LAPACK  3.6.1
LAPACK: Linear Algebra PACKage
dlatb4.f
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1 *> \brief \b DLATB4
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 DLATB4( PATH, IMAT, M, N, TYPE, KL, KU, ANORM, MODE,
12 * CNDNUM, DIST )
13 *
14 * .. Scalar Arguments ..
15 * CHARACTER DIST, TYPE
16 * CHARACTER*3 PATH
17 * INTEGER IMAT, KL, KU, M, MODE, N
18 * DOUBLE PRECISION ANORM, CNDNUM
19 * ..
20 *
21 *
22 *> \par Purpose:
23 * =============
24 *>
25 *> \verbatim
26 *>
27 *> DLATB4 sets parameters for the matrix generator based on the type of
28 *> matrix to be generated.
29 *> \endverbatim
30 *
31 * Arguments:
32 * ==========
33 *
34 *> \param[in] PATH
35 *> \verbatim
36 *> PATH is CHARACTER*3
37 *> The LAPACK path name.
38 *> \endverbatim
39 *>
40 *> \param[in] IMAT
41 *> \verbatim
42 *> IMAT is INTEGER
43 *> An integer key describing which matrix to generate for this
44 *> path.
45 *> \endverbatim
46 *>
47 *> \param[in] M
48 *> \verbatim
49 *> M is INTEGER
50 *> The number of rows in the matrix to be generated.
51 *> \endverbatim
52 *>
53 *> \param[in] N
54 *> \verbatim
55 *> N is INTEGER
56 *> The number of columns in the matrix to be generated.
57 *> \endverbatim
58 *>
59 *> \param[out] TYPE
60 *> \verbatim
61 *> TYPE is CHARACTER*1
62 *> The type of the matrix to be generated:
63 *> = 'S': symmetric matrix
64 *> = 'P': symmetric positive (semi)definite matrix
65 *> = 'N': nonsymmetric matrix
66 *> \endverbatim
67 *>
68 *> \param[out] KL
69 *> \verbatim
70 *> KL is INTEGER
71 *> The lower band width of the matrix to be generated.
72 *> \endverbatim
73 *>
74 *> \param[out] KU
75 *> \verbatim
76 *> KU is INTEGER
77 *> The upper band width of the matrix to be generated.
78 *> \endverbatim
79 *>
80 *> \param[out] ANORM
81 *> \verbatim
82 *> ANORM is DOUBLE PRECISION
83 *> The desired norm of the matrix to be generated. The diagonal
84 *> matrix of singular values or eigenvalues is scaled by this
85 *> value.
86 *> \endverbatim
87 *>
88 *> \param[out] MODE
89 *> \verbatim
90 *> MODE is INTEGER
91 *> A key indicating how to choose the vector of eigenvalues.
92 *> \endverbatim
93 *>
94 *> \param[out] CNDNUM
95 *> \verbatim
96 *> CNDNUM is DOUBLE PRECISION
97 *> The desired condition number.
98 *> \endverbatim
99 *>
100 *> \param[out] DIST
101 *> \verbatim
102 *> DIST is CHARACTER*1
103 *> The type of distribution to be used by the random number
104 *> generator.
105 *> \endverbatim
106 *
107 * Authors:
108 * ========
109 *
110 *> \author Univ. of Tennessee
111 *> \author Univ. of California Berkeley
112 *> \author Univ. of Colorado Denver
113 *> \author NAG Ltd.
114 *
115 *> \date November 2011
116 *
117 *> \ingroup double_lin
118 *
119 * =====================================================================
120  SUBROUTINE dlatb4( PATH, IMAT, M, N, TYPE, KL, KU, ANORM, MODE,
121  $ cndnum, dist )
122 *
123 * -- LAPACK test routine (version 3.4.0) --
124 * -- LAPACK is a software package provided by Univ. of Tennessee, --
125 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
126 * November 2011
127 *
128 * .. Scalar Arguments ..
