LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ zlatb4()

subroutine zlatb4 ( character*3  path,
integer  imat,
integer  m,
integer  n,
character  type,
integer  kl,
integer  ku,
double precision  anorm,
integer  mode,
double precision  cndnum,
character  dist 
)

ZLATB4

Purpose:
 ZLATB4 sets parameters for the matrix generator based on the type of
 matrix to be generated.
Parameters
[in]PATH
          PATH is CHARACTER*3
          The LAPACK path name.
[in]IMAT
          IMAT is INTEGER
          An integer key describing which matrix to generate for this
          path.
[in]M
          M is INTEGER
          The number of rows in the matrix to be generated.
[in]N
          N is INTEGER
          The number of columns in the matrix to be generated.
[out]TYPE
          TYPE is CHARACTER*1
          The type of the matrix to be generated:
          = 'S':  symmetric matrix
          = 'H':  Hermitian matrix
          = 'P':  Hermitian positive (semi)definite matrix
          = 'N':  nonsymmetric matrix
[out]KL
          KL is INTEGER
          The lower band width of the matrix to be generated.
[out]KU
          KU is INTEGER
          The upper band width of the matrix to be generated.
[out]ANORM
          ANORM is DOUBLE PRECISION
          The desired norm of the matrix to be generated.  The diagonal
          matrix of singular values or eigenvalues is scaled by this
          value.
[out]MODE
          MODE is INTEGER
          A key indicating how to choose the vector of eigenvalues.
[out]CNDNUM
          CNDNUM is DOUBLE PRECISION
          The desired condition number.
[out]DIST
          DIST is CHARACTER*1
          The type of distribution to be used by the random number
          generator.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 119 of file zlatb4.f.

121*
122* -- LAPACK test routine --
123* -- LAPACK is a software package provided by Univ. of Tennessee, --
124* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
125*
126* .. Scalar Arguments ..
127 CHARACTER DIST, TYPE
128 CHARACTER*3 PATH
129 INTEGER IMAT, KL, KU, M, MODE, N
130 DOUBLE PRECISION ANORM, CNDNUM
131* ..
132*
133* =====================================================================
134*
135* .. Parameters ..
136 DOUBLE PRECISION SHRINK, TENTH
137 parameter( shrink = 0.25d0, tenth = 0.1d+0 )
138 DOUBLE PRECISION ONE
139 parameter( one = 1.0d+0 )
140 DOUBLE PRECISION TWO
141 parameter( two = 2.0d+0 )
142* ..
143* .. Local Scalars ..
144 LOGICAL FIRST
145 CHARACTER*2 C2
146 INTEGER MAT
147 DOUBLE PRECISION BADC1, BADC2, EPS, LARGE, SMALL
148* ..
149* .. External Functions ..
150 LOGICAL LSAMEN
151 DOUBLE PRECISION DLAMCH
152 EXTERNAL lsamen, dlamch
153* ..
154* .. Intrinsic Functions ..
155 INTRINSIC abs, max, sqrt
156* ..
157* .. Save statement ..
158 SAVE eps, small, large, badc1, badc2, first
159* ..
160* .. Data statements ..
161 DATA first / .true. /
162* ..
163* .. Executable Statements ..
164*
165* Set some constants for use in the subroutine.
166*
167 IF( first ) THEN
168 first = .false.
169 eps = dlamch( 'Precision' )
170 badc2 = tenth / eps
171 badc1 = sqrt( badc2 )
172 small = dlamch( 'Safe minimum' )
173 large = one / small
174 small = shrink*( small / eps )
175 large = one / small
176 END IF
177*
178 c2 = path( 2: 3 )
179*
180* Set some parameters we don't plan to change.
181*
182 dist = 'S'
183 mode = 3
184*
185* xQR, xLQ, xQL, xRQ: Set parameters to generate a general
186* M x N matrix.
187*
188 IF( lsamen( 2, c2, 'QR' ) .OR. lsamen( 2, c2, 'LQ' ) .OR.
189 $ lsamen( 2, c2, 'QL' ) .OR. lsamen( 2, c2, 'RQ' ) ) THEN
190*
191* Set TYPE, the type of matrix to be generated.
192*
193 TYPE = 'N'
194*
195* Set the lower and upper bandwidths.
