LAPACK  3.10.1 LAPACK: Linear Algebra PACKage
zlatme.f
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1 *> \brief \b ZLATME
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 ZLATME( N, DIST, ISEED, D, MODE, COND, DMAX,
12 * RSIGN,
13 * UPPER, SIM, DS, MODES, CONDS, KL, KU, ANORM,
14 * A,
15 * LDA, WORK, INFO )
16 *
17 * .. Scalar Arguments ..
18 * CHARACTER DIST, RSIGN, SIM, UPPER
19 * INTEGER INFO, KL, KU, LDA, MODE, MODES, N
20 * DOUBLE PRECISION ANORM, COND, CONDS
21 * COMPLEX*16 DMAX
22 * ..
23 * .. Array Arguments ..
24 * INTEGER ISEED( 4 )
25 * DOUBLE PRECISION DS( * )
26 * COMPLEX*16 A( LDA, * ), D( * ), WORK( * )
27 * ..
28 *
29 *
30 *> \par Purpose:
31 * =============
32 *>
33 *> \verbatim
34 *>
35 *> ZLATME generates random non-symmetric square matrices with
36 *> specified eigenvalues for testing LAPACK programs.
37 *>
38 *> ZLATME operates by applying the following sequence of
39 *> operations:
40 *>
41 *> 1. Set the diagonal to D, where D may be input or
42 *> computed according to MODE, COND, DMAX, and RSIGN
43 *> as described below.
44 *>
45 *> 2. If UPPER='T', the upper triangle of A is set to random values
46 *> out of distribution DIST.
47 *>
48 *> 3. If SIM='T', A is multiplied on the left by a random matrix
49 *> X, whose singular values are specified by DS, MODES, and
50 *> CONDS, and on the right by X inverse.
51 *>
52 *> 4. If KL < N-1, the lower bandwidth is reduced to KL using
53 *> Householder transformations. If KU < N-1, the upper
54 *> bandwidth is reduced to KU.
55 *>
56 *> 5. If ANORM is not negative, the matrix is scaled to have
57 *> maximum-element-norm ANORM.
58 *>
59 *> (Note: since the matrix cannot be reduced beyond Hessenberg form,
60 *> no packing options are available.)
61 *> \endverbatim
62 *
63 * Arguments:
64 * ==========
65 *
66 *> \param[in] N
67 *> \verbatim
68 *> N is INTEGER
69 *> The number of columns (or rows) of A. Not modified.
70 *> \endverbatim
71 *>
72 *> \param[in] DIST
73 *> \verbatim
74 *> DIST is CHARACTER*1
75 *> On entry, DIST specifies the type of distribution to be used
76 *> to generate the random eigen-/singular values, and on the
77 *> upper triangle (see UPPER).
78 *> 'U' => UNIFORM( 0, 1 ) ( 'U' for uniform )
79 *> 'S' => UNIFORM( -1, 1 ) ( 'S' for symmetric )
80 *> 'N' => NORMAL( 0, 1 ) ( 'N' for normal )
81 *> 'D' => uniform on the complex disc |z| < 1.
82 *> Not modified.
83 *> \endverbatim
84 *>
85 *> \param[in,out] ISEED
86 *> \verbatim
87 *> ISEED is INTEGER array, dimension ( 4 )
88 *> On entry ISEED specifies the seed of the random number
89 *> generator. They should lie between 0 and 4095 inclusive,
90 *> and ISEED(4) should be odd. The random number generator
91 *> uses a linear congruential sequence limited to small
92 *> integers, and so should produce machine independent
93 *> random numbers. The values of ISEED are changed on
94 *> exit, and can be used in the next call to ZLATME
95 *> to continue the same random number sequence.
96 *> Changed on exit.
97 *> \endverbatim
98 *>
99 *> \param[in,out] D
100 *> \verbatim
101 *> D is COMPLEX*16 array, dimension ( N )
102 *> This array is used to specify the eigenvalues of A. If
103 *> MODE=0, then D is assumed to contain the eigenvalues
104 *> otherwise they will be computed according to MODE, COND,
105 *> DMAX, and RSIGN and placed in D.
106 *> Modified if MODE is nonzero.