129  CHARACTER DIST, TYPE
130  CHARACTER*3 PATH
131  INTEGER IMAT, KL, KU, M, MODE, N
132  DOUBLE PRECISION ANORM, CNDNUM
133 * ..
134 *
135 * =====================================================================
136 *
137 * .. Parameters ..
138  DOUBLE PRECISION SHRINK, TENTH
139  parameter ( shrink = 0.25d0, tenth = 0.1d+0 )
140  DOUBLE PRECISION ONE
141  parameter ( one = 1.0d+0 )
142  DOUBLE PRECISION TWO
143  parameter ( two = 2.0d+0 )
144 * ..
145 * .. Local Scalars ..
146  LOGICAL FIRST
147  CHARACTER*2 C2
148  INTEGER MAT
149  DOUBLE PRECISION BADC1, BADC2, EPS, LARGE, SMALL
150 * ..
151 * .. External Functions ..
152  LOGICAL LSAMEN
153  DOUBLE PRECISION DLAMCH
154  EXTERNAL lsamen, dlamch
155 * ..
156 * .. Intrinsic Functions ..
157  INTRINSIC abs, max, sqrt
158 * ..
159 * .. External Subroutines ..
160  EXTERNAL dlabad
161 * ..
162 * .. Save statement ..
163  SAVE eps, small, large, badc1, badc2, first
164 * ..
165 * .. Data statements ..
166  DATA first / .true. /
167 * ..
168 * .. Executable Statements ..
169 *
170 * Set some constants for use in the subroutine.
171 *
172  IF( first ) THEN
173  first = .false.
174  eps = dlamch( 'Precision' )
175  badc2 = tenth / eps
176  badc1 = sqrt( badc2 )
177  small = dlamch( 'Safe minimum' )
178  large = one / small
179 *
180 * If it looks like we're on a Cray, take the square root of
181 * SMALL and LARGE to avoid overflow and underflow problems.
182 *
183  CALL dlabad( small, large )
184  small = shrink*( small / eps )
185  large = one / small
186  END IF
187 *
188  c2 = path( 2: 3 )
189 *
190 * Set some parameters we don't plan to change.
191 *
192  dist = 'S'
193  mode = 3
194 *
195  IF( lsamen( 2, c2, 'QR' ) .OR. lsamen( 2, c2, 'LQ' ) .OR.
196  $ lsamen( 2, c2, 'QL' ) .OR. lsamen( 2, c2, 'RQ' ) ) THEN
197 *
198 * xQR, xLQ, xQL, xRQ: Set parameters to generate a general
199 * M x N matrix.
200 *
201 * Set TYPE, the type of matrix to be generated.
202 *
203  TYPE = 'N'
204 *
205 * Set the lower and upper bandwidths.
206 *
207  IF( imat.EQ.1 ) THEN
208  kl = 0
209  ku = 0
210  ELSE IF( imat.EQ.2 ) THEN
211  kl = 0
212  ku = max( n-1, 0 )
213  ELSE IF( imat.EQ.3 ) THEN
214  kl = max( m-1, 0 )
215  ku = 0
216  ELSE
217  kl = max( m-1, 0 )
218  ku = max( n-1, 0 )
219  END IF
220 *
221 * Set the condition number and norm.
222 *
223  IF( imat.EQ.5 ) THEN
224  cndnum = badc1
225  ELSE IF( imat.EQ.6 ) THEN
226  cndnum = badc2
227  ELSE
228  cndnum = two
229  END IF
230 *
231  IF( imat.EQ.7 ) THEN
232  anorm = small
233  ELSE IF( imat.EQ.8 ) THEN
234  anorm = large
235  ELSE
236  anorm = one
237  END IF
238 *
239  ELSE IF( lsamen( 2, c2, 'GE' ) ) THEN
240 *
241 * xGE: Set parameters to generate a general M x N matrix.