196*
197 IF( imat.EQ.1 ) THEN
198 kl = 0
199 ku = 0
200 ELSE IF( imat.EQ.2 ) THEN
201 kl = 0
202 ku = max( n-1, 0 )
203 ELSE IF( imat.EQ.3 ) THEN
204 kl = max( m-1, 0 )
205 ku = 0
206 ELSE
207 kl = max( m-1, 0 )
208 ku = max( n-1, 0 )
209 END IF
210*
211* Set the condition number and norm.
212*
213 IF( imat.EQ.5 ) THEN
214 cndnum = badc1
215 ELSE IF( imat.EQ.6 ) THEN
216 cndnum = badc2
217 ELSE
218 cndnum = two
219 END IF
220*
221 IF( imat.EQ.7 ) THEN
222 anorm = small
223 ELSE IF( imat.EQ.8 ) THEN
224 anorm = large
225 ELSE
226 anorm = one
227 END IF
228*
229 ELSE IF( lsamen( 2, c2, 'QK' ) ) THEN
230*
231* xQK: truncated QR with pivoting.
232* Set parameters to generate a general
233* M x N matrix.
234*
235* Set TYPE, the type of matrix to be generated. 'N' is nonsymmetric.
236*
237 TYPE = 'N'
238*
239* Set DIST, the type of distribution for the random
240* number generator. 'S' is
241*
242 dist = 'S'
243*
244* Set the lower and upper bandwidths.
245*
246 IF( imat.EQ.2 ) THEN
247*
248* 2. Random, Diagonal, CNDNUM = 2
249*
250 kl = 0
251 ku = 0
252 cndnum = two
253 anorm = one
254 mode = 3
255 ELSE IF( imat.EQ.3 ) THEN
256*
257* 3. Random, Upper triangular, CNDNUM = 2
258*
259 kl = 0
260 ku = max( n-1, 0 )
261 cndnum = two
262 anorm = one
263 mode = 3
264 ELSE IF( imat.EQ.4 ) THEN
265*
266* 4. Random, Lower triangular, CNDNUM = 2
267*
268 kl = max( m-1, 0 )
269 ku = 0
270 cndnum = two
271 anorm = one
272 mode = 3
273 ELSE
274*
275* 5.-19. Rectangular matrix
276*
277 kl = max( m-1, 0 )
278 ku = max( n-1, 0 )
279*
280 IF( imat.GE.5 .AND. imat.LE.14 ) THEN
281*
282* 5.-14. Random, CNDNUM = 2.
283*
284 cndnum = two
285 anorm = one
286 mode = 3
287*
288 ELSE IF( imat.EQ.15 ) THEN
289*
290* 15. Random, CNDNUM = sqrt(0.1/EPS)
291*
292 cndnum = badc1
293 anorm = one
294 mode = 3
295*
296 ELSE IF( imat.EQ.16 ) THEN
297*
298* 16. Random, CNDNUM = 0.1/EPS
299*
300 cndnum = badc2
301 anorm = one
302 mode = 3
303*
304 ELSE IF( imat.EQ.17 ) THEN
305*
306* 17. Random, CNDNUM = 0.1/EPS,
307* one small singular value S(N)=1/CNDNUM
308*
309 cndnum = badc2
310 anorm = one
311 mode = 2
312*
313 ELSE IF( imat.EQ.18 ) THEN
314*
315* 18. Random, scaled near underflow
316*
317 cndnum = two
318 anorm = small
319 mode = 3
320*
321 ELSE IF( imat.EQ.19 ) THEN
322*
323* 19. Random, scaled near overflow
324*
325 cndnum = two
326 anorm = large
327 mode = 3
328*
329 END IF
330*
331 END IF
332*
333 ELSE IF( lsamen( 2, c2, 'GE' ) ) THEN
334*
335* xGE: Set parameters to generate a general M x N matrix.
336*
337* Set TYPE, the type of matrix to be generated.
338*
339 TYPE = 'N'
340*
341* Set the lower and upper bandwidths.
342*
343 IF( imat.EQ.1 ) THEN
344 kl = 0
345 ku = 0
346 ELSE IF( imat.EQ.2 ) THEN
347 kl = 0
348 ku = max( n-1, 0 )
349 ELSE IF( imat.EQ.3 ) THEN
350 kl = max( m-1, 0 )
351 ku = 0
352 ELSE
353 kl = max( m-1, 0 )
354 ku = max( n-1, 0 )
355 END IF
356*
357* Set the condition number and norm.
