QOD

using System;
using System.Collections.Generic;
using System.ComponentModel;
using System.Data;
using System.Drawing;
using System.Linq;
using System.Text;
using System.Windows.Forms;

namespace v0._1
{
    public partial class Form1 : Form
    {
        public Form1()
        {
            InitializeComponent();
        }

        /*

         -1/h^2(G[i+1,j]-2G[i,j]+G[i-1,j])
         -1/(h*r[i])(G[i+1,j]-G[i-1,j])
         -1/(k^2r[i]^2)(G[i,j+1]-2G[i,j]+G[i,j-1])
         -cot(t[j])/(2kr[i])(G[i,j+1]-G[i,j-1])+V[i,j]G[i,j]
         =Em(M,N)G[i,j]

         h=R/(M+1) k=pi/(2N+2)
         r[i]=(i-1)h t[j]=(j-1)k; 1=<i=<M+2, 1=<j=<N;

         formula se moze zapisati kao
         Em(M,N)G[i,j]=A[i,j]*G[i,j] + B[i,j]*G[i-1,j] + C[i,j]*G[i+1,j]
                                     + D[i,j]*G[i,j-1] + F[i,j]*G[i,j+1]
         A[i,j]= 2/h^2+2/(k^2r[i]^2)+V[i,j]
         B[i,j]= -1/h^2+1/(h*r[i])
         C[i,j]= -1/h^2-1/(h*r[i])
         D[i,j]= -1/(k^2r[i]^2)+cot(t[j])/(2kr[i])
         F[i,j]= -1/(k^2r[i]^2)-cot(t[j])/(2kr[i])
         V[i,j]= m*gama+m^2/(r[i] sin(t[j]))^2+(gama/2)^2 (r[i] sin(t[j]))^2-2/r[i]
        */




        private void Form1_Load(object sender, EventArgs e)
        {

        }

        private void button1_Click(object sender, EventArgs e)
        {
            double R = Convert.ToDouble(textBox1.Text); //poluprecnik QODa
            double gama=Convert.ToDouble(textBox4.Text); //jacina magnetnog polja
            double m=Convert.ToDouble(textBox5.Text); //magnetni kvantni broj

            int N = Convert.ToInt32(textBox2.Text);
            int M = Convert.ToInt32(textBox3.Text);  //dimenzije
            double h = R / (M + 1); // korak za r
            double k = Math.PI / (2 * N + 2); // korak za k
            double[] r = new double[M];
            double[] t = new double[N];



            for (int i = 1; i < M+3; i++)
            {
                r[i]=(i-1)*h;
            }

            for (int j = 1; j < N+3; j++)
            {
                t[j] = (j - 1) * k;
            }

            //Clanovi: V, A, B, C, D, F

            double[,] V = new double[M, N];
            for (int i = 1; i < M+3; i++)
            {
                for (int j = 1; j < N+3; j++)
                {
                    V[i, j] = m * gama + Math.Pow(m, 2) / Math.Pow((r[i] * Math.Sin(t[j])), 2) + Math.Pow((gama * r[i] * Math.Sin(t[j]) / 2), 2) - 2 / r[i];
                    j++;
                }
                i++;
            }

            double[,] A = new double[M, N];
            for (int i = 1; i < M + 3; i++)
            {
                for (int j = 1; j < N + 3; j++)
                {
                    A[i, j] = 2 / Math.Pow(h, 2) + 2 / Math.Pow(k * r[i], 2) + V[i, j];
                    j++;
                }
                i++;
            }

            double[,] B = new double[M, N];
            for (int i = 1; i < M + 3; i++)
            {
                for (int j = 1; j < N + 3; j++)
                {
                    B[i, j] = -1 / Math.Pow(h, 2) + 1 / (h * r[i]);
                    j++;
                }
                i++;
            }

            double[,] C = new double[M, N];
            for (int i = 1; i < M + 3; i++)
            {
                for (int j = 1; j < N + 3; j++)
                {
                    C[i, j] = -1 / Math.Pow(h, 2) - 1 / (h * r[i]);
                    j++;
                }
                i++;
            }

            double[,] D = new double[M, N];
            for (int i = 1; i < M + 3; i++)
            {
                for (int j = 1; j < N + 3; j++)
                {
                    D[i, j] = -1 / Math.Pow(k * r[i], 2) + 1 / (Math.Tan(t[j]) * 2 * k * Math.Pow(r[i], 2));
                    j++;
                }
                i++;
            }

            double[,] F = new double[M, N];
            for (int i = 1; i < M + 3; i++)
            {
                for (int j = 1; j < N + 3; j++)
                {
                    D[i, j] = -1 / Math.Pow(k * r[i], 2) - 1 / (Math.Tan(t[j]) * 2 * k * Math.Pow(r[i], 2));
                    j++;
                }
                i++;
            }

            // Matrica Lambda L
            double[,] L = new double[M * N, M * N];

            //postavljanje na 0
            for (int i = 1; i < M + 3; i++)
            {
                for (int j = 1; j < N + 3; j++)
                {
                    L[i, j] = 0;
                    j++;
                }
                i++;
            }
            //metoda za invernzne koordinate


            //postavljanje clanova
            {
                for (int i = 1; i < M+3; i++)
                {
                    int p = 0; int q = 0;


                    L[i, i] = A[i, i];
                    L[i, i - 1] = B[p, q];
                    L[i, i + 1] = C[p, q];
                    L[i, i - N] = D[p, q];
                    L[i, i + N] = F[p, q];
                }
            }


        }
    }
}