reflections.h

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/*************************************************************************
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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modification, are permitted provided that the following conditions are
met:
 
- Redistributions of source code must retain the above copyright
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- Redistributions in binary form must reproduce 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
  this software without specific prior written permission.
 
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*************************************************************************/
 
#ifndef _reflections_h
#define _reflections_h
 
#include "ap.h"
#include "amp.h"
namespace reflections
{
    template<unsigned int Precision>
    void generatereflection(ap::template_1d_array< amp::ampf<Precision> >& x,
        int n,
        amp::ampf<Precision>& tau);
    template<unsigned int Precision>
    void applyreflectionfromtheleft(ap::template_2d_array< amp::ampf<Precision> >& c,
        amp::ampf<Precision> tau,
        const ap::template_1d_array< amp::ampf<Precision> >& v,
        int m1,
        int m2,
        int n1,
        int n2,
        ap::template_1d_array< amp::ampf<Precision> >& work);
    template<unsigned int Precision>
    void applyreflectionfromtheright(ap::template_2d_array< amp::ampf<Precision> >& c,
        amp::ampf<Precision> tau,
        const ap::template_1d_array< amp::ampf<Precision> >& v,
        int m1,
        int m2,
        int n1,
        int n2,
        ap::template_1d_array< amp::ampf<Precision> >& work);
 
 
    /*************************************************************************
    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
    *************************************************************************/
    template<unsigned int Precision>
    void generatereflection(ap::template_1d_array< amp::ampf<Precision> >& x,
        int n,
        amp::ampf<Precision>& tau)
    {
        int j;
        amp::ampf<Precision> alpha;
        amp::ampf<Precision> xnorm;
        amp::ampf<Precision> v;
        amp::ampf<Precision> beta;
        amp::ampf<Precision> mx;
 
 
 
        //
        // 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 = amp::maximum<Precision>(amp::abs<Precision>(x(j)), mx);
        }
        xnorm = 0;
        if( mx!=0 )
        {
            for(j=2; j<=n; j++)
            {
                xnorm = xnorm+amp::sqr<Precision>(x(j)/mx);
            }
            xnorm = amp::sqrt<Precision>(xnorm)*mx;
        }
        if( xnorm==0 )
        {
 
            //
            // H  =  I
            //
            tau = 0;
            return;
        }
 
        //
        // general case
        //
        mx = amp::maximum<Precision>(amp::abs<Precision>(alpha), amp::abs<Precision>(xnorm));
        beta = -mx*amp::sqrt<Precision>(amp::sqr<Precision>(alpha/mx)+amp::sqr<Precision>(xnorm/mx));
        if( alpha<0 )
        {
            beta = -beta;
        }
        tau = (beta-alpha)/beta;
        v = 1/(alpha-beta);
        ap::vmul(x.getvector(2, n), v);
        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
    *************************************************************************/
    template<unsigned int Precision>
    void applyreflectionfromtheleft(ap::template_2d_array< amp::ampf<Precision> >& c,
        amp::ampf<Precision> tau,
        const ap::template_1d_array< amp::ampf<Precision> >& v,
        int m1,
        int m2,
        int n1,
        int n2,
        ap::template_1d_array< amp::ampf<Precision> >& work)
    {
        amp::ampf<Precision> t;
        int i;
        int vm;
 
 
        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);
            ap::vadd(work.getvector(n1, n2), c.getrow(i, n1, n2), t);
        }
 
        //
        // C := C - tau * v * w'
        //
        for(i=m1; i<=m2; i++)
        {
            t = v(i-m1+1)*tau;
            ap::vsub(c.getrow(i, n1, n2), work.getvector(n1, n2), t);
        }
    }
 
 
    /*************************************************************************
    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
    *************************************************************************/
    template<unsigned int Precision>
    void applyreflectionfromtheright(ap::template_2d_array< amp::ampf<Precision> >& c,
        amp::ampf<Precision> tau,
        const ap::template_1d_array< amp::ampf<Precision> >& v,
        int m1,
        int m2,
        int n1,
        int n2,
        ap::template_1d_array< amp::ampf<Precision> >& work)
    {
        amp::ampf<Precision> t;
        int i;
        int vm;
 
 
        if( tau==0 || n1>n2 || m1>m2 )
        {
            return;
        }
 
        //
        // w := C * v
        //
        vm = n2-n1+1;
        for(i=m1; i<=m2; i++)
        {
            t = ap::vdotproduct(c.getrow(i, n1, n2), v.getvector(1, vm));
            work(i) = t;
        }
 
        //
        // C := C - w * v'
        //
        for(i=m1; i<=m2; i++)
        {
            t = work(i)*tau;
            ap::vsub(c.getrow(i, n1, n2), v.getvector(1, vm), t);
        }
    }
} // namespace
 
#endif