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
|
//------------------------------------------------------------------------------
// CHOLMOD/Cholesky/cholmod_spsolve: solve a linear system with sparse x and b
//------------------------------------------------------------------------------
// CHOLMOD/Cholesky Module. Copyright (C) 2005-2023, Timothy A. Davis
// All Rights Reserved.
// SPDX-License-Identifier: LGPL-2.1+
//------------------------------------------------------------------------------
// Given an LL' or LDL' factorization of A, solve one of the following systems:
//
// Ax=b 0: CHOLMOD_A also applies the permutation L->Perm
// LDL'x=b 1: CHOLMOD_LDLt does not apply L->Perm
// LDx=b 2: CHOLMOD_LD
// DL'x=b : CHOLMOD_DLt
// Lx=b 4: CHOLMOD_L
// L'x=b 5: CHOLMOD_Lt
// Dx=b 6: CHOLMOD_D
// x=Pb 7: CHOLMOD_P apply a permutation (P is L->Perm)
// x=P'b 8: CHOLMOD_Pt apply an inverse permutation
//
// where b and x are sparse. If L and b are real, then x is real. Otherwise,
// x is complex or zomplex, depending on the Common->prefer_zomplex parameter.
// All xtypes of x and b are supported (real, complex, and zomplex), and
// all dtypes.
#include "cholmod_internal.h"
#ifndef NCHOLESKY
//------------------------------------------------------------------------------
// t_cholmod_spsolve_worker
//------------------------------------------------------------------------------
#define DOUBLE
#define REAL
#include "t_cholmod_spsolve_worker.c"
#define COMPLEX
#include "t_cholmod_spsolve_worker.c"
#define ZOMPLEX
#include "t_cholmod_spsolve_worker.c"
#undef DOUBLE
#define SINGLE
#define REAL
#include "t_cholmod_spsolve_worker.c"
#define COMPLEX
#include "t_cholmod_spsolve_worker.c"
#define ZOMPLEX
#include "t_cholmod_spsolve_worker.c"
//------------------------------------------------------------------------------
// cholmod_spsolve
//------------------------------------------------------------------------------
cholmod_sparse *CHOLMOD(spsolve) // returns the sparse solution X
(
// input:
int sys, // system to solve
cholmod_factor *L, // factorization to use
cholmod_sparse *B, // right-hand-side
cholmod_common *Common
)
{
//--------------------------------------------------------------------------
// check inputs
//--------------------------------------------------------------------------
cholmod_dense *X4 = NULL, *B4 = NULL ;
cholmod_sparse *X = NULL ;
RETURN_IF_NULL_COMMON (NULL) ;
RETURN_IF_NULL (L, NULL) ;
RETURN_IF_NULL (B, NULL) ;
RETURN_IF_XTYPE_INVALID (L, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, NULL) ;
RETURN_IF_XTYPE_INVALID (B, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, NULL) ;
if (L->n != B->nrow)
{
ERROR (CHOLMOD_INVALID, "dimensions of L and B do not match") ;
return (NULL) ;
}
if (B->stype)
{
ERROR (CHOLMOD_INVALID, "B cannot be stored in symmetric mode") ;
return (NULL) ;
}
if (L->dtype != B->dtype)
{
ERROR (CHOLMOD_INVALID, "dtype of L and B must match") ;
return (NULL) ;
}
Common->status = CHOLMOD_OK ;
//--------------------------------------------------------------------------
// allocate workspace B4 and initial result X
//--------------------------------------------------------------------------
Int n = L->n ;
Int nrhs = B->ncol ;
// X is real if both L and B are real, complex/zomplex otherwise
int X_xtype =
(L->xtype == CHOLMOD_REAL && B->xtype == CHOLMOD_REAL) ? CHOLMOD_REAL :
(Common->prefer_zomplex ? CHOLMOD_ZOMPLEX : CHOLMOD_COMPLEX) ;
// solve up to 4 columns at a time
Int block = MIN (nrhs, 4) ;
// initial size of X is at most 4*n
size_t nzmax = ((size_t) n) * ((size_t) block) ;
X = CHOLMOD(spzeros) (n, nrhs, nzmax, X_xtype + B->dtype, Common) ;
B4 = CHOLMOD(zeros) (n, block, B->xtype + B->dtype, Common) ;
if (Common->status < CHOLMOD_OK)
{
CHOLMOD(free_sparse) (&X, Common) ;
CHOLMOD(free_dense) (&B4, Common) ;
return (NULL) ;
}
size_t xnz = 0 ;
//--------------------------------------------------------------------------
// solve in chunks of 4 columns at a time
//--------------------------------------------------------------------------
