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
|
/* lapack/complex16/zunghr.f -- translated by f2c (version 20050501).
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
*/
#ifdef __cplusplus
extern "C" {
#endif
#include "v3p_netlib.h"
/* Table of constant values */
static integer c__1 = 1;
static integer c_n1 = -1;
/*< SUBROUTINE ZUNGHR( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO ) >*/
/* Subroutine */ int zunghr_(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;
/* Local variables */
integer i__, j, nb, nh, iinfo;
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
integer lwkopt=0;
logical lquery;
extern /* Subroutine */ int zungqr_(integer *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *, integer *);
/* -- LAPACK routine (version 3.0) -- */
/* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
/* Courant Institute, Argonne National Lab, and Rice University */
/* June 30, 1999 */
/* .. Scalar Arguments .. */
/*< INTEGER IHI, ILO, INFO, LDA, LWORK, N >*/
/* .. */
/* .. Array Arguments .. */
/*< COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) >*/
/* .. */
/* Purpose */
/* ======= */
/* ZUNGHR generates a complex unitary matrix Q which is defined as the */
/* product of IHI-ILO elementary reflectors of order N, as returned by */
/* ZGEHRD: */
/* Q = H(ilo) H(ilo+1) . . . H(ihi-1). */
/* Arguments */
/* ========= */
/* N (input) INTEGER */
/* The order of the matrix Q. N >= 0. */
/* ILO (input) INTEGER */
/* IHI (input) INTEGER */
/* ILO and IHI must have the same values as in the previous call */
/* of ZGEHRD. Q is equal to the unit matrix except in the */
/* submatrix Q(ilo+1:ihi,ilo+1:ihi). */
/* 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 vectors which define the elementary reflectors, */
/* as returned by ZGEHRD. */
/* On exit, the N-by-N unitary matrix Q. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,N). */
/* TAU (input) COMPLEX*16 array, dimension (N-1) */
/* TAU(i) must contain the scalar factor of the elementary */
/* reflector H(i), as returned by ZGEHRD. */
/* WORK (workspace/output) COMPLEX*16 array, dimension (LWORK) */
/* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
/* LWORK (input) INTEGER */
/* The dimension of the array WORK. LWORK >= IHI-ILO. */
/* For optimum performance LWORK >= (IHI-ILO)*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 */
/* ===================================================================== */
/* .. Parameters .. */
/*< COMPLEX*16 ZERO, ONE >*/
/*< >*/
/* .. */
/* .. Local Scalars .. */
/*< LOGICAL LQUERY >*/
/*< INTEGER I, IINFO, J, LWKOPT, NB, NH >*/
/* .. */
/* .. External Subroutines .. */
/*< EXTERNAL XERBLA, ZUNGQR >*/
/* .. */
/* .. External Functions .. */
/*< INTEGER ILAENV >*/
/*< EXTERNAL ILAENV >*/
/* .. */
/* .. Intrinsic Functions .. */
/*< INTRINSIC MAX, MIN >*/
/* .. */
/* .. Executable Statements .. */
/* Test the input arguments */
/*< INFO = 0 >*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--tau;
--work;
/* Function Body */
*info = 0;
/*< NH = IHI - ILO >*/
nh = *ihi - *ilo;
/*< LQUERY = ( LWORK.EQ.-1 ) >*/
lquery = *lwork == -1;
/*< IF( N.LT.0 ) THEN >*/
if (*n < 0) {
/*< INFO = -1 >*/
*info = -1;
/*< ELSE IF( ILO.LT.1 .OR. ILO.GT.MAX( 1, N ) ) THEN >*/
} else if (*ilo < 1 || *ilo > max(1,*n)) {
