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
|
#define WSOLVE
/* ========================================================================== */
/* === UMFPACK_solve ======================================================== */
/* ========================================================================== */
/* -------------------------------------------------------------------------- */
/* UMFPACK Version 4.1 (Apr. 30, 2003), Copyright (c) 2003 by Timothy A. */
/* Davis. All Rights Reserved. See ../README for License. */
/* email: davis@cise.ufl.edu CISE Department, Univ. of Florida. */
/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
/* -------------------------------------------------------------------------- */
/*
User-callable. Solves a linear system using the numerical factorization
computed by UMFPACK_numeric. See umfpack_solve.h for more details.
For umfpack_*_solve:
Dynamic memory usage: UMFPACK_solve calls UMF_malloc twice, for
workspace of size c*n*sizeof(double) + n*sizeof(Int), where c is
defined below. On return, all of this workspace is free'd via UMF_free.
For umfpack_*_wsolve:
No dynamic memory usage. Input arrays are used for workspace instead.
Pattern is a workspace of size n Integers. The double array W must be
at least of size c*n, where c is defined below.
If iterative refinement is requested, and Ax=b, A'x=b or A.'x=b is being
solved, and the matrix A is not singular, then c is 5 for the real version
and 10 for the complex version. Otherwise, c is 1 for the real version and
4 for the complex version.
*/
#include "umf_internal.h"
#include "umf_valid_numeric.h"
#include "umf_solve.h"
#ifndef WSOLVE
#include "umf_malloc.h"
#include "umf_free.h"
#ifndef NDEBUG
PRIVATE Int init_count ;
#endif
#endif
GLOBAL Int
#ifdef WSOLVE
UMFPACK_wsolve
#else
UMFPACK_solve
#endif
(
Int sys,
const Int Ap [ ],
const Int Ai [ ],
const double Ax [ ],
#ifdef COMPLEX
const double Az [ ],
#endif
double Xx [ ],
#ifdef COMPLEX
double Xz [ ],
#endif
const double Bx [ ],
#ifdef COMPLEX
const double Bz [ ],
#endif
void *NumericHandle,
const double Control [UMFPACK_CONTROL],
double User_Info [UMFPACK_INFO]
#ifdef WSOLVE
, Int Pattern [ ],
double W [ ]
#endif
)
{
/* ---------------------------------------------------------------------- */
/* local variables */
/* ---------------------------------------------------------------------- */
NumericType *Numeric ;
Int n, i, irstep, status ;
double Info2 [UMFPACK_INFO], *Info, /* tstart, tend */ stats [2] ;
#ifndef WSOLVE
Int *Pattern, wsize ;
double *W ;
#endif
/* ---------------------------------------------------------------------- */
/* get the amount of time used by the process so far */
/* ---------------------------------------------------------------------- */
umfpack_tic (stats) ;
#ifndef WSOLVE
#ifndef NDEBUG
init_count = UMF_malloc_count ;
#endif
#endif
/* ---------------------------------------------------------------------- */
/* get parameters */
/* ---------------------------------------------------------------------- */
irstep = GET_CONTROL (UMFPACK_IRSTEP, UMFPACK_DEFAULT_IRSTEP) ;
if (User_Info != (double *) NULL)
{
/* return Info in user's array */
Info = User_Info ;
/* clear the parts of Info that are set by UMFPACK_solve */
for (i = UMFPACK_IR_TAKEN ; i <= UMFPACK_SOLVE_TIME ; i++)
{
Info [i] = EMPTY ;
}
}
else
{
/* no Info array passed - use local one instead */
Info = Info2 ;
for (i = 0 ; i < UMFPACK_INFO ; i++)
{
Info [i] = EMPTY ;
}
}
Info [UMFPACK_STATUS] = UMFPACK_OK ;
Info [UMFPACK_SOLVE_FLOPS] = 0 ;
Numeric = (NumericType *) NumericHandle ;
if (!UMF_valid_numeric (Numeric))
{
Info [UMFPACK_STATUS] = UMFPACK_ERROR_invalid_Numeric_object ;
return (UMFPACK_ERROR_invalid_Numeric_object) ;
}
Info [UMFPACK_NROW] = Numeric->n_row ;
Info [UMFPACK_NCOL] = Numeric->n_col ;
if (Numeric->n_row != Numeric->n_col)
{
/* only square systems can be handled */
Info [UMFPACK_STATUS] = UMFPACK_ERROR_invalid_system ;
return (UMFPACK_ERROR_invalid_system) ;
}
n = Numeric->n_row ;
if (Numeric->nnzpiv < n
|| SCALAR_IS_ZERO (Numeric->rcond) || SCALAR_IS_NAN (Numeric->rcond))
{
/* turn off iterative refinement if A is singular */
/* or if U has NaN's on the diagonal. */
irstep = 0 ;
}
if (!Xx || !Bx
#ifdef COMPLEX
|| !Xz || !Bz
#endif
)
{
Info [UMFPACK_STATUS] = UMFPACK_ERROR_argument_missing ;
return (UMFPACK_ERROR_argument_missing) ;
}
if (sys >= UMFPACK_Pt_L)
{
/* no iterative refinement except for nonsingular Ax=b, A'x=b, A.'x=b */
irstep = 0 ;
}
/* ---------------------------------------------------------------------- */
/* allocate or check the workspace */
/* ---------------------------------------------------------------------- */
#ifdef WSOLVE
if (!W || !Pattern)
{
Info [UMFPACK_STATUS] = UMFPACK_ERROR_argument_missing ;
return (UMFPACK_ERROR_argument_missing) ;
}
#else
#ifdef COMPLEX
if (irstep > 0)
{
wsize = 10*n ; /* W, X, Z, S, Y, B2 */
}
else
{
wsize = 4*n ; /* W, X */
}
#else
if (irstep > 0)
{
wsize = 5*n ; /* W, Z, S, Y, B2 */
}
else
{
wsize = n ; /* W */
}
#endif
Pattern = (Int *) UMF_malloc (n, sizeof (Int)) ;
W = (double *) UMF_malloc (wsize, sizeof (double)) ;
if (!W || !Pattern)
{
DEBUGm4 (("out of memory: solve work\n")) ;
Info [UMFPACK_STATUS] = UMFPACK_ERROR_out_of_memory ;
(void) UMF_free ((void *) W) ;
(void) UMF_free ((void *) Pattern) ;
return (UMFPACK_ERROR_out_of_memory) ;
}
#endif /* WSOLVE */
/* ---------------------------------------------------------------------- */
/* solve the system */
/* ---------------------------------------------------------------------- */
status = UMF_solve (sys, Ap, Ai, Ax, Xx, Bx,
#ifdef COMPLEX
Az, Xz, Bz,
#endif
Numeric, irstep, Info, Pattern, W) ;
/* ---------------------------------------------------------------------- */
/* free the workspace (if allocated) */
/* ---------------------------------------------------------------------- */
#ifndef WSOLVE
(void) UMF_free ((void *) W) ;
(void) UMF_free ((void *) Pattern) ;
ASSERT (UMF_malloc_count == init_count) ;
#endif
/* ---------------------------------------------------------------------- */
/* get the time used by UMFPACK_*solve */
/* ---------------------------------------------------------------------- */
Info [UMFPACK_STATUS] = status ;
if (status >= 0)
{
umfpack_toc (stats) ;
Info [UMFPACK_SOLVE_WALLTIME] = stats [0] ;
Info [UMFPACK_SOLVE_TIME] = stats [1] ;
}
return (status) ;
}
|
