LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ dlatb4()

 subroutine dlatb4 ( 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 )

DLATB4

Purpose:
``` DLATB4 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 = 'P': symmetric 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.```

Definition at line 118 of file dlatb4.f.

120 *
121 * -- LAPACK test routine --
122 * -- LAPACK is a software package provided by Univ. of Tennessee, --
123 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
124 *
125 * .. Scalar Arguments ..
126  CHARACTER DIST, TYPE
127  CHARACTER*3 PATH
128  INTEGER IMAT, KL, KU, M, MODE, N
129  DOUBLE PRECISION ANORM, CNDNUM
130 * ..
131 *
132 * =====================================================================
133 *
134 * .. Parameters ..
135  DOUBLE PRECISION SHRINK, TENTH
136  parameter( shrink = 0.25d0, tenth = 0.1d+0 )
137  DOUBLE PRECISION ONE
138  parameter( one = 1.0d+0 )
139  DOUBLE PRECISION TWO
140  parameter( two = 2.0d+0 )
141 * ..
142 * .. Local Scalars ..
143  LOGICAL FIRST
144  CHARACTER*2 C2
145  INTEGER MAT
147 * ..
148 * .. External Functions ..
149  LOGICAL LSAMEN
150  DOUBLE PRECISION DLAMCH
151  EXTERNAL lsamen, dlamch
152 * ..
153 * .. Intrinsic Functions ..
154  INTRINSIC abs, max, sqrt
155 * ..
156 * .. External Subroutines ..
158 * ..
159 * .. Save statement ..
161 * ..
162 * .. Data statements ..
163  DATA first / .true. /
164 * ..
165 * .. Executable Statements ..
166 *
167 * Set some constants for use in the subroutine.
168 *
169  IF( first ) THEN
170  first = .false.
171  eps = dlamch( 'Precision' )
172  badc2 = tenth / eps
174  small = dlamch( 'Safe minimum' )
175  large = one / small
176 *
177 * If it looks like we're on a Cray, take the square root of
178 * SMALL and LARGE to avoid overflow and underflow problems.
179 *
180  CALL dlabad( small, large )
181  small = shrink*( small / eps )
182  large = one / small
183  END IF
184 *
185  c2 = path( 2: 3 )
186 *
187 * Set some parameters we don't plan to change.
188 *
189  dist = 'S'
190  mode = 3
191 *
192  IF( lsamen( 2, c2, 'QR' ) .OR. lsamen( 2, c2, 'LQ' ) .OR.
193  \$ lsamen( 2, c2, 'QL' ) .OR. lsamen( 2, c2, 'RQ' ) ) THEN
194 *
195 * xQR, xLQ, xQL, xRQ: Set parameters to generate a general
196 * M x N matrix.
197 *
198 * Set TYPE, the type of matrix to be generated.
199 *
200  TYPE = 'N'
201 *
202 * Set the lower and upper bandwidths.
203 *
204  IF( imat.EQ.1 ) THEN
205  kl = 0
206  ku = 0
207  ELSE IF( imat.EQ.2 ) THEN
208  kl = 0
209  ku = max( n-1, 0 )
210  ELSE IF( imat.EQ.3 ) THEN
211  kl = max( m-1, 0 )
212  ku = 0
213  ELSE
214  kl = max( m-1, 0 )
215  ku = max( n-1, 0 )
216  END IF
217 *
218 * Set the condition number and norm.
219 *
220  IF( imat.EQ.5 ) THEN
222  ELSE IF( imat.EQ.6 ) THEN
224  ELSE
225  cndnum = two
226  END IF
227 *
228  IF( imat.EQ.7 ) THEN
229  anorm = small
230  ELSE IF( imat.EQ.8 ) THEN
231  anorm = large
232  ELSE
233  anorm = one
234  END IF
235 *
236  ELSE IF( lsamen( 2, c2, 'GE' ) ) THEN
237 *
238 * xGE: Set parameters to generate a general M x N matrix.
239 *
240 * Set TYPE, the type of matrix to be generated.
241 *
242  TYPE = 'N'
243 *
244 * Set the lower and upper bandwidths.
