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
|
/* zhbgvd.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 doublecomplex c_b1 = {1.,0.};
static doublecomplex c_b2 = {0.,0.};
/* Subroutine */ int zhbgvd_(char *jobz, char *uplo, integer *n, integer *ka,
integer *kb, doublecomplex *ab, integer *ldab, doublecomplex *bb,
integer *ldbb, doublereal *w, doublecomplex *z__, integer *ldz,
doublecomplex *work, integer *lwork, doublereal *rwork, integer *
lrwork, integer *iwork, integer *liwork, integer *info)
{
/* System generated locals */
integer ab_dim1, ab_offset, bb_dim1, bb_offset, z_dim1, z_offset, i__1;
/* Local variables */
integer inde;
char vect[1];
integer llwk2;
extern logical lsame_(char *, char *);
integer iinfo;
extern /* Subroutine */ int zgemm_(char *, char *, integer *, integer *,
integer *, doublecomplex *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *);
integer lwmin;
logical upper;
integer llrwk;
logical wantz;
integer indwk2;
extern /* Subroutine */ int xerbla_(char *, integer *), dsterf_(
integer *, doublereal *, doublereal *, integer *), zstedc_(char *,
integer *, doublereal *, doublereal *, doublecomplex *, integer *
, doublecomplex *, integer *, doublereal *, integer *, integer *,
integer *, integer *), zhbtrd_(char *, char *, integer *,
integer *, doublecomplex *, integer *, doublereal *, doublereal *,
doublecomplex *, integer *, doublecomplex *, integer *);
integer indwrk, liwmin;
extern /* Subroutine */ int zhbgst_(char *, char *, integer *, integer *,
integer *, doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, doublereal *,
integer *), zlacpy_(char *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *);
integer lrwmin;
extern /* Subroutine */ int zpbstf_(char *, integer *, integer *,
doublecomplex *, integer *, integer *);
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 */
/* ======= */
/* ZHBGVD computes all the eigenvalues, and optionally, the eigenvectors */
/* of a complex generalized Hermitian-definite banded eigenproblem, of */
/* the form A*x=(lambda)*B*x. Here A and B are assumed to be Hermitian */
/* and banded, and B is also positive definite. 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 triangles of A and B are stored; */
/* = 'L': Lower triangles of A and B are stored. */
/* N (input) INTEGER */
/* The order of the matrices A and B. N >= 0. */
/* KA (input) INTEGER */
/* The number of superdiagonals of the matrix A if UPLO = 'U', */
/* or the number of subdiagonals if UPLO = 'L'. KA >= 0. */
/* KB (input) INTEGER */
/* The number of superdiagonals of the matrix B if UPLO = 'U', */
/* or the number of subdiagonals if UPLO = 'L'. KB >= 0. */
/* AB (input/output) COMPLEX*16 array, dimension (LDAB, N) */
/* On entry, the upper or lower triangle of the Hermitian band */
/* matrix A, stored in the first ka+1 rows of the array. The */
/* j-th column of A is stored in the j-th column of the array AB */
/* as follows: */
/* if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j; */
/* if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka). */
/* On exit, the contents of AB are destroyed. */
/* LDAB (input) INTEGER */
/* The leading dimension of the array AB. LDAB >= KA+1. */
/* BB (input/output) COMPLEX*16 array, dimension (LDBB, N) */
/* On entry, the upper or lower triangle of the Hermitian band */
/* matrix B, stored in the first kb+1 rows of the array. The */
/* j-th column of B is stored in the j-th column of the array BB */
/* as follows: */
/* if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j; */
/* if UPLO = 'L', BB(1+i-j,j) = B(i,j) for j<=i<=min(n,j+kb). */
/* On exit, the factor S from the split Cholesky factorization */
/* B = S**H*S, as returned by ZPBSTF. */
/* LDBB (input) INTEGER */
/* The leading dimension of the array BB. LDBB >= KB+1. */
/* W (output) DOUBLE PRECISION array, dimension (N) */
/* If INFO = 0, the eigenvalues in ascending order. */
/* Z (output) COMPLEX*16 array, dimension (LDZ, N) */
/* If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of */
/* eigenvectors, with the i-th column of Z holding the */
/* eigenvector associated with W(i). The eigenvectors are */
/* normalized so that Z**H*B*Z = I. */