107 *> \endverbatim
108 *>
109 *> \param[in] MODE
110 *> \verbatim
111 *> MODE is INTEGER
112 *> On entry this describes how the eigenvalues are to
113 *> be specified:
114 *> MODE = 0 means use D as input
115 *> MODE = 1 sets D(1)=1 and D(2:N)=1.0/COND
116 *> MODE = 2 sets D(1:N-1)=1 and D(N)=1.0/COND
117 *> MODE = 3 sets D(I)=COND**(-(I-1)/(N-1))
118 *> MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND)
119 *> MODE = 5 sets D to random numbers in the range
120 *> ( 1/COND , 1 ) such that their logarithms
121 *> are uniformly distributed.
122 *> MODE = 6 set D to random numbers from same distribution
123 *> as the rest of the matrix.
124 *> MODE < 0 has the same meaning as ABS(MODE), except that
125 *> the order of the elements of D is reversed.
126 *> Thus if MODE is between 1 and 4, D has entries ranging
127 *> from 1 to 1/COND, if between -1 and -4, D has entries
128 *> ranging from 1/COND to 1,
129 *> Not modified.
130 *> \endverbatim
131 *>
132 *> \param[in] COND
133 *> \verbatim
134 *> COND is DOUBLE PRECISION
135 *> On entry, this is used as described under MODE above.
136 *> If used, it must be >= 1. Not modified.
137 *> \endverbatim
138 *>
139 *> \param[in] DMAX
140 *> \verbatim
141 *> DMAX is COMPLEX*16
142 *> If MODE is neither -6, 0 nor 6, the contents of D, as
143 *> computed according to MODE and COND, will be scaled by
144 *> DMAX / max(abs(D(i))). Note that DMAX need not be
145 *> positive or real: if DMAX is negative or complex (or zero),
146 *> D will be scaled by a negative or complex number (or zero).
147 *> If RSIGN='F' then the largest (absolute) eigenvalue will be
148 *> equal to DMAX.
149 *> Not modified.
150 *> \endverbatim
151 *>
152 *> \param[in] RSIGN
153 *> \verbatim
154 *> RSIGN is CHARACTER*1
155 *> If MODE is not 0, 6, or -6, and RSIGN='T', then the
156 *> elements of D, as computed according to MODE and COND, will
157 *> be multiplied by a random complex number from the unit
158 *> circle |z| = 1. If RSIGN='F', they will not be. RSIGN may
159 *> only have the values 'T' or 'F'.
160 *> Not modified.
161 *> \endverbatim
162 *>
163 *> \param[in] UPPER
164 *> \verbatim
165 *> UPPER is CHARACTER*1
166 *> If UPPER='T', then the elements of A above the diagonal
167 *> will be set to random numbers out of DIST. If UPPER='F',
168 *> they will not. UPPER may only have the values 'T' or 'F'.
169 *> Not modified.
170 *> \endverbatim
171 *>
172 *> \param[in] SIM
173 *> \verbatim
174 *> SIM is CHARACTER*1
175 *> If SIM='T', then A will be operated on by a "similarity
176 *> transform", i.e., multiplied on the left by a matrix X and
177 *> on the right by X inverse. X = U S V, where U and V are
178 *> random unitary matrices and S is a (diagonal) matrix of
179 *> singular values specified by DS, MODES, and CONDS. If
180 *> SIM='F', then A will not be transformed.
181 *> Not modified.
182 *> \endverbatim
183 *>
184 *> \param[in,out] DS
185 *> \verbatim
186 *> DS is DOUBLE PRECISION array, dimension ( N )
187 *> This array is used to specify the singular values of X,
188 *> in the same way that D specifies the eigenvalues of A.
189 *> If MODE=0, the DS contains the singular values, which
190 *> may not be zero.
191 *> Modified if MODE is nonzero.
192 *> \endverbatim
193 *>
194 *> \param[in] MODES
195 *> \verbatim
196 *> MODES is INTEGER
197 *> \endverbatim
198 *>
199 *> \param[in] CONDS
200 *> \verbatim
201 *> CONDS is DOUBLE PRECISION
202 *> Similar to MODE and COND, but for specifying the diagonal
203 *> of S. MODES=-6 and +6 are not allowed (since they would
204 *> result in randomly ill-conditioned eigenvalues.)
205 *> \endverbatim
206 *>
207 *> \param[in] KL
208 *> \verbatim
209 *> KL is INTEGER
210 *> This specifies the lower bandwidth of the matrix. KL=1
211 *> specifies upper Hessenberg form. If KL is at least N-1,
212 *> then A will have full lower bandwidth.
213 *> Not modified.
