aboutsummaryrefslogtreecommitdiffstats
path: root/contrib/libs/clapack/cheevd.c
blob: 0cade89b4ee77cb060e20a5eeec7a1fdcfb36c59 (plain) (blame)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
/* cheevd.f -- translated by f2c (version 20061008).
   You must link the resulting object file with libf2c:
	on Microsoft Windows system, link with libf2c.lib;
	on Linux or Unix systems, link with .../path/to/libf2c.a -lm
	or, if you install libf2c.a in a standard place, with -lf2c -lm
	-- in that order, at the end of the command line, as in
		cc *.o -lf2c -lm
	Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,

		http://www.netlib.org/f2c/libf2c.zip
*/

#include "f2c.h"
#include "blaswrap.h"

/* Table of constant values */

static integer c__1 = 1;
static integer c_n1 = -1;
static integer c__0 = 0;
static real c_b18 = 1.f;

/* Subroutine */ int cheevd_(char *jobz, char *uplo, integer *n, complex *a, 
	integer *lda, real *w, complex *work, integer *lwork, real *rwork, 
	integer *lrwork, integer *iwork, integer *liwork, integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, i__1, i__2;
    real r__1;

    /* Builtin functions */
    double sqrt(doublereal);

    /* Local variables */
    real eps;
    integer inde;
    real anrm;
    integer imax;
    real rmin, rmax;
    integer lopt;
    real sigma;
    extern logical lsame_(char *, char *);
    integer iinfo;
    extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *);
    integer lwmin, liopt;
    logical lower;
    integer llrwk, lropt;
    logical wantz;
    integer indwk2, llwrk2;
    extern doublereal clanhe_(char *, char *, integer *, complex *, integer *, 
	     real *);
    integer iscale;
    extern /* Subroutine */ int clascl_(char *, integer *, integer *, real *, 
	    real *, integer *, integer *, complex *, integer *, integer *), cstedc_(char *, integer *, real *, real *, complex *, 
	    integer *, complex *, integer *, real *, integer *, integer *, 
	    integer *, integer *);
    extern doublereal slamch_(char *);
    extern /* Subroutine */ int chetrd_(char *, integer *, complex *, integer 
	    *, real *, real *, complex *, complex *, integer *, integer *), clacpy_(char *, integer *, integer *, complex *, integer 
	    *, complex *, integer *);
    real safmin;
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
	    integer *, integer *);
    extern /* Subroutine */ int xerbla_(char *, integer *);
    real bignum;
    integer indtau, indrwk, indwrk, liwmin;
    extern /* Subroutine */ int ssterf_(integer *, real *, real *, integer *);
    integer lrwmin;
    extern /* Subroutine */ int cunmtr_(char *, char *, char *, integer *, 
	    integer *, complex *, integer *, complex *, complex *, integer *, 
	    complex *, integer *, integer *);
    integer llwork;
    real smlnum;
    logical lquery;


/*  -- LAPACK driver routine (version 3.2) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/*     November 2006 */

/*     .. Scalar Arguments .. */
/*     .. */
/*     .. Array Arguments .. */
/*     .. */

/*  Purpose */
/*  ======= */

/*  CHEEVD computes all eigenvalues and, optionally, eigenvectors of a */
/*  complex Hermitian matrix A.  If eigenvectors are desired, it uses a */
/*  divide and conquer algorithm. */

/*  The divide and conquer algorithm makes very mild assumptions about */
/*  floating point arithmetic. It will work on machines with a guard */
/*  digit in add/subtract, or on those binary machines without guard */
/*  digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or */
/*  Cray-2. It could conceivably fail on hexadecimal or decimal machines */
/*  without guard digits, but we know of none. */

/*  Arguments */
/*  ========= */

/*  JOBZ    (input) CHARACTER*1 */
/*          = 'N':  Compute eigenvalues only; */
/*          = 'V':  Compute eigenvalues and eigenvectors. */

/*  UPLO    (input) CHARACTER*1 */
/*          = 'U':  Upper triangle of A is stored; */
/*          = 'L':  Lower triangle of A is stored. */

/*  N       (input) INTEGER */
/*          The order of the matrix A.  N >= 0. */

/*  A       (input/output) COMPLEX array, dimension (LDA, N) */
/*          On entry, the Hermitian matrix A.  If UPLO = 'U', the */
/*          leading N-by-N upper triangular part of A contains the */
/*          upper triangular part of the matrix A.  If UPLO = 'L', */
/*          the leading N-by-N lower triangular part of A contains */
/*          the lower triangular part of the matrix A. */
/*          On exit, if JOBZ = 'V', then if INFO = 0, A contains the */
/*          orthonormal eigenvectors of the matrix A. */
/*          If JOBZ = 'N', then on exit the lower triangle (if UPLO='L') */
/*          or the upper triangle (if UPLO='U') of A, including the */
/*          diagonal, is destroyed. */

