99 lines
2.6 KiB
C++
99 lines
2.6 KiB
C++
#include <iostream>
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#include <vector>
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#include "hdnum.hh"
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template<class N>
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class EllipseProblem
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{
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public:
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// Exportiere Größentyp
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typedef std::size_t size_type;
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// Exportiere Zahlentyp
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typedef N number_type;
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// Dimension der untenstehenden Funktion
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std::size_t size () const
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{
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return 2;
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}
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// Funktionsauswertung
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void F (const hdnum::Vector<N>& x, hdnum::Vector<N>& result) const
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{
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result[0] = pow(x[0], 2) + pow(x[1], 2) - 4;
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result[1] = pow(x[0], 2)/9 + pow(x[1], 2) - 1;
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}
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// Jacobimatrix
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void F_x (const hdnum::Vector<N>& x, hdnum::DenseMatrix<N>& result) const
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{
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result[0][0] = 2*x[0]; result[0][1] = 2*x[1];
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result[1][0] = 2*x[0]/9; result[1][1] = 2*x[1];
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}
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};
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int main ()
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{
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typedef double Number; // Zahlentyp
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typedef EllipseProblem<Number> Problem;
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Problem problem;
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hdnum::Vector<Number> u(problem.size()); // Vektor für Startpunkt bzw Lösung
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hdnum::Vector<Number> result(problem.size()); // Vektor für Funktionswerte
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// Newton
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hdnum::Newton newton;
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newton.set_maxit(20);
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newton.set_verbosity(2);
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newton.set_reduction(1e-10);
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newton.set_abslimit(1e-20);
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newton.set_linesearchsteps(3);
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// 1. Quadrant
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u[0] = 2.0; u[1] = 1.0;
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newton.solve(problem,u);
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std::cout << "Nullstelle im 1. Quadrant: " << std::setprecision(15) << u << std::endl;
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problem.F(u, result);
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std::cout << "Funktionswert: " << std::setprecision(15) << result << std::endl;
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// 2. Quadrant
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u[0] = -2.0; u[1] = 1.0;
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newton.solve(problem,u);
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std::cout << "Nullstelle im 2. Quadrant: " << std::setprecision(15) << u << std::endl;
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problem.F(u, result);
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std::cout << "Funktionswert: " << std::setprecision(15) << result << std::endl;
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// 3. Quadrant
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u[0] = -2.0; u[1] = -1.0;
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newton.solve(problem,u);
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std::cout << "Nullstelle im 3. Quadrant: " << std::setprecision(15) << u << std::endl;
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problem.F(u, result);
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std::cout << "Funktionswert: " << std::setprecision(15) << result << std::endl;
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// 4. Quadrant
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u[0] = 2.0; u[1] = -1.0;
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newton.solve(problem,u);
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std::cout << "Nullstelle im 4. Quadrant: " << std::setprecision(15) << u << std::endl;
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problem.F(u, result);
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std::cout << "Funktionswert: " << std::setprecision(15) << result << std::endl;
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// Relaxation
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hdnum::Banach banach;
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banach.set_maxit(5000); // set parameters
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banach.set_verbosity(2);
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banach.set_reduction(1e-15);
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banach.set_abslimit(1e-20);
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banach.set_sigma(0.375);
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u[0] = 2.0; u[1] = 1.0; // Startwert
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banach.solve(problem,u);
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std::cout << "Ergebnis: " << std::setprecision(15) << u << std::endl;
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return 0;
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}
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