source: branches/CEDMA-Exporter-715/sources/HeuristicLab.LinearRegression/3.2/alglib/lq.cs @ 2273

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

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  in this license in the documentation and/or other materials
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  contributors may be used to endorse or promote products derived from
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"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
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*************************************************************************/

using System;

class lq
{
    /*************************************************************************
    LQ decomposition of a rectangular matrix of size MxN

    Input parameters:
        A   -   matrix A whose indexes range within [0..M-1, 0..N-1].
        M   -   number of rows in matrix A.
        N   -   number of columns in matrix A.

    Output parameters:
        A   -   matrices L and Q in compact form (see below)
        Tau -   array of scalar factors which are used to form
                matrix Q. Array whose index ranges within [0..Min(M,N)-1].

    Matrix A is represented as A = LQ, where Q is an orthogonal matrix of size
    MxM, L - lower triangular (or lower trapezoid) matrix of size M x N.

    The elements of matrix L are located on and below  the  main  diagonal  of
    matrix A. The elements which are located in Tau array and above  the  main
    diagonal of matrix A are used to form matrix Q as follows:

    Matrix Q is represented as a product of elementary reflections

    Q = H(k-1)*H(k-2)*...*H(1)*H(0),

    where k = min(m,n), and each H(i) is of the form

    H(i) = 1 - tau * v * (v^T)

    where tau is a scalar stored in Tau[I]; v - real vector, so that v(0:i-1)=0,
    v(i) = 1, v(i+1:n-1) stored in A(i,i+1:n-1).

      -- ALGLIB --
         Copyright 2005-2007 by Bochkanov Sergey
    *************************************************************************/
    public static void rmatrixlq(ref double[,] a,
        int m,
        int n,
        ref double[] tau)
    {
        double[] work = new double[0];
        double[] t = new double[0];
        int i = 0;
        int k = 0;
        int minmn = 0;
        int maxmn = 0;
        double tmp = 0;
        int i_ = 0;
        int i1_ = 0;

        minmn = Math.Min(m, n);
        maxmn = Math.Max(m, n);
        work = new double[m+1];
        t = new double[n+1];
        tau = new double[minmn-1+1];
        k = Math.Min(m, n);
        for(i=0; i<=k-1; i++)
        {
            
            //
            // Generate elementary reflector H(i) to annihilate A(i,i+1:n-1)
            //
            i1_ = (i) - (1);
            for(i_=1; i_<=n-i;i_++)
            {
                t[i_] = a[i,i_+i1_];
            }
            reflections.generatereflection(ref t, n-i, ref tmp);
            tau[i] = tmp;
            i1_ = (1) - (i);
            for(i_=i; i_<=n-1;i_++)
            {
                a[i,i_] = t[i_+i1_];
            }
            t[1] = 1;
            if( i<n )
            {
                
                //
                // Apply H(i) to A(i+1:m,i:n) from the right
                //
                reflections.applyreflectionfromtheright(ref a, tau[i], ref t, i+1, m-1, i, n-1, ref work);
            }
        }
    }


    /*************************************************************************
    Partial unpacking of matrix Q from the LQ decomposition of a matrix A

    Input parameters:
        A       -   matrices L and Q in compact form.
                    Output of RMatrixLQ subroutine.
        M       -   number of rows in given matrix A. M>=0.
        N       -   number of columns in given matrix A. N>=0.
        Tau     -   scalar factors which are used to form Q.
                    Output of the RMatrixLQ subroutine.
        QRows   -   required number of rows in matrix Q. N>=QRows>=0.

    Output parameters:
        Q       -   first QRows rows of matrix Q. Array whose indexes range
                    within [0..QRows-1, 0..N-1]. If QRows=0, the array remains
                    unchanged.

      -- ALGLIB --
         Copyright 2005 by Bochkanov Sergey
    *************************************************************************/
    public static void rmatrixlqunpackq(ref double[,] a,
        int m,
        int n,
        ref double[] tau,
        int qrows,
        ref double[,] q)
    {
        int i = 0;
        int j = 0;
        int k = 0;
        int minmn = 0;
        double[] v = new double[0];
        double[] work = new double[0];
        int i_ = 0;
        int i1_ = 0;

        System.Diagnostics.Debug.Assert(qrows<=n, "RMatrixLQUnpackQ: QRows>N!");
        if( m<=0 | n<=0 | qrows<=0 )
        {
            return;
        }
        
        //
        // init
        //
        minmn = Math.Min(m, n);
        k = Math.Min(minmn, qrows);
        q = new double[qrows-1+1, n-1+1];
        v = new double[n+1];
        work = new double[qrows+1];
        for(i=0; i<=qrows-1; i++)
        {
            for(j=0; j<=n-1; j++)
            {
                if( i==j )
                {
                    q[i,j] = 1;
                }
                else
                {
                    q[i,j] = 0;
                }
            }
        }
        
        //
        // unpack Q
        //
        for(i=k-1; i>=0; i--)
        {
            
            //
            // Apply H(i)
            //
            i1_ = (i) - (1);
            for(i_=1; i_<=n-i;i_++)
            {
                v[i_] = a[i,i_+i1_];
            }
            v[1] = 1;
            reflections.applyreflectionfromtheright(ref q, tau[i], ref v, 0, qrows-1, i, n-1, ref work);
        }
    }


    /*************************************************************************
    Unpacking of matrix L from the LQ decomposition of a matrix A

    Input parameters:
        A       -   matrices Q and L in compact form.
                    Output of RMatrixLQ subroutine.
        M       -   number of rows in given matrix A. M>=0.
        N       -   number of columns in given matrix A. N>=0.

