add num8

2020-06-26 20:19:29 +02:00
parent 333cd04e58
commit 0c6d5e130e
8 changed files with 499 additions and 0 deletions
@@ -0,0 +1,98 @@
+#include <iostream>
+#include <vector>
+#include "hdnum.hh"
+
+template<class N>
+class EllipseProblem
+{
+public:
+  // Exportiere Größentyp
+  typedef std::size_t size_type;
+
+  // Exportiere Zahlentyp
+  typedef N number_type;
+
+  // Dimension der untenstehenden Funktion
+  std::size_t size () const
+  {
+    return 2;
+  }
+
+  // Funktionsauswertung
+  void F (const hdnum::Vector<N>& x, hdnum::Vector<N>& result) const
+  {
+    result[0] = pow(x[0], 2) + pow(x[1], 2) - 4;
+    result[1] = pow(x[0], 2)/9 + pow(x[1], 2) - 1;
+  }
+
+  // Jacobimatrix
+  void F_x (const hdnum::Vector<N>& x, hdnum::DenseMatrix<N>& result) const
+  {
+    result[0][0] = 2*x[0]; result[0][1] = 2*x[1];
+    result[1][0] = 2*x[0]/9; result[1][1] = 2*x[1];
+  }
+};
+
+int main ()
+{
+  typedef double Number; // Zahlentyp
+
+
+  typedef EllipseProblem<Number> Problem;
+  Problem problem;
+
+
+  hdnum::Vector<Number> u(problem.size()); // Vektor für Startpunkt bzw Lösung
+  hdnum::Vector<Number> result(problem.size()); // Vektor für Funktionswerte
+
+  // Newton
+  hdnum::Newton newton;
+  newton.set_maxit(20);
+  newton.set_verbosity(2);
+  newton.set_reduction(1e-10);
+  newton.set_abslimit(1e-20);
+  newton.set_linesearchsteps(3);
+
+  // 1. Quadrant
+  u[0] = 2.0; u[1] = 1.0;
+  newton.solve(problem,u);
+  std::cout << "Nullstelle im 1. Quadrant: " <<  std::setprecision(15) << u << std::endl;
+  problem.F(u, result);
+  std::cout << "Funktionswert: " <<  std::setprecision(15) << result << std::endl;
+
+  // 2. Quadrant
+  u[0] = -2.0; u[1] = 1.0;
+  newton.solve(problem,u);
+  std::cout << "Nullstelle im 2. Quadrant: " <<  std::setprecision(15) << u << std::endl;
+  problem.F(u, result);
+  std::cout << "Funktionswert: " <<  std::setprecision(15) << result << std::endl;
+
+  // 3. Quadrant
+  u[0] = -2.0; u[1] = -1.0;
+  newton.solve(problem,u);
+  std::cout << "Nullstelle im 3. Quadrant: " <<  std::setprecision(15) << u << std::endl;
+  problem.F(u, result);
+  std::cout << "Funktionswert: " <<  std::setprecision(15) << result << std::endl;
+
+  // 4. Quadrant
+  u[0] = 2.0; u[1] = -1.0;
+  newton.solve(problem,u);
+  std::cout << "Nullstelle im 4. Quadrant: " <<  std::setprecision(15) << u << std::endl;
+  problem.F(u, result);
+  std::cout << "Funktionswert: " <<  std::setprecision(15) << result << std::endl;
+
+  // Relaxation
+  hdnum::Banach banach;
+  banach.set_maxit(5000);                  // set parameters
+  banach.set_verbosity(2);
+  banach.set_reduction(1e-15);
+  banach.set_abslimit(1e-20);
+  banach.set_sigma(0.375);
+
+  u[0] = 2.0; u[1] = 1.0; // Startwert
+  banach.solve(problem,u);
+
+   std::cout << "Ergebnis: " <<  std::setprecision(15) << u << std::endl;
+
+  return 0;
+}