iter_track.h

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/* This file is part of Cloudy and is copyright (C)1978-2013 by Gary J. Ferland and
 * others.  For conditions of distribution and use see copyright notice in license.txt */
 
#ifndef ITER_TRACK_H_
#define ITER_TRACK_H_
 
// The class iter_track was derived from this original source:                //
//          http://www.mymathlib.webtrellis.net/roots/amsterdam.html          //
//                                                                            //
// The original code was heavily modified by: Peter van Hoof, ROB             //
 
double Amsterdam_Method( double (*f)(double), double a, double fa, double c, double fc,
                         double tol, int max_iter, int& err );
 
class iter_track
{
        vector< pair<double,double> > p_history;
        double p_result;
        double p_tol;
        int p_a;
        int p_b;
        int p_c;
        bool p_lgRootFound;
 
        void p_clear0()
        {
                p_history.clear();
        }
        void p_clear1()
        {
                p_history.reserve( 10 );
                set_NaN( p_result );
                p_tol = numeric_limits<double>::max();
                p_a = -1;
                p_b = -1;
                p_c = -1;
                p_lgRootFound = false;
        }
        void p_set_root(double x)
        {
                p_result = x;
                p_lgRootFound = true;
        }
        double p_x(int ip) const
        {
                return p_history[ip].first;
        }
        double p_y(int ip) const
        {
                return p_history[ip].second;
        }
        double p_midpoint() const
        {
                return 0.5*(p_x(p_a) + p_x(p_c));
        }
        double p_numerator(double dab, double dcb, double fa, double fb, double fc)
        {
                return fb*(dab*fc*(fc-fb)-fa*dcb*(fa-fb));
        }
        double p_denominator(double fa, double fb, double fc)
        {
                return (fc-fb)*(fa-fb)*(fa-fc);
        }
 
public:
        iter_track()
        {
                p_clear1();
        }
        ~iter_track()
        {
                p_clear0();
        }
        void clear()
        {
                p_clear0();
                p_clear1();
        }
        void set_tol(double tol)
        {
                p_tol = tol;
        }
        double bracket_width() const
        {
                return p_x(p_c) - p_x(p_a);
        }
        bool lgConverged()
        {
                if( p_lgRootFound )
                        return true;
                if( bracket_width() < p_tol )
                {
                        p_result = p_midpoint();
                        return true;
                }
                return false;
        }
        double root() const
        {
                return p_result;
        }
        int init_bracket( double x1, double fx1, double x2, double fx2 )
        {
                // fx1 and fx2 must have opposite sign, or be zero
                int s1 = sign3(fx1);
                int test = s1*sign3(fx2);
                if( test > 0 )
                        return -1;
                if( test == 0 )
                        p_set_root( ( s1 == 0 ) ? x1 : x2 );
 
                p_history.push_back( pair<double,double>(x1,fx1) );
                p_history.push_back( pair<double,double>(x2,fx2) );
                p_a = ( x1 < x2 ) ? 0 : 1;
                p_c = ( x1 < x2 ) ? 1 : 0;
                return 0;
        }
        void add( double x, double fx )
        {
                p_history.push_back( pair<double,double>(x,fx) );
                p_b = p_history.size()-1;
                if( fx == 0. )
                        p_set_root( x );
        }
        double next_val();
        double next_val(double max_rel_step)
        {
                double next = next_val();
                double last = p_history.back().first;
                double rel_step = safe_div( next, last ) - 1.;
                rel_step = sign( min(abs(rel_step),abs(max_rel_step)), rel_step );
                return (1.+rel_step)*last;
        }
        // these routines return a numerical estimate of the derivative
        // by making a linear least squares fit of y(x) to the last n steps
        double deriv(int n, double& sigma) const;
        double deriv(double& sigma) const
        {
                return deriv( p_history.size(), sigma );
        }
        double deriv(int n) const
        {
                double sigma;
                return deriv( n, sigma );
        }
        double deriv() const
        {
                double sigma;
                return deriv( p_history.size(), sigma );
        }
        // these routines return a numerical estimate of the root
        // by making a linear least squares fit of x(y) to the last n steps
        double zero_fit(int n, double& sigma) const;
        double zero_fit(double& sigma) const
        {
                return zero_fit( p_history.size(), sigma );
        }
        double zero_fit(int n) const
        {
                double sigma;
                return zero_fit( n, sigma );
        }
        double zero_fit() const
        {
                double sigma;
                return zero_fit( p_history.size(), sigma );
        }
        int in_bounds(double x) const
        {
                if( x < p_x(p_a) )
                        return -1;
                else if( x > p_x(p_c) )
                        return 1;
                else
                        return 0;
        }
        // the following two methods are debugging aids
        void print_status() const
        {
                dprintf( ioQQQ, "a %i %.15e %.15e\n", p_a, p_x(p_a), p_y(p_a) );
                dprintf( ioQQQ, "b %i %.15e %.15e\n", p_b, p_x(p_b), p_y(p_b) );
                dprintf( ioQQQ, "c %i %.15e %.15e\n", p_c, p_x(p_c), p_y(p_c) );
        }
        void print_history() const
        {
                fprintf( ioQQQ, " x(i)                 y(i)  iter_track history\n" );
                for( unsigned int i=0; i < p_history.size(); ++i )
                        fprintf( ioQQQ, "%.15e %.15e\n", p_x(i), p_y(i) );
        }
};
 
//
//
template<class T>
class iter_track_basic
{
        T p_lo_bound;
        T p_hi_bound;
        void p_clear1()
        {
                // invalidate the bracket
                p_lo_bound = numeric_limits<T>::max();
                p_hi_bound = numeric_limits<T>::min();
        }
public:
        iter_track_basic()
        {
                p_clear1();
        }
        void clear()
        {
                p_clear1();
        }
        T next_val( T current, T next_est )
        {
                // update the bounds of the bracket
                if( next_est < current )
                        p_hi_bound = current;
                else
                        p_lo_bound = current;
                // if the bracket has been established, do a bisection
                // otherwise simply return next_est.
                if( p_lo_bound < p_hi_bound )
                        return (T)0.5*(p_lo_bound + p_hi_bound);
                else
                        return next_est;
        }
};
 
#endif