init

P2/CMyMatrix.cpp

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+#include "CMyMatrix.h"
+#include "CMyVektor.h"
+#include <iostream>
+#include <iomanip>
+#include <math.h>
+
+// Konstruktor
+CMyMatrix::CMyMatrix(int z, int s) {
+    zeilen = z;
+    spalten = s;
+    matrix.resize(zeilen);
+    for (int i = 0; i < zeilen; ++i)
+        matrix[i].resize(spalten);
+}
+
+double CMyMatrix::getZeilen() {
+    return zeilen;
+}
+
+double CMyMatrix::getSpalten() {
+    return spalten;
+}
+
+void CMyMatrix::setWert(double wert, int zeile, int spalte) {
+    matrix[zeile][spalte] = wert;
+}
+
+double CMyMatrix::getWert(int zeile, int spalte) {
+    return matrix[zeile][spalte];
+}
+
+double& CMyMatrix::operator()(int zeile, int spalte) {
+    return matrix[zeile][spalte];
+}
+
+CMyMatrix CMyMatrix::invers() {
+    if (this->getZeilen() != 2 || this->getSpalten() != 2)
+        throw std::runtime_error("Keine 2x2 Matrix");
+
+    double a = this->getWert(0, 0);
+    double b = this->getWert(1, 0);
+    double c = this->getWert(0, 1);
+    double d = this->getWert(1, 1);
+
+    double determinate = a * d - b * c;
+
+    if (determinate == 0)
+        throw std::runtime_error("detA == 0");
+
+    double kehrwertDeterminante = 1 / determinate;
+    CMyMatrix inverse(2,2);
+
+    inverse.setWert(kehrwertDeterminante * d, 0, 0);
+    inverse.setWert(kehrwertDeterminante * -c, 0, 1);
+    inverse.setWert(kehrwertDeterminante * -b, 1, 0);
+    inverse.setWert(kehrwertDeterminante * a, 1, 1);
+
+    return inverse;
+}
+
+// Matrix-Vektor Multiplikation
+CMyVektor operator*(CMyMatrix A, CMyVektor x) {
+    // M Spalten == V Zeilen
+    if (A.getSpalten() != x.getDimension())
+        throw std::runtime_error("Matrix(m x n) * Vektor(i) n != i");
+
+    CMyVektor ergebnis(A.getZeilen());
+
+    for (int i = 0; i < A.getZeilen(); i++) {                                            // Zeile
+        for (int j = 0; j < A.getSpalten(); j++) // Spalte
+            ergebnis[i] += A(i, j) * x[j];       // Aufsummierung
+    }
+    return ergebnis;
+}
+
+std::ostream& operator<<(std::ostream& os, CMyMatrix x) {
+
+    for (int i = 0; i < x.getZeilen(); ++i) {
+        os << "\t\t\t(";
+        for (int j = 0; j < x.getSpalten(); ++j)
+            j == x.getSpalten() - 1 ? os << std::fixed << std::setprecision(10) << x(i, j) : os << std::fixed << std::setprecision(10) << x(i, j) << "|";
+
+        os << ")\n";
+    }
+    return os;
+}
+
+CMyMatrix jacobi(CMyVektor x, CMyVektor(*f)(CMyVektor)) {
+    double const h = pow(10, -4);
+    CMyVektor f_x = f(x);
+    CMyVektor tmp{ x };
+
+    CMyMatrix jacobiMatrix(f_x.getDimension(), x.getDimension());
+
+    for (int i = 0; i < f_x.getDimension(); ++i) { // Zeile bzw. Teilfunktion f_i
+        for (int j = 0; j < x.getDimension(); ++j) { // Spalte bzw. Variable x_j
+            tmp[j] += h;
+            jacobiMatrix(i, j) = (f(tmp)[i] - f_x[i]) / h;
+            tmp[j] -= h;
+        }
+    }
+    return jacobiMatrix;
+};
+
+void newtonverfahren(CMyVektor x, CMyVektor(*f)(CMyVektor)) {
+    int schritt = 0;
+    CMyVektor f_x = f(x);
+    CMyMatrix jacobi_f_x = jacobi(x, f);
+    CMyMatrix jacobiInvers = jacobi_f_x.invers();
+
+    double funktionLaenge = f_x.length();
+
+    CMyVektor dx = -1 * (jacobiInvers * f_x);
+
+    while (schritt != 50 && funktionLaenge >= 1e-5) {
+        std::cout << "Schritt " << schritt << ":"
+        << "\n\t            𝐱 = " << x
+        << "\n\t         𝑓(𝐱) = " << f_x << "\n"
+        << "\n\t        ∂𝑓(𝐱) = \n " << jacobi_f_x
+        << "\n\t      ∂𝑓(𝐱)⁻¹ = \n" << jacobiInvers
+        << "\n\t           Δ𝐱 = " << dx
+        << "\n\t     ||𝑓(𝐱)|| = " << funktionLaenge << std::endl << std::endl;
+
+        schritt++;
+        x = x + dx;
+        f_x = f(x);
+        jacobi_f_x = jacobi(x, f);
+        jacobiInvers = jacobi_f_x.invers();
+        dx = -1 * (jacobiInvers * f_x);
+        funktionLaenge = f_x.length();
+
+        if (schritt == 50) {
+            std::cout << "Ende wegen Schrittanzahl = 50 bei";
+            std::cout << "\n\t             x = " << x
+                << "\n\t          𝑓(𝐱) = " << f_x
+                << "\n\t      ||𝑓(𝐱)|| = " << funktionLaenge << std::endl;
+        }
+        else if (funktionLaenge < 1e-5) {
+            std::cout << "Ende wegen ||𝑓(𝐱)||<1e-5 bei";
+            std::cout << "\n\t             x = " << x
+                << "\n\t          𝑓(𝐱) = " << f_x
+                << "\n\t      ||𝑓(𝐱)|| = " << funktionLaenge << std::endl;
+        }
+    }
+};