245 *
246  IF( imat.EQ.1 ) THEN
247  kl = 0
248  ku = 0
249  ELSE IF( imat.EQ.2 ) THEN
250  kl = 0
251  ku = max( n-1, 0 )
252  ELSE IF( imat.EQ.3 ) THEN
253  kl = max( m-1, 0 )
254  ku = 0
255  ELSE
256  kl = max( m-1, 0 )
257  ku = max( n-1, 0 )
258  END IF
259 *
260 * Set the condition number and norm.
261 *
262  IF( imat.EQ.8 ) THEN
264  ELSE IF( imat.EQ.9 ) THEN
266  ELSE
267  cndnum = two
268  END IF
269 *
270  IF( imat.EQ.10 ) THEN
271  anorm = small
272  ELSE IF( imat.EQ.11 ) THEN
273  anorm = large
274  ELSE
275  anorm = one
276  END IF
277 *
278  ELSE IF( lsamen( 2, c2, 'GB' ) ) THEN
279 *
280 * xGB: Set parameters to generate a general banded matrix.
281 *
282 * Set TYPE, the type of matrix to be generated.
283 *
284  TYPE = 'N'
285 *
286 * Set the condition number and norm.
287 *
288  IF( imat.EQ.5 ) THEN
290  ELSE IF( imat.EQ.6 ) THEN
292  ELSE
293  cndnum = two
294  END IF
295 *
296  IF( imat.EQ.7 ) THEN
297  anorm = small
298  ELSE IF( imat.EQ.8 ) THEN
299  anorm = large
300  ELSE
301  anorm = one
302  END IF
303 *
304  ELSE IF( lsamen( 2, c2, 'GT' ) ) THEN
305 *
306 * xGT: Set parameters to generate a general tridiagonal matrix.
307 *
308 * Set TYPE, the type of matrix to be generated.
309 *
310  TYPE = 'N'
311 *
312 * Set the lower and upper bandwidths.
313 *
314  IF( imat.EQ.1 ) THEN
315  kl = 0
316  ELSE
317  kl = 1
318  END IF
319  ku = kl
320 *
321 * Set the condition number and norm.
322 *
323  IF( imat.EQ.3 ) THEN
325  ELSE IF( imat.EQ.4 ) THEN
327  ELSE
328  cndnum = two
329  END IF
330 *
331  IF( imat.EQ.5 .OR. imat.EQ.11 ) THEN
332  anorm = small
333  ELSE IF( imat.EQ.6 .OR. imat.EQ.12 ) THEN
334  anorm = large
335  ELSE
336  anorm = one
337  END IF
338 *
339  ELSE IF( lsamen( 2, c2, 'PO' ) .OR. lsamen( 2, c2, 'PP' ) ) THEN
340 *
341 * xPO, xPP: Set parameters to generate a
342 * symmetric positive definite matrix.
343 *
344 * Set TYPE, the type of matrix to be generated.
345 *
346  TYPE = c2( 1: 1 )
347 *
348 * Set the lower and upper bandwidths.
349 *
350  IF( imat.EQ.1 ) THEN
351  kl = 0
352  ELSE
353  kl = max( n-1, 0 )
354  END IF
355  ku = kl
356 *
357 * Set the condition number and norm.
358 *
359  IF( imat.EQ.6 ) THEN
361  ELSE IF( imat.EQ.7 ) THEN
363  ELSE
364  cndnum = two
365  END IF
366 *
367  IF( imat.EQ.8 ) THEN
368  anorm = small
369  ELSE IF( imat.EQ.9 ) THEN
370  anorm = large
371  ELSE
372  anorm = one
373  END IF
374 *
375 *
376  ELSE IF( lsamen( 2, c2, 'SY' ) .OR. lsamen( 2, c2, 'SP' ) ) THEN
377 *
378 * xSY, xSP: Set parameters to generate a
379 * symmetric matrix.
380 *
381 * Set TYPE, the type of matrix to be generated.
382 *
383  TYPE = c2( 1: 1 )
384 *
385 * Set the lower and upper bandwidths.
386 *
387  IF( imat.EQ.1 ) THEN
388  kl = 0
389  ELSE
390  kl = max( n-1, 0 )
391  END IF
392  ku = kl
393 *
394 * Set the condition number and norm.
