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
|
/* zgehrd.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_b2 = {1.,0.};
static integer c__1 = 1;
static integer c_n1 = -1;
static integer c__3 = 3;
static integer c__2 = 2;
static integer c__65 = 65;
/* Subroutine */ int zgehrd_(integer *n, integer *ilo, integer *ihi,
doublecomplex *a, integer *lda, doublecomplex *tau, doublecomplex *
work, integer *lwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
doublecomplex z__1;
/* Local variables */
integer i__, j;
doublecomplex t[4160] /* was [65][64] */;
integer ib;
doublecomplex ei;
integer nb, nh, nx, iws, nbmin, iinfo;
extern /* Subroutine */ int zgemm_(char *, char *, integer *, integer *,
integer *, doublecomplex *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *), ztrmm_(char *, char *, char *, char *,
integer *, integer *, doublecomplex *, doublecomplex *, integer *
, doublecomplex *, integer *),
zaxpy_(integer *, doublecomplex *, doublecomplex *, integer *,
doublecomplex *, integer *), zgehd2_(integer *, integer *,
integer *, doublecomplex *, integer *, doublecomplex *,
doublecomplex *, integer *), zlahr2_(integer *, integer *,
integer *, doublecomplex *, integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *), xerbla_(
char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *);
extern /* Subroutine */ int zlarfb_(char *, char *, char *, char *,
integer *, integer *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *);
integer ldwork, lwkopt;
logical lquery;
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZGEHRD reduces a complex general matrix A to upper Hessenberg form H by */
/* an unitary similarity transformation: Q' * A * Q = H . */
/* Arguments */
/* ========= */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. */
/* ILO (input) INTEGER */
/* IHI (input) INTEGER */
/* It is assumed that A is already upper triangular in rows */
/* and columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally */
/* set by a previous call to ZGEBAL; otherwise they should be */
/* set to 1 and N respectively. See Further Details. */
/* 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0. */
/* A (input/output) COMPLEX*16 array, dimension (LDA,N) */
/* On entry, the N-by-N general matrix to be reduced. */
/* On exit, the upper triangle and the first subdiagonal of A */
/* are overwritten with the upper Hessenberg matrix H, and the */
/* elements below the first subdiagonal, with the array TAU, */
/* represent the unitary matrix Q as a product of elementary */
/* reflectors. See Further Details. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,N). */
/* TAU (output) COMPLEX*16 array, dimension (N-1) */
/* The scalar factors of the elementary reflectors (see Further */
/* Details). Elements 1:ILO-1 and IHI:N-1 of TAU are set to */
/* zero. */
/* WORK (workspace/output) COMPLEX*16 array, dimension (LWORK) */
/* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
/* LWORK (input) INTEGER */
/* The length of the array WORK. LWORK >= max(1,N). */
/* For optimum performance LWORK >= N*NB, where NB is the */
/* optimal blocksize. */
/* If LWORK = -1, then a workspace query is assumed; the routine */
/* only calculates the optimal size of the WORK array, returns */
/* this value as the first entry of the WORK array, and no error */
/* message related to LWORK is issued by XERBLA. */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value. */
/* Further Details */
/* =============== */
/* The matrix Q is represented as a product of (ihi-ilo) elementary */
/* reflectors */
/* Q = H(ilo) H(ilo+1) . . . H(ihi-1). */
/* Each H(i) has the form */
/* H(i) = I - tau * v * v' */
/* where tau is a complex scalar, and v is a complex vector with */
/* v(1:i) = 0, v(i+1) = 1 and v(ihi+1:n) = 0; v(i+2:ihi) is stored on */
/* exit in A(i+2:ihi,i), and tau in TAU(i). */
/* The contents of A are illustrated by the following example, with */
/* n = 7, ilo = 2 and ihi = 6: */
/* on entry, on exit, */
/* ( a a a a a a a ) ( a a h h h h a ) */
/* ( a a a a a a ) ( a h h h h a ) */
/* ( a a a a a a ) ( h h h h h h ) */
/* ( a a a a a a ) ( v2 h h h h h ) */
/* ( a a a a a a ) ( v2 v3 h h h h ) */
/* ( a a a a a a ) ( v2 v3 v4 h h h ) */
/* ( a ) ( a ) */
/* where a denotes an element of the original matrix A, h denotes a */