242 *
243 * Set TYPE, the type of matrix to be generated.
244 *
245  TYPE = 'N'
246 *
247 * Set the lower and upper bandwidths.
248 *
249  IF( imat.EQ.1 ) THEN
250  kl = 0
251  ku = 0
252  ELSE IF( imat.EQ.2 ) THEN
253  kl = 0
254  ku = max( n-1, 0 )
255  ELSE IF( imat.EQ.3 ) THEN
256  kl = max( m-1, 0 )
257  ku = 0
258  ELSE
259  kl = max( m-1, 0 )
260  ku = max( n-1, 0 )
261  END IF
262 *
263 * Set the condition number and norm.
264 *
265  IF( imat.EQ.8 ) THEN
266  cndnum = badc1
267  ELSE IF( imat.EQ.9 ) THEN
268  cndnum = badc2
269  ELSE
270  cndnum = two
271  END IF
272 *
273  IF( imat.EQ.10 ) THEN
274  anorm = small
275  ELSE IF( imat.EQ.11 ) THEN
276  anorm = large
277  ELSE
278  anorm = one
279  END IF
280 *
281  ELSE IF( lsamen( 2, c2, 'GB' ) ) THEN
282 *
283 * xGB: Set parameters to generate a general banded matrix.
284 *
285 * Set TYPE, the type of matrix to be generated.
286 *
287  TYPE = 'N'
288 *
289 * Set the condition number and norm.
290 *
291  IF( imat.EQ.5 ) THEN
292  cndnum = badc1
293  ELSE IF( imat.EQ.6 ) THEN
294  cndnum = tenth*badc2
295  ELSE
296  cndnum = two
297  END IF
298 *
299  IF( imat.EQ.7 ) THEN
300  anorm = small
301  ELSE IF( imat.EQ.8 ) THEN
302  anorm = large
303  ELSE
304  anorm = one
305  END IF
306 *
307  ELSE IF( lsamen( 2, c2, 'GT' ) ) THEN
308 *
309 * xGT: Set parameters to generate a general tridiagonal matrix.
310 *
311 * Set TYPE, the type of matrix to be generated.
312 *
313  TYPE = 'N'
314 *
315 * Set the lower and upper bandwidths.
316 *
317  IF( imat.EQ.1 ) THEN
318  kl = 0
319  ELSE
320  kl = 1
321  END IF
322  ku = kl
323 *
324 * Set the condition number and norm.
325 *
326  IF( imat.EQ.3 ) THEN
327  cndnum = badc1
328  ELSE IF( imat.EQ.4 ) THEN
329  cndnum = badc2
330  ELSE
331  cndnum = two
332  END IF
333 *
334  IF( imat.EQ.5 .OR. imat.EQ.11 ) THEN
335  anorm = small
336  ELSE IF( imat.EQ.6 .OR. imat.EQ.12 ) THEN
337  anorm = large
338  ELSE
339  anorm = one
340  END IF
341 *
342  ELSE IF( lsamen( 2, c2, 'PO' ) .OR. lsamen( 2, c2, 'PP' ) .OR.
343  $ lsamen( 2, c2, 'SY' ) .OR. lsamen( 2, c2, 'SP' ) ) THEN
344 *
345 * xPO, xPP, xSY, xSP: Set parameters to generate a
346 * symmetric matrix.
347 *
348 * Set TYPE, the type of matrix to be generated.
349 *
350  TYPE = c2( 1: 1 )
351 *
352 * Set the lower and upper bandwidths.
353 *
354  IF( imat.EQ.1 ) THEN
355  kl = 0
356  ELSE
357  kl = max( n-1, 0 )
358  END IF
359  ku = kl
360 *
361 * Set the condition number and norm.
