source: trunk/sources/HeuristicLab.LinearRegression/3.2/alglib/reflections.cs @ 2211

/*************************************************************************
Copyright (c) 1992-2007 The University of Tennessee.  All rights reserved.

Contributors:
    * Sergey Bochkanov (ALGLIB project). Translation from FORTRAN to
      pseudocode.

See subroutines comments for additional copyrights.

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- Redistributions of source code must retain the above copyright
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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
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*************************************************************************/

using System;

class reflections
{
    /*************************************************************************
    Generation of an elementary reflection transformation

    The subroutine generates elementary reflection H of order N, so that, for
    a given X, the following equality holds true:

        ( X(1) )   ( Beta )
    H * (  ..  ) = (  0   )
        ( X(n) )   (  0   )

    where
                  ( V(1) )
    H = 1 - Tau * (  ..  ) * ( V(1), ..., V(n) )
                  ( V(n) )

    where the first component of vector V equals 1.

    Input parameters:
        X   -   vector. Array whose index ranges within [1..N].
        N   -   reflection order.

    Output parameters:
        X   -   components from 2 to N are replaced with vector V.
                The first component is replaced with parameter Beta.
        Tau -   scalar value Tau. If X is a null vector, Tau equals 0,
                otherwise 1 <= Tau <= 2.

    This subroutine is the modification of the DLARFG subroutines from
    the LAPACK library. It has a similar functionality except for the
    fact that it doesn’t handle errors when the intermediate results
    cause an overflow.


    MODIFICATIONS:
        24.12.2005 sign(Alpha) was replaced with an analogous to the Fortran SIGN code.

      -- LAPACK auxiliary routine (version 3.0) --
         Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
         Courant Institute, Argonne National Lab, and Rice University
         September 30, 1994
    *************************************************************************/
    public static void generatereflection(ref double[] x,
        int n,
        ref double tau)
    {
        int j = 0;
        double alpha = 0;
        double xnorm = 0;
        double v = 0;
        double beta = 0;
        double mx = 0;
        int i_ = 0;

        
        //
        // Executable Statements ..
        //
        if( n<=1 )
        {
            tau = 0;
            return;
        }
        
        //
        // XNORM = DNRM2( N-1, X, INCX )
        //
        alpha = x[1];
        mx = 0;
        for(j=2; j<=n; j++)
        {
            mx = Math.Max(Math.Abs(x[j]), mx);
        }
        xnorm = 0;
        if( mx!=0 )
        {
            for(j=2; j<=n; j++)
            {
                xnorm = xnorm+AP.Math.Sqr(x[j]/mx);
            }
            xnorm = Math.Sqrt(xnorm)*mx;
        }
        if( xnorm==0 )
        {
            
            //
            // H  =  I
            //
            tau = 0;
            return;
        }
        
        //
        // general case
        //
        mx = Math.Max(Math.Abs(alpha), Math.Abs(xnorm));
        beta = -(mx*Math.Sqrt(AP.Math.Sqr(alpha/mx)+AP.Math.Sqr(xnorm/mx)));
        if( alpha<0 )
        {
            beta = -beta;
        }
        tau = (beta-alpha)/beta;
        v = 1/(alpha-beta);
        for(i_=2; i_<=n;i_++)
        {
            x[i_] = v*x[i_];
        }
        x[1] = beta;
    }


    /*************************************************************************
    Application of an elementary reflection to a rectangular matrix of size MxN

    The algorithm pre-multiplies the matrix by an elementary reflection transformation
    which is given by column V and scalar Tau (see the description of the
    GenerateReflection procedure). Not the whole matrix but only a part of it
    is transformed (rows from M1 to M2, columns from N1 to N2). Only the elements
    of this submatrix are changed.

    Input parameters:
        C       -   matrix to be transformed.
        Tau     -   scalar defining the transformation.
        V       -   column defining the transformation.
                    Array whose index ranges within [1..M2-M1+1].
        M1, M2  -   range of rows to be transformed.
        N1, N2  -   range of columns to be transformed.
        WORK    -   working array whose indexes goes from N1 to N2.

    Output parameters:
        C       -   the result of multiplying the input matrix C by the
                    transformation matrix which is given by Tau and V.
                    If N1>N2 or M1>M2, C is not modified.