/* If JOBZ = 'N', then Z is not referenced. */
/* LDZ (input) INTEGER */
/* The leading dimension of the array Z. LDZ >= 1, and if */
/* JOBZ = 'V', LDZ >= N. */
/* WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK)) */
/* On exit, if INFO=0, WORK(1) returns the optimal LWORK. */
/* LWORK (input) INTEGER */
/* The dimension of the array WORK. */
/* If N <= 1, LWORK >= 1. */
/* If JOBZ = 'N' and N > 1, LWORK >= N. */
/* If JOBZ = 'V' and N > 1, LWORK >= 2*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) DOUBLE PRECISION array, dimension (MAX(1,LRWORK)) */
/* On exit, if INFO=0, RWORK(1) returns the optimal LRWORK. */
/* LRWORK (input) INTEGER */
/* The dimension of array RWORK. */
/* If N <= 1, LRWORK >= 1. */
/* If JOBZ = 'N' and N > 1, LRWORK >= N. */
/* If JOBZ = 'V' and N > 1, LRWORK >= 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 array IWORK. */
/* If JOBZ = 'N' or N <= 1, LIWORK >= 1. */
/* If JOBZ = 'V' and N > 1, LIWORK >= 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 i is: */
/* <= N: the algorithm failed to converge: */
/* i off-diagonal elements of an intermediate */
/* tridiagonal form did not converge to zero; */
/* > N: if INFO = N + i, for 1 <= i <= N, then ZPBSTF */
/* returned INFO = i: B is not positive definite. */
/* The factorization of B could not be completed and */
/* no eigenvalues or eigenvectors were computed. */
/* Further Details */
/* =============== */
/* Based on contributions by */
/* Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
ab_dim1 = *ldab;
ab_offset = 1 + ab_dim1;
ab -= ab_offset;
bb_dim1 = *ldbb;
bb_offset = 1 + bb_dim1;
bb -= bb_offset;
--w;
z_dim1 = *ldz;
z_offset = 1 + z_dim1;
z__ -= z_offset;
--work;
--rwork;
--iwork;
/* Function Body */
wantz = lsame_(jobz, "V");
upper = lsame_(uplo, "U");
lquery = *lwork == -1 || *lrwork == -1 || *liwork == -1;
*info = 0;
if (*n <= 1) {
lwmin = 1;
lrwmin = 1;
liwmin = 1;
} else if (wantz) {
/* Computing 2nd power */
i__1 = *n;
lwmin = i__1 * i__1 << 1;
/* Computing 2nd power */
i__1 = *n;
lrwmin = *n * 5 + 1 + (i__1 * i__1 << 1);
liwmin = *n * 5 + 3;
} else {
lwmin = *n;
lrwmin = *n;
liwmin = 1;
}
if (! (wantz || lsame_(jobz, "N"))) {
*info = -1;
} else if (! (upper || lsame_(uplo, "L"))) {
*info = -2;
} else if (*n < 0) {
*info = -3;
} else if (*ka < 0) {
*info = -4;
} else if (*kb < 0 || *kb > *ka) {
*info = -5;
} else if (*ldab < *ka + 1) {
*info = -7;
} else if (*ldbb < *kb + 1) {
*info = -9;
} else if (*ldz < 1 || wantz && *ldz < *n) {
*info = -12;
}
if (*info == 0) {
work[1].r = (doublereal) lwmin, work[1].i = 0.;
rwork[1] = (doublereal) lrwmin;
iwork[1] = liwmin;
if (*lwork < lwmin && ! lquery) {
*info = -14;
} else if (*lrwork < lrwmin && ! lquery) {
*info = -16;
} else if (*liwork < liwmin && ! lquery) {
*info = -18;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZHBGVD", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
/* Form a split Cholesky factorization of B. */
zpbstf_(uplo, n, kb, &bb[bb_offset], ldbb, info);
if (*info != 0) {
*info = *n + *info;
return 0;
}
/* Transform problem to standard eigenvalue problem. */
inde = 1;
indwrk = inde + *n;
indwk2 = *n * *n + 1;
llwk2 = *lwork - indwk2 + 2;
llrwk = *lrwork - indwrk + 2;
zhbgst_(jobz, uplo, n, ka, kb, &ab[ab_offset], ldab, &bb[bb_offset], ldbb,
&z__[z_offset], ldz, &work[1], &rwork[indwrk], &iinfo);
/* Reduce Hermitian band matrix to tridiagonal form. */
if (wantz) {
*(unsigned char *)vect = 'U';
} else {
*(unsigned char *)vect = 'N';
}
zhbtrd_(vect, uplo, n, ka, &ab[ab_offset], ldab, &w[1], &rwork[inde], &
z__[z_offset], ldz, &work[1], &iinfo);
/* For eigenvalues only, call DSTERF. For eigenvectors, call ZSTEDC. */
if (! wantz) {
dsterf_(n, &w[1], &rwork[inde], info);
} else {
zstedc_("I", n, &w[1], &rwork[inde], &work[1], n, &work[indwk2], &
llwk2, &rwork[indwrk], &llrwk, &iwork[1], liwork, info);
zgemm_("N", "N", n, n, n, &c_b1, &z__[z_offset], ldz, &work[1], n, &
c_b2, &work[indwk2], n);
zlacpy_("A", n, n, &work[indwk2], n, &z__[z_offset], ldz);
}
work[1].r = (doublereal) lwmin, work[1].i = 0.;
rwork[1] = (doublereal) lrwmin;
iwork[1] = liwmin;
return 0;
/* End of ZHBGVD */
} /* zhbgvd_ */
|
