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/*
* conjugate_gradient.cpp
*
* Copyright 2006 Nathan Hurst <njh@mail.csse.monash.edu.au>
*
* This library is free software; you can redistribute it and/or
* modify it either under the terms of the GNU Lesser General Public
* License version 2.1 as published by the Free Software Foundation
* (the "LGPL") or, at your option, under the terms of the Mozilla
* Public License Version 1.1 (the "MPL"). If you do not alter this
* notice, a recipient may use your version of this file under either
* the MPL or the LGPL.
*
* You should have received a copy of the LGPL along with this library
* in the file COPYING-LGPL-2.1; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
* You should have received a copy of the MPL along with this library
* in the file COPYING-MPL-1.1
*
* The contents of this file are subject to the Mozilla Public License
* Version 1.1 (the "License"); you may not use this file except in
* compliance with the License. You may obtain a copy of the License at
* http://www.mozilla.org/MPL/
*
* This software is distributed on an "AS IS" basis, WITHOUT WARRANTY
* OF ANY KIND, either express or implied. See the LGPL or the MPL for
* the specific language governing rights and limitations.
*
*/
#include <math.h>
#include <stdlib.h>
#include <valarray>
#include <cassert>
#include <2geom/conjugate_gradient.h>
/* lifted wholely from wikipedia. */
using std::valarray;
static void
matrix_times_vector(valarray<double> const &matrix, /* m * n */
valarray<double> const &vec, /* n */
valarray<double> &result) /* m */
{
unsigned n = vec.size();
unsigned m = result.size();
assert(m*n == matrix.size());
const double* mp = &const_cast<valarray<double>&>(matrix)[0];
for (unsigned i = 0; i < m; i++) {
double res = 0;
for (unsigned j = 0; j < n; j++)
res += *mp++ * vec[j];
result[i] = res;
}
}
/**
// only used in commented code below
static double Linfty(valarray<double> const &vec) {
return std::max(vec.max(), -vec.min());
}
**/
double
inner(valarray<double> const &x,
valarray<double> const &y) {
double total = 0;
for(unsigned i = 0; i < x.size(); i++)
total += x[i]*y[i];
return total;// (x*y).sum(); <- this is more concise, but ineff
}
void
conjugate_gradient(double **A,
double *x,
double *b,
unsigned n,
double tol,
int max_iterations,
bool ortho1) {
valarray<double> vA(n*n);
valarray<double> vx(n);
valarray<double> vb(n);
for(unsigned i=0;i<n;i++) {
vx[i]=x[i];
vb[i]=b[i];
for(unsigned j=0;j<n;j++) {
vA[i*n+j]=A[i][j];
}
}
conjugate_gradient(vA,vx,vb,n,tol,max_iterations,ortho1);
for(unsigned i=0;i<n;i++) {
x[i]=vx[i];
}
}
void
conjugate_gradient(valarray<double> const &A,
valarray<double> &x,
valarray<double> const &b,
unsigned n, double tol,
unsigned max_iterations, bool /*ortho1*/) {
valarray<double> Ap(n), p(n), r(n);
matrix_times_vector(A,x,Ap);
r=b-Ap;
double r_r = inner(r,r);
unsigned k = 0;
tol *= tol;
while(k < max_iterations && r_r > tol) {
k++;
double r_r_new = r_r;
if(k == 1)
p = r;
else {
r_r_new = inner(r,r);
p = r + (r_r_new/r_r)*p;
}
matrix_times_vector(A, p, Ap);
double alpha_k = r_r_new / inner(p, Ap);
x += alpha_k*p;
r -= alpha_k*Ap;
r_r = r_r_new;
}
//printf("njh: %d iters, Linfty = %g L2 = %g\n", k,
//std::max(-r.min(), r.max()), sqrt(r_r));
// x is solution
}
/*
Local Variables:
mode:c++
c-file-style:"stroustrup"
c-file-offsets:((innamespace . 0)(inline-open . 0)(case-label . +))
indent-tabs-mode:nil
fill-column:99
End:
*/
// vim: filetype=cpp:expandtab:shiftwidth=4:tabstop=8:softtabstop=4:encoding=utf-8:textwidth=99 :
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