      -- LAPACK auxiliary routine (version 3.0) --
         Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
         Courant Institute, Argonne National Lab, and Rice University
         September 30, 1994
    *************************************************************************/
    public static void applyreflectionfromtheleft(ref double[,] c,
        double tau,
        ref double[] v,
        int m1,
        int m2,
        int n1,
        int n2,
        ref double[] work)
    {
        double t = 0;
        int i = 0;
        int vm = 0;
        int i_ = 0;

        if( tau==0 | n1>n2 | m1>m2 )
        {
            return;
        }
        
        //
        // w := C' * v
        //
        vm = m2-m1+1;
        for(i=n1; i<=n2; i++)
        {
            work[i] = 0;
        }
        for(i=m1; i<=m2; i++)
        {
            t = v[i+1-m1];
            for(i_=n1; i_<=n2;i_++)
            {
                work[i_] = work[i_] + t*c[i,i_];
            }
        }
        
        //
        // C := C - tau * v * w'
        //
        for(i=m1; i<=m2; i++)
        {
            t = v[i-m1+1]*tau;
            for(i_=n1; i_<=n2;i_++)
            {
                c[i,i_] = c[i,i_] - t*work[i_];
            }
        }
    }


    /*************************************************************************
    Application of an elementary reflection to a rectangular matrix of size MxN

    The algorithm post-multiplies the matrix by an elementary reflection transformation
    which is given by column V and scalar Tau (see the description of the
    GenerateReflection procedure). Not the whole matrix but only a part of it
    is transformed (rows from M1 to M2, columns from N1 to N2). Only the
    elements of this submatrix are changed.

    Input parameters:
        C       -   matrix to be transformed.
        Tau     -   scalar defining the transformation.
        V       -   column defining the transformation.
                    Array whose index ranges within [1..N2-N1+1].
        M1, M2  -   range of rows to be transformed.
        N1, N2  -   range of columns to be transformed.
        WORK    -   working array whose indexes goes from M1 to M2.

    Output parameters:
        C       -   the result of multiplying the input matrix C by the
                    transformation matrix which is given by Tau and V.
                    If N1>N2 or M1>M2, C is not modified.

      -- LAPACK auxiliary routine (version 3.0) --
         Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
         Courant Institute, Argonne National Lab, and Rice University
         September 30, 1994
    *************************************************************************/
    public static void applyreflectionfromtheright(ref double[,] c,
        double tau,
        ref double[] v,
        int m1,
        int m2,
        int n1,
        int n2,
        ref double[] work)
    {
        double t = 0;
        int i = 0;
        int vm = 0;
        int i_ = 0;
        int i1_ = 0;

        if( tau==0 | n1>n2 | m1>m2 )
        {
            return;
        }
        
        //
        // w := C * v
        //
        vm = n2-n1+1;
        for(i=m1; i<=m2; i++)
        {
            i1_ = (1)-(n1);
            t = 0.0;
            for(i_=n1; i_<=n2;i_++)
            {
                t += c[i,i_]*v[i_+i1_];
            }
            work[i] = t;
        }
        
        //
        // C := C - w * v'
        //
        for(i=m1; i<=m2; i++)
        {
            t = work[i]*tau;
            i1_ = (1) - (n1);
            for(i_=n1; i_<=n2;i_++)
            {
                c[i,i_] = c[i,i_] - t*v[i_+i1_];
            }
        }
    }


    private static void testreflections()
    {
        int i = 0;
        int j = 0;
        int n = 0;
        int m = 0;
        int maxmn = 0;
        double[] x = new double[0];
        double[] v = new double[0];
        double[] work = new double[0];
        double[,] h = new double[0,0];
        double[,] a = new double[0,0];
        double[,] b = new double[0,0];
        double[,] c = new double[0,0];
        double tmp = 0;
        double beta = 0;
        double tau = 0;
        double err = 0;
        double mer = 0;
        double mel = 0;
        double meg = 0;
        int pass = 0;
        int passcount = 0;
        int i_ = 0;

        passcount = 1000;
        mer = 0;
        mel = 0;
        meg = 0;
        for(pass=1; pass<=passcount; pass++)
        {
            
            //
            // Task
            //
            n = 1+AP.Math.RandomInteger(10);
            m = 1+AP.Math.RandomInteger(10);
            maxmn = Math.Max(m, n);
            
            //
            // Initialize
            //
            x = new double[maxmn+1];
            v = new double[maxmn+1];
            work = new double[maxmn+1];
            h = new double[maxmn+1, maxmn+1];
            a = new double[maxmn+1, maxmn+1];
            b = new double[maxmn+1, maxmn+1];
            c = new double[maxmn+1, maxmn+1];
            