358*
359 IF( imat.EQ.8 ) THEN
360 cndnum = badc1
361 ELSE IF( imat.EQ.9 ) THEN
362 cndnum = badc2
363 ELSE
364 cndnum = two
365 END IF
366*
367 IF( imat.EQ.10 ) THEN
368 anorm = small
369 ELSE IF( imat.EQ.11 ) THEN
370 anorm = large
371 ELSE
372 anorm = one
373 END IF
374*
375 ELSE IF( lsamen( 2, c2, 'GB' ) ) THEN
376*
377* xGB: Set parameters to generate a general banded matrix.
378*
379* Set TYPE, the type of matrix to be generated.
380*
381 TYPE = 'N'
382*
383* Set the condition number and norm.
384*
385 IF( imat.EQ.5 ) THEN
386 cndnum = badc1
387 ELSE IF( imat.EQ.6 ) THEN
388 cndnum = tenth*badc2
389 ELSE
390 cndnum = two
391 END IF
392*
393 IF( imat.EQ.7 ) THEN
394 anorm = small
395 ELSE IF( imat.EQ.8 ) THEN
396 anorm = large
397 ELSE
398 anorm = one
399 END IF
400*
401 ELSE IF( lsamen( 2, c2, 'GT' ) ) THEN
402*
403* xGT: Set parameters to generate a general tridiagonal matrix.
404*
405* Set TYPE, the type of matrix to be generated.
406*
407 TYPE = 'N'
408*
409* Set the lower and upper bandwidths.
410*
411 IF( imat.EQ.1 ) THEN
412 kl = 0
413 ELSE
414 kl = 1
415 END IF
416 ku = kl
417*
418* Set the condition number and norm.
419*
420 IF( imat.EQ.3 ) THEN
421 cndnum = badc1
422 ELSE IF( imat.EQ.4 ) THEN
423 cndnum = badc2
424 ELSE
425 cndnum = two
426 END IF
427*
428 IF( imat.EQ.5 .OR. imat.EQ.11 ) THEN
429 anorm = small
430 ELSE IF( imat.EQ.6 .OR. imat.EQ.12 ) THEN
431 anorm = large
432 ELSE
433 anorm = one
434 END IF
435*
436 ELSE IF( lsamen( 2, c2, 'PO' ) .OR. lsamen( 2, c2, 'PP' ) ) THEN
437*
438* xPO, xPP: Set parameters to generate a
439* symmetric or Hermitian positive definite matrix.
440*
441* Set TYPE, the type of matrix to be generated.
442*
443 TYPE = c2( 1: 1 )
444*
445* Set the lower and upper bandwidths.
446*
447 IF( imat.EQ.1 ) THEN
448 kl = 0
449 ELSE
450 kl = max( n-1, 0 )
451 END IF
452 ku = kl
453*
454* Set the condition number and norm.
455*
456 IF( imat.EQ.6 ) THEN
457 cndnum = badc1
458 ELSE IF( imat.EQ.7 ) THEN
459 cndnum = badc2
460 ELSE
461 cndnum = two
462 END IF
463*
464 IF( imat.EQ.8 ) THEN
465 anorm = small
466 ELSE IF( imat.EQ.9 ) THEN
467 anorm = large
468 ELSE
469 anorm = one
470 END IF
471*
472 ELSE IF( lsamen( 2, c2, 'HE' ) .OR. lsamen( 2, c2, 'HP' ) .OR.
473 $ lsamen( 2, c2, 'SY' ) .OR. lsamen( 2, c2, 'SP' ) ) THEN
474*
475* xHE, xHP, xSY, xSP: Set parameters to generate a
476* symmetric or Hermitian matrix.
477*
478* Set TYPE, the type of matrix to be generated.
479*
480 TYPE = c2( 1: 1 )
481*
482* Set the lower and upper bandwidths.
483*
484 IF( imat.EQ.1 ) THEN
485 kl = 0
486 ELSE
487 kl = max( n-1, 0 )
488 END IF
489 ku = kl
490*
491* Set the condition number and norm.
