occt/src/math/math_Householder.cxx

// Copyright (c) 1997-1999 Matra Datavision
// Copyright (c) 1999-2014 OPEN CASCADE SAS
//
// This file is part of Open CASCADE Technology software library.
//
// This library is free software; you can redistribute it and/or modify it under
// the terms of the GNU Lesser General Public License version 2.1 as published
// by the Free Software Foundation, with special exception defined in the file
// OCCT_LGPL_EXCEPTION.txt. Consult the file LICENSE_LGPL_21.txt included in OCCT
// distribution for complete text of the license and disclaimer of any warranty.
//
// Alternatively, this file may be used under the terms of Open CASCADE
// commercial license or contractual agreement.

// #ifndef OCCT_DEBUG
#define No_Standard_RangeError
#define No_Standard_OutOfRange
#define No_Standard_DimensionError

// #endif

#include <math_Householder.hxx>
#include <math_Matrix.hxx>
#include <Standard_DimensionError.hxx>
#include <StdFail_NotDone.hxx>

// Cette classe decrit la methode de Householder qui transforme A en un
// produit de matrice orthogonale par une triangulaire superieure. Les seconds
// membres sont modifies dans le meme temps.
// Les references sur le cote sont celles de l'algorithme explique en page
// 90 du livre "Introduction a l'analyse numerique matricielle et a
// l'optimisation." par P.G. CIARLET, edition MASSON. Les secondes
// references sont celles du sous-programme HOUSEO d'Euclid.
// A la difference du sous-programme Houseo, la premiere colonne n'est pas
// traitee separement. Les tests effectues ont montre que le code effectue
// specialement pour celle-ci etait plus long qu'une simple recopie. C'est
// donc cette solution de recopie initiale qui a ete retenue.
math_Householder::math_Householder(const math_Matrix&  A,
                                   const math_Vector&  B,
                                   const Standard_Real EPS)
    : Sol(1, A.ColNumber(), 1, 1),
      Q(1, A.RowNumber(), 1, A.ColNumber()),
      Done(Standard_False)
{

  mylowerArow = A.LowerRow();
  mylowerAcol = A.LowerCol();
  myupperArow = A.UpperRow();
  myupperAcol = A.UpperCol();
  math_Matrix B1(1, B.Length(), 1, 1);
  B1.SetCol(1, B);
  Perform(A, B1, EPS);
}

math_Householder::math_Householder(const math_Matrix&  A,
                                   const math_Matrix&  B,
                                   const Standard_Real EPS)
    : Sol(1, A.ColNumber(), 1, B.ColNumber()),
      Q(1, A.RowNumber(), A.LowerCol(), A.UpperCol()),
      Done(Standard_False)
{

  mylowerArow = A.LowerRow();
  mylowerAcol = A.LowerCol();
  myupperArow = A.UpperRow();
  myupperAcol = A.UpperCol();
  Perform(A, B, EPS);
}

math_Householder::math_Householder(const math_Matrix&     A,
                                   const math_Matrix&     B,
                                   const Standard_Integer lowerArow,
                                   const Standard_Integer upperArow,
                                   const Standard_Integer lowerAcol,
                                   const Standard_Integer upperAcol,
                                   const Standard_Real    EPS)
    : Sol(1, upperAcol - lowerAcol + 1, 1, B.ColNumber()),
      Q(1, upperArow - lowerArow + 1, 1, upperAcol - lowerAcol + 1),
      Done(Standard_False)
{
  mylowerArow = lowerArow;
  myupperArow = upperArow;
  mylowerAcol = lowerAcol;
  myupperAcol = upperAcol;

  Perform(A, B, EPS);
}

void math_Householder::Perform(const math_Matrix& A, const math_Matrix& B, const Standard_Real EPS)
{

  Standard_Integer i, j, k, n, l, m;
  Standard_Real    f, g, h = 0., alfaii;
  Standard_Real    qki;
  Standard_Real    cj;
  n = Q.ColNumber();
  l = Q.RowNumber();
  m = B.ColNumber();
  math_Matrix B2(1, l, 1, m);

  Standard_Integer lbrow = B.LowerRow();
  for (i = 1; i <= l; i++)
  {
    for (j = 1; j <= n; j++)
    {
      Q(i, j) = A(i + mylowerArow - 1, j + mylowerAcol - 1);
    }
    for (j = 1; j <= m; j++)
    {
      B2(i, j) = B(i + lbrow - 1, j);
    }
  }

  Standard_DimensionError_Raise_if(l != B.RowNumber() || n > l, " ");

  // Traitement de chaque colonne de A:
  for (i = 1; i <= n; i++)
  {
    h = 0.0;
    for (k = i; k <= l; k++)
    {
      qki = Q(k, i);
      h += qki * qki; // = ||a||*||a||     = EUAI
    }
    f = Q(i, i); // = a1              = AII
    g = f < 1.e-15 ? Sqrt(h) : -Sqrt(h);
    if (fabs(g) <= EPS)
    {
      Done = Standard_False;
      return;
    }
    h -= f * g;     // = (v*v)/2         = C1
    alfaii = g - f; // = v               = ALFAII
    for (j = i + 1; j <= n; j++)
    {
      Standard_Real scale = 0.0;
      for (k = i; k <= l; k++)
      {
        scale += Q(k, i) * Q(k, j); //                   = SCAL
      }
      cj      = (g * Q(i, j) - scale) / h;
      Q(i, j) = Q(i, j) - alfaii * cj;
      for (k = i + 1; k <= l; k++)
      {
        Q(k, j) = Q(k, j) + cj * Q(k, i);
      }
    }

    // Modification de B:

    for (j = 1; j <= m; j++)
    {
      Standard_Real scale = Q(i, i) * B2(i, j);
      for (k = i + 1; k <= l; k++)
      {
        scale += Q(k, i) * B2(k, j);
      }
      cj       = (g * B2(i, j) - scale) / h;
      B2(i, j) = B2(i, j) - cj * alfaii;
      for (k = i + 1; k <= l; k++)
      {
        B2(k, j) = B2(k, j) + cj * Q(k, i);
      }
    }
    Q(i, i) = g;
  }

  // Remontee:
  for (j = 1; j <= m; j++)
  {
    Sol(n, j) = B2(n, j) / Q(n, n);
    for (i = n - 1; i >= 1; i--)
    {
      Standard_Real scale = 0.0;
      for (k = i + 1; k <= n; k++)
      {
        scale += Q(i, k) * Sol(k, j);
      }
      Sol(i, j) = (B2(i, j) - scale) / Q(i, i);
    }
  }
  Done = Standard_True;
}

void math_Householder::Dump(Standard_OStream& o) const
{

  o << "math_Householder ";
  if (Done)
  {
    o << " Status = Done \n";
  }
  else
  {
    o << "Status = not Done \n";
  }
}