source: src/main/java/agents/Jama/CholeskyDecomposition.java

package agents.Jama;

   /** Cholesky Decomposition.
   <P>
   For a symmetric, positive definite matrix A, the Cholesky decomposition
   is an lower triangular matrix L so that A = L*L'.
   <P>
   If the matrix is not symmetric or positive definite, the constructor
   returns a partial decomposition and sets an internal flag that may
   be queried by the isSPD() method.
   */

public class CholeskyDecomposition implements java.io.Serializable {

/* ------------------------
   Class variables
 * ------------------------ */

   /** Array for internal storage of decomposition.
   @serial internal array storage.
   */
   private double[][] L;

   /** Row and column dimension (square matrix).
   @serial matrix dimension.
   */
   private int n;

   /** Symmetric and positive definite flag.
   @serial is symmetric and positive definite flag.
   */
   private boolean isspd;

/* ------------------------
   Constructor
 * ------------------------ */

   /** Cholesky algorithm for symmetric and positive definite matrix.
       Structure to access L and isspd flag.
   @param  Arg   Square, symmetric matrix.
   */

   public CholeskyDecomposition (Matrix Arg) {


     // Initialize.
      double[][] A = Arg.getArray();
      n = Arg.getRowDimension();
      L = new double[n][n];
      isspd = (Arg.getColumnDimension() == n);
      // Main loop.
      for (int j = 0; j < n; j++) {
         double[] Lrowj = L[j];
         double d = 0.0;
         for (int k = 0; k < j; k++) {
            double[] Lrowk = L[k];
            double s = 0.0;
            for (int i = 0; i < k; i++) {
               s += Lrowk[i]*Lrowj[i];
            }
            Lrowj[k] = s = (A[j][k] - s)/L[k][k];
            d = d + s*s;
            isspd = isspd & (A[k][j] == A[j][k]); 
         }
         d = A[j][j] - d;
         isspd = isspd & (d > 0.0);
         L[j][j] = Math.sqrt(Math.max(d,0.0));
         for (int k = j+1; k < n; k++) {
            L[j][k] = 0.0;
         }
      }
   }

/* ------------------------
   Temporary, experimental code.
 * ------------------------ *\

   \** Right Triangular Cholesky Decomposition.
   <P>
   For a symmetric, positive definite matrix A, the Right Cholesky
   decomposition is an upper triangular matrix R so that A = R'*R.
   This constructor computes R with the Fortran inspired column oriented
   algorithm used in LINPACK and MATLAB.  In Java, we suspect a row oriented,
   lower triangular decomposition is faster.  We have temporarily included
   this constructor here until timing experiments confirm this suspicion.
   *\

   \** Array for internal storage of right triangular decomposition. **\
   private transient double[][] R;

   \** Cholesky algorithm for symmetric and positive definite matrix.
   @param  A           Square, symmetric matrix.
   @param  rightflag   Actual value ignored.
   @return             Structure to access R and isspd flag.
   *\

   public CholeskyDecomposition (Matrix Arg, int rightflag) {
      // Initialize.
      double[][] A = Arg.getArray();
      n = Arg.getColumnDimension();
      R = new double[n][n];
      isspd = (Arg.getColumnDimension() == n);
      // Main loop.
      for (int j = 0; j < n; j++) {
         double d = 0.0;
         for (int k = 0; k < j; k++) {
            double s = A[k][j];
            for (int i = 0; i < k; i++) {
               s = s - R[i][k]*R[i][j];
            }
            R[k][j] = s = s/R[k][k];
            d = d + s*s;
            isspd = isspd & (A[k][j] == A[j][k]); 
         }
         d = A[j][j] - d;
         isspd = isspd & (d > 0.0);
         R[j][j] = Math.sqrt(Math.max(d,0.0));
         for (int k = j+1; k < n; k++) {
            R[k][j] = 0.0;
         }
      }
   }

   \** Return upper triangular factor.
   @return     R
   *\

   public Matrix getR () {
      return new Matrix(R,n,n);
   }

\* ------------------------
   End of temporary code.
 * ------------------------ */

/* ------------------------
   Public Methods
 * ------------------------ */

   /** Is the matrix symmetric and positive definite?
   @return     true if A is symmetric and positive definite.
   */

   public boolean isSPD () {
      return isspd;
   }

   /** Return triangular factor.
   @return     L
   */

   public Matrix getL () {
      return new Matrix(L,n,n);
   }

   /** Solve A*X = B
   @param  B   A Matrix with as many rows as A and any number of columns.
   @return     X so that L*L'*X = B
   @exception  IllegalArgumentException  Matrix row dimensions must agree.
   @exception  RuntimeException  Matrix is not symmetric positive definite.
   */

   public Matrix solve (Matrix B) {
      if (B.getRowDimension() != n) {
         throw new IllegalArgumentException("Matrix row dimensions must agree.");
      }
      if (!isspd) {
         throw new RuntimeException("Matrix is not symmetric positive definite.");
      }

      // Copy right hand side.
      double[][] X = B.getArrayCopy();
      int nx = B.getColumnDimension();

              // Solve L*Y = B;
              for (int k = 0; k < n; k++) {
                for (int j = 0; j < nx; j++) {
                   for (int i = 0; i < k ; i++) {
                       X[k][j] -= X[i][j]*L[k][i];
                   }
                   X[k][j] /= L[k][k];
                }
              }
        
              // Solve L'*X = Y;
              for (int k = n-1; k >= 0; k--) {
                for (int j = 0; j < nx; j++) {
                   for (int i = k+1; i < n ; i++) {
                       X[k][j] -= X[i][j]*L[i][k];
                   }
                   X[k][j] /= L[k][k];
                }
              }
      
      
      return new Matrix(X,n,nx);
   }
  private static final long serialVersionUID = 1;

}