492*
493 IF( imat.EQ.7 ) THEN
494 cndnum = badc1
495 ELSE IF( imat.EQ.8 ) THEN
496 cndnum = badc2
497 ELSE
498 cndnum = two
499 END IF
500*
501 IF( imat.EQ.9 ) THEN
502 anorm = small
503 ELSE IF( imat.EQ.10 ) THEN
504 anorm = large
505 ELSE
506 anorm = one
507 END IF
508*
509 ELSE IF( lsamen( 2, c2, 'PB' ) ) THEN
510*
511* xPB: Set parameters to generate a symmetric band matrix.
512*
513* Set TYPE, the type of matrix to be generated.
514*
515 TYPE = 'P'
516*
517* Set the norm and condition number.
518*
519 IF( imat.EQ.5 ) THEN
520 cndnum = badc1
521 ELSE IF( imat.EQ.6 ) THEN
522 cndnum = badc2
523 ELSE
524 cndnum = two
525 END IF
526*
527 IF( imat.EQ.7 ) THEN
528 anorm = small
529 ELSE IF( imat.EQ.8 ) THEN
530 anorm = large
531 ELSE
532 anorm = one
533 END IF
534*
535 ELSE IF( lsamen( 2, c2, 'PT' ) ) THEN
536*
537* xPT: Set parameters to generate a symmetric positive definite
538* tridiagonal matrix.
539*
540 TYPE = 'P'
541 IF( imat.EQ.1 ) THEN
542 kl = 0
543 ELSE
544 kl = 1
545 END IF
546 ku = kl
547*
548* Set the condition number and norm.
549*
550 IF( imat.EQ.3 ) THEN
551 cndnum = badc1
552 ELSE IF( imat.EQ.4 ) THEN
553 cndnum = badc2
554 ELSE
555 cndnum = two
556 END IF
557*
558 IF( imat.EQ.5 .OR. imat.EQ.11 ) THEN
559 anorm = small
560 ELSE IF( imat.EQ.6 .OR. imat.EQ.12 ) THEN
561 anorm = large
562 ELSE
563 anorm = one
564 END IF
565*
566 ELSE IF( lsamen( 2, c2, 'TR' ) .OR. lsamen( 2, c2, 'TP' ) ) THEN
567*
568* xTR, xTP: Set parameters to generate a triangular matrix
569*
570* Set TYPE, the type of matrix to be generated.
571*
572 TYPE = 'N'
573*
574* Set the lower and upper bandwidths.
575*
576 mat = abs( imat )
577 IF( mat.EQ.1 .OR. mat.EQ.7 ) THEN
578 kl = 0
579 ku = 0
580 ELSE IF( imat.LT.0 ) THEN
581 kl = max( n-1, 0 )
582 ku = 0
583 ELSE
584 kl = 0
585 ku = max( n-1, 0 )
586 END IF
587*
588* Set the condition number and norm.
589*
590 IF( mat.EQ.3 .OR. mat.EQ.9 ) THEN
591 cndnum = badc1
592 ELSE IF( mat.EQ.4 .OR. mat.EQ.10 ) THEN
593 cndnum = badc2
594 ELSE
595 cndnum = two
596 END IF
597*
598 IF( mat.EQ.5 ) THEN
599 anorm = small
600 ELSE IF( mat.EQ.6 ) THEN
601 anorm = large
602 ELSE
603 anorm = one
604 END IF
605*
606 ELSE IF( lsamen( 2, c2, 'TB' ) ) THEN
607*
608* xTB: Set parameters to generate a triangular band matrix.
609*
610* Set TYPE, the type of matrix to be generated.
611*
612 TYPE = 'N'
613*
614* Set the norm and condition number.
615*
616 mat = abs( imat )
617 IF( mat.EQ.2 .OR. mat.EQ.8 ) THEN
618 cndnum = badc1
619 ELSE IF( mat.EQ.3 .OR. mat.EQ.9 ) THEN
620 cndnum = badc2
621 ELSE
622 cndnum = two
623 END IF
624*
625 IF( mat.EQ.4 ) THEN
626 anorm = small
627 ELSE IF( mat.EQ.5 ) THEN
628 anorm = large
629 ELSE
630 anorm = one
631 END IF
632 END IF
633 IF( n.LE.1 )
634 $ cndnum = one
635*
636 RETURN
637*
638* End of ZLATB4
639*
dlamch
double precision function dlamch(cmach)
DLAMCH
Definition dlamch.f:69
lsamen
logical function lsamen(n, ca, cb)
LSAMEN
Definition lsamen.f:74
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