Class VisualNumerics.math.ComplexCholesky 
All Packages  Class Hierarchy  This Package  Previous  Next  Index

Class VisualNumerics.math.ComplexCholesky 

java.lang.Object
   |
   +----VisualNumerics.math.ComplexCholesky
public class ComplexCholesky
extends Object
Cholesky Decomposition of a Complex Hermitian positive definite matrix.

Constructor Index

o ComplexCholesky(Complex[][])
Construct the Cholesky decomposition of a Complex Hermitian positive definite matrix.

Method Index

o condition()
Return an estimate of the reciprocal of the L1 condition number of the Complex matrix used to construct this instance.
o determinant()
Return the determinant of the matrix used to construct this instance.
o inverse()
Return the inverse of the matrix used to construct this instance.
o R()
Return the Cholesky factorization of the Complex Hermitian positive definite matrix used to construct this instance.
o solve(Complex[])
Solve a complex Hermitian positive definite system of linear equations.

Constructors

o ComplexCholesky 
  public ComplexCholesky(Complex a[][]) throws IllegalArgumentException, MathException
Construct the Cholesky decomposition of a Complex Hermitian positive definite matrix.
Parameters:
a - Complex Hermitian positive definite matrix to be factored.
Throws: IllegalArgumentException
This exception is issued when the row lengths of input matrix a are not equal (i.e. the matrix edges are "jagged".)
Throws: MathException
This exception is issued when the input matrix a is not square or is not positive definite or some diagonal element is not real.
Algorithm:
The constructor computes an RHR Cholesky factorization of a complex matrix. The constructor is based on the LINPACK routine ZPOFA.
Dongarra, J.J., J.R. Bunch, C.B. Moler, and G.W. Stewart(1979), LINPACK Users' Guide, SIAM, Philadelphia.
Example: 
 import VisualNumerics.math.*;
 import java.io.*;
 class testCCholesky {
    public static void main(String args[]) {
       int      i, j, n=3;
       double   cond=0.0e0, dtrm=0.0e0;
       Complex r[][]=null, ainv[][], x[];
       Complex a[][] = new Complex[n][n];
       Complex b[] = new Complex[n];
       for(i=0; i < n; i++){
          for(int j=0; j < n; j++){
             a[i][j] = new Complex((double)(j+3*i), (double)(j-i));
             a[j][i] = new Complex(a[i][j].re, 0.0e0);
          }
          b[i] = new Complex((double)(7+i));
       }
       a = ComplexMatrix.multiply(a, ComplexMatrix.adjoint(a));
       try {
         ComplexCholesky cholesky = new ComplexCholesky(a);
         r = cholesky.R();
         x = cholesky.solve(b[i]);
         ainv = cholesky.inverse();
         cond = cholesky.condition();
         dtrm = cholesky.determinant();
           ... print output ...
       } catch (IllegalArgumentException e) {
         System.err.println("From testcomplexcholesky "+e);
       } catch (MathException e) {
         System.err.println("From testcomplexcholesky "+e);
       }
    }
 }

Methods

o solve 
  public static Complex[] solve(Complex b[]) throws MathException
Solve a complex Hermitian positive definite system of linear equations.
Parameters:
b - Complex vector containing the right-hand side of the linear system.
Returns:
A Complex vector containing the solution to the system of linear equations.
Throws: MathException
This exception is issued when the input matrix a is singular.
Algorithm:
The Cholesky constructor computes an RHR Cholesky factorization of a complex matrix. This factorization is then used to compute the solution for the system of linear equations. This method is based on the LINPACK routine ZPOSL.
o inverse 
  public static Complex[][] inverse() throws MathException
Return the inverse of the matrix used to construct this instance.
Returns:
A Complex[][] matrix containing the inverse of the matrix used to construct this instance.
Throws: MathException
This exception is issued when the input matrix a is singular.
o condition 
  public static double condition()
Return an estimate of the reciprocal of the L1 condition number of the Complex matrix used to construct this instance.
Returns:
A scalar of type double containing an estimate of the reciprocal of the L1 condition number of the Complex matrix used to construct this instance.
Algorithm:
The Cholesky constructor computes an RHR Cholesky factorization of a complex matrix. This factorization is then used by this method in determining the condition number. The L1 condition number of a matrix A is defined to be the 1-norm of A times the 1-norm of A inverse. Since it is expensive to compute the 1-norm of A inverse, the condition number is only estimated. The estimation algorithm is the same as used by LINPACK routine ZPOCO. A condition number less than approximately 2.22e-16 indicates that very small changes in A can cause very large changes in the solution x of a linear system involving A.
o R 
  public static Complex[][] R()
Return the Cholesky factorization of the Complex Hermitian positive definite matrix used to construct this instance.
Returns:
A Complex matrix containing the upper triangular matrix R of the factorization of the matrix used to construct this instance in the upper triangle.
Algorithm:
The Cholesky constructor computes an RHR Cholesky factorization of a complex matrix. This method returns the saved factorization.
o determinant 
  public static double determinant()
Return the determinant of the matrix used to construct this instance.
Returns:
A double scalar containing the determinant of the matrix used to construct this instance.
Algorithm:
The ComplexCholesky constructor computes an RHR factorization of the complex matrix. The product of the diagonal elements of R is then obtained. The product squared is the determinant of the input matrix. This method is based on LINPACK routine ZPODI. 
All Packages  Class Hierarchy  This Package  Previous  Next  Index