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
|
/* zgtsv.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"
/* Subroutine */ int zgtsv_(integer *n, integer *nrhs, doublecomplex *dl,
doublecomplex *d__, doublecomplex *du, doublecomplex *b, integer *ldb,
integer *info)
{
/* System generated locals */
integer b_dim1, b_offset, i__1, i__2, i__3, i__4, i__5, i__6, i__7;
doublereal d__1, d__2, d__3, d__4;
doublecomplex z__1, z__2, z__3, z__4, z__5;
/* Builtin functions */
double d_imag(doublecomplex *);
void z_div(doublecomplex *, doublecomplex *, doublecomplex *);
/* Local variables */
integer j, k;
doublecomplex temp, mult;
extern /* Subroutine */ int 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 */
/* ======= */
/* ZGTSV solves the equation */
/* A*X = B, */
/* where A is an N-by-N tridiagonal matrix, by Gaussian elimination with */
/* partial pivoting. */
/* Note that the equation A'*X = B may be solved by interchanging the */
/* order of the arguments DU and DL. */
/* Arguments */
/* ========= */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. */
/* NRHS (input) INTEGER */
/* The number of right hand sides, i.e., the number of columns */
/* of the matrix B. NRHS >= 0. */
/* DL (input/output) COMPLEX*16 array, dimension (N-1) */
/* On entry, DL must contain the (n-1) subdiagonal elements of */
/* A. */
/* On exit, DL is overwritten by the (n-2) elements of the */
/* second superdiagonal of the upper triangular matrix U from */
/* the LU factorization of A, in DL(1), ..., DL(n-2). */
/* D (input/output) COMPLEX*16 array, dimension (N) */
/* On entry, D must contain the diagonal elements of A. */
/* On exit, D is overwritten by the n diagonal elements of U. */
/* DU (input/output) COMPLEX*16 array, dimension (N-1) */
/* On entry, DU must contain the (n-1) superdiagonal elements */
/* of A. */
/* On exit, DU is overwritten by the (n-1) elements of the first */
/* superdiagonal of U. */
/* B (input/output) COMPLEX*16 array, dimension (LDB,NRHS) */
/* On entry, the N-by-NRHS right hand side matrix B. */
/* On exit, if INFO = 0, the N-by-NRHS solution matrix X. */
/* 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 */
/* > 0: if INFO = i, U(i,i) is exactly zero, and the solution */
/* has not been computed. The factorization has not been */
/* completed unless i = N. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Statement Functions .. */
/* .. */
/* .. Statement Function definitions .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
--dl;
--d__;
--du;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
/* Function Body */
*info = 0;
if (*n < 0) {
*info = -1;
} else if (*nrhs < 0) {
*info = -2;
} else if (*ldb < max(1,*n)) {
*info = -7;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZGTSV ", &i__1);
return 0;
}
if (*n == 0) {
return 0;
}
i__1 = *n - 1;
for (k = 1; k <= i__1; ++k) {
i__2 = k;
if (dl[i__2].r == 0. && dl[i__2].i == 0.) {
/* Subdiagonal is zero, no elimination is required. */
i__2 = k;
if (d__[i__2].r == 0. && d__[i__2].i == 0.) {
/* Diagonal is zero: set INFO = K and return; a unique */
/* solution can not be found. */
*info = k;
return 0;
}
} else /* if(complicated condition) */ {
i__2 = k;
i__3 = k;
if ((d__1 = d__[i__2].r, abs(d__1)) + (d__2 = d_imag(&d__[k]),
abs(d__2)) >= (d__3 = dl[i__3].r, abs(d__3)) + (d__4 =
