//Equipo: Norberto Suaste Hernandez (3088785) y Ana Patricia Diosdado Trejo (2980620)

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using System;

using System.Collections.Generic;

using System.Linq;

​

class Program

{

    static void Main()

    {

        // Definir los puntos de datos

        List<DataPoint> dataPoints = new List<DataPoint>

        {

            new DataPoint(1, 7.2074),

            new DataPoint(2, 10.5465),

            new DataPoint(3, 9.7056),

            new DataPoint(4, 8.2160),

            new DataPoint(5, 10.2054),

            new DataPoint(6, 16.6029),

            new DataPoint(7, 24.2849),

            new DataPoint(8, 28.9468),

            new DataPoint(9, 29.0606),

            new DataPoint(10, 27.2799)

        };

​

        // Estimación inicial de los parámetros

        double x1 = 1.0;

        double x2 = 1.0;

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        // Realizar ajuste de curva

        (double fittedX1, double fittedX2) = FitCurve(dataPoints, x1, x2);

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        Console.WriteLine($"Los parámetros ajustados son x1 = {fittedX1:F4}, x2 = {fittedX2:F4} y se aplicarán de la siguiente manera: ");

​

        // Imprimir los datos originales y los valores ajustados

        Console.WriteLine("\nt\tf(t)\tFitted f(t)");

        foreach (var point in dataPoints)

        {

            double fittedValue = FittedFunction(point.T, fittedX1, fittedX2);

            Console.WriteLine($"{point.T}\t{point.FT:F4}\t{fittedValue:F4}");

        }

    }

​

    static (double x1, double x2) FitCurve(List<DataPoint> dataPoints, double initialX1, double initialX2)

    {

        double x1 = initialX1;

        double x2 = initialX2;

        double learningRate = 0.0001;

        int iterations = 10000;

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        for (int i = 0; i < iterations; i++)

        {

            double sumErrorX1 = 0;

            double sumErrorX2 = 0;

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            foreach (var point in dataPoints)

            {

                double predicted = FittedFunction(point.T, x1, x2);

                double error = predicted - point.FT;

​

                sumErrorX1 += error * point.T;

                sumErrorX2 += error * Math.Sin(point.T);

            }

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            x1 -= learningRate * sumErrorX1 / dataPoints.Count;

            x2 -= learningRate * sumErrorX2 / dataPoints.Count;

        }

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        return (x1, x2);

    }

​

    static double FittedFunction(double t, double x1, double x2)

    {

        return x1 * t + x2 * Math.Sin(t);

    }

}

​

class DataPoint

{

    public double T { get; }

    public double FT { get; }

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    public DataPoint(double t, double ft)

    {

        T = t;

        FT = ft;

    }

}