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/*
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This is java program to find the solution to the linear equations of any number of variables.
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The class provides a simple implementation of the Gauss-Seidel method.
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If the matrix isn’t diagonally dominant the program tries to convert it(if possible) by rearranging the rows.
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*/
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//This class provides a simple implementation of the GaussSeidel method for solving systems of linear equations.
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//If the matrix isn't diagonally dominant the program tries to convert it(if possible) by rearranging the rows.
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import java.io.BufferedReader;
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import java.io.IOException;
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import java.io.InputStreamReader;
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import java.io.PrintWriter;
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import java.util.Arrays;
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import java.util.StringTokenizer;
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public class Gauss_Seidel
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{
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public static final int MAX_ITERATIONS = 100;
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private double[][] M;
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public Gauss_Seidel(double [][] matrix)
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{
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M = matrix;
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}
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public void print()
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{
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int n = M.length;
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for (int i = 0; i < n; i++)
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{
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for (int j = 0; j < n + 1; j++)
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System.out.print(M[i][j] + " ");
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System.out.println();
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}
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}
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public boolean transformToDominant(int r, boolean[] V, int[] R)
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{
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int n = M.length;
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if (r == M.length)
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{
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double[][] T = new double[n][n+1];
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for (int i = 0; i < R.length; i++)
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{
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for (int j = 0; j < n + 1; j++)
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T[i][j] = M[R[i]][j];
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}
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M = T;
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return true;
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}
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for (int i = 0; i < n; i++)
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{
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if (V[i]) continue;
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double sum = 0;
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for (int j = 0; j < n; j++)
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sum += Math.abs(M[i][j]);
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if (2 * Math.abs(M[i][r]) > sum)
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{
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// diagonally dominant?
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V[i] = true;
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R[r] = i;
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if (transformToDominant(r + 1, V, R))
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return true;
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V[i] = false;
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}
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}
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return false;
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}
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public boolean makeDominant()
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{
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boolean[] visited = new boolean[M.length];
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int[] rows = new int[M.length];
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Arrays.fill(visited, false);
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return transformToDominant(0, visited, rows);
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}
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public void solve()
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{
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int iterations = 0;
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int n = M.length;
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double epsilon = 1e-15;
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double[] X = new double[n]; // Approximations
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double[] P = new double[n]; // Prev
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Arrays.fill(X, 0);
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while (true)
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{
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for (int i = 0; i < n; i++)
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{
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double sum = M[i][n]; // b_n
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for (int j = 0; j < n; j++)
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if (j != i)
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sum -= M[i][j] * X[j];
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// Update x_i to use in the next row calculation
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X[i] = 1/M[i][i] * sum;
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}
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System.out.print("X_" + iterations + " = {");
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for (int i = 0; i < n; i++)
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System.out.print(X[i] + " ");
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System.out.println("}");
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iterations++;
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if (iterations == 1)
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continue;
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boolean stop = true;
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for (int i = 0; i < n && stop; i++)
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if (Math.abs(X[i] - P[i]) > epsilon)
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stop = false;
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if (stop || iterations == MAX_ITERATIONS) break;
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P = (double[])X.clone();
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}
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}
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public static void main(String[] args) throws IOException
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{
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int n;
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double[][] M;
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BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
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PrintWriter writer = new PrintWriter(System.out, true);
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System.out.println("Enter the number of variables in the equation:");
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n = Integer.parseInt(reader.readLine());
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M = new double[n][n+1];
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System.out.println("Enter the augmented matrix:");
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for (int i = 0; i < n; i++)
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{
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StringTokenizer strtk = new StringTokenizer(reader.readLine());
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while (strtk.hasMoreTokens())
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for (int j = 0; j < n + 1 && strtk.hasMoreTokens(); j++)
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M[i][j] = Integer.parseInt(strtk.nextToken());
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}
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Gauss_Seidel gausSeidel = new Gauss_Seidel(M);
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if (!gausSeidel.makeDominant())
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{
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writer.println("The system isn't diagonally dominant: " +
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"The method cannot guarantee convergence.");
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}
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writer.println();
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gausSeidel.print();
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gausSeidel.solve();
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}
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}
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/*
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Enter the number of variables in the equation:
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2
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Enter the augmented matrix:
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1 2 3
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6 5 4
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6.0 5.0 4.0
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1.0 2.0 3.0
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X_0 = {0.6666666666666666 1.1666666666666667 }
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X_1 = {-0.30555555555555564 1.652777777777778 }
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X_2 = {-0.7106481481481481 1.855324074074074 }
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X_3 = {-0.8794367283950617 1.9397183641975309 }
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X_4 = {-0.9497653034979425 1.9748826517489713 }
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X_5 = {-0.9790688764574759 1.9895344382287379 }
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X_6 = {-0.9912786985239483 1.9956393492619742 }
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X_7 = {-0.9963661243849785 1.9981830621924892 }
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X_8 = {-0.9984858851604077 1.9992429425802039 }
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X_9 = {-0.9993691188168363 1.999684559408418 }
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X_10 = {-0.9997371328403484 1.999868566420174 }
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X_11 = {-0.9998904720168117 1.9999452360084058 }
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X_12 = {-0.999954363340338 1.999977181670169 }
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X_13 = {-0.9999809847251406 1.9999904923625702 }
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X_14 = {-0.9999920769688085 1.9999960384844042 }
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X_15 = {-0.9999966987370034 1.9999983493685016 }
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X_16 = {-0.9999986244737512 1.9999993122368755 }
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X_17 = {-0.9999994268640631 1.9999997134320315 }
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X_18 = {-0.9999997611933598 1.9999998805966799 }
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X_19 = {-0.9999999004972331 1.9999999502486165 }
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X_20 = {-0.9999999585405137 1.9999999792702567 }
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X_21 = {-0.999999982725214 1.999999991362607 }
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X_22 = {-0.9999999928021724 1.9999999964010862 }
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X_23 = {-0.999999997000905 1.9999999985004524 }
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X_24 = {-0.999999998750377 1.9999999993751885 }
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X_25 = {-0.9999999994793237 1.9999999997396618 }
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X_26 = {-0.9999999997830514 1.9999999998915257 }
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X_27 = {-0.9999999999096048 1.9999999999548024 }
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X_28 = {-0.9999999999623352 1.9999999999811675 }
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X_29 = {-0.9999999999843061 1.999999999992153 }
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X_30 = {-0.9999999999934606 1.9999999999967302 }
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X_31 = {-0.9999999999972751 1.9999999999986375 }
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X_32 = {-0.9999999999988646 1.9999999999994322 }
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X_33 = {-0.9999999999995268 1.9999999999997633 }
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X_34 = {-0.9999999999998028 1.9999999999999014 }
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X_35 = {-0.9999999999999176 1.9999999999999587 }
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X_36 = {-0.9999999999999656 1.9999999999999827 }
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X_37 = {-0.9999999999999855 1.9999999999999927 }
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X_38 = {-0.9999999999999938 1.999999999999997 }
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X_39 = {-0.9999999999999973 1.9999999999999987 }
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X_40 = {-0.9999999999999988 1.9999999999999993 }
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X_41 = {-0.9999999999999993 1.9999999999999996 } |