// @(#)root/matrix:$Name:  $:$Id: TMatrixTLazy.cxx,v 1.2 2005/12/23 19:55:50 brun Exp $
// Authors: Fons Rademakers, Eddy Offermann  Nov 2003

/*************************************************************************
 * Copyright (C) 1995-2000, Rene Brun and Fons Rademakers.               *
 * All rights reserved.                                                  *
 *                                                                       *
 * For the licensing terms see $ROOTSYS/LICENSE.                         *
 * For the list of contributors see $ROOTSYS/README/CREDITS.             *
 *************************************************************************/

//////////////////////////////////////////////////////////////////////////
//                                                                      //
// Templates of Lazy Matrix classes.                                    //
//                                                                      //
//   TMatrixTLazy                                                       //
//   TMatrixTSymLazy                                                    //
//   THaarMatrixT                                                       //
//   THilbertMatrixT                                                    //
//   THilbertMatrixTSym                                                 //
//                                                                      //
//////////////////////////////////////////////////////////////////////////

#include "TMatrixT.h"
#include "TMatrixTSym.h"
#include "TMatrixTLazy.h"

#ifndef R__ALPHA
templateClassImp(TMatrixTLazy)
templateClassImp(TMatrixTSymLazy)
templateClassImp(THaarMatrixT)
templateClassImp(THilbertMatrixT)
templateClassImp(THilbertMatrixTSym)
#endif

//______________________________________________________________________________
template<class Element>
THaarMatrixT<Element>::THaarMatrixT(Int_t order,Int_t no_cols)
    : TMatrixTLazy<Element>(1<<order, no_cols == 0 ? 1<<order : no_cols)
{
  Assert(order > 0 && no_cols >= 0);
}

//______________________________________________________________________________
template<class Element>
void MakeHaarMat(TMatrixT<Element> &m)
{
  // Create an orthonormal (2^n)*(no_cols) Haar (sub)matrix, whose columns
  // are Haar functions. If no_cols is 0, create the complete matrix with
  // 2^n columns. Example, the complete Haar matrix of the second order is:
  // column 1: [ 1  1  1  1]/2
  // column 2: [ 1  1 -1 -1]/2
  // column 3: [ 1 -1  0  0]/sqrt(2)
  // column 4: [ 0  0  1 -1]/sqrt(2)
  // Matrix m is assumed to be zero originally.

  Assert(m.IsValid());
  const Int_t no_rows = m.GetNrows();
  const Int_t no_cols = m.GetNcols();
  Assert(no_rows >= no_cols && no_cols > 0);

  // It is easier to calculate a Haar matrix when the elements are stored
  // column-wise . Since we are row-wise, the transposed Haar is calculted

  TMatrixT<Element> mtr(no_cols,no_rows);
        Element *cp    = mtr.GetMatrixArray();
  const Element *m_end = mtr.GetMatrixArray()+no_rows*no_cols;

  Element norm_factor = 1/TMath::Sqrt((Element)no_rows);

  // First row is always 1 (up to normalization)
  Int_t j;
  for (j = 0; j < no_rows; j++)
    *cp++ = norm_factor;

  // The other functions are kind of steps: stretch of 1 followed by the
  // equally long stretch of -1. The functions can be grouped in families
  // according to their order (step size), differing only in the location
  // of the step
  Int_t step_length = no_rows/2;
  while (cp < m_end && step_length > 0) {
    for (Int_t step_position = 0; cp < m_end && step_position < no_rows;
           step_position += 2*step_length, cp += no_rows) {
      Element *ccp = cp+step_position;
      for (j = 0; j < step_length; j++)
        *ccp++ = norm_factor;
      for (j = 0; j < step_length; j++)
        *ccp++ = -norm_factor;
    }
    step_length /= 2;
    norm_factor *= TMath::Sqrt(2.0);
  }

  Assert(step_length != 0       || cp == m_end);
  Assert(no_rows     != no_cols || step_length == 0);

  m.Transpose(mtr);
}

//______________________________________________________________________________
template<class Element>
void THaarMatrixT<Element>::FillIn(TMatrixT<Element> &m) const
{
  MakeHaarMat(m);
}

//______________________________________________________________________________
template<class Element>
THilbertMatrixT<Element>::THilbertMatrixT(Int_t no_rows,Int_t no_cols)
    : TMatrixTLazy<Element>(no_rows,no_cols)
{
  Assert(no_rows > 0 && no_cols > 0);
}

//______________________________________________________________________________
template<class Element>
THilbertMatrixT<Element>::THilbertMatrixT(Int_t row_lwb,Int_t row_upb,Int_t col_lwb,Int_t col_upb)
    : TMatrixTLazy<Element>(row_lwb,row_upb,col_lwb,col_upb)
{
  Assert(row_upb-row_lwb+1 > 0 && col_upb-col_lwb+1 > 0);
}

//______________________________________________________________________________
template<class Element>
void MakeHilbertMat(TMatrixT<Element> &m)
{
  // Make a Hilbert matrix. Hilb[i,j] = 1/(i+j+1),
  // i,j=0...max-1 (matrix need not be a square one).

  Assert(m.IsValid());
  const Int_t no_rows = m.GetNrows();
  const Int_t no_cols = m.GetNcols();
  Assert(no_rows > 0 && no_cols > 0);

  Element *cp = m.GetMatrixArray();
  for (Int_t i = 0; i < no_rows; i++)
    for (Int_t j = 0; j < no_cols; j++)
      *cp++ = 1.0/(i+j+1.0);
}

//______________________________________________________________________________
template<class Element>
void THilbertMatrixT<Element>::FillIn(TMatrixT<Element> &m) const
{
  MakeHilbertMat(m);
}

//______________________________________________________________________________
template<class Element>
THilbertMatrixTSym<Element>::THilbertMatrixTSym(Int_t no_rows)
    : TMatrixTSymLazy<Element>(no_rows)
{
  Assert(no_rows > 0);
}

//______________________________________________________________________________
template<class Element>
THilbertMatrixTSym<Element>::THilbertMatrixTSym(Int_t row_lwb,Int_t row_upb)
    : TMatrixTSymLazy<Element>(row_lwb,row_upb)
{
  Assert(row_upb-row_lwb+1 > 0);
}

//______________________________________________________________________________
template<class Element>
void MakeHilbertMat(TMatrixTSym<Element> &m)
{
  // Make a Hilbert matrix. Hilb[i,j] = 1/(i+j+1),
  // i,j=0...max-1 (matrix must be square).

  Assert(m.IsValid());
  const Int_t no_rows = m.GetNrows();
  Assert(no_rows > 0);

  Element *cp = m.GetMatrixArray();
  for (Int_t i = 0; i < no_rows; i++)
    for (Int_t j = 0; j < no_rows; j++)
      *cp++ = 1.0/(i+j+1.0);
}

//______________________________________________________________________________
template<class Element>
void THilbertMatrixTSym<Element>::FillIn(TMatrixTSym<Element> &m) const
{
  MakeHilbertMat(m);
}

template class TMatrixTLazy      <Float_t>;
template class TMatrixTSymLazy   <Float_t>;
template class THaarMatrixT      <Float_t>;
template class THilbertMatrixT   <Float_t>;
template class THilbertMatrixTSym<Float_t>;

template class TMatrixTLazy      <Double_t>;
template class TMatrixTSymLazy   <Double_t>;
template class THaarMatrixT      <Double_t>;
template class THilbertMatrixT   <Double_t>;
template class THilbertMatrixTSym<Double_t>;