    Output parameters:
        L       -   matrix L, array[0..M-1, 0..N-1].

      -- ALGLIB --
         Copyright 2005 by Bochkanov Sergey
    *************************************************************************/
    public static void rmatrixlqunpackl(ref double[,] a,
        int m,
        int n,
        ref double[,] l)
    {
        int i = 0;
        int k = 0;
        int i_ = 0;

        if( m<=0 | n<=0 )
        {
            return;
        }
        l = new double[m-1+1, n-1+1];
        for(i=0; i<=n-1; i++)
        {
            l[0,i] = 0;
        }
        for(i=1; i<=m-1; i++)
        {
            for(i_=0; i_<=n-1;i_++)
            {
                l[i,i_] = l[0,i_];
            }
        }
        for(i=0; i<=m-1; i++)
        {
            k = Math.Min(i, n-1);
            for(i_=0; i_<=k;i_++)
            {
                l[i,i_] = a[i,i_];
            }
        }
    }


    /*************************************************************************
    Obsolete 1-based subroutine
    See RMatrixLQ for 0-based replacement.
    *************************************************************************/
    public static void lqdecomposition(ref double[,] a,
        int m,
        int n,
        ref double[] tau)
    {
        double[] work = new double[0];
        double[] t = new double[0];
        int i = 0;
        int k = 0;
        int nmip1 = 0;
        int minmn = 0;
        int maxmn = 0;
        double tmp = 0;
        int i_ = 0;
        int i1_ = 0;

        minmn = Math.Min(m, n);
        maxmn = Math.Max(m, n);
        work = new double[m+1];
        t = new double[n+1];
        tau = new double[minmn+1];
        
        //
        // Test the input arguments
        //
        k = Math.Min(m, n);
        for(i=1; i<=k; i++)
        {
            
            //
            // Generate elementary reflector H(i) to annihilate A(i,i+1:n)
            //
            nmip1 = n-i+1;
            i1_ = (i) - (1);
            for(i_=1; i_<=nmip1;i_++)
            {
                t[i_] = a[i,i_+i1_];
            }
            reflections.generatereflection(ref t, nmip1, ref tmp);
            tau[i] = tmp;
            i1_ = (1) - (i);
            for(i_=i; i_<=n;i_++)
            {
                a[i,i_] = t[i_+i1_];
            }
            t[1] = 1;
            if( i<n )
            {
                
                //
                // Apply H(i) to A(i+1:m,i:n) from the right
                //
                reflections.applyreflectionfromtheright(ref a, tau[i], ref t, i+1, m, i, n, ref work);
            }
        }
    }


    /*************************************************************************
    Obsolete 1-based subroutine
    See RMatrixLQUnpackQ for 0-based replacement.
    *************************************************************************/
    public static void unpackqfromlq(ref double[,] a,
        int m,
        int n,
        ref double[] tau,
        int qrows,
        ref double[,] q)
    {
        int i = 0;
        int j = 0;
        int k = 0;
        int minmn = 0;
        double[] v = new double[0];
        double[] work = new double[0];
        int vm = 0;
        int i_ = 0;
        int i1_ = 0;

        System.Diagnostics.Debug.Assert(qrows<=n, "UnpackQFromLQ: QRows>N!");
        if( m==0 | n==0 | qrows==0 )
        {
            return;
        }
        
        //
        // init
        //
        minmn = Math.Min(m, n);
        k = Math.Min(minmn, qrows);
        q = new double[qrows+1, n+1];
        v = new double[n+1];
        work = new double[qrows+1];
        for(i=1; i<=qrows; i++)
        {
            for(j=1; j<=n; j++)
            {
                if( i==j )
                {
                    q[i,j] = 1;
                }
                else
                {
                    q[i,j] = 0;
                }
            }
        }
        
        //
        // unpack Q
        //
        for(i=k; i>=1; i--)
        {
            
            //
            // Apply H(i)
            //
            vm = n-i+1;
            i1_ = (i) - (1);
            for(i_=1; i_<=vm;i_++)
            {
                v[i_] = a[i,i_+i1_];
            }
            v[1] = 1;
            reflections.applyreflectionfromtheright(ref q, tau[i], ref v, 1, qrows, i, n, ref work);
        }
    }


    /*************************************************************************
    Obsolete 1-based subroutine
    *************************************************************************/
    public static void lqdecompositionunpacked(double[,] a,
        int m,
        int n,
        ref double[,] l,
        ref double[,] q)
    {
        int i = 0;
        int j = 0;
        double[] tau = new double[0];

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

        if( n<=0 )
        {
            return;
        }
        q = new double[n+1, n+1];
        l = new double[m+1, n+1];
        
        //
        // LQDecomposition
        //
        lqdecomposition(ref a, m, n, ref tau);
        
        //
        // L
        //
        for(i=1; i<=m; i++)
        {
            for(j=1; j<=n; j++)
            {
                if( j>i )
                {
                    l[i,j] = 0;
                }
                else
                {
                    l[i,j] = a[i,j];
                }
            }
        }
        
        //
        // Q
        //
        unpackqfromlq(ref a, m, n, ref tau, n, ref q);
    }
}