source: trunk/sources/ALGLIB/hevd.cs @ 2636

/*************************************************************************
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 hevd
    {
        /*************************************************************************
        Finding the eigenvalues and eigenvectors of a Hermitian matrix

        The algorithm finds eigen pairs of a Hermitian matrix by  reducing  it  to
        real tridiagonal form and using the QL/QR algorithm.

        Input parameters:
            A       -   Hermitian matrix which is given  by  its  upper  or  lower
                        triangular part.
                        Array whose indexes range within [0..N-1, 0..N-1].
            N       -   size of matrix A.
            IsUpper -   storage format.
            ZNeeded -   flag controlling whether the eigenvectors  are  needed  or
                        not. If ZNeeded is equal to:
                         * 0, the eigenvectors are not returned;
                         * 1, the eigenvectors are returned.

        Output parameters:
            D       -   eigenvalues in ascending order.
                        Array whose index ranges within [0..N-1].
            Z       -   if ZNeeded is equal to:
                         * 0, Z hasn’t changed;
                         * 1, Z contains the eigenvectors.
                        Array whose indexes range within [0..N-1, 0..N-1].
                        The eigenvectors are stored in the matrix columns.

        Result:
            True, if the algorithm has converged.
            False, if the algorithm hasn't converged (rare case).

        Note:
            eigen vectors of Hermitian matrix are defined up to multiplication  by
            a complex number L, such as |L|=1.

          -- ALGLIB --
             Copyright 2005, 23 March 2007 by Bochkanov Sergey
        *************************************************************************/
        public static bool hmatrixevd(AP.Complex[,] a,
            int n,
            int zneeded,
            bool isupper,
            ref double[] d,
            ref AP.Complex[,] z)
        {
            bool result = new bool();
            AP.Complex[] tau = new AP.Complex[0];
            double[] e = new double[0];
            double[] work = new double[0];
            double[,] t = new double[0,0];
            AP.Complex[,] q = new AP.Complex[0,0];
            int i = 0;
            int k = 0;
            double v = 0;
            int i_ = 0;

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

            System.Diagnostics.Debug.Assert(zneeded==0 | zneeded==1, "HermitianEVD: incorrect ZNeeded");
            
            //
            // Reduce to tridiagonal form
            //
            htridiagonal.hmatrixtd(ref a, n, isupper, ref tau, ref d, ref e);
            if( zneeded==1 )
            {
                htridiagonal.hmatrixtdunpackq(ref a, n, isupper, ref tau, ref q);
                zneeded = 2;
            }
            
            //
            // TDEVD
            //
            result = tdevd.smatrixtdevd(ref d, e, n, zneeded, ref t);
            
            //
            // Eigenvectors are needed
            // Calculate Z = Q*T = Re(Q)*T + i*Im(Q)*T
            //
            if( result & zneeded!=0 )
            {
                work = new double[n-1+1];
                z = new AP.Complex[n-1+1, n-1+1];
                for(i=0; i<=n-1; i++)
                {
                    
                    //
                    // Calculate real part
                    //
                    for(k=0; k<=n-1; k++)
                    {
                        work[k] = 0;
                    }
                    for(k=0; k<=n-1; k++)
                    {
                        v = q[i,k].x;
                        for(i_=0; i_<=n-1;i_++)
                        {
                            work[i_] = work[i_] + v*t[k,i_];
                        }
                    }
                    for(k=0; k<=n-1; k++)
                    {
                        z[i,k].x = work[k];
                    }
                    
                    //
                    // Calculate imaginary part
                    //
                    for(k=0; k<=n-1; k++)
                    {
                        work[k] = 0;
                    }
                    for(k=0; k<=n-1; k++)
                    {
                        v = q[i,k].y;
                        for(i_=0; i_<=n-1;i_++)
                        {
                            work[i_] = work[i_] + v*t[k,i_];
                        }
                    }
                    for(k=0; k<=n-1; k++)
                    {
                        z[i,k].y = work[k];
                    }
                }
            }
            return result;
        }


        /*************************************************************************

          -- ALGLIB --
             Copyright 2005, 23 March 2007 by Bochkanov Sergey
        *************************************************************************/
        public static bool hermitianevd(AP.Complex[,] a,
            int n,
            int zneeded,
            bool isupper,
            ref double[] d,
            ref AP.Complex[,] z)
        {
            bool result = new bool();
            AP.Complex[] tau = new AP.Complex[0];
            double[] e = new double[0];
            double[] work = new double[0];
            double[,] t = new double[0,0];
            AP.Complex[,] q = new AP.Complex[0,0];
            int i = 0;
            int k = 0;
            double v = 0;
            int i_ = 0;

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

            System.Diagnostics.Debug.Assert(zneeded==0 | zneeded==1, "HermitianEVD: incorrect ZNeeded");
            
            //
            // Reduce to tridiagonal form
            //
            htridiagonal.hermitiantotridiagonal(ref a, n, isupper, ref tau, ref d, ref e);
            if( zneeded==1 )
            {
                htridiagonal.unpackqfromhermitiantridiagonal(ref a, n, isupper, ref tau, ref q);
                zneeded = 2;
            }
            
            //
            // TDEVD
            //
            result = tdevd.tridiagonalevd(ref d, e, n, zneeded, ref t);
            
            //
            // Eigenvectors are needed
            // Calculate Z = Q*T = Re(Q)*T + i*Im(Q)*T
            //
            if( result & zneeded!=0 )
            {
                work = new double[n+1];
                z = new AP.Complex[n+1, n+1];
                for(i=1; i<=n; i++)
                {
                    
                    //
                    // Calculate real part
                    //
                    for(k=1; k<=n; k++)
                    {
                        work[k] = 0;
                    }
                    for(k=1; k<=n; k++)
                    {
                        v = q[i,k].x;
                        for(i_=1; i_<=n;i_++)
                        {
                            work[i_] = work[i_] + v*t[k,i_];
                        }
                    }
                    for(k=1; k<=n; k++)
                    {
                        z[i,k].x = work[k];
                    }
                    
                    //
                    // Calculate imaginary part
                    //
                    for(k=1; k<=n; k++)
                    {
                        work[k] = 0;
                    }
                    for(k=1; k<=n; k++)
                    {
                        v = q[i,k].y;
                        for(i_=1; i_<=n;i_++)
                        {
                            work[i_] = work[i_] + v*t[k,i_];
                        }
                    }
                    for(k=1; k<=n; k++)
                    {
                        z[i,k].y = work[k];
                    }
                }
            }
            return result;
        }
    }
}