214 *> \endverbatim
215 *>
216 *> \param[in] KU
217 *> \verbatim
218 *> KU is INTEGER
219 *> This specifies the upper bandwidth of the matrix. KU=1
220 *> specifies lower Hessenberg form. If KU is at least N-1,
221 *> then A will have full upper bandwidth; if KU and KL
222 *> are both at least N-1, then A will be dense. Only one of
223 *> KU and KL may be less than N-1.
224 *> Not modified.
225 *> \endverbatim
226 *>
227 *> \param[in] ANORM
228 *> \verbatim
229 *> ANORM is DOUBLE PRECISION
230 *> If ANORM is not negative, then A will be scaled by a non-
231 *> negative real number to make the maximum-element-norm of A
232 *> to be ANORM.
233 *> Not modified.
234 *> \endverbatim
235 *>
236 *> \param[out] A
237 *> \verbatim
238 *> A is COMPLEX*16 array, dimension ( LDA, N )
239 *> On exit A is the desired test matrix.
240 *> Modified.
241 *> \endverbatim
242 *>
243 *> \param[in] LDA
244 *> \verbatim
245 *> LDA is INTEGER
246 *> LDA specifies the first dimension of A as declared in the
247 *> calling program. LDA must be at least M.
248 *> Not modified.
249 *> \endverbatim
250 *>
251 *> \param[out] WORK
252 *> \verbatim
253 *> WORK is COMPLEX*16 array, dimension ( 3*N )
254 *> Workspace.
255 *> Modified.
256 *> \endverbatim
257 *>
258 *> \param[out] INFO
259 *> \verbatim
260 *> INFO is INTEGER
261 *> Error code. On exit, INFO will be set to one of the
262 *> following values:
263 *> 0 => normal return
264 *> -1 => N negative
265 *> -2 => DIST illegal string
266 *> -5 => MODE not in range -6 to 6
267 *> -6 => COND less than 1.0, and MODE neither -6, 0 nor 6
268 *> -9 => RSIGN is not 'T' or 'F'
269 *> -10 => UPPER is not 'T' or 'F'
270 *> -11 => SIM is not 'T' or 'F'
271 *> -12 => MODES=0 and DS has a zero singular value.
272 *> -13 => MODES is not in the range -5 to 5.
273 *> -14 => MODES is nonzero and CONDS is less than 1.
274 *> -15 => KL is less than 1.
275 *> -16 => KU is less than 1, or KL and KU are both less than
276 *> N-1.
277 *> -19 => LDA is less than M.
278 *> 1 => Error return from ZLATM1 (computing D)
279 *> 2 => Cannot scale to DMAX (max. eigenvalue is 0)
280 *> 3 => Error return from DLATM1 (computing DS)
281 *> 4 => Error return from ZLARGE
282 *> 5 => Zero singular value from DLATM1.
283 *> \endverbatim
284 *
285 * Authors:
286 * ========
287 *
288 *> \author Univ. of Tennessee
289 *> \author Univ. of California Berkeley
290 *> \author Univ. of Colorado Denver
291 *> \author NAG Ltd.
292 *
293 *> \ingroup complex16_matgen
294 *
295 * =====================================================================
296  SUBROUTINE zlatme( N, DIST, ISEED, D, MODE, COND, DMAX,
297  \$ RSIGN,
298  \$ UPPER, SIM, DS, MODES, CONDS, KL, KU, ANORM,
299  \$ A,
300  \$ LDA, WORK, INFO )
301 *
302 * -- LAPACK computational routine --
303 * -- LAPACK is a software package provided by Univ. of Tennessee, --
304 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
305 *
306 * .. Scalar Arguments ..
307  CHARACTER DIST, RSIGN, SIM, UPPER
308  INTEGER INFO, KL, KU, LDA, MODE, MODES, N
309  DOUBLE PRECISION ANORM, COND, CONDS
310  COMPLEX*16 DMAX
311 * ..
312 * .. Array Arguments ..
313  INTEGER ISEED( 4 )
314  DOUBLE PRECISION DS( * )
315  COMPLEX*16 A( LDA, * ), D( * ), WORK( * )
316 * ..
317 *
318 * =====================================================================
319 *
320 * .. Parameters ..
321  DOUBLE PRECISION ZERO
322  PARAMETER ( ZERO = 0.0d+0 )
323  DOUBLE PRECISION ONE
324  PARAMETER ( ONE = 1.0d+0 )
325  COMPLEX*16 CZERO
326  parameter( czero = ( 0.0d+0, 0.0d+0 ) )
327  COMPLEX*16 CONE
328  parameter( cone = ( 1.0d+0, 0.0d+0 ) )
329 * ..
