// Norberto Suaste Hernandez  3088785

// Ana Patricia Diosdado Trejo  2980620

​

using System;

​

public class ModeloTemperatura

{

    private readonly double[] _meses;

    private readonly double[] _temperaturas;

​

    public ModeloTemperatura(double[] meses, double[] temperaturas)

    {

        _meses = meses;

        _temperaturas = temperaturas;

    }

​

    public double[] AjustarModeloSenoidal()

    {

        int n = _meses.Length;

​

        double sumY = 0, sumSinX = 0, sumCosX = 0, sumYSinX = 0, sumYCosX = 0;

        double sumSinXSquared = 0, sumCosXSquared = 0, sumSinXCosX = 0;

​

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

        {

            double sinX = Math.Sin(_meses[i]);

            double cosX = Math.Cos(_meses[i]);

​

            sumY += _temperaturas[i];

            sumSinX += sinX;

            sumCosX += cosX;

            sumYSinX += _temperaturas[i] * sinX;

            sumYCosX += _temperaturas[i] * cosX;

            sumSinXSquared += sinX * sinX;

            sumCosXSquared += cosX * cosX;

            sumSinXCosX += sinX * cosX;

        }

​

        double[,] A = {

            { n, sumSinX, sumCosX },

            { sumSinX, sumSinXSquared, sumSinXCosX },

            { sumCosX, sumSinXCosX, sumCosXSquared }

        };

​

        double[] B = { sumY, sumYSinX, sumYCosX };

​

        double[] coeficientes = ResolverSistemaLineal(A, B);

        return coeficientes;

    }

​

    private static double[] ResolverSistemaLineal(double[,] A, double[] B)

    {

        int n = B.Length;

        double[,] augmentedMatrix = new double[n, n + 1];

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

        {

            for (int j = 0; j < n; j++)

            {

                augmentedMatrix[i, j] = A[i, j];

            }

            augmentedMatrix[i, n] = B[i];

        }

        for (int i = 0; i < n - 1; i++)

        {

            for (int k = i + 1; k < n; k++)

            {

                double factor = augmentedMatrix[k, i] / augmentedMatrix[i, i];

                for (int j = i; j <= n; j++)

                {

                    augmentedMatrix[k, j] -= factor * augmentedMatrix[i, j];

                }

            }

        }

        double[] x = new double[n];

        for (int i = n - 1; i >= 0; i--)

        {

            x[i] = augmentedMatrix[i, n];

            for (int j = i + 1; j < n; j++)

            {

                x[i] -= augmentedMatrix[i, j] * x[j];

            }

            x[i] /= augmentedMatrix[i, i];

        }

​

        return x;

    }

​

    public static void Main()

    {

        double[] mesesNuevaYork = { 1, 3, 4, 5, 8, 10, 11 };

        double[] temperaturasNuevaYork = { -8, 11, 23, 29, 35, 10, 2 };

        double[] mesesSantiago = { 1, 2, 4, 6, 8, 10, 12 };

        double[] temperaturasSantiago = { 25, 22, 16, 7, -2, 13, 21 };

        ModeloTemperatura modeloNuevaYork = new ModeloTemperatura(mesesNuevaYork, temperaturasNuevaYork);

        ModeloTemperatura modeloSantiago = new ModeloTemperatura(mesesSantiago, temperaturasSantiago);

        double[] coeficientesNuevaYork = modeloNuevaYork.AjustarModeloSenoidal();

        double[] coeficientesSantiago = modeloSantiago.AjustarModeloSenoidal();

        Console.WriteLine("Modelo para Nueva York:");

        Console.WriteLine($"f(x) = {coeficientesNuevaYork[0]} + {coeficientesNuevaYork[1]} * sin(x) + {coeficientesNuevaYork[2]} * cos(x)");

​

        Console.WriteLine("Modelo para Santiago de Chile:");

        Console.WriteLine($"f(x) = {coeficientesSantiago[0]} + {coeficientesSantiago[1]} * sin(x) + {coeficientesSantiago[2]} * cos(x)");

    }

}