            //
            // GenerateReflection
            //
            for(i=1; i<=n; i++)
            {
                x[i] = 2*AP.Math.RandomReal()-1;
                v[i] = x[i];
            }
            generatereflection(ref v, n, ref tau);
            beta = v[1];
            v[1] = 1;
            for(i=1; i<=n; i++)
            {
                for(j=1; j<=n; j++)
                {
                    if( i==j )
                    {
                        h[i,j] = 1-tau*v[i]*v[j];
                    }
                    else
                    {
                        h[i,j] = -(tau*v[i]*v[j]);
                    }
                }
            }
            err = 0;
            for(i=1; i<=n; i++)
            {
                tmp = 0.0;
                for(i_=1; i_<=n;i_++)
                {
                    tmp += h[i,i_]*x[i_];
                }
                if( i==1 )
                {
                    err = Math.Max(err, Math.Abs(tmp-beta));
                }
                else
                {
                    err = Math.Max(err, Math.Abs(tmp));
                }
            }
            meg = Math.Max(meg, err);
            
            //
            // ApplyReflectionFromTheLeft
            //
            for(i=1; i<=m; i++)
            {
                x[i] = 2*AP.Math.RandomReal()-1;
                v[i] = x[i];
            }
            for(i=1; i<=m; i++)
            {
                for(j=1; j<=n; j++)
                {
                    a[i,j] = 2*AP.Math.RandomReal()-1;
                    b[i,j] = a[i,j];
                }
            }
            generatereflection(ref v, m, ref tau);
            beta = v[1];
            v[1] = 1;
            applyreflectionfromtheleft(ref b, tau, ref v, 1, m, 1, n, ref work);
            for(i=1; i<=m; i++)
            {
                for(j=1; j<=m; j++)
                {
                    if( i==j )
                    {
                        h[i,j] = 1-tau*v[i]*v[j];
                    }
                    else
                    {
                        h[i,j] = -(tau*v[i]*v[j]);
                    }
                }
            }
            for(i=1; i<=m; i++)
            {
                for(j=1; j<=n; j++)
                {
                    tmp = 0.0;
                    for(i_=1; i_<=m;i_++)
                    {
                        tmp += h[i,i_]*a[i_,j];
                    }
                    c[i,j] = tmp;
                }
            }
            err = 0;
            for(i=1; i<=m; i++)
            {
                for(j=1; j<=n; j++)
                {
                    err = Math.Max(err, Math.Abs(b[i,j]-c[i,j]));
                }
            }
            mel = Math.Max(mel, err);
            
            //
            // ApplyReflectionFromTheRight
            //
            for(i=1; i<=n; i++)
            {
                x[i] = 2*AP.Math.RandomReal()-1;
                v[i] = x[i];
            }
            for(i=1; i<=m; i++)
            {
                for(j=1; j<=n; j++)
                {
                    a[i,j] = 2*AP.Math.RandomReal()-1;
                    b[i,j] = a[i,j];
                }
            }
            generatereflection(ref v, n, ref tau);
            beta = v[1];
            v[1] = 1;
            applyreflectionfromtheright(ref b, tau, ref v, 1, m, 1, n, ref work);
            for(i=1; i<=n; i++)
            {
                for(j=1; j<=n; j++)
                {
                    if( i==j )
                    {
                        h[i,j] = 1-tau*v[i]*v[j];
                    }
                    else
                    {
                        h[i,j] = -(tau*v[i]*v[j]);
                    }
                }
            }
            for(i=1; i<=m; i++)
            {
                for(j=1; j<=n; j++)
                {
                    tmp = 0.0;
                    for(i_=1; i_<=n;i_++)
                    {
                        tmp += a[i,i_]*h[i_,j];
                    }
                    c[i,j] = tmp;
                }
            }
            err = 0;
            for(i=1; i<=m; i++)
            {
                for(j=1; j<=n; j++)
                {
                    err = Math.Max(err, Math.Abs(b[i,j]-c[i,j]));
                }
            }
            mer = Math.Max(mer, err);
        }
        
        //
        // Overflow crash test
        //
        x = new double[10+1];
        v = new double[10+1];
        for(i=1; i<=10; i++)
        {
            v[i] = AP.Math.MaxRealNumber*0.01*(2*AP.Math.RandomReal()-1);
        }
        generatereflection(ref v, 10, ref tau);
        System.Console.Write("TESTING REFLECTIONS");
        System.Console.WriteLine();
        System.Console.Write("Pass count is ");
        System.Console.Write("{0,0:d}",passcount);
        System.Console.WriteLine();
        System.Console.Write("Generate     absolute error is       ");
        System.Console.Write("{0,5:E3}",meg);
        System.Console.WriteLine();
        System.Console.Write("Apply(Left)  absolute error is       ");
        System.Console.Write("{0,5:E3}",mel);
        System.Console.WriteLine();
        System.Console.Write("Apply(Right) absolute error is       ");
        System.Console.Write("{0,5:E3}",mer);
        System.Console.WriteLine();
        System.Console.Write("Overflow crash test passed");
        System.Console.WriteLine();
    }
}