', a1, ' | / ( |A| n ulp ) ',
873  $ ' 4= | I - U U', a1, ' | / ( n ulp )' / ' Eig check:',
874  $ /' 5= | D1 - D2', '', ' | / ( |D1| ulp ) ',
875  $ ' 6= | D1 - D3', '', ' | / ( |D1| ulp ) ' )
876  9993 FORMAT( ' N=', i5, ', K=', i4, ', seed=', 4( i4, ',' ), ' type ',
877  $ i2, ', test(', i2, ')=', g10.3 )
878 *
879 * End of SCHKSB2STG
880 *
881  END
subroutine slaset(UPLO, M, N, ALPHA, BETA, A, LDA)
SLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition: slaset.f:110
subroutine 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 ssteqr(COMPZ, N, D, E, Z, LDZ, WORK, INFO)
SSTEQR
Definition: ssteqr.f:131
subroutine slatms(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, KL, KU, PACK, A, LDA, WORK, INFO)
SLATMS
Definition: slatms.f:321
subroutine slatmr(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, RSIGN, GRADE, DL, MODEL, CONDL, DR, MODER, CONDR, PIVTNG, IPIVOT, KL, KU, SPARSE, ANORM, PACK, A, LDA, IWORK, INFO)
SLATMR
Definition: slatmr.f:471
subroutine ssbtrd(VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ, WORK, INFO)
SSBTRD
Definition: ssbtrd.f:163
subroutine scopy(N, SX, INCX, SY, INCY)
SCOPY
Definition: scopy.f:82
subroutine schksb2stg(NSIZES, NN, NWDTHS, KK, NTYPES, DOTYPE, ISEED, THRESH, NOUNIT, A, LDA, SD, SE, D1, D2, D3, U, LDU, WORK, LWORK, RESULT, INFO)
SCHKSB2STG
Definition: schksb2stg.f:332
subroutine ssbt21(UPLO, N, KA, KS, A, LDA, D, E, U, LDU, WORK, RESULT)
SSBT21
Definition: ssbt21.f:147
subroutine slasum(TYPE, IOUNIT, IE, NRUN)
SLASUM
Definition: slasum.f:41
subroutine ssytrd_sb2st(STAGE1, VECT, UPLO, N, KD, AB, LDAB, D, E, HOUS, LHOUS, WORK, LWORK, INFO)
SSYTRD_SB2ST reduces a real symmetric band matrix A to real symmetric tridiagonal form T
Definition: ssytrd_sb2st.F:230