1 /*
2 * Copyright (C) 1998, 2000-2007, 2010, 2011, 2012, 2013 SINTEF ICT,
3 * Applied Mathematics, Norway.
4 *
5 * Contact information: E-mail: tor.dokken@sintef.no
6 * SINTEF ICT, Department of Applied Mathematics,
7 * P.O. Box 124 Blindern,
8 * 0314 Oslo, Norway.
9 *
10 * This file is part of SISL.
11 *
12 * SISL is free software: you can redistribute it and/or modify
13 * it under the terms of the GNU Affero General Public License as
14 * published by the Free Software Foundation, either version 3 of the
15 * License, or (at your option) any later version.
16 *
17 * SISL is distributed in the hope that it will be useful,
18 * but WITHOUT ANY WARRANTY; without even the implied warranty of
19 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
20 * GNU Affero General Public License for more details.
21 *
22 * You should have received a copy of the GNU Affero General Public
23 * License along with SISL. If not, see
24 * <http://www.gnu.org/licenses/>.
25 *
26 * In accordance with Section 7(b) of the GNU Affero General Public
27 * License, a covered work must retain the producer line in every data
28 * file that is created or manipulated using SISL.
29 *
30 * Other Usage
31 * You can be released from the requirements of the license by purchasing
32 * a commercial license. Buying such a license is mandatory as soon as you
33 * develop commercial activities involving the SISL library without
34 * disclosing the source code of your own applications.
35 *
36 * This file may be used in accordance with the terms contained in a
37 * written agreement between you and SINTEF ICT.
38 */
39
40 #include "sisl-copyright.h"
41
42 /*
43 *
44 * $Id: s6lufacp.c,v 1.2 2001-03-19 15:59:02 afr Exp $
45 *
46 */
47
48
49 #define S6LUFACP
50
51 #include "sislP.h"
52
53 #if defined(SISLNEEDPROTOTYPES)
54 void
s6lufacp(double ea[],int nl[],int im,int * jstat)55 s6lufacp(double ea[],int nl[],int im,int *jstat)
56 #else
57 void s6lufacp(ea,nl,im,jstat)
58 double ea[];
59 int nl[];
60 int im;
61 int *jstat;
62 #endif
63 /*
64 ***********************************************************************
65 *
66 ************************************************************************
67 *
68 * PURPOSE : LU-factorisation of a full matrix. The matrix is stored
69 * in a one-dimensional array.
70 *
71 *
72 * INPUT : im - The number of equations.
73 *
74 *
75 *
76 * INPUT/OUTPUT : eb - the array in which the matrix is stored.
77 * The elements are stored row-wise.
78 *
79 *
80 * OUTPUT : nl - Array that indicates order of rows after pivoting.
81 * jstat - Status variable.
82 * < 0 : error
83 * = 0 : ok
84 * > 0 : warning
85 *
86 *
87 * METHOD : Gauss-elimination with partial pivoting.
88 *
89 *
90 * REFERENCES : Cheney & Kincaid : Numerical Mathematics and
91 * Computing.
92 *
93 *-
94 * CALLS :
95 *
96 * WRITTEN BY : Vibeke Skytt, SI, 86-12.
97 *
98 ************************************************************************
99 */
100 {
101 int kpos = 0; /* Position of error. */
102 int ki,kj,kk; /* Counters. */
103 int kmax = 0; /* Number of row with maximum greates element. */
104 int kchange; /* Help variable to change order of two rows. */
105 double tmult; /* Factor with which to multiply a row before it is
106 added to another. */
107 double t1; /* Help variabel to find maximum of a number of elements.*/
108 double tmax; /* Maximum of a number of elements. */
109 double tdiv; /* Dividend in expression. */
110 double *smax = SISL_NULL; /* Maximum elements in the rows of ea. */
111
112 /* Allocate space for local array. */
113
114 if ((smax = new0array(im,double)) == SISL_NULL) goto err101;
115
116 /* Find largest element in each row. */
117
118 for (ki=0; ki<im; ki++)
119 {
120 nl[ki] = ki;
121 for (kj=0; kj<im; kj++)
122 smax[ki] = MAX(smax[ki],fabs(ea[ki*im+kj]));
123 }
124
125 for (ki=0; ki<im-1; ki++)
126 {
127
128 /* Find row with maximum greates element to treat now. */
129
130 tmax = DZERO;
131 for (kj=ki; kj<im; kj++)
132 {
133 tdiv = smax[nl[kj]];
134 if (DEQUAL(tdiv,DZERO)) goto warn1;
135 t1 = fabs(ea[nl[kj]*im+ki]/tdiv);
136 if (t1 > tmax)
137 {
138 tmax = t1;
139 kmax = kj;
140 }
141 }
142 kchange = nl[kmax];
143 nl[kmax] = nl[ki];
144 nl[ki] = kchange;
145
146 /* Add a multiplum of current row to all later rows in order to
147 get an upper triangular matrix ea. */
148
149 for (kj=ki+1; kj<im; kj++)
150 {
151 tdiv = ea[ki+kchange*im];
152 if (DEQUAL(tdiv,DZERO)) goto warn1;
153 tmult = ea[ki+nl[kj]*im]/tdiv;
154 ea[ki+nl[kj]*im] = tmult;
155
156 for (kk=ki+1; kk<im; kk++)
157 ea[kk+nl[kj]*im] -= ea[kk+kchange*im]*tmult;
158 }
159 }
160
161 /* LU-factorizing performed. */
162
163 *jstat = 0;
164 goto out;
165
166 /* Singular equation system. */
167
168 warn1 : *jstat = 1;
169 goto out;
170
171 /* Error in space allocation. */
172
173 err101: *jstat = -101;
174 s6err("s6lufacp",*jstat,kpos);
175 goto out;
176
177 out:
178
179 /* Free space occupied by local array. */
180
181 if (smax != SISL_NULL) freearray(smax);
182
183 return;
184 }
185
186
187
188
189