395 *
396  IF( imat.EQ.7 ) THEN
398  ELSE IF( imat.EQ.8 ) THEN
400  ELSE
401  cndnum = two
402  END IF
403 *
404  IF( imat.EQ.9 ) THEN
405  anorm = small
406  ELSE IF( imat.EQ.10 ) THEN
407  anorm = large
408  ELSE
409  anorm = one
410  END IF
411 *
412  ELSE IF( lsamen( 2, c2, 'PB' ) ) THEN
413 *
414 * xPB: Set parameters to generate a symmetric band matrix.
415 *
416 * Set TYPE, the type of matrix to be generated.
417 *
418  TYPE = 'P'
419 *
420 * Set the norm and condition number.
421 *
422  IF( imat.EQ.5 ) THEN
424  ELSE IF( imat.EQ.6 ) THEN
426  ELSE
427  cndnum = two
428  END IF
429 *
430  IF( imat.EQ.7 ) THEN
431  anorm = small
432  ELSE IF( imat.EQ.8 ) THEN
433  anorm = large
434  ELSE
435  anorm = one
436  END IF
437 *
438  ELSE IF( lsamen( 2, c2, 'PT' ) ) THEN
439 *
440 * xPT: Set parameters to generate a symmetric positive definite
441 * tridiagonal matrix.
442 *
443  TYPE = 'P'
444  IF( imat.EQ.1 ) THEN
445  kl = 0
446  ELSE
447  kl = 1
448  END IF
449  ku = kl
450 *
451 * Set the condition number and norm.
452 *
453  IF( imat.EQ.3 ) THEN
455  ELSE IF( imat.EQ.4 ) THEN
457  ELSE
458  cndnum = two
459  END IF
460 *
461  IF( imat.EQ.5 .OR. imat.EQ.11 ) THEN
462  anorm = small
463  ELSE IF( imat.EQ.6 .OR. imat.EQ.12 ) THEN
464  anorm = large
465  ELSE
466  anorm = one
467  END IF
468 *
469  ELSE IF( lsamen( 2, c2, 'TR' ) .OR. lsamen( 2, c2, 'TP' ) ) THEN
470 *
471 * xTR, xTP: Set parameters to generate a triangular matrix
472 *
473 * Set TYPE, the type of matrix to be generated.
474 *
475  TYPE = 'N'
476 *
477 * Set the lower and upper bandwidths.
478 *
479  mat = abs( imat )
480  IF( mat.EQ.1 .OR. mat.EQ.7 ) THEN
481  kl = 0
482  ku = 0
483  ELSE IF( imat.LT.0 ) THEN
484  kl = max( n-1, 0 )
485  ku = 0
486  ELSE
487  kl = 0
488  ku = max( n-1, 0 )
489  END IF
490 *
491 * Set the condition number and norm.
492 *
493  IF( mat.EQ.3 .OR. mat.EQ.9 ) THEN
495  ELSE IF( mat.EQ.4 ) THEN
497  ELSE IF( mat.EQ.10 ) THEN
499  ELSE
500  cndnum = two
501  END IF
502 *
503  IF( mat.EQ.5 ) THEN
504  anorm = small
505  ELSE IF( mat.EQ.6 ) THEN
506  anorm = large
507  ELSE
508  anorm = one
509  END IF
510 *
511  ELSE IF( lsamen( 2, c2, 'TB' ) ) THEN
512 *
513 * xTB: Set parameters to generate a triangular band matrix.
514 *
515 * Set TYPE, the type of matrix to be generated.
516 *
517  TYPE = 'N'
518 *
519 * Set the norm and condition number.
520 *
521  IF( imat.EQ.2 .OR. imat.EQ.8 ) THEN
523  ELSE IF( imat.EQ.3 .OR. imat.EQ.9 ) THEN
525  ELSE
526  cndnum = two
527  END IF
528 *
529  IF( imat.EQ.4 ) THEN
530  anorm = small
531  ELSE IF( imat.EQ.5 ) THEN
532  anorm = large
533  ELSE
534  anorm = one
535  END IF
536  END IF
537  IF( n.LE.1 )
538  \$ cndnum = one
539 *
540  RETURN
541 *
542 * End of DLATB4
543 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
logical function lsamen(N, CA, CB)
LSAMEN
Definition: lsamen.f:74