/*  LDA     (input) INTEGER */
/*          The leading dimension of the array A.  LDA >= max(1,N). */

/*  W       (output) REAL array, dimension (N) */
/*          If INFO = 0, the eigenvalues in ascending order. */

/*  WORK    (workspace/output) COMPLEX array, dimension (MAX(1,LWORK)) */
/*          On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */

/*  LWORK   (input) INTEGER */
/*          The length of the array WORK. */
/*          If N <= 1,                LWORK must be at least 1. */
/*          If JOBZ  = 'N' and N > 1, LWORK must be at least N + 1. */
/*          If JOBZ  = 'V' and N > 1, LWORK must be at least 2*N + N**2. */

/*          If LWORK = -1, then a workspace query is assumed; the routine */
/*          only calculates the optimal sizes of the WORK, RWORK and */
/*          IWORK arrays, returns these values as the first entries of */
/*          the WORK, RWORK and IWORK arrays, and no error message */
/*          related to LWORK or LRWORK or LIWORK is issued by XERBLA. */

/*  RWORK   (workspace/output) REAL array, */
/*                                         dimension (LRWORK) */
/*          On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK. */

/*  LRWORK  (input) INTEGER */
/*          The dimension of the array RWORK. */
/*          If N <= 1,                LRWORK must be at least 1. */
/*          If JOBZ  = 'N' and N > 1, LRWORK must be at least N. */
/*          If JOBZ  = 'V' and N > 1, LRWORK must be at least */
/*                         1 + 5*N + 2*N**2. */

/*          If LRWORK = -1, then a workspace query is assumed; the */
/*          routine only calculates the optimal sizes of the WORK, RWORK */
/*          and IWORK arrays, returns these values as the first entries */
/*          of the WORK, RWORK and IWORK arrays, and no error message */
/*          related to LWORK or LRWORK or LIWORK is issued by XERBLA. */

/*  IWORK   (workspace/output) INTEGER array, dimension (MAX(1,LIWORK)) */
/*          On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. */

/*  LIWORK  (input) INTEGER */
/*          The dimension of the array IWORK. */
/*          If N <= 1,                LIWORK must be at least 1. */
/*          If JOBZ  = 'N' and N > 1, LIWORK must be at least 1. */
/*          If JOBZ  = 'V' and N > 1, LIWORK must be at least 3 + 5*N. */

/*          If LIWORK = -1, then a workspace query is assumed; the */
/*          routine only calculates the optimal sizes of the WORK, RWORK */
/*          and IWORK arrays, returns these values as the first entries */
/*          of the WORK, RWORK and IWORK arrays, and no error message */
/*          related to LWORK or LRWORK or LIWORK is issued by XERBLA. */

/*  INFO    (output) INTEGER */
/*          = 0:  successful exit */
/*          < 0:  if INFO = -i, the i-th argument had an illegal value */
/*          > 0:  if INFO = i and JOBZ = 'N', then the algorithm failed */
/*                to converge; i off-diagonal elements of an intermediate */
/*                tridiagonal form did not converge to zero; */
/*                if INFO = i and JOBZ = 'V', then the algorithm failed */
/*                to compute an eigenvalue while working on the submatrix */
/*                lying in rows and columns INFO/(N+1) through */
/*                mod(INFO,N+1). */

/*  Further Details */
/*  =============== */

/*  Based on contributions by */
/*     Jeff Rutter, Computer Science Division, University of California */
/*     at Berkeley, USA */

/*  Modified description of INFO. Sven, 16 Feb 05. */
/*  ===================================================================== */

/*     .. Parameters .. */
/*     .. */
/*     .. Local Scalars .. */
/*     .. */
/*     .. External Functions .. */
/*     .. */
/*     .. External Subroutines .. */
/*     .. */
/*     .. Intrinsic Functions .. */
/*     .. */
/*     .. Executable Statements .. */

/*     Test the input parameters. */

    /* Parameter adjustments */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1;
    a -= a_offset;
    --w;
    --work;
    --rwork;
    --iwork;

    /* Function Body */
    wantz = lsame_(jobz, "V");
    lower = lsame_(uplo, "L");
    lquery = *lwork == -1 || *lrwork == -1 || *liwork == -1;

