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Gauss Jordan JAVA

ini adalah algoritma gauss jordan untuk menyelesaikan persamaan linier
ini adalah class Gauss_Jordan_Elimination

package gausjordan;


import gauss_jordan.*;
import Database.Data;
import java.util.LinkedList;
 import java.util.Scanner;
 

 public class Gauss_Jordan_Elimination 

 {

 private static final double EPSILON = 1e-8;

 

 private final int N; // N-by-N system

 private double[][] a; // N-by-N+1 augmented matrix

 

 // Gauss-Jordan elimination with partial pivoting
 
 public Gauss_Jordan_Elimination(){
 N=0;
 }
 
 public Gauss_Jordan_Elimination(double[][] A, double[] b) 

 {

 N = b.length;

 

 // build augmented matrix

 a = new double[N][N+N+1];

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

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

 a[i][j] = A[i][j];

 

 // only need if you want to find certificate of infeasibility (or compute inverse)

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

 a[i][N+i] = 1.0;

 

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

 a[i][N+N] = b[i];

 

 solve();

 

 assert check(A, b);

 }
 
 

 private void solve() 

 {

 // Gauss-Jordan elimination

 for (int p = 0; p < N; p++) 

 {

 int max = p;

 for (int i = p+1; i < N; i++) 

 {

 if (Math.abs(a[i][p]) > Math.abs(a[max][p])) 

 {

 max = i;

 }

 }

 

 // exchange row p with row max

 swap(p, max);

 

 // singular or nearly singular

 if (Math.abs(a[p][p]) <= EPSILON) 

 {

 continue;

 // throw new RuntimeException("Matrix is singular or nearly singular");

 }

 

 // pivot

 pivot(p, p);

 }

 // show();

 }

 

 // swap row1 and row2

 private void swap(int row1, int row2) 

 {

 double[] temp = a[row1];

 a[row1] = a[row2];

 a[row2] = temp;

 }

 

 

 // pivot on entry (p, q) using Gauss-Jordan elimination

 private void pivot(int p, int q) 

 { // everything but row p and column q

 for (int i = 0; i < N; i++) {

 double alpha = a[i][q] / a[p][q];

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

 {

 if (i != p && j != q) a[i][j] -= alpha * a[p][j];

 }

 }

 

 // zero out column q

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

 if (i != p) a[i][q] = 0.0;

 

 // scale row p (ok to go from q+1 to N, but do this for consistency with simplex pivot)

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

 if (j != q) a[p][j] /= a[p][q];

 a[p][q] = 1.0;

 }

 

 // extract solution to Ax = b

 public double[] primal() 

 {

 double[] x = new double[N];

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

 {

 if (Math.abs(a[i][i]) > EPSILON)

 x[i] = a[i][N+N] / a[i][i];

 else if (Math.abs(a[i][N+N]) > EPSILON)

 return null;

 }

 return x;

 }

 

 // extract solution to yA = 0, yb != 0

 public double[] dual() 

 {

 double[] y = new double[N];

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

 {

 if ( (Math.abs(a[i][i]) <= EPSILON) && (Math.abs(a[i][N+N]) > EPSILON) ) 

 {

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

 y[j] = a[i][N+j];

 return y;

 }

 }

 return null;

 }

 

 // does the system have a solution?

 public boolean isFeasible() 

 {

 return primal() != null;

 }

 

 // print the tableaux

 private void show() 

 {

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

 {

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

 {

 System.out.print(" "+a[i][j]);

 }

 System.out.print("| ");

 for (int j = N; j < N+N; j++) 

 {

 System.out.print(" "+a[i][j]);

 }

 System.out.print("| "+a[i][N+N]);

 }

 System.out.println();

 }

 

 

 // check that Ax = b or yA = 0, yb != 0

 private boolean check(double[][] A, double[] b) 

 {

 

 // check that Ax = b

 if (isFeasible()) 

 {

 double[] x = primal();

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

 {

 double sum = 0.0;

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

 {

 sum += A[i][j] * x[j];

 }

 if (Math.abs(sum - b[i]) > EPSILON) 

 {

 System.out.println("not feasible");

 System.out.println(i+" = "+b[i]+", sum = "+sum+" ");

 return false;

 }

 }

 return true;

 }

 

 // or that yA = 0, yb != 0

 else 

 {

 double[] y = dual();

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

 {

 double sum = 0.0;

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

 {

 sum += A[i][j] * y[i];

 }

 if (Math.abs(sum) > EPSILON) 

 {

 System.out.println("invalid certificate of infeasibility");

 System.out.println("sum = "+sum+" ");

 return false;

 }

 }

 double sum = 0.0;

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

 {

 sum += y[i] * b[i];

 }

 if (Math.abs(sum) < EPSILON) 

 {

 System.out.println("invalid certificate of infeasibility");

 System.out.println("yb = "+sum+" ");

 

 return false;

 }

 return true;

 }

 }

 

 

 public double[] test(double[][] A, double[] b) 

 {

 Gauss_Jordan_Elimination gaussian = new Gauss_Jordan_Elimination(A, b);

 if (gaussian.isFeasible()) 

 {

 System.out.println("Solution to Ax = b");

 double[] x = gaussian.primal();

 for (int i = 0; i < x.length; i++) 

 {

 System.out.println(" "+x[i]+" ");

 }
 return x;
 }

 else 

 {

 System.out.println("Certificate of infeasibility");

 double[] y = gaussian.dual();

 for (int j = 0; j < y.length; j++) 

 {

 System.out.println(" "+y[j]+" ");

 }

 }

 System.out.println();
 return null;
 }

 

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