330 * .. Local Scalars ..
332  INTEGER I, IC, ICOLS, IDIST, IINFO, IR, IROWS, IRSIGN,
333  \$ ISIM, IUPPER, J, JC, JCR
334  DOUBLE PRECISION RALPHA, TEMP
335  COMPLEX*16 ALPHA, TAU, XNORMS
336 * ..
337 * .. Local Arrays ..
338  DOUBLE PRECISION TEMPA( 1 )
339 * ..
340 * .. External Functions ..
341  LOGICAL LSAME
342  DOUBLE PRECISION ZLANGE
343  COMPLEX*16 ZLARND
344  EXTERNAL LSAME, ZLANGE, ZLARND
345 * ..
346 * .. External Subroutines ..
347  EXTERNAL dlatm1, xerbla, zcopy, zdscal, zgemv, zgerc,
349  \$ zscal
350 * ..
351 * .. Intrinsic Functions ..
352  INTRINSIC abs, dconjg, max, mod
353 * ..
354 * .. Executable Statements ..
355 *
356 * 1) Decode and Test the input parameters.
357 * Initialize flags & seed.
358 *
359  info = 0
360 *
361 * Quick return if possible
362 *
363  IF( n.EQ.0 )
364  \$ RETURN
365 *
366 * Decode DIST
367 *
368  IF( lsame( dist, 'U' ) ) THEN
369  idist = 1
370  ELSE IF( lsame( dist, 'S' ) ) THEN
371  idist = 2
372  ELSE IF( lsame( dist, 'N' ) ) THEN
373  idist = 3
374  ELSE IF( lsame( dist, 'D' ) ) THEN
375  idist = 4
376  ELSE
377  idist = -1
378  END IF
379 *
380 * Decode RSIGN
381 *
382  IF( lsame( rsign, 'T' ) ) THEN
383  irsign = 1
384  ELSE IF( lsame( rsign, 'F' ) ) THEN
385  irsign = 0
386  ELSE
387  irsign = -1
388  END IF
389 *
390 * Decode UPPER
391 *
392  IF( lsame( upper, 'T' ) ) THEN
393  iupper = 1
394  ELSE IF( lsame( upper, 'F' ) ) THEN
395  iupper = 0
396  ELSE
397  iupper = -1
398  END IF
399 *
400 * Decode SIM
401 *
402  IF( lsame( sim, 'T' ) ) THEN
403  isim = 1
404  ELSE IF( lsame( sim, 'F' ) ) THEN
405  isim = 0
406  ELSE
407  isim = -1
408  END IF
409 *
410 * Check DS, if MODES=0 and ISIM=1
411 *
412  bads = .false.
413  IF( modes.EQ.0 .AND. isim.EQ.1 ) THEN
414  DO 10 j = 1, n
415  IF( ds( j ).EQ.zero )
416  \$ bads = .true.
417  10 CONTINUE
418  END IF
419 *
420 * Set INFO if an error
421 *
422  IF( n.LT.0 ) THEN
423  info = -1
424  ELSE IF( idist.EQ.-1 ) THEN
425  info = -2
426  ELSE IF( abs( mode ).GT.6 ) THEN
427  info = -5
428  ELSE IF( ( mode.NE.0 .AND. abs( mode ).NE.6 ) .AND. cond.LT.one )
429  \$ THEN
430  info = -6
431  ELSE IF( irsign.EQ.-1 ) THEN
432  info = -9
433  ELSE IF( iupper.EQ.-1 ) THEN
434  info = -10
435  ELSE IF( isim.EQ.-1 ) THEN
436  info = -11
437  ELSE IF( bads ) THEN
438  info = -12
439  ELSE IF( isim.EQ.1 .AND. abs( modes ).GT.5 ) THEN
440  info = -13
441  ELSE IF( isim.EQ.1 .AND. modes.NE.0 .AND. conds.LT.one ) THEN
442  info = -14
443  ELSE IF( kl.LT.1 ) THEN
444  info = -15
445  ELSE IF( ku.LT.1 .OR. ( ku.LT.n-1 .AND. kl.LT.n-1 ) ) THEN
446  info = -16
447  ELSE IF( lda.LT.max( 1, n ) ) THEN
448  info = -19
449  END IF
450 *
451  IF( info.NE.0 ) THEN
452  CALL xerbla( 'ZLATME', -info )
453  RETURN
454  END IF
455 *
456 * Initialize random number generator
457 *
458  DO 20 i = 1, 4
459  iseed( i ) = mod( abs( iseed( i ) ), 4096 )
460  20 CONTINUE
461 *
462  IF( mod( iseed( 4 ), 2 ).NE.1 )
463  \$ iseed( 4 ) = iseed( 4 ) + 1
464 *
465 * 2) Set up diagonal of A
466 *
