occt/src/FEmTool/FEmTool_LinearFlexion.cxx

// Created on: 1998-11-06
// Created by: Igor FEOKTISTOV
// Copyright (c) 1998-1999 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.

#include <FEmTool_ElementsOfRefMatrix.hxx>
#include <FEmTool_LinearFlexion.hxx>
#include <math.hxx>
#include <math_GaussSetIntegration.hxx>
#include <math_IntegerVector.hxx>
#include <math_Matrix.hxx>
#include <math_Vector.hxx>
#include <PLib.hxx>
#include <PLib_HermitJacobi.hxx>
#include <Standard_ConstructionError.hxx>
#include <Standard_DomainError.hxx>
#include <Standard_NotImplemented.hxx>
#include <Standard_Type.hxx>
#include <TColStd_HArray2OfInteger.hxx>
#include <TColStd_HArray2OfReal.hxx>

IMPLEMENT_STANDARD_RTTIEXT(FEmTool_LinearFlexion, FEmTool_ElementaryCriterion)

//=================================================================================================

FEmTool_LinearFlexion::FEmTool_LinearFlexion(const Standard_Integer WorkDegree,
                                             const GeomAbs_Shape    ConstraintOrder)
    : RefMatrix(0, WorkDegree, 0, WorkDegree)
{
  static Standard_Integer Order = -333, WDeg = 14;
  static math_Vector      MatrixElemts(0, ((WDeg + 2) * (WDeg + 1)) / 2 - 1);

  myOrder = PLib::NivConstr(ConstraintOrder);

  if (myOrder != Order)
  {
    // Calculating RefMatrix
    if (WorkDegree > WDeg)
      throw Standard_ConstructionError("Degree too high");
    Order                                 = myOrder;
    Standard_Integer            DerOrder  = 2;
    Handle(PLib_HermitJacobi)   theBase   = new PLib_HermitJacobi(WDeg, ConstraintOrder);
    FEmTool_ElementsOfRefMatrix Elem      = FEmTool_ElementsOfRefMatrix(theBase, DerOrder);
    Standard_Integer            maxDegree = WDeg + 1;
    math_IntegerVector          anOrder(1, 1, Min(4 * (maxDegree / 2 + 1), math::GaussPointsMax()));
    math_Vector                 Lower(1, 1, -1.), Upper(1, 1, 1.);
    math_GaussSetIntegration    anInt(Elem, Lower, Upper, anOrder);

    MatrixElemts = anInt.Value();
  }

  Standard_Integer i, j, ii, jj;
  for (ii = i = 0; i <= WorkDegree; i++)
  {
    RefMatrix(i, i) = MatrixElemts(ii);
    for (j = i + 1, jj = ii + 1; j <= WorkDegree; j++, jj++)
    {
      RefMatrix(j, i) = RefMatrix(i, j) = MatrixElemts(jj);
    }
    ii += WDeg + 1 - i;
  }
}

//=================================================================================================

Handle(TColStd_HArray2OfInteger) FEmTool_LinearFlexion::DependenceTable() const
{
  if (myCoeff.IsNull())
    throw Standard_DomainError("FEmTool_LinearFlexion::DependenceTable");

  Handle(TColStd_HArray2OfInteger) DepTab = new TColStd_HArray2OfInteger(myCoeff->LowerCol(),
                                                                         myCoeff->UpperCol(),
                                                                         myCoeff->LowerCol(),
                                                                         myCoeff->UpperCol(),
                                                                         0);
  Standard_Integer                 i;
  for (i = myCoeff->LowerCol(); i <= myCoeff->UpperCol(); i++)
    DepTab->SetValue(i, i, 1);

  return DepTab;
}

//=================================================================================================

Standard_Real FEmTool_LinearFlexion::Value()
{
  Standard_Integer deg = Min(myCoeff->ColLength() - 1, RefMatrix.UpperRow()), i, j,
                   j0 = myCoeff->LowerRow(), degH = Min(2 * myOrder + 1, deg),
                   NbDim = myCoeff->RowLength(), dim;

  TColStd_Array2OfReal NewCoeff(1, NbDim, 0, deg);

