# aewallin/opencamlib

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 /* \$Id\$ * * Copyright 2010 Anders Wallin (anders.e.e.wallin "at" gmail.com) * * This file is part of OpenCAMlib. * * OpenCAMlib is free software: you can redistribute it and/or modify * it under the terms of the GNU General Public License as published by * the Free Software Foundation, either version 3 of the License, or * (at your option) any later version. * * OpenCAMlib is distributed in the hope that it will be useful, * but WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the * GNU General Public License for more details. * * You should have received a copy of the GNU General Public License * along with OpenCAMlib. If not, see . */ #ifndef BRENT_ZERO_H #define BRENT_ZERO_H namespace ocl { /// Brent's root finding algorithm /// http://en.wikipedia.org/wiki/Brent's_method /// /// find a zero of function f in the interval [a,b] /// a and b must bracket the root, i.e. f(a) must have different sign than f(b) /// needs a pointer to an ErrObj which must provide a function /// double ErrObj::error(double x) for which we try to find a zero /// /// FIXME: describe tolerance parameters eps and t template double brent_zero( double a, double b, double eps, double t, ErrObj* ell) { // f must have unequal sign at a and b, i.e. // f(a)*f(b) < 0 // returns the location of a root c where f(c)=0 // to within 6*eps*abs(c)+2*t tolerance double c,d,e; double fa,fb,fc; // function values double m,p,q,r,s; double tol; fa = ell->error(a); // f(a); fb = ell->error(b); // f(b); if (fa*fb >= 0.0) {// check for opposite signs std::cout << " brent_zero() called with invalid interval [a,b] !\n"; assert(0); } c = a; // set c sln equal to a sln fc = fa; e = b-a; // interval width d = e; // interval width while (true) { if (fabs(fc)b was small, or fa is a better solution e = m; d = e; // bisection? } else { s = fb/fa; if (a == c) { p=2.0*m*s; q=1.0-s; } else { q = fa/fc; r = fb/fc; p = s*(2.0*m*a*(q-r)-(b-a)*(r-1.0)); q = (q-1.0)*(r-1.0)*(s-1.0); } if (p>0.0) q=-q; else p=-p; // make p negative s=e; e=d; if ( (2.0*p < (3.0*m*q-fabs(tol*q))) && (p tol ) // if d is "large" b = b+d; // push the root by d else if ( m > 0.0 ) b = b+tol; // otherwise, push root by tol in direction of m else b = b-tol; // std::cout << " brent_zero b=" << b << "\n"; fb = ell->error(b); // f(b); if ( ((fb>0.0) && (fc>0.0)) || ((fb<=0.0) && (fc<=0.0)) ) { // fb and fc have the same sign c = a; // so change c to a fc = fa; e = b-a; // interval width d = e; } } // end iteration-loop return b; } } // end namespace #endif // end file brent_zero.hpp