source: trunk/sources/ALGLIB/sdet.cs @ 2578

/*************************************************************************
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 >>>
*************************************************************************/

using System;

namespace alglib
{
    public class sdet
    {
        /*************************************************************************
        Determinant calculation of the matrix given by LDLT decomposition.

        Input parameters:
            A       -   LDLT-decomposition of the matrix,
                        output of subroutine SMatrixLDLT.
            Pivots  -   table of permutations which were made during
                        LDLT decomposition, output of subroutine SMatrixLDLT.
            N       -   size of matrix A.
            IsUpper -   matrix storage format. The value is equal to the input
                        parameter of subroutine SMatrixLDLT.

        Result:
            matrix determinant.

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

            result = 1;
            if( isupper )
            {
                k = 0;
                while( k<n )
                {
                    if( pivots[k]>=0 )
                    {
                        result = result*a[k,k];
                        k = k+1;
                    }
                    else
                    {
                        result = result*(a[k,k]*a[k+1,k+1]-a[k,k+1]*a[k,k+1]);
                        k = k+2;
                    }
                }
            }
            else
            {
                k = n-1;
                while( k>=0 )
                {
                    if( pivots[k]>=0 )
                    {
                        result = result*a[k,k];
                        k = k-1;
                    }
                    else
                    {
                        result = result*(a[k-1,k-1]*a[k,k]-a[k,k-1]*a[k,k-1]);
                        k = k-2;
                    }
                }
            }
            return result;
        }


        /*************************************************************************
        Determinant calculation of the symmetric matrix

        Input parameters:
            A       -   matrix. Array with elements [0..N-1, 0..N-1].
            N       -   size of matrix A.
            IsUpper -   if IsUpper = True, then 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.

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

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

            ldlt.smatrixldlt(ref a, n, isupper, ref pivots);
            result = smatrixldltdet(ref a, ref pivots, n, isupper);
            return result;
        }


        public static double determinantldlt(ref double[,] a,
            ref int[] pivots,
            int n,
            bool isupper)
        {
            double result = 0;
            int k = 0;

            result = 1;
            if( isupper )
            {
                k = 1;
                while( k<=n )
                {
                    if( pivots[k]>0 )
                    {
                        result = result*a[k,k];
                        k = k+1;
                    }
                    else
                    {
                        result = result*(a[k,k]*a[k+1,k+1]-a[k,k+1]*a[k,k+1]);
                        k = k+2;
                    }
                }
            }
            else
            {
                k = n;
                while( k>=1 )
                {
                    if( pivots[k]>0 )
                    {
                        result = result*a[k,k];
                        k = k-1;
                    }
                    else
                    {
                        result = result*(a[k-1,k-1]*a[k,k]-a[k,k-1]*a[k,k-1]);
                        k = k-2;
                    }
                }
            }
            return result;
        }


        public static double determinantsymmetric(double[,] a,
            int n,
            bool isupper)
        {
            double result = 0;
            int[] pivots = new int[0];

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

            ldlt.ldltdecomposition(ref a, n, isupper, ref pivots);
            result = determinantldlt(ref a, ref pivots, n, isupper);
            return result;
        }
    }
}