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
|
/* chegs2.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 complex c_b1 = {1.f,0.f};
static integer c__1 = 1;
/* Subroutine */ int chegs2_(integer *itype, char *uplo, integer *n, complex *
a, integer *lda, complex *b, integer *ldb, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2;
real r__1, r__2;
complex q__1;
/* Local variables */
integer k;
complex ct;
real akk, bkk;
extern /* Subroutine */ int cher2_(char *, integer *, complex *, complex *
, integer *, complex *, integer *, complex *, integer *);
extern logical lsame_(char *, char *);
extern /* Subroutine */ int caxpy_(integer *, complex *, complex *,
integer *, complex *, integer *);
logical upper;
extern /* Subroutine */ int ctrmv_(char *, char *, char *, integer *,
complex *, integer *, complex *, integer *), ctrsv_(char *, char *, char *, integer *, complex *,
integer *, complex *, integer *), clacgv_(
integer *, complex *, integer *), csscal_(integer *, real *,
complex *, integer *), xerbla_(char *, integer *);
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CHEGS2 reduces a complex Hermitian-definite generalized */
/* eigenproblem to standard form. */
/* If ITYPE = 1, the problem is A*x = lambda*B*x, */
/* and A is overwritten by inv(U')*A*inv(U) or inv(L)*A*inv(L') */
/* If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or */
/* B*A*x = lambda*x, and A is overwritten by U*A*U` or L'*A*L. */
/* B must have been previously factorized as U'*U or L*L' by CPOTRF. */
/* Arguments */
/* ========= */
/* ITYPE (input) INTEGER */
/* = 1: compute inv(U')*A*inv(U) or inv(L)*A*inv(L'); */
/* = 2 or 3: compute U*A*U' or L'*A*L. */
/* UPLO (input) CHARACTER*1 */
/* Specifies whether the upper or lower triangular part of the */
/* Hermitian matrix A is stored, and how B has been factorized. */
/* = 'U': Upper triangular */
/* = 'L': Lower triangular */
/* N (input) INTEGER */
/* The order of the matrices A and B. 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, and the strictly lower */
/* triangular part of A is not referenced. If UPLO = 'L', the */
/* leading n by n lower triangular part of A contains the lower */
/* triangular part of the matrix A, and the strictly upper */
/* triangular part of A is not referenced. */
/* On exit, if INFO = 0, the transformed matrix, stored in the */
/* same format as A. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,N). */
/* B (input) COMPLEX array, dimension (LDB,N) */
/* The triangular factor from the Cholesky factorization of B, */
/* as returned by CPOTRF. */
/* LDB (input) INTEGER */
/* The leading dimension of the array B. LDB >= max(1,N). */
/* INFO (output) INTEGER */
/* = 0: successful exit. */
/* < 0: if INFO = -i, the i-th argument had an illegal value. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
/* Function Body */
*info = 0;
upper = lsame_(uplo, "U");
if (*itype < 1 || *itype > 3) {
*info = -1;
} else if (! upper && ! lsame_(uplo, "L")) {
*info = -2;
} else if (*n < 0) {
*info = -3;
} else if (*lda < max(1,*n)) {
*info = -5;
} else if (*ldb < max(1,*n)) {
*info = -7;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CHEGS2", &i__1);
return 0;
}
if (*itype == 1) {
if (upper) {
/* Compute inv(U')*A*inv(U) */
i__1 = *n;
for (k = 1; k <= i__1; ++k) {
/* Update the upper triangle of A(k:n,k:n) */
i__2 = k + k * a_dim1;
akk = a[i__2].r;
i__2 = k + k * b_dim1;
bkk = b[i__2].r;
/* Computing 2nd power */
r__1 = bkk;
akk /= r__1 * r__1;
i__2 = k + k * a_dim1;
a[i__2].r = akk, a[i__2].i = 0.f;
if (k < *n) {
i__2 = *n - k;
r__1 = 1.f / bkk;
csscal_(&i__2, &r__1, &a[k + (k + 1) * a_dim1], lda);
r__1 = akk * -.5f;