362 *
363  IF( imat.EQ.6 ) THEN
364  cndnum = badc1
365  ELSE IF( imat.EQ.7 ) THEN
366  cndnum = badc2
367  ELSE
368  cndnum = two
369  END IF
370 *
371  IF( imat.EQ.8 ) THEN
372  anorm = small
373  ELSE IF( imat.EQ.9 ) THEN
374  anorm = large
375  ELSE
376  anorm = one
377  END IF
378 *
379  ELSE IF( lsamen( 2, c2, 'PB' ) ) THEN
380 *
381 * xPB: Set parameters to generate a symmetric band matrix.
382 *
383 * Set TYPE, the type of matrix to be generated.
384 *
385  TYPE = 'P'
386 *
387 * Set the norm and condition number.
388 *
389  IF( imat.EQ.5 ) THEN
390  cndnum = badc1
391  ELSE IF( imat.EQ.6 ) THEN
392  cndnum = badc2
393  ELSE
394  cndnum = two
395  END IF
396 *
397  IF( imat.EQ.7 ) THEN
398  anorm = small
399  ELSE IF( imat.EQ.8 ) THEN
400  anorm = large
401  ELSE
402  anorm = one
403  END IF
404 *
405  ELSE IF( lsamen( 2, c2, 'PT' ) ) THEN
406 *
407 * xPT: Set parameters to generate a symmetric positive definite
408 * tridiagonal matrix.
409 *
410  TYPE = 'P'
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, 'TR' ) .OR. lsamen( 2, c2, 'TP' ) ) THEN
437 *
438 * xTR, xTP: Set parameters to generate a triangular matrix
439 *
440 * Set TYPE, the type of matrix to be generated.
441 *
442  TYPE = 'N'
443 *
444 * Set the lower and upper bandwidths.
445 *
446  mat = abs( imat )
447  IF( mat.EQ.1 .OR. mat.EQ.7 ) THEN
448  kl = 0
449  ku = 0
450  ELSE IF( imat.LT.0 ) THEN
451  kl = max( n-1, 0 )
452  ku = 0
453  ELSE
454  kl = 0
455  ku = max( n-1, 0 )
456  END IF
457 *
458 * Set the condition number and norm.
459 *
460  IF( mat.EQ.3 .OR. mat.EQ.9 ) THEN
461  cndnum = badc1
462  ELSE IF( mat.EQ.4 ) THEN
463  cndnum = badc2
464  ELSE IF( mat.EQ.10 ) THEN
465  cndnum = badc2
466  ELSE
467  cndnum = two
468  END IF
469 *
470  IF( mat.EQ.5 ) THEN
471  anorm = small
472  ELSE IF( mat.EQ.6 ) THEN
473  anorm = large
474  ELSE
475  anorm = one
476  END IF
477 *
478  ELSE IF( lsamen( 2, c2, 'TB' ) ) THEN
479 *
480 * xTB: Set parameters to generate a triangular band matrix.
481 *
482 * Set TYPE, the type of matrix to be generated.
483 *
484  TYPE = 'N'
485 *
486 * Set the norm and condition number.
487 *
488  IF( imat.EQ.2 .OR. imat.EQ.8 ) THEN
489  cndnum = badc1
490  ELSE IF( imat.EQ.3 .OR. imat.EQ.9 ) THEN
491  cndnum = badc2
492  ELSE
493  cndnum = two
494  END IF
495 *
496  IF( imat.EQ.4 ) THEN
497  anorm = small
498  ELSE IF( imat.EQ.5 ) THEN
499  anorm = large
500  ELSE
501  anorm = one
502  END IF
503  END IF
504  IF( n.LE.1 )
505  $ cndnum = one
506 *
507  RETURN
508 *
509 * End of DLATB4
510 *
511  END
dlabad
subroutine dlabad(SMALL, LARGE)
DLABAD
Definition: dlabad.f:76
dlatb4
subroutine dlatb4(PATH, IMAT, M, N, TYPE, KL, KU, ANORM, MODE, CNDNUM, DIST)
DLATB4
Definition: dlatb4.f:122