01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
 
package algs91; // section 9.9
import stdlib.*;
/* ***********************************************************************
 *  Compilation:  javac Cholesky.java
 *  Execution:    java Cholesky
 *
 *  Compute XCholesky decomposition of symmetric positive definite
 *  matrix A = LL^T.
 *
 *  % java Cholesky
 *  2.00000  0.00000  0.00000
 *  0.50000  2.17945  0.00000
 *  0.50000  1.26179  3.62738
 *
 *************************************************************************/

public class XCholesky {
  //private static final double EPSILON = 1e-10;

  // is symmetric
  public static boolean isSymmetric(double[][] A) {
    int N = A.length;
    for (int i = 0; i < N; i++) {
      for (int j = 0; j < i; j++) {
        if (A[i][j] != A[j][i]) return false;
      }
    }
    return true;
  }

  // is symmetric
  public static boolean isSquare(double[][] A) {
    int N = A.length;
    for (int i = 0; i < N; i++) {
      if (A[i].length != N) return false;
    }
    return true;
  }


  // return XCholesky factor L of psd matrix A = L L^T
  public static double[][] cholesky(double[][] A) {
    if (!isSquare(A)) {
      throw new Error("Matrix is not square");
    }
    if (!isSymmetric(A)) {
      throw new Error("Matrix is not symmetric");
    }

    int N  = A.length;
    double[][] L = new double[N][N];

    for (int i = 0; i < N; i++)  {
      for (int j = 0; j <= i; j++) {
        double sum = 0.0;
        for (int k = 0; k < j; k++) {
          sum += L[i][k] * L[j][k];
        }
        if (i == j) L[i][i] = Math.sqrt(A[i][i] - sum);
        else        L[i][j] = 1.0 / L[j][j] * (A[i][j] - sum);
      }
      if (L[i][i] <= 0) {
        throw new Error("Matrix not positive definite");
      }
    }
    return L;
  }


  // sample client
  public static void main(String[] args) {
    int N = 3;
    double[][] A = {
        { 4, 1,  1 },
        { 1, 5,  3 },
        { 1, 3, 15 }
    };
    double[][] L = cholesky(A);
    for (int i = 0; i < N; i++) {
      for (int j = 0; j < N; j++) {
        StdOut.format("%8.5f ", L[i][j]);
      }
      StdOut.println();
    }

  }

}