8/code/Chisl2sem1homework.cpp - master - levg/numm

8/code/Chisl2sem1homework.cpp
102 строки3 KB
Лев Черняховский
29 окт 2024, 10:38
29 окт 2024, 10:38d9048cd
#include <iostream>
#include <fstream>
#include <cmath>
#include <vector>
#include <string>
#define M_PI 3.141592653589793238462643383279
using namespace std;

double customFunction1(double x) {
    return x * log(x) - 0.5;
}

double customFunction2(double x) {
    return pow(x, 3) + (x >= 0 ? 1 : -1) * pow(x, 2) + 2;
}

double interpolateLagrange(const vector<double>& xValues, const vector<double>& yValues, double x) {
    double result = 0.0;
    int n = xValues.size();

    for (int i = 0; i < n; ++i) {
        double term = yValues[i];
        for (int j = 0; j < n; ++j) {
            if (i != j)
                term *= (x - xValues[j]) / (xValues[i] - xValues[j]);
        }
        result += term;
    }

    return result;
}

vector<double> generateUniformPoints(double a, double b, int n) {
    vector<double> points(n);
    for (int i = 0; i < n; ++i)
        points[i] = a + i * (b - a) / (n - 1);
    return points;
}

vector<double> generateChebyshevPoints(double a, double b, int n) {
    vector<double> points(n);
    for (int i = 0; i < n; ++i)
        points[i] = 0.5 * ((b - a) * cos(M_PI * (2 * i + 1) / (2 * n)) + (b + a));
    return points;
}

void computeErrorAndSave(const vector<double>& xValues, const vector<double>& yValues, double(*function)(double), const string& filename, int testPoints = 100) {
    ofstream outFile(filename);
    double a = xValues.front(), b = xValues.back();
    double maxError = 0.0;

    for (int i = 0; i <= testPoints; ++i) {
        double x = a + i * (b - a) / testPoints;
        double actualValue = function(x);
        double interpolatedValue = interpolateLagrange(xValues, yValues, x);
        double error = fabs(actualValue - interpolatedValue);
        maxError = max(maxError, error);

        outFile << x << " " << actualValue << " " << interpolatedValue << " " << error << endl;
    }

    outFile.close();
    cout << "Max error saved in " << filename << ": " << maxError << endl;
}

int main() {
    double intervalStart = 1.0, intervalEnd = 5.0;
    vector<int> nodeCounts;
    for (int n = 5; n <= 100; ++n) {
        nodeCounts.push_back(n);
    }

    for (int n : nodeCounts) {
        vector<double> uniformX = generateUniformPoints(intervalStart, intervalEnd, n);
        vector<double> chebyshevX = generateChebyshevPoints(intervalStart, intervalEnd, n);
        vector<double> uniformY(n), chebyshevY(n);

        for (int i = 0; i < n; ++i) {
            uniformY[i] = customFunction1(uniformX[i]);
            chebyshevY[i] = customFunction1(chebyshevX[i]);
        }

        computeErrorAndSave(uniformX, uniformY, customFunction1, "error_uniform_func1_" + to_string(n) + ".txt");
        computeErrorAndSave(chebyshevX, chebyshevY, customFunction1, "error_chebyshev_func1_" + to_string(n) + ".txt");
    }

    for (int n : nodeCounts) {
        vector<double> uniformX2 = generateUniformPoints(intervalStart, intervalEnd, n);
        vector<double> chebyshevX2 = generateChebyshevPoints(intervalStart, intervalEnd, n);
        vector<double> uniformY2(n), chebyshevY2(n);

        for (int i = 0; i < n; ++i) {
            uniformY2[i] = customFunction2(uniformX2[i]);
            chebyshevY2[i] = customFunction2(chebyshevX2[i]);
        }

        computeErrorAndSave(uniformX2, uniformY2, customFunction2, "error_uniform_func2_" + to_string(n) + ".txt");
        computeErrorAndSave(chebyshevX2, chebyshevY2, customFunction2, "error_chebyshev_func2_" + to_string(n) + ".txt");
    }

    return 0;
}