/*************************************************************** * Sample program ldim2tayl_ex2.cpp to calculate an enclosure * * of the Taylor coefficient f[2][1] of the function * * f(x,y) = sqrt( 1+(x+y)^2) at (x,y) = (10^8,2.1*10^8) * ***************************************************************/ #include #include "ldim2taylor.hpp" using namespace std; using namespace cxsc; using namespace taylor; ldim2taylor f(ldim2taylor_vector& x) { // f = sqrt( 1+(x+y)^2 ); ldim2taylor erg; erg = sqrt( 1+sqr(x[1]+x[2]) ); return erg; } ldim2taylor g(ldim2taylor_vector& x) { // g = sqrt( 1+(x+y)^2 ); ldim2taylor erg; erg = sqrt1px2( x[1]+x[2] ); return erg; } int main() { int p = 3; // Maximal order of Taylor expansion stagprec = 3; // Desired precision of 3*16=48 digits string string1 = "[1e8,1e8]"; string string2 = "[2.1e8,2.1e8]"; l_interval z1,z2; string1 >> z1; string2 >> z2; l_ivector iv(2); // 2 components with Lb=1 and Ub=2; iv[1] = z1; // x-value, x_0 = 4; iv[2] = z2; // y-value, y_0 = 2; ldim2taylor_vector tv; // Default constructor call tv = init_var(p,iv); // Initialization with vector iv ldim2taylor t; // Default constructor call t = f(tv); // function call cout << SetDotPrecision(16*stagprec,16*stagprec-3) << Scientific; cout << "Function f(x,y): t[2][1] = " << t[2][1] << endl; t = g(tv); cout << "Function g(x,y): t[2][1] = " << t[2][1] << endl; }