ct.r = r__1, ct.i = 0.f;
i__2 = *n - k;
clacgv_(&i__2, &a[k + (k + 1) * a_dim1], lda);
i__2 = *n - k;
clacgv_(&i__2, &b[k + (k + 1) * b_dim1], ldb);
i__2 = *n - k;
caxpy_(&i__2, &ct, &b[k + (k + 1) * b_dim1], ldb, &a[k + (
k + 1) * a_dim1], lda);
i__2 = *n - k;
q__1.r = -1.f, q__1.i = -0.f;
cher2_(uplo, &i__2, &q__1, &a[k + (k + 1) * a_dim1], lda,
&b[k + (k + 1) * b_dim1], ldb, &a[k + 1 + (k + 1)
* a_dim1], lda);
i__2 = *n - k;
caxpy_(&i__2, &ct, &b[k + (k + 1) * b_dim1], ldb, &a[k + (
k + 1) * a_dim1], lda);
i__2 = *n - k;
clacgv_(&i__2, &b[k + (k + 1) * b_dim1], ldb);
i__2 = *n - k;
ctrsv_(uplo, "Conjugate transpose", "Non-unit", &i__2, &b[
k + 1 + (k + 1) * b_dim1], ldb, &a[k + (k + 1) *
a_dim1], lda);
i__2 = *n - k;
clacgv_(&i__2, &a[k + (k + 1) * a_dim1], lda);
}
/* L10: */
}
} else {
/* Compute inv(L)*A*inv(L') */
i__1 = *n;
for (k = 1; k <= i__1; ++k) {
/* Update the lower triangle of A(k:n,k:n) */
i__2 = k + k * a_dim1;
akk = a[i__2].r;
i__2 = k + k * b_dim1;
bkk = b[i__2].r;
/* Computing 2nd power */
r__1 = bkk;
akk /= r__1 * r__1;
i__2 = k + k * a_dim1;
a[i__2].r = akk, a[i__2].i = 0.f;
if (k < *n) {
i__2 = *n - k;
r__1 = 1.f / bkk;
csscal_(&i__2, &r__1, &a[k + 1 + k * a_dim1], &c__1);
r__1 = akk * -.5f;
ct.r = r__1, ct.i = 0.f;
i__2 = *n - k;
caxpy_(&i__2, &ct, &b[k + 1 + k * b_dim1], &c__1, &a[k +
1 + k * a_dim1], &c__1);
i__2 = *n - k;
q__1.r = -1.f, q__1.i = -0.f;
cher2_(uplo, &i__2, &q__1, &a[k + 1 + k * a_dim1], &c__1,
&b[k + 1 + k * b_dim1], &c__1, &a[k + 1 + (k + 1)
* a_dim1], lda);
i__2 = *n - k;
caxpy_(&i__2, &ct, &b[k + 1 + k * b_dim1], &c__1, &a[k +
1 + k * a_dim1], &c__1);
i__2 = *n - k;
ctrsv_(uplo, "No transpose", "Non-unit", &i__2, &b[k + 1
+ (k + 1) * b_dim1], ldb, &a[k + 1 + k * a_dim1],
&c__1);
}
/* L20: */
}
}
} else {
if (upper) {
/* Compute U*A*U' */
i__1 = *n;
for (k = 1; k <= i__1; ++k) {
/* Update the upper triangle of A(1:k,1:k) */
i__2 = k + k * a_dim1;
akk = a[i__2].r;
i__2 = k + k * b_dim1;
bkk = b[i__2].r;
i__2 = k - 1;
ctrmv_(uplo, "No transpose", "Non-unit", &i__2, &b[b_offset],
ldb, &a[k * a_dim1 + 1], &c__1);
r__1 = akk * .5f;
ct.r = r__1, ct.i = 0.f;
i__2 = k - 1;
caxpy_(&i__2, &ct, &b[k * b_dim1 + 1], &c__1, &a[k * a_dim1 +
1], &c__1);
i__2 = k - 1;
cher2_(uplo, &i__2, &c_b1, &a[k * a_dim1 + 1], &c__1, &b[k *
b_dim1 + 1], &c__1, &a[a_offset], lda);
i__2 = k - 1;
caxpy_(&i__2, &ct, &b[k * b_dim1 + 1], &c__1, &a[k * a_dim1 +
1], &c__1);
i__2 = k - 1;
csscal_(&i__2, &bkk, &a[k * a_dim1 + 1], &c__1);
i__2 = k + k * a_dim1;
/* Computing 2nd power */
r__2 = bkk;
r__1 = akk * (r__2 * r__2);
a[i__2].r = r__1, a[i__2].i = 0.f;
/* L30: */
}
} else {
/* Compute L'*A*L */
i__1 = *n;
for (k = 1; k <= i__1; ++k) {
/* Update the lower triangle of A(1:k,1:k) */
i__2 = k + k * a_dim1;
akk = a[i__2].r;
i__2 = k + k * b_dim1;
bkk = b[i__2].r;
i__2 = k - 1;
clacgv_(&i__2, &a[k + a_dim1], lda);
i__2 = k - 1;
ctrmv_(uplo, "Conjugate transpose", "Non-unit", &i__2, &b[
b_offset], ldb, &a[k + a_dim1], lda);
r__1 = akk * .5f;
ct.r = r__1, ct.i = 0.f;
i__2 = k - 1;
clacgv_(&i__2, &b[k + b_dim1], ldb);
i__2 = k - 1;
caxpy_(&i__2, &ct, &b[k + b_dim1], ldb, &a[k + a_dim1], lda);
i__2 = k - 1;
cher2_(uplo, &i__2, &c_b1, &a[k + a_dim1], lda, &b[k + b_dim1]
, ldb, &a[a_offset], lda);
i__2 = k - 1;
caxpy_(&i__2, &ct, &b[k + b_dim1], ldb, &a[k + a_dim1], lda);
i__2 = k - 1;
clacgv_(&i__2, &b[k + b_dim1], ldb);
i__2 = k - 1;
csscal_(&i__2, &bkk, &a[k + a_dim1], lda);
i__2 = k - 1;
clacgv_(&i__2, &a[k + a_dim1], lda);
i__2 = k + k * a_dim1;
/* Computing 2nd power */
r__2 = bkk;
r__1 = akk * (r__2 * r__2);
a[i__2].r = r__1, a[i__2].i = 0.f;
/* L40: */
}
}
}
return 0;
/* End of CHEGS2 */
} /* chegs2_ */
|