  Standard_Real coeff = (myLast - myFirst) / 2., cteh3 = 2. / Pow(coeff, 3), mfact, Jline;

  Standard_Integer k1;

  Standard_Real J = 0.;

  for (i = 0; i <= degH; i++)
  {
    k1    = (i <= myOrder) ? i : i - myOrder - 1;
    mfact = Pow(coeff, k1);
    for (dim = 1; dim <= NbDim; dim++)
      NewCoeff(dim, i) = myCoeff->Value(j0 + i, dim) * mfact;
  }

  for (i = degH + 1; i <= deg; i++)
  {
    for (dim = 1; dim <= NbDim; dim++)
      NewCoeff(dim, i) = myCoeff->Value(j0 + i, dim);
  }

  for (dim = 1; dim <= NbDim; dim++)
  {
    for (i = 0; i <= deg; i++)
    {
      Jline = 0.5 * RefMatrix(i, i) * NewCoeff(dim, i);
      for (j = 0; j < i; j++)
        Jline += RefMatrix(i, j) * NewCoeff(dim, j);
      J += Jline * NewCoeff(dim, i);
    }
  }

  if (J < 0.)
    J = 0.;
  return cteh3 * J;
}

//=================================================================================================

void FEmTool_LinearFlexion::Hessian(const Standard_Integer Dimension1,
                                    const Standard_Integer Dimension2,
                                    math_Matrix&           H)
{

  Handle(TColStd_HArray2OfInteger) DepTab = DependenceTable();

  if (Dimension1 < DepTab->LowerRow() || Dimension1 > DepTab->UpperRow()
      || Dimension2 < DepTab->LowerCol() || Dimension2 > DepTab->UpperCol())
    throw Standard_OutOfRange("FEmTool_LinearJerk::Hessian");

  if (DepTab->Value(Dimension1, Dimension2) == 0)
    throw Standard_DomainError("FEmTool_LinearJerk::Hessian");

  Standard_Integer deg  = Min(RefMatrix.UpperRow(), H.RowNumber() - 1),
                   degH = Min(2 * myOrder + 1, deg);

  Standard_Real    coeff = (myLast - myFirst) / 2., cteh3 = 2. / Pow(coeff, 3), mfact;
  Standard_Integer k1, k2, i, j;

  H.Init(0.);

  for (i = 0; i <= degH; i++)
  {
    k1    = (i <= myOrder) ? i : i - myOrder - 1;
    mfact = Pow(coeff, k1) * cteh3;
    // Hermite*Hermite part of matrix
    for (j = i; j <= degH; j++)
    {
      k2      = (j <= myOrder) ? j : j - myOrder - 1;
      H(i, j) = mfact * Pow(coeff, k2) * RefMatrix(i, j);
      if (i != j)
        H(j, i) = H(i, j);
    }
    // Hermite*Jacobi part of matrix
    for (j = degH + 1; j <= deg; j++)
    {
      H(i, j) = H(j, i) = mfact * RefMatrix(i, j);
    }
  }

  // Jacoby*Jacobi part of matrix
  for (i = degH + 1; i <= deg; i++)
  {
    for (j = i; j <= deg; j++)
    {
      H(i, j) = cteh3 * RefMatrix(i, j);
      if (i != j)
        H(j, i) = H(i, j);
    }
  }
}

//=================================================================================================

void FEmTool_LinearFlexion::Gradient(const Standard_Integer Dimension, math_Vector& G)
{
  if (Dimension < myCoeff->LowerCol() || Dimension > myCoeff->UpperCol())
    throw Standard_OutOfRange("FEmTool_LinearFlexion::Gradient");

  Standard_Integer deg = Min(G.Length() - 1, myCoeff->ColLength() - 1);

  math_Vector      X(0, deg);
  math_Matrix      H(0, deg, 0, deg);
  Standard_Integer i, i1 = myCoeff->LowerRow();
  for (i = 0; i <= deg; i++)
    X(i) = myCoeff->Value(i1 + i, Dimension);

  Hessian(Dimension, Dimension, H);

  G.Multiply(H, X);
}