467 * Compute D according to COND and MODE
468 *
469  CALL zlatm1( mode, cond, irsign, idist, iseed, d, n, iinfo )
470  IF( iinfo.NE.0 ) THEN
471  info = 1
472  RETURN
473  END IF
474  IF( mode.NE.0 .AND. abs( mode ).NE.6 ) THEN
475 *
476 * Scale by DMAX
477 *
478  temp = abs( d( 1 ) )
479  DO 30 i = 2, n
480  temp = max( temp, abs( d( i ) ) )
481  30 CONTINUE
482 *
483  IF( temp.GT.zero ) THEN
484  alpha = dmax / temp
485  ELSE
486  info = 2
487  RETURN
488  END IF
489 *
490  CALL zscal( n, alpha, d, 1 )
491 *
492  END IF
493 *
494  CALL zlaset( 'Full', n, n, czero, czero, a, lda )
495  CALL zcopy( n, d, 1, a, lda+1 )
496 *
497 * 3) If UPPER='T', set upper triangle of A to random numbers.
498 *
499  IF( iupper.NE.0 ) THEN
500  DO 40 jc = 2, n
501  CALL zlarnv( idist, iseed, jc-1, a( 1, jc ) )
502  40 CONTINUE
503  END IF
504 *
505 * 4) If SIM='T', apply similarity transformation.
506 *
507 * -1
508 * Transform is X A X , where X = U S V, thus
509 *
510 * it is U S V A V' (1/S) U'
511 *
512  IF( isim.NE.0 ) THEN
513 *
514 * Compute S (singular values of the eigenvector matrix)
515 * according to CONDS and MODES
516 *
517  CALL dlatm1( modes, conds, 0, 0, iseed, ds, n, iinfo )
518  IF( iinfo.NE.0 ) THEN
519  info = 3
520  RETURN
521  END IF
522 *
523 * Multiply by V and V'
524 *
525  CALL zlarge( n, a, lda, iseed, work, iinfo )
526  IF( iinfo.NE.0 ) THEN
527  info = 4
528  RETURN
529  END IF
530 *
531 * Multiply by S and (1/S)
532 *
533  DO 50 j = 1, n
534  CALL zdscal( n, ds( j ), a( j, 1 ), lda )
535  IF( ds( j ).NE.zero ) THEN
536  CALL zdscal( n, one / ds( j ), a( 1, j ), 1 )
537  ELSE
538  info = 5
539  RETURN
540  END IF
541  50 CONTINUE
542 *
543 * Multiply by U and U'
544 *
545  CALL zlarge( n, a, lda, iseed, work, iinfo )
546  IF( iinfo.NE.0 ) THEN
547  info = 4
548  RETURN
549  END IF
550  END IF
551 *
552 * 5) Reduce the bandwidth.
553 *
554  IF( kl.LT.n-1 ) THEN
555 *
556 * Reduce bandwidth -- kill column
557 *
558  DO 60 jcr = kl + 1, n - 1
559  ic = jcr - kl
560  irows = n + 1 - jcr
561  icols = n + kl - jcr
562 *
563  CALL zcopy( irows, a( jcr, ic ), 1, work, 1 )
564  xnorms = work( 1 )
565  CALL zlarfg( irows, xnorms, work( 2 ), 1, tau )
566  tau = dconjg( tau )
567  work( 1 ) = cone
568  alpha = zlarnd( 5, iseed )
569 *
570  CALL zgemv( 'C', irows, icols, cone, a( jcr, ic+1 ), lda,
571  \$ work, 1, czero, work( irows+1 ), 1 )
572  CALL zgerc( irows, icols, -tau, work, 1, work( irows+1 ), 1,
573  \$ a( jcr, ic+1 ), lda )
574 *
575  CALL zgemv( 'N', n, irows, cone, a( 1, jcr ), lda, work, 1,
576  \$ czero, work( irows+1 ), 1 )
577  CALL zgerc( n, irows, -dconjg( tau ), work( irows+1 ), 1,
578  \$ work, 1, a( 1, jcr ), lda )
579 *
580  a( jcr, ic ) = xnorms
581  CALL zlaset( 'Full', irows-1, 1, czero, czero,
582  \$ a( jcr+1, ic ), lda )
583 *
584  CALL zscal( icols+1, alpha, a( jcr, ic ), lda )
585  CALL zscal( n, dconjg( alpha ), a( 1, jcr ), 1 )
586  60 CONTINUE
587  ELSE IF( ku.LT.n-1 ) THEN
588 *
589 * Reduce upper bandwidth -- kill a row at a time.