for (Int jfirst = 0 ; jfirst < nrhs ; jfirst += block)
{
//----------------------------------------------------------------------
// adjust the number of columns of B4
//----------------------------------------------------------------------
Int jlast = MIN (nrhs, jfirst + block) ;
B4->ncol = jlast - jfirst ;
//----------------------------------------------------------------------
// scatter B(jfirst:jlast-1) into B4
//----------------------------------------------------------------------
switch ((B->xtype + B->dtype) % 8)
{
case CHOLMOD_REAL + CHOLMOD_SINGLE:
rs_cholmod_spsolve_B_scatter_worker (B4, B, jfirst, jlast) ;
break ;
case CHOLMOD_COMPLEX + CHOLMOD_SINGLE:
cs_cholmod_spsolve_B_scatter_worker (B4, B, jfirst, jlast) ;
break ;
case CHOLMOD_ZOMPLEX + CHOLMOD_SINGLE:
zs_cholmod_spsolve_B_scatter_worker (B4, B, jfirst, jlast) ;
break ;
case CHOLMOD_REAL + CHOLMOD_DOUBLE:
rd_cholmod_spsolve_B_scatter_worker (B4, B, jfirst, jlast) ;
break ;
case CHOLMOD_COMPLEX + CHOLMOD_DOUBLE:
cd_cholmod_spsolve_B_scatter_worker (B4, B, jfirst, jlast) ;
break ;
case CHOLMOD_ZOMPLEX + CHOLMOD_DOUBLE:
zd_cholmod_spsolve_B_scatter_worker (B4, B, jfirst, jlast) ;
break ;
}
//----------------------------------------------------------------------
// solve the system (X4 = A\B4 or other system)
//----------------------------------------------------------------------
X4 = CHOLMOD(solve) (sys, L, B4, Common) ;
if (Common->status < CHOLMOD_OK)
{
CHOLMOD(free_sparse) (&X, Common) ;
CHOLMOD(free_dense) (&B4, Common) ;
CHOLMOD(free_dense) (&X4, Common) ;
return (NULL) ;
}
ASSERT (X4->xtype == X_xtype) ;
//----------------------------------------------------------------------
// append the solution onto X
//----------------------------------------------------------------------
bool ok = true ;
switch ((X->xtype + X->dtype) % 8)
{
case CHOLMOD_REAL + CHOLMOD_SINGLE:
ok = rs_cholmod_spsolve_X_worker (X, X4, jfirst, jlast, &xnz,
Common) ;
break ;
case CHOLMOD_COMPLEX + CHOLMOD_SINGLE:
ok = cs_cholmod_spsolve_X_worker (X, X4, jfirst, jlast, &xnz,
Common) ;
break ;
case CHOLMOD_ZOMPLEX + CHOLMOD_SINGLE:
ok = zs_cholmod_spsolve_X_worker (X, X4, jfirst, jlast, &xnz,
Common) ;
break ;
case CHOLMOD_REAL + CHOLMOD_DOUBLE:
ok = rd_cholmod_spsolve_X_worker (X, X4, jfirst, jlast, &xnz,
Common) ;
break ;
case CHOLMOD_COMPLEX + CHOLMOD_DOUBLE:
ok = cd_cholmod_spsolve_X_worker (X, X4, jfirst, jlast, &xnz,
Common) ;
break ;
case CHOLMOD_ZOMPLEX + CHOLMOD_DOUBLE:
ok = zd_cholmod_spsolve_X_worker (X, X4, jfirst, jlast, &xnz,
Common) ;
break ;
}
CHOLMOD(free_dense) (&X4, Common) ;
if (!ok)
{
// out of memory
CHOLMOD(free_sparse) (&X, Common) ;
CHOLMOD(free_dense) (&B4, Common) ;
return (NULL) ;
}
//----------------------------------------------------------------------
// clear B4 for next iteration
//----------------------------------------------------------------------
if (jlast < nrhs)
{
switch ((B->xtype + B->dtype) % 8)
{
case CHOLMOD_REAL + CHOLMOD_SINGLE:
rs_cholmod_spsolve_B_clear_worker (B4, B, jfirst, jlast) ;
break ;
case CHOLMOD_COMPLEX + CHOLMOD_SINGLE:
cs_cholmod_spsolve_B_clear_worker (B4, B, jfirst, jlast) ;
break ;
case CHOLMOD_ZOMPLEX + CHOLMOD_SINGLE:
zs_cholmod_spsolve_B_clear_worker (B4, B, jfirst, jlast) ;
break ;
case CHOLMOD_REAL + CHOLMOD_DOUBLE:
rd_cholmod_spsolve_B_clear_worker (B4, B, jfirst, jlast) ;
break ;
case CHOLMOD_COMPLEX + CHOLMOD_DOUBLE:
cd_cholmod_spsolve_B_clear_worker (B4, B, jfirst, jlast) ;
break ;
case CHOLMOD_ZOMPLEX + CHOLMOD_DOUBLE:
zd_cholmod_spsolve_B_clear_worker (B4, B, jfirst, jlast) ;
break ;
}
}
}
//--------------------------------------------------------------------------
// finalize X, reduce it in size, free workspace, and return result
//--------------------------------------------------------------------------
Int *Xp = X->p ;
Xp [nrhs] = xnz ;
ASSERT (xnz <= X->nzmax) ;
CHOLMOD(reallocate_sparse) (xnz, X, Common) ;
ASSERT (Common->status == CHOLMOD_OK) ;
CHOLMOD(free_dense) (&B4, Common) ;
return (X) ;
}
#endif
|
