121 lines
3.7 KiB
Java
121 lines
3.7 KiB
Java
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/*
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This is a Java Program to Implement Gaussian Elimination Algorithm. Gaussian elimination (also known as row reduction) is an algorithm for solving systems of linear equations.
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*/
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/**
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** Java Program to Implement Gaussian Elimination Algorithm
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**/
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import java.util.Scanner;
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/** Class GaussianElimination **/
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public class GaussianElimination
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{
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public void solve(double[][] A, double[] B)
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{
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int N = B.length;
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for (int k = 0; k < N; k++)
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{
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/** find pivot row **/
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int max = k;
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for (int i = k + 1; i < N; i++)
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if (Math.abs(A[i][k]) > Math.abs(A[max][k]))
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max = i;
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/** swap row in A matrix **/
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double[] temp = A[k];
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A[k] = A[max];
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A[max] = temp;
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/** swap corresponding values in constants matrix **/
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double t = B[k];
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B[k] = B[max];
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B[max] = t;
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/** pivot within A and B **/
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for (int i = k + 1; i < N; i++)
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{
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double factor = A[i][k] / A[k][k];
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B[i] -= factor * B[k];
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for (int j = k; j < N; j++)
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A[i][j] -= factor * A[k][j];
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}
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}
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/** Print row echelon form **/
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printRowEchelonForm(A, B);
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/** back substitution **/
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double[] solution = new double[N];
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for (int i = N - 1; i >= 0; i--)
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{
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double sum = 0.0;
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for (int j = i + 1; j < N; j++)
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sum += A[i][j] * solution[j];
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solution[i] = (B[i] - sum) / A[i][i];
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}
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/** Print solution **/
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printSolution(solution);
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}
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/** function to print in row echleon form **/
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public void printRowEchelonForm(double[][] A, double[] B)
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{
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int N = B.length;
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System.out.println("\nRow Echelon form : ");
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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; j++)
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System.out.printf("%.3f ", A[i][j]);
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System.out.printf("| %.3f\n", B[i]);
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}
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System.out.println();
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}
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/** function to print solution **/
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public void printSolution(double[] sol)
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{
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int N = sol.length;
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System.out.println("\nSolution : ");
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for (int i = 0; i < N; i++)
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System.out.printf("%.3f ", sol[i]);
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System.out.println();
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}
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/** Main function **/
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public static void main (String[] args)
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{
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Scanner scan = new Scanner(System.in);
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System.out.println("Gaussian Elimination Algorithm Test\n");
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/** Make an object of GaussianElimination class **/
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GaussianElimination ge = new GaussianElimination();
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System.out.println("\nEnter number of variables");
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int N = scan.nextInt();
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double[] B = new double[N];
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double[][] A = new double[N][N];
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System.out.println("\nEnter "+ N +" equations coefficients ");
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for (int i = 0; i < N; i++)
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for (int j = 0; j < N; j++)
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A[i][j] = scan.nextDouble();
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System.out.println("\nEnter "+ N +" solutions");
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for (int i = 0; i < N; i++)
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B[i] = scan.nextDouble();
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ge.solve(A,B);
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}
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}
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/*
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Enter number of variables
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3
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Enter 3 equations coefficients
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2 1 -1
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-3 -1 2
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-2 1 2
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Enter 3 solutions
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8
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-11
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-3
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Row Echelon form :
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-3.000 -1.000 2.000 | -11.000
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0.000 1.667 0.667 | 4.333
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0.000 0.000 0.200 | -0.200
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Solution :
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2.000 3.000 -1.000
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