# Java Program to Perform LU Decomposition of any Matrix

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This is a java program to LU Decomposition of a given matrix. LU decomposition is the process of reducing single matrix into 2 matrices such that, upon multiplication we get the original matrix, having property that one of them is lower trinagular matrix and other one is upper trinagular matrix.

Here is the source code of the Java Program to Perform LU Decomposition of any Matrix. The Java program is successfully compiled and run on a Windows system. The program output is also shown below.

1. `//This is a sample program to calulate the LU decomposition of the given matrix`
2. `import java.util.Scanner;`
3. ` `
4. `public class LUDecomposition`
5. `{`
6. `    public static void main(String args[])`
7. `    {`
8. `        System.out.println("Enter the dimension of the matrix:");`
9. `        Scanner sc = new Scanner(System.in);`
10. `        int n = sc.nextInt();`
11. `        double [][]mat = new double[n][n];`
12. `        for(int i=0; i<n; i++)`
13. `            for(int j=0; j<n; j++)`
14. `                mat[i][j] = sc.nextDouble();`
15. ` `
16. `        if(n==2)`
17. `        {`
18. `            double [][]l = new double[n][n];`
19. `            l[0][0] = l[1][1] = 1;`
20. `            l[0][1] = 0;`
21. ` `
22. `            double [][]u = new double[n][n];`
23. `            u[1][0] = 0;`
24. ` `
25. `            u[0][0] = mat[0][0];`
26. `            u[0][1] = mat[0][1];`
27. ` `
28. `            l[1][0] = mat[1][0]/mat[0][0];`
29. `            u[1][1] = mat[1][1] - (l[1][0]*u[0][1]);   //mat[2][2]-(mat[2][1]*mat[1][2]/mat[1][1]);`
30. ` `
31. `            System.out.println("The L Component is:");`
32. `            for(int i=0; i<n; i++)`
33. `            {`
34. `                for(int j=0; j<n; j++)`
35. `                    System.out.print(" "+l[i][j]);`
36. `                System.out.println();`
37. `            }`
38. `            System.out.println("The U Component is:");`
39. `            for(int i=0; i<n; i++)`
40. `            {`
41. `                for(int j=0; j<n; j++)`
42. `                    System.out.print(" "+u[i][j]);`
43. `                System.out.println();`
44. `            }`
45. ` `
46. `        }`
47. `        if(n==3)`
48. `        {`
49. `            double [][]l = new double[n][n];`
50. `            l[0][0] = l[1][1] = l[2][2] = 1;`
51. `            l[0][1] = l[0][2] = l[1][2] = 0;`
52. ` `
53. `            double [][]u = new double[n][n];`
54. `            u[1][0] = u[2][0] = u[2][1] = 0;`
55. ` `
56. `            u[0][0] = mat[0][0];`
57. `            u[0][1] = mat[0][1];`
58. `            u[0][2] = mat[0][2];`
59. ` `
60. `            l[1][0] = mat[1][0]/mat[0][0];`
61. `            u[1][1] = mat[1][1] - (l[1][0]*u[0][1]);   //mat[2][2]-(mat[2][1]*mat[1][2]/mat[1][1]);`
62. `            u[1][2] = mat[1][2] - (l[1][0]*u[0][2]);`
63. ` `
64. `            l[2][0] = mat[2][0]/u[0][0];`
65. `            l[2][1] = (mat[2][1] - l[2][1]*u[0][1])/u[1][1];`
66. `            u[2][2] = mat[2][2] - (l[2][0]*u[0][2]) - (l[2][1]*u[1][2]);`
67. ` `
68. `            System.out.println("The L Component is:");`
69. `            for(int i=0; i<n; i++)`
70. `            {`
71. `                for(int j=0; j<n; j++)`
72. `                    System.out.print(" "+l[i][j]);`
73. `                System.out.println();`
74. `            }`
75. `            System.out.println("The U Component is:");`
76. `            for(int i=0; i<n; i++)`
77. `            {`
78. `                for(int j=0; j<n; j++)`
79. `                    System.out.print(" "+u[i][j]);`
80. `                System.out.println();`
81. `            }`
82. `        }`
83. `        sc.close();`
84. `    }`
85. `}`

Output:

```\$ javac LUDecomposition.java
\$ java LUDecomposition.java
Enter the dimension of the matrix:
3
2 3 1
4 5 1
1 1 1
The L Component is:
1.0 0.0 0.0
2.0 1.0 0.0
0.5 -1.0 1.0
The U Component is:
2.0 3.0 1.0
0.0 -1.0 -1.0
0.0 0.0 -0.5```

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