d_imag(&dl[k]), abs(d__4))) {
/* No row interchange required */
z_div(&z__1, &dl[k], &d__[k]);
mult.r = z__1.r, mult.i = z__1.i;
i__2 = k + 1;
i__3 = k + 1;
i__4 = k;
z__2.r = mult.r * du[i__4].r - mult.i * du[i__4].i, z__2.i =
mult.r * du[i__4].i + mult.i * du[i__4].r;
z__1.r = d__[i__3].r - z__2.r, z__1.i = d__[i__3].i - z__2.i;
d__[i__2].r = z__1.r, d__[i__2].i = z__1.i;
i__2 = *nrhs;
for (j = 1; j <= i__2; ++j) {
i__3 = k + 1 + j * b_dim1;
i__4 = k + 1 + j * b_dim1;
i__5 = k + j * b_dim1;
z__2.r = mult.r * b[i__5].r - mult.i * b[i__5].i, z__2.i =
mult.r * b[i__5].i + mult.i * b[i__5].r;
z__1.r = b[i__4].r - z__2.r, z__1.i = b[i__4].i - z__2.i;
b[i__3].r = z__1.r, b[i__3].i = z__1.i;
/* L10: */
}
if (k < *n - 1) {
i__2 = k;
dl[i__2].r = 0., dl[i__2].i = 0.;
}
} else {
/* Interchange rows K and K+1 */
z_div(&z__1, &d__[k], &dl[k]);
mult.r = z__1.r, mult.i = z__1.i;
i__2 = k;
i__3 = k;
d__[i__2].r = dl[i__3].r, d__[i__2].i = dl[i__3].i;
i__2 = k + 1;
temp.r = d__[i__2].r, temp.i = d__[i__2].i;
i__2 = k + 1;
i__3 = k;
z__2.r = mult.r * temp.r - mult.i * temp.i, z__2.i = mult.r *
temp.i + mult.i * temp.r;
z__1.r = du[i__3].r - z__2.r, z__1.i = du[i__3].i - z__2.i;
d__[i__2].r = z__1.r, d__[i__2].i = z__1.i;
if (k < *n - 1) {
i__2 = k;
i__3 = k + 1;
dl[i__2].r = du[i__3].r, dl[i__2].i = du[i__3].i;
i__2 = k + 1;
z__2.r = -mult.r, z__2.i = -mult.i;
i__3 = k;
z__1.r = z__2.r * dl[i__3].r - z__2.i * dl[i__3].i,
z__1.i = z__2.r * dl[i__3].i + z__2.i * dl[i__3]
.r;
du[i__2].r = z__1.r, du[i__2].i = z__1.i;
}
i__2 = k;
du[i__2].r = temp.r, du[i__2].i = temp.i;
i__2 = *nrhs;
for (j = 1; j <= i__2; ++j) {
i__3 = k + j * b_dim1;
temp.r = b[i__3].r, temp.i = b[i__3].i;
i__3 = k + j * b_dim1;
i__4 = k + 1 + j * b_dim1;
b[i__3].r = b[i__4].r, b[i__3].i = b[i__4].i;
i__3 = k + 1 + j * b_dim1;
i__4 = k + 1 + j * b_dim1;
z__2.r = mult.r * b[i__4].r - mult.i * b[i__4].i, z__2.i =
mult.r * b[i__4].i + mult.i * b[i__4].r;
z__1.r = temp.r - z__2.r, z__1.i = temp.i - z__2.i;
b[i__3].r = z__1.r, b[i__3].i = z__1.i;
/* L20: */
}
}
}
/* L30: */
}
i__1 = *n;
if (d__[i__1].r == 0. && d__[i__1].i == 0.) {
*info = *n;
return 0;
}
/* Back solve with the matrix U from the factorization. */
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
i__2 = *n + j * b_dim1;
z_div(&z__1, &b[*n + j * b_dim1], &d__[*n]);
b[i__2].r = z__1.r, b[i__2].i = z__1.i;
if (*n > 1) {
i__2 = *n - 1 + j * b_dim1;
i__3 = *n - 1 + j * b_dim1;
i__4 = *n - 1;
i__5 = *n + j * b_dim1;
z__3.r = du[i__4].r * b[i__5].r - du[i__4].i * b[i__5].i, z__3.i =
du[i__4].r * b[i__5].i + du[i__4].i * b[i__5].r;
z__2.r = b[i__3].r - z__3.r, z__2.i = b[i__3].i - z__3.i;
z_div(&z__1, &z__2, &d__[*n - 1]);
b[i__2].r = z__1.r, b[i__2].i = z__1.i;
}
for (k = *n - 2; k >= 1; --k) {
i__2 = k + j * b_dim1;
i__3 = k + j * b_dim1;
i__4 = k;
i__5 = k + 1 + j * b_dim1;
z__4.r = du[i__4].r * b[i__5].r - du[i__4].i * b[i__5].i, z__4.i =
du[i__4].r * b[i__5].i + du[i__4].i * b[i__5].r;
z__3.r = b[i__3].r - z__4.r, z__3.i = b[i__3].i - z__4.i;
i__6 = k;
i__7 = k + 2 + j * b_dim1;
z__5.r = dl[i__6].r * b[i__7].r - dl[i__6].i * b[i__7].i, z__5.i =
dl[i__6].r * b[i__7].i + dl[i__6].i * b[i__7].r;
z__2.r = z__3.r - z__5.r, z__2.i = z__3.i - z__5.i;
z_div(&z__1, &z__2, &d__[k]);
b[i__2].r = z__1.r, b[i__2].i = z__1.i;
/* L40: */
}
/* L50: */
}
return 0;
/* End of ZGTSV */
} /* zgtsv_ */
|
