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/*
* functions.h -- ePiX auxiliary functions; Deriv, Integral classes
*
* This file is part of ePiX, a C++ library for creating high-quality
* figures in LaTeX
*
* Version 1.1.22
* Last Change: September 24, 2007
*/
/*
* Copyright (C) 2001, 2002, 2003, 2004, 2005, 2006, 2007
* Andrew D. Hwang <rot 13 nujnat at zngupf dot ubylpebff dot rqh>
* Department of Mathematics and Computer Science
* College of the Holy Cross
* Worcester, MA, 01610-2395, USA
*/
/*
* ePiX 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 2 of the License, or
* (at your option) any later version.
*
* ePiX 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 ePiX; if not, write to the Free Software Foundation, Inc.,
* 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*/
#ifndef EPIX_FUNCTIONS
#define EPIX_FUNCTIONS
namespace ePiX {
class P;
// sensitive to angle units
double Cos(double t);
double Sin(double t);
double Tan(double t);
double Sec(double t);
double Csc(double t);
double Cot(double t);
double Acos(double t);
double Asin(double t);
double Atan(double t);
double Atan2(double y, double x);
// additional hyperbolic functions and inverses
double sech(double);
double csch(double);
double coth(double);
double asech(double);
double acsch(double);
double acoth(double);
// zero functions
double zero(double);
double zero(double, double);
double zero(double, double, double);
double zero(const P&);
// P constructors
P xyz(double x, double y, double z=0);
P cyl(double r, double t, double z);
P sph(double r, double t, double phi);
// for log data plotting
P log_log(double x, double y, double z=0);
P log_lin(double x, double y, double z=0);
P lin_log(double x, double y, double z=0);
P cylindrical(P); // not const P&
P spherical(P);
P polar(double r, double t);
P cis(double t);
// utility functions
double recip (double);
double sinx (double); // discontinuity removed
double sgn (double);
// period-2 extension of absolute value on [-1,1]: \/\/\/
double cb (double);
int gcd (int, int);
double min(double, double);
double max(double, double);
double snip_to(double var, double arg1, double arg2);
double inf (double f(double), double, double);
double sup (double f(double), double, double);
// derivative class
class Deriv {
private:
double (*f)(double);
double dt;
public:
Deriv(double func(double));
Deriv(double func(double), double eps);
P operator() (const P&) const; // for plotting
// numerical values
double eval(double t) const;
// one-sided derivatives
double right(double t) const;
double left(double t) const;
}; // end of class Deriv
// definite integral class
class Integral {
private:
double (*f)(double);
double x0; // lower limit
public:
Integral(double func(double), double a=0);
P operator() (const P&) const;
double eval(double) const;
}; // end of class Integral
double newton (double f(double), double g(double), double start);
double newton (double f(double), double start);
} // end of namespace
#endif /* EPIX_FUNCTIONS */
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