x027.h

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#pragma once

#include <algorithm>
#include <cmath>
#include <iostream>
#include <numeric>
#include <vector>

namespace nmx::apps::x027 {

inline void ex1() {
    //----------------------------------------------------------
    // Berechnung der Geraden a1 x + a0, die durch die Punkte
    // (x0,y0) und (x1,y1) geht
    //--------------------------------------------------------
    auto line = [](double x0, double y0, double x1, double y1) {
        double a1 = (y1 - y0) / (x1 - x0);
        double a0 = y1 - a1 * x1;
        return std::make_pair(a0, a1);
    };

    //----------------------------------------------------------
    //für eine Gerade y(x) = a1 * x + a0 berechne y(x)
    //----------------------------------------------------------
    auto lininterp = [](double a0, double a1, double x) { //
        return a0 + a1 * x;
    };

    //**
    //---------------------------------------------
    //Erstellung von Beispieldaten (x,y)
    //-----------------------------------------------
    //reserviere Speicher für 20 Elemente
    std::vector<double> xvalues(20), yvalues(20);
    //fülle x = 0.1,0.2,...
    double xval = 0;
    std::generate(xvalues.begin(), xvalues.end(), [&xval]() { //
        return xval += 0.1;
    });
    //fülle y = cos(x)
    std::transform(xvalues.begin(),
                   xvalues.end(), //
                   std::begin(yvalues),
                   [](double x) { return std::cos(x); });

    //**
    //-------------------------------------
    //Berechnung von y(x=1.23)
    //----------------------------------------
    const double x = 1.23;
    // suche 1.tes x_i >= x
    auto itr = std::upper_bound(xvalues.begin(), xvalues.end(), x);
    //  wenn gefunden...
    if (itr != xvalues.end()) {
        // finde Index im Feld
        auto idx = static_cast<size_t>(std::distance(xvalues.begin(), itr));
        std::cout << "found  index: " << idx //
                  << " with x=" << xvalues[idx] //
                  << " and y=" << yvalues[idx] << std::endl;
        const double x0 = xvalues[idx - 1];
        const double x1 = xvalues[idx];
        const double y0 = yvalues[idx - 1];
        const double y1 = yvalues[idx];
        auto [a0, a1] = line(x0, y0, x1, y1);
        std::cout << "(x0,y0)=(" << x0 << "," << y0 << ")" << std::endl;
        std::cout << "(x1,y1)=(" << x1 << "," << y1 << ")" << std::endl;
        std::cout << "(a0,a1)=(" << a0 << "," << a1 << ")" << std::endl;
        std::cout << "x=" << x << std::endl;
        std::cout << "interpolated value:" << lininterp(a0, a1, x) << std::endl;
        std::cout << "true value:" << std::cos(x) << std::endl;
    }
}

} // namespace nmx::apps::x027