    *info = 0;
    if (! (wantz || lsame_(jobz, "N"))) {
	*info = -1;
    } else if (! (lower || lsame_(uplo, "U"))) {
	*info = -2;
    } else if (*n < 0) {
	*info = -3;
    } else if (*lda < max(1,*n)) {
	*info = -5;
    }

    if (*info == 0) {
	if (*n <= 1) {
	    lwmin = 1;
	    lrwmin = 1;
	    liwmin = 1;
	    lopt = lwmin;
	    lropt = lrwmin;
	    liopt = liwmin;
	} else {
	    if (wantz) {
		lwmin = (*n << 1) + *n * *n;
/* Computing 2nd power */
		i__1 = *n;
		lrwmin = *n * 5 + 1 + (i__1 * i__1 << 1);
		liwmin = *n * 5 + 3;
	    } else {
		lwmin = *n + 1;
		lrwmin = *n;
		liwmin = 1;
	    }
/* Computing MAX */
	    i__1 = lwmin, i__2 = *n + ilaenv_(&c__1, "CHETRD", uplo, n, &c_n1, 
		     &c_n1, &c_n1);
	    lopt = max(i__1,i__2);
	    lropt = lrwmin;
	    liopt = liwmin;
	}
	work[1].r = (real) lopt, work[1].i = 0.f;
	rwork[1] = (real) lropt;
	iwork[1] = liopt;

	if (*lwork < lwmin && ! lquery) {
	    *info = -8;
	} else if (*lrwork < lrwmin && ! lquery) {
	    *info = -10;
	} else if (*liwork < liwmin && ! lquery) {
	    *info = -12;
	}
    }

    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("CHEEVD", &i__1);
	return 0;
    } else if (lquery) {
	return 0;
    }

/*     Quick return if possible */

    if (*n == 0) {
	return 0;
    }

    if (*n == 1) {
	i__1 = a_dim1 + 1;
	w[1] = a[i__1].r;
	if (wantz) {
	    i__1 = a_dim1 + 1;
	    a[i__1].r = 1.f, a[i__1].i = 0.f;
	}
	return 0;
    }

/*     Get machine constants. */

    safmin = slamch_("Safe minimum");
    eps = slamch_("Precision");
    smlnum = safmin / eps;
    bignum = 1.f / smlnum;
    rmin = sqrt(smlnum);
    rmax = sqrt(bignum);

/*     Scale matrix to allowable range, if necessary. */

    anrm = clanhe_("M", uplo, n, &a[a_offset], lda, &rwork[1]);
    iscale = 0;
    if (anrm > 0.f && anrm < rmin) {
	iscale = 1;
	sigma = rmin / anrm;
    } else if (anrm > rmax) {
	iscale = 1;
	sigma = rmax / anrm;
    }
    if (iscale == 1) {
	clascl_(uplo, &c__0, &c__0, &c_b18, &sigma, n, n, &a[a_offset], lda, 
		info);
    }

/*     Call CHETRD to reduce Hermitian matrix to tridiagonal form. */

    inde = 1;
    indtau = 1;
    indwrk = indtau + *n;
    indrwk = inde + *n;
    indwk2 = indwrk + *n * *n;
    llwork = *lwork - indwrk + 1;
    llwrk2 = *lwork - indwk2 + 1;
    llrwk = *lrwork - indrwk + 1;
    chetrd_(uplo, n, &a[a_offset], lda, &w[1], &rwork[inde], &work[indtau], &
	    work[indwrk], &llwork, &iinfo);

/*     For eigenvalues only, call SSTERF.  For eigenvectors, first call */
/*     CSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the */
/*     tridiagonal matrix, then call CUNMTR to multiply it to the */
/*     Householder transformations represented as Householder vectors in */
/*     A. */

    if (! wantz) {
	ssterf_(n, &w[1], &rwork[inde], info);
    } else {
	cstedc_("I", n, &w[1], &rwork[inde], &work[indwrk], n, &work[indwk2], 
		&llwrk2, &rwork[indrwk], &llrwk, &iwork[1], liwork, info);
	cunmtr_("L", uplo, "N", n, n, &a[a_offset], lda, &work[indtau], &work[
		indwrk], n, &work[indwk2], &llwrk2, &iinfo);
	clacpy_("A", n, n, &work[indwrk], n, &a[a_offset], lda);
    }

/*     If matrix was scaled, then rescale eigenvalues appropriately. */

    if (iscale == 1) {
	if (*info == 0) {
	    imax = *n;
	} else {
	    imax = *info - 1;
	}
	r__1 = 1.f / sigma;
	sscal_(&imax, &r__1, &w[1], &c__1);
    }

    work[1].r = (real) lopt, work[1].i = 0.f;
    rwork[1] = (real) lropt;
    iwork[1] = liopt;

    return 0;

/*     End of CHEEVD */

} /* cheevd_ */