590 *
591  DO 70 jcr = ku + 1, n - 1
592  ir = jcr - ku
593  irows = n + ku - jcr
594  icols = n + 1 - jcr
595 *
596  CALL zcopy( icols, a( ir, jcr ), lda, work, 1 )
597  xnorms = work( 1 )
598  CALL zlarfg( icols, xnorms, work( 2 ), 1, tau )
599  tau = dconjg( tau )
600  work( 1 ) = cone
601  CALL zlacgv( icols-1, work( 2 ), 1 )
602  alpha = zlarnd( 5, iseed )
603 *
604  CALL zgemv( 'N', irows, icols, cone, a( ir+1, jcr ), lda,
605  \$ work, 1, czero, work( icols+1 ), 1 )
606  CALL zgerc( irows, icols, -tau, work( icols+1 ), 1, work, 1,
607  \$ a( ir+1, jcr ), lda )
608 *
609  CALL zgemv( 'C', icols, n, cone, a( jcr, 1 ), lda, work, 1,
610  \$ czero, work( icols+1 ), 1 )
611  CALL zgerc( icols, n, -dconjg( tau ), work, 1,
612  \$ work( icols+1 ), 1, a( jcr, 1 ), lda )
613 *
614  a( ir, jcr ) = xnorms
615  CALL zlaset( 'Full', 1, icols-1, czero, czero,
616  \$ a( ir, jcr+1 ), lda )
617 *
618  CALL zscal( irows+1, alpha, a( ir, jcr ), 1 )
619  CALL zscal( n, dconjg( alpha ), a( jcr, 1 ), lda )
620  70 CONTINUE
621  END IF
622 *
623 * Scale the matrix to have norm ANORM
624 *
625  IF( anorm.GE.zero ) THEN
626  temp = zlange( 'M', n, n, a, lda, tempa )
627  IF( temp.GT.zero ) THEN
628  ralpha = anorm / temp
629  DO 80 j = 1, n
630  CALL zdscal( n, ralpha, a( 1, j ), 1 )
631  80 CONTINUE
632  END IF
633  END IF
634 *
635  RETURN
636 *
637 * End of ZLATME
638 *
639  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine zdscal(N, DA, ZX, INCX)
ZDSCAL
Definition: zdscal.f:78
subroutine zscal(N, ZA, ZX, INCX)
ZSCAL
Definition: zscal.f:78
subroutine zcopy(N, ZX, INCX, ZY, INCY)
ZCOPY
Definition: zcopy.f:81
subroutine zgerc(M, N, ALPHA, X, INCX, Y, INCY, A, LDA)
ZGERC
Definition: zgerc.f:130
subroutine zgemv(TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
ZGEMV
Definition: zgemv.f:158
subroutine zlarge(N, A, LDA, ISEED, WORK, INFO)
ZLARGE
Definition: zlarge.f:87
subroutine zlatm1(MODE, COND, IRSIGN, IDIST, ISEED, D, N, INFO)
ZLATM1
Definition: zlatm1.f:137
subroutine zlatme(N, DIST, ISEED, D, MODE, COND, DMAX, RSIGN, UPPER, SIM, DS, MODES, CONDS, KL, KU, ANORM, A, LDA, WORK, INFO)
ZLATME
Definition: zlatme.f:301
subroutine zlarnv(IDIST, ISEED, N, X)
ZLARNV returns a vector of random numbers from a uniform or normal distribution.
Definition: zlarnv.f:99
subroutine zlaset(UPLO, M, N, ALPHA, BETA, A, LDA)
ZLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition: zlaset.f:106
subroutine zlacgv(N, X, INCX)
ZLACGV conjugates a complex vector.
Definition: zlacgv.f:74
subroutine zlarfg(N, ALPHA, X, INCX, TAU)
ZLARFG generates an elementary reflector (Householder matrix).
Definition: zlarfg.f:106
subroutine dlatm1(MODE, COND, IRSIGN, IDIST, ISEED, D, N, INFO)
DLATM1
Definition: dlatm1.f:135