/*--------------------------------------------------------------- Sample program litayl_ex2.cpp for staggered Taylor arithmetic. Calculating guaranteed inclusions of the derivatives of the function f = atan(x^2/(1+x^2)) in interval staggered arithmetic. -----------------------------------------------------------------*/ #include "litaylor.hpp" // Header file for class l_itaylor #include // Interval staggered arithmetic #include // Input, output using namespace std; using namespace taylor; using namespace cxsc; l_itaylor f1(const l_itaylor& x) { l_itaylor w; l_real S( abs( Sup(get_j_derive(x,0)) ) ); if (S<1) { w = sqr(x); atan( w/(1+w) ); } else w = atan(1/(1+sqr(1/x))); // to avoid overflow return w; } int main() { stagprec = 3; // Provides a precision of about 3*16=48 // decimal digits. int p = 2; // Taylor expansion of order p l_itaylor x(p,comp(0.5,134)); // Constructor call for // independentvariable x of order p=2; l_itaylor f,g,h; // Default constructor call f = f1(x); // After assignment: f is Taylor object of order p. cout << SetDotPrecision(16*stagprec,16*stagprec) << Scientific << "Derivatives of function f1(x):" << endl; cout << "1. derivative: " << get_j_derive(f,1) << endl; cout << "2. derivative: " << get_j_derive(f,2) << endl; cout << "Derivatives of function g(x):" << endl; g = sqr(x); g = atan(g/(1+g)); // suitable for |(x)_0| < 1; cout << "1. derivative: " << get_j_derive(g,1) << endl; cout << "2. derivative: " << get_j_derive(g,2) << endl; cout << "Derivatives of function h(x):" << endl; h = atan(1/(1+sqr(1/x))); // suitable for |(x)_0| >= 1; cout << "1. derivative: " << get_j_derive(h,1) << endl; cout << "2. derivative: " << get_j_derive(h,2) << endl; return 0; }