/*< INFO = -2 >*/
*info = -2;
/*< ELSE IF( IHI.LT.MIN( ILO, N ) .OR. IHI.GT.N ) THEN >*/
} else if (*ihi < min(*ilo,*n) || *ihi > *n) {
/*< INFO = -3 >*/
*info = -3;
/*< ELSE IF( LDA.LT.MAX( 1, N ) ) THEN >*/
} else if (*lda < max(1,*n)) {
/*< INFO = -5 >*/
*info = -5;
/*< ELSE IF( LWORK.LT.MAX( 1, NH ) .AND. .NOT.LQUERY ) THEN >*/
} else if (*lwork < max(1,nh) && ! lquery) {
/*< INFO = -8 >*/
*info = -8;
/*< END IF >*/
}
/*< IF( INFO.EQ.0 ) THEN >*/
if (*info == 0) {
/*< NB = ILAENV( 1, 'ZUNGQR', ' ', NH, NH, NH, -1 ) >*/
nb = ilaenv_(&c__1, "ZUNGQR", " ", &nh, &nh, &nh, &c_n1, (ftnlen)6, (
ftnlen)1);
/*< LWKOPT = MAX( 1, NH )*NB >*/
lwkopt = max(1,nh) * nb;
/*< WORK( 1 ) = LWKOPT >*/
work[1].r = (doublereal) lwkopt, work[1].i = 0.;
/*< END IF >*/
}
/*< IF( INFO.NE.0 ) THEN >*/
if (*info != 0) {
/*< CALL XERBLA( 'ZUNGHR', -INFO ) >*/
i__1 = -(*info);
xerbla_("ZUNGHR", &i__1, (ftnlen)6);
/*< RETURN >*/
return 0;
/*< ELSE IF( LQUERY ) THEN >*/
} else if (lquery) {
/*< RETURN >*/
return 0;
/*< END IF >*/
}
/* Quick return if possible */
/*< IF( N.EQ.0 ) THEN >*/
if (*n == 0) {
/*< WORK( 1 ) = 1 >*/
work[1].r = 1., work[1].i = 0.;
/*< RETURN >*/
return 0;
/*< END IF >*/
}
/* Shift the vectors which define the elementary reflectors one */
/* column to the right, and set the first ilo and the last n-ihi */
/* rows and columns to those of the unit matrix */
/*< DO 40 J = IHI, ILO + 1, -1 >*/
i__1 = *ilo + 1;
for (j = *ihi; j >= i__1; --j) {
/*< DO 10 I = 1, J - 1 >*/
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
/*< A( I, J ) = ZERO >*/
i__3 = i__ + j * a_dim1;
a[i__3].r = 0., a[i__3].i = 0.;
/*< 10 CONTINUE >*/
/* L10: */
}
/*< DO 20 I = J + 1, IHI >*/
i__2 = *ihi;
for (i__ = j + 1; i__ <= i__2; ++i__) {
/*< A( I, J ) = A( I, J-1 ) >*/
i__3 = i__ + j * a_dim1;
i__4 = i__ + (j - 1) * a_dim1;
a[i__3].r = a[i__4].r, a[i__3].i = a[i__4].i;
/*< 20 CONTINUE >*/
/* L20: */
}
/*< DO 30 I = IHI + 1, N >*/
i__2 = *n;
for (i__ = *ihi + 1; i__ <= i__2; ++i__) {
/*< A( I, J ) = ZERO >*/
i__3 = i__ + j * a_dim1;
a[i__3].r = 0., a[i__3].i = 0.;
/*< 30 CONTINUE >*/
/* L30: */
}
/*< 40 CONTINUE >*/
/* L40: */
}
/*< DO 60 J = 1, ILO >*/
i__1 = *ilo;
for (j = 1; j <= i__1; ++j) {
/*< DO 50 I = 1, N >*/
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
/*< A( I, J ) = ZERO >*/
i__3 = i__ + j * a_dim1;
a[i__3].r = 0., a[i__3].i = 0.;
/*< 50 CONTINUE >*/
/* L50: */
}
/*< A( J, J ) = ONE >*/
i__2 = j + j * a_dim1;
a[i__2].r = 1., a[i__2].i = 0.;
/*< 60 CONTINUE >*/
/* L60: */
}
/*< DO 80 J = IHI + 1, N >*/
i__1 = *n;
for (j = *ihi + 1; j <= i__1; ++j) {
/*< DO 70 I = 1, N >*/
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
/*< A( I, J ) = ZERO >*/
i__3 = i__ + j * a_dim1;
a[i__3].r = 0., a[i__3].i = 0.;
/*< 70 CONTINUE >*/
/* L70: */
}
/*< A( J, J ) = ONE >*/
i__2 = j + j * a_dim1;
a[i__2].r = 1., a[i__2].i = 0.;
/*< 80 CONTINUE >*/
/* L80: */
}
/*< IF( NH.GT.0 ) THEN >*/
if (nh > 0) {
/* Generate Q(ilo+1:ihi,ilo+1:ihi) */
/*< >*/
zungqr_(&nh, &nh, &nh, &a[*ilo + 1 + (*ilo + 1) * a_dim1], lda, &tau[*
ilo], &work[1], lwork, &iinfo);
/*< END IF >*/
}
/*< WORK( 1 ) = LWKOPT >*/
work[1].r = (doublereal) lwkopt, work[1].i = 0.;
/*< RETURN >*/
return 0;
/* End of ZUNGHR */
/*< END >*/
} /* zunghr_ */
#ifdef __cplusplus
}
#endif
|
