95 lines
3.4 KiB
Java
95 lines
3.4 KiB
Java
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/*
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This is a java program to LU Decomposition of a given matrix. LU decomposition is the process of
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reducing single matrix into 2 matrices such that, upon multiplication we get the original matrix,
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having property that one of them is lower trinagular matrix and other one is upper trinagular matrix.
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*/
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//This is a sample program to calulate the LU decomposition of the given matrix
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import java.util.Scanner;
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public class LUDecomposition
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{
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public static void main(String args[])
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{
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System.out.println("Enter the dimension of the matrix:");
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Scanner sc = new Scanner(System.in);
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int n = sc.nextInt();
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double [][]mat = new double[n][n];
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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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mat[i][j] = sc.nextDouble();
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if(n==2)
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{
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double [][]l = new double[n][n];
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l[0][0] = l[1][1] = 1;
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l[0][1] = 0;
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double [][]u = new double[n][n];
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u[1][0] = 0;
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u[0][0] = mat[0][0];
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u[0][1] = mat[0][1];
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l[1][0] = mat[1][0]/mat[0][0];
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u[1][1] = mat[1][1] - (l[1][0]*u[0][1]); //mat[2][2]-(mat[2][1]*mat[1][2]/mat[1][1]);
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System.out.println("The L Component is:");
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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.print(" "+l[i][j]);
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System.out.println();
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}
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System.out.println("The U Component is:");
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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.print(" "+u[i][j]);
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System.out.println();
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}
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}
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if(n==3)
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{
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double [][]l = new double[n][n];
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l[0][0] = l[1][1] = l[2][2] = 1;
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l[0][1] = l[0][2] = l[1][2] = 0;
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double [][]u = new double[n][n];
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u[1][0] = u[2][0] = u[2][1] = 0;
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u[0][0] = mat[0][0];
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u[0][1] = mat[0][1];
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u[0][2] = mat[0][2];
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l[1][0] = mat[1][0]/mat[0][0];
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u[1][1] = mat[1][1] - (l[1][0]*u[0][1]); //mat[2][2]-(mat[2][1]*mat[1][2]/mat[1][1]);
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u[1][2] = mat[1][2] - (l[1][0]*u[0][2]);
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l[2][0] = mat[2][0]/u[0][0];
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l[2][1] = (mat[2][1] - l[2][1]*u[0][1])/u[1][1];
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u[2][2] = mat[2][2] - (l[2][0]*u[0][2]) - (l[2][1]*u[1][2]);
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System.out.println("The L Component is:");
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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.print(" "+l[i][j]);
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System.out.println();
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}
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System.out.println("The U Component is:");
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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.print(" "+u[i][j]);
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System.out.println();
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}
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}
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sc.close();
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}
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}
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/*
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Enter the dimension of the matrix:
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3
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2 3 1
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4 5 1
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1 1 1
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The L Component is:
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1.0 0.0 0.0
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2.0 1.0 0.0
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0.5 -1.0 1.0
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The U Component is:
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2.0 3.0 1.0
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0.0 -1.0 -1.0
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0.0 0.0 -0.5
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