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// This file is part of fityk program. Copyright 2001-2013 Marcin Wojdyr
// Licence: GNU General Public License ver. 2+
#ifndef FITYK_NUMFUNCS_H_
#define FITYK_NUMFUNCS_H_
#include <stdlib.h>
#include "fityk.h"
#include "common.h" // S
namespace fityk {
/// Point used for linear interpolation and polyline convex hull algorithm.
struct PointD
{
double x, y;
PointD() {}
PointD(double x_, double y_) : x(x_), y(y_) {}
bool operator< (const PointD& b) const { return x < b.x; }
};
/// Point used for spline/polyline interpolation.
/// The q parameter is used for cubic spline computation.
struct PointQ
{
double x, y;
double q; /* q is used for spline */
PointQ() {}
PointQ(double x_, double y_) : x(x_), y(y_) {}
bool operator< (const PointQ& b) const { return x < b.x; }
};
/// must be run before computing value of cubic spline in point x
/// results are written in PointQ::q
/// based on Numerical Recipes www.nr.com
FITYK_API void prepare_spline_interpolation (std::vector<PointQ> &bb);
// instantiated for T = PointQ, PointD
template<typename T>
typename std::vector<T>::iterator
get_interpolation_segment(std::vector<T> &bb, double x);
FITYK_API double get_spline_interpolation(std::vector<PointQ> &bb, double x);
FITYK_API double get_linear_interpolation(std::vector<PointD> &bb, double x);
FITYK_API double get_linear_interpolation(std::vector<PointQ> &bb, double x);
// random number utilities
inline double rand_1_1() { return 2.0 * rand() / RAND_MAX - 1.; }
inline double rand_0_1() { return static_cast<double>(rand()) / RAND_MAX; }
inline double rand_uniform(double a, double b) { return a + rand_0_1()*(b-a); }
inline bool rand_bool() { return rand() < RAND_MAX / 2; }
double rand_gauss();
double rand_cauchy();
// very simple matrix utils
void jordan_solve(std::vector<realt>& A, std::vector<realt>& b, int n);
FITYK_API void invert_matrix(std::vector<realt>&A, int n);
// format (for printing) matrix m x n stored in vec. `mname' is name/comment.
std::string format_matrix(const std::vector<realt>& vec,
int m, int n, const char *mname);
// Simple Polyline Convex Hull Algorithms
// takes as input a sequence of points (x,y), with increasing x coord (added
// in push_point()) and returns points of convex hull (get_vertices())
class FITYK_API SimplePolylineConvex
{
public:
void push_point(double x, double y) { push_point(PointD(x, y)); }
void push_point(PointD const& p);
std::vector<PointD> const& get_vertices() const { return vertices_; }
// test if point p2 left of the line through p0 and p1
static bool is_left(PointD const& p0, PointD const& p1, PointD const& p2)
{ return (p1.x - p0.x)*(p2.y - p0.y) > (p2.x - p0.x)*(p1.y - p0.y); }
private:
std::vector<PointD> vertices_;
};
/// search x in [x1, x2] for which %f(x)==val,
/// x1, x2, val: f(x1) <= val <= f(x2) or f(x2) <= val <= f(x1)
/// bisection + Newton-Raphson
template<typename T>
realt find_x_with_value(T *func, realt x1, realt x2, realt val)
{
const int max_iter = 1000;
std::vector<realt> dy_da(func->max_param_pos() + 1, 0);
// we don't need derivatives here, but to make it simpler..
realt y1 = func->calculate_value_and_deriv(x1, dy_da) - val;
realt y2 = func->calculate_value_and_deriv(x2, dy_da) - val;
if ((y1 > 0 && y2 > 0) || (y1 < 0 && y2 < 0))
throw ExecuteError("Value " + S(val) + " is not bracketed by "
+ S(x1) + "(" + S(y1+val) + ") and "
+ S(x2) + "(" + S(y2+val) + ").");
if (y1 == 0)
return x1;
if (y2 == 0)
return x2;
if (y1 > 0)
std::swap(x1, x2);
realt t = (x1 + x2) / 2.;
for (int i = 0; i < max_iter; ++i) {
//check if converged
if (is_eq(x1, x2))
return (x1+x2) / 2.;
// calculate f and df
dy_da.back() = 0;
realt f = func->calculate_value_and_deriv(t, dy_da) - val;
realt df = dy_da.back();
// narrow the range
if (f == 0.)
return t;
else if (f < 0)
x1 = t;
else // f > 0
x2 = t;
// select new guess point
realt dx = -f/df * 1.02; // 1.02 is to jump to the other side of point
if ((t+dx > x2 && t+dx > x1) || (t+dx < x2 && t+dx < x1) // outside
|| i % 20 == 19) { // precaution
//bisection
t = (x1 + x2) / 2.;
} else {
t += dx;
}
}
throw ExecuteError("The search has not converged.");
}
/// finds root of derivative, using bisection method
template<typename T>
realt find_extremum(T *func, realt x1, realt x2)
{
const int max_iter = 1000;
std::vector<realt> dy_da(func->max_param_pos() + 1, 0);
// calculate df
dy_da.back() = 0;
func->calculate_value_and_deriv(x1, dy_da);
realt y1 = dy_da.back();
dy_da.back() = 0;
func->calculate_value_and_deriv(x2, dy_da);
realt y2 = dy_da.back();
if ((y1 > 0 && y2 > 0) || (y1 < 0 && y2 < 0))
throw ExecuteError("Derivatives at " + S(x1) + " and " + S(x2)
+ " have the same sign.");
if (y1 == 0)
return x1;
if (y2 == 0)
return x2;
if (y1 > 0)
std::swap(x1, x2);
for (int i = 0; i < max_iter; ++i) {
realt t = (x1 + x2) / 2.;
// calculate df
dy_da.back() = 0;
func->calculate_value_and_deriv(t, dy_da);
realt df = dy_da.back();
// narrow the range
if (df == 0.)
return t;
else if (df < 0)
x1 = t;
else // df > 0
x2 = t;
//check if converged
if (is_eq(x1, x2))
return (x1+x2) / 2.;
}
throw ExecuteError("The search has not converged.");
}
} // namespace fityk
#endif
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