source: trunk/sources/HeuristicLab.ExtLibs/HeuristicLab.ALGLIB/2.5.0/ALGLIB-2.5.0/matdet.cs @ 4068

/*************************************************************************
Copyright (c) 2005-2007, Sergey Bochkanov (ALGLIB project).

>>> SOURCE LICENSE >>>
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation (www.fsf.org); either version 2 of the 
License, or (at your option) any later version.

This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU General Public License for more details.

A copy of the GNU General Public License is available at
http://www.fsf.org/licensing/licenses

>>> END OF LICENSE >>>
*************************************************************************/


namespace alglib {
  public class matdet {
    /*************************************************************************
    Determinant calculation of the matrix given by its LU decomposition.

    Input parameters:
        A       -   LU decomposition of the matrix (output of
                    RMatrixLU subroutine).
        Pivots  -   table of permutations which were made during
                    the LU decomposition.
                    Output of RMatrixLU subroutine.
        N       -   size of matrix A.

    Result: matrix determinant.

      -- ALGLIB --
         Copyright 2005 by Bochkanov Sergey
    *************************************************************************/
    public static double rmatrixludet(ref double[,] a,
        ref int[] pivots,
        int n) {
      double result = 0;
      int i = 0;
      int s = 0;

      result = 1;
      s = 1;
      for (i = 0; i <= n - 1; i++) {
        result = result * a[i, i];
        if (pivots[i] != i) {
          s = -s;
        }
      }
      result = result * s;
      return result;
    }


    /*************************************************************************
    Calculation of the determinant of a general matrix

    Input parameters:
        A       -   matrix, array[0..N-1, 0..N-1]
        N       -   size of matrix A.

    Result: determinant of matrix A.

      -- ALGLIB --
         Copyright 2005 by Bochkanov Sergey
    *************************************************************************/
    public static double rmatrixdet(double[,] a,
        int n) {
      double result = 0;
      int[] pivots = new int[0];

      a = (double[,])a.Clone();

      trfac.rmatrixlu(ref a, n, n, ref pivots);
      result = rmatrixludet(ref a, ref pivots, n);
      return result;
    }


    /*************************************************************************
    Determinant calculation of the matrix given by its LU decomposition.

    Input parameters:
        A       -   LU decomposition of the matrix (output of
                    RMatrixLU subroutine).
        Pivots  -   table of permutations which were made during
                    the LU decomposition.
                    Output of RMatrixLU subroutine.
        N       -   size of matrix A.

    Result: matrix determinant.

      -- ALGLIB --
         Copyright 2005 by Bochkanov Sergey
    *************************************************************************/
    public static AP.Complex cmatrixludet(ref AP.Complex[,] a,
        ref int[] pivots,
        int n) {
      AP.Complex result = 0;
      int i = 0;
      int s = 0;

      result = 1;
      s = 1;
      for (i = 0; i <= n - 1; i++) {
        result = result * a[i, i];
        if (pivots[i] != i) {
          s = -s;
        }
      }
      result = result * s;
      return result;
    }


    /*************************************************************************
    Calculation of the determinant of a general matrix

    Input parameters:
        A       -   matrix, array[0..N-1, 0..N-1]
        N       -   size of matrix A.

    Result: determinant of matrix A.

      -- ALGLIB --
         Copyright 2005 by Bochkanov Sergey
    *************************************************************************/
    public static AP.Complex cmatrixdet(AP.Complex[,] a,
        int n) {
      AP.Complex result = 0;
      int[] pivots = new int[0];

      a = (AP.Complex[,])a.Clone();

      trfac.cmatrixlu(ref a, n, n, ref pivots);
      result = cmatrixludet(ref a, ref pivots, n);
      return result;
    }


    /*************************************************************************
    Determinant calculation of the matrix given by the Cholesky decomposition.

    Input parameters:
        A   -   Cholesky decomposition,
                output of SMatrixCholesky subroutine.
        N   -   size of matrix A.

    As the determinant is equal to the product of squares of diagonal elements,
    it’s not necessary to specify which triangle - lower or upper - the matrix
    is stored in.

    Result:
        matrix determinant.

      -- ALGLIB --
         Copyright 2005-2008 by Bochkanov Sergey
    *************************************************************************/
    public static double spdmatrixcholeskydet(ref double[,] a,
        int n) {
      double result = 0;
      int i = 0;

      result = 1;
      for (i = 0; i <= n - 1; i++) {
        result = result * AP.Math.Sqr(a[i, i]);
      }
      return result;
    }


    /*************************************************************************
    Determinant calculation of the symmetric positive definite matrix.

    Input parameters:
        A       -   matrix. Array with elements [0..N-1, 0..N-1].
        N       -   size of matrix A.
        IsUpper -   if IsUpper = True, then the symmetric matrix A is given by
                    its upper triangle, and the lower triangle isn’t used by
                    subroutine. Similarly, if IsUpper = False, then A is given
                    by its lower triangle.

    Result:
        determinant of matrix A.
        If matrix A is not positive definite, then subroutine returns -1.

      -- ALGLIB --
         Copyright 2005-2008 by Bochkanov Sergey
    *************************************************************************/
    public static double spdmatrixdet(double[,] a,
        int n,
        bool isupper) {
      double result = 0;

      a = (double[,])a.Clone();

      if (!trfac.spdmatrixcholesky(ref a, n, isupper)) {
        result = -1;
      } else {
        result = spdmatrixcholeskydet(ref a, n);
      }
      return result;
    }
  }
}