/* modified element of the upper Hessenberg matrix H, and vi denotes an */
/* element of the vector defining H(i). */
/* This file is a slight modification of LAPACK-3.0's ZGEHRD */
/* subroutine incorporating improvements proposed by Quintana-Orti and */
/* Van de Geijn (2005). */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. 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;
--tau;
--work;
/* Function Body */
*info = 0;
/* Computing MIN */
i__1 = 64, i__2 = ilaenv_(&c__1, "ZGEHRD", " ", n, ilo, ihi, &c_n1);
nb = min(i__1,i__2);
lwkopt = *n * nb;
work[1].r = (doublereal) lwkopt, work[1].i = 0.;
lquery = *lwork == -1;
if (*n < 0) {
*info = -1;
} else if (*ilo < 1 || *ilo > max(1,*n)) {
*info = -2;
} else if (*ihi < min(*ilo,*n) || *ihi > *n) {
*info = -3;
} else if (*lda < max(1,*n)) {
*info = -5;
} else if (*lwork < max(1,*n) && ! lquery) {
*info = -8;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZGEHRD", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Set elements 1:ILO-1 and IHI:N-1 of TAU to zero */
i__1 = *ilo - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
tau[i__2].r = 0., tau[i__2].i = 0.;
/* L10: */
}
i__1 = *n - 1;
for (i__ = max(1,*ihi); i__ <= i__1; ++i__) {
i__2 = i__;
tau[i__2].r = 0., tau[i__2].i = 0.;
/* L20: */
}
/* Quick return if possible */
nh = *ihi - *ilo + 1;
if (nh <= 1) {
work[1].r = 1., work[1].i = 0.;
return 0;
}
/* Determine the block size */
/* Computing MIN */
i__1 = 64, i__2 = ilaenv_(&c__1, "ZGEHRD", " ", n, ilo, ihi, &c_n1);
nb = min(i__1,i__2);
nbmin = 2;
iws = 1;
if (nb > 1 && nb < nh) {
/* Determine when to cross over from blocked to unblocked code */
/* (last block is always handled by unblocked code) */
/* Computing MAX */
i__1 = nb, i__2 = ilaenv_(&c__3, "ZGEHRD", " ", n, ilo, ihi, &c_n1);
nx = max(i__1,i__2);
if (nx < nh) {
/* Determine if workspace is large enough for blocked code */
iws = *n * nb;
if (*lwork < iws) {
/* Not enough workspace to use optimal NB: determine the */
/* minimum value of NB, and reduce NB or force use of */
/* unblocked code */
/* Computing MAX */
i__1 = 2, i__2 = ilaenv_(&c__2, "ZGEHRD", " ", n, ilo, ihi, &
c_n1);
nbmin = max(i__1,i__2);
if (*lwork >= *n * nbmin) {
nb = *lwork / *n;
} else {
nb = 1;
}
}
}
}
ldwork = *n;
if (nb < nbmin || nb >= nh) {
/* Use unblocked code below */
i__ = *ilo;
} else {
/* Use blocked code */
i__1 = *ihi - 1 - nx;
i__2 = nb;
for (i__ = *ilo; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
/* Computing MIN */
i__3 = nb, i__4 = *ihi - i__;
ib = min(i__3,i__4);
/* Reduce columns i:i+ib-1 to Hessenberg form, returning the */
/* matrices V and T of the block reflector H = I - V*T*V' */
/* which performs the reduction, and also the matrix Y = A*V*T */
zlahr2_(ihi, &i__, &ib, &a[i__ * a_dim1 + 1], lda, &tau[i__], t, &
c__65, &work[1], &ldwork);
/* Apply the block reflector H to A(1:ihi,i+ib:ihi) from the */
/* right, computing A := A - Y * V'. V(i+ib,ib-1) must be set */
/* to 1 */
i__3 = i__ + ib + (i__ + ib - 1) * a_dim1;
ei.r = a[i__3].r, ei.i = a[i__3].i;
i__3 = i__ + ib + (i__ + ib - 1) * a_dim1;
a[i__3].r = 1., a[i__3].i = 0.;
i__3 = *ihi - i__ - ib + 1;
z__1.r = -1., z__1.i = -0.;
zgemm_("No transpose", "Conjugate transpose", ihi, &i__3, &ib, &
z__1, &work[1], &ldwork, &a[i__ + ib + i__ * a_dim1], lda,
&c_b2, &a[(i__ + ib) * a_dim1 + 1], lda);
i__3 = i__ + ib + (i__ + ib - 1) * a_dim1;
a[i__3].r = ei.r, a[i__3].i = ei.i;
/* Apply the block reflector H to A(1:i,i+1:i+ib-1) from the */
/* right */
i__3 = ib - 1;
ztrmm_("Right", "Lower", "Conjugate transpose", "Unit", &i__, &
i__3, &c_b2, &a[i__ + 1 + i__ * a_dim1], lda, &work[1], &
ldwork);
i__3 = ib - 2;
for (j = 0; j <= i__3; ++j) {
z__1.r = -1., z__1.i = -0.;
zaxpy_(&i__, &z__1, &work[ldwork * j + 1], &c__1, &a[(i__ + j
+ 1) * a_dim1 + 1], &c__1);
/* L30: */
}
/* Apply the block reflector H to A(i+1:ihi,i+ib:n) from the */
/* left */
i__3 = *ihi - i__;
i__4 = *n - i__ - ib + 1;
zlarfb_("Left", "Conjugate transpose", "Forward", "Columnwise", &
i__3, &i__4, &ib, &a[i__ + 1 + i__ * a_dim1], lda, t, &
c__65, &a[i__ + 1 + (i__ + ib) * a_dim1], lda, &work[1], &
ldwork);
/* L40: */
}
}
/* Use unblocked code to reduce the rest of the matrix */
zgehd2_(n, &i__, ihi, &a[a_offset], lda, &tau[1], &work[1], &iinfo);
work[1].r = (doublereal) iws, work[1].i = 0.;
return 0;
/* End of ZGEHRD */
} /* zgehrd_ */
|
