occt/src/math/math_BrentMinimum.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.

#include <math_BrentMinimum.hxx>
#include <math_Function.hxx>
#include <StdFail_NotDone.hxx>

static const Standard_Real CGOLD = 0.3819660; // 0.5*(3 - sqrt(5));

//=======================================================================
// function : SHFT
// purpose  : Shifts arguments
//=======================================================================
inline void SHFT(Standard_Real& theA, Standard_Real& theB, Standard_Real& theC, Standard_Real& theD)
{
  theA = theB;
  theB = theC;
  theC = theD;
}

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

math_BrentMinimum::math_BrentMinimum(const Standard_Real    theTolX,
                                     const Standard_Integer theNbIterations,
                                     const Standard_Real    theZEPS)
    : a(0.0),
      b(0.0),
      x(0.0),
      fx(0.0),
      fv(0.0),
      fw(0.0),
      XTol(theTolX),
      EPSZ(theZEPS),
      Done(Standard_False),
      iter(0),
      Itermax(theNbIterations),
      myF(Standard_False)
{
}

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

math_BrentMinimum::math_BrentMinimum(const Standard_Real    theTolX,
                                     const Standard_Real    theFbx,
                                     const Standard_Integer theNbIterations,
                                     const Standard_Real    theZEPS)
    : a(0.0),
      b(0.0),
      x(0.0),
      fx(theFbx),
      fv(0.0),
      fw(0.0),
      XTol(theTolX),
      EPSZ(theZEPS),
      Done(Standard_False),
      iter(0),
      Itermax(theNbIterations),
      myF(Standard_True)
{
}

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

math_BrentMinimum::~math_BrentMinimum() {}

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

void math_BrentMinimum::Perform(math_Function&      F,
                                const Standard_Real ax,
                                const Standard_Real bx,
                                const Standard_Real cx)
{
  Standard_Boolean OK;
  Standard_Real    etemp, fu, p, q, r;
  Standard_Real    tol1, tol2, u, v, w, xm;
  Standard_Real    e = 0.0;
  Standard_Real    d = RealLast();

  a = ((ax < cx) ? ax : cx);
  b = ((ax > cx) ? ax : cx);
  x = w = v = bx;
  if (!myF)
  {
    OK = F.Value(x, fx);
    if (!OK)
      return;
  }
  fw = fv = fx;
  for (iter = 1; iter <= Itermax; iter++)
  {
    xm   = 0.5 * (a + b);
    tol1 = XTol * fabs(x) + EPSZ;
    tol2 = 2.0 * tol1;
    if (IsSolutionReached(F))
    {
      Done = Standard_True;
      return;
    }
    if (fabs(e) > tol1)
    {
      r = (x - w) * (fx - fv);
      q = (x - v) * (fx - fw);
      p = (x - v) * q - (x - w) * r;
      q = 2.0 * (q - r);
      if (q > 0.0)
        p = -p;
      q     = fabs(q);
      etemp = e;
      e     = d;
      if (fabs(p) >= fabs(0.5 * q * etemp) || p <= q * (a - x) || p >= q * (b - x))
      {
        e = (x >= xm ? a - x : b - x);
        d = CGOLD * e;
      }
      else
      {
        d = p / q;
        u = x + d;
        if (u - a < tol2 || b - u < tol2)
          d = Sign(tol1, xm - x);
      }
    }
    else
    {
      e = (x >= xm ? a - x : b - x);
      d = CGOLD * e;
    }
    u  = (fabs(d) >= tol1 ? x + d : x + Sign(tol1, d));
    OK = F.Value(u, fu);
    if (!OK)
      return;
    if (fu <= fx)
    {
      if (u >= x)
        a = x;
      else
        b = x;
      SHFT(v, w, x, u);
      SHFT(fv, fw, fx, fu);
    }
    else
    {
      if (u < x)
        a = u;
      else
        b = u;
      if (fu <= fw || w == x)
      {
        v  = w;
        w  = u;
        fv = fw;
        fw = fu;
      }
      else if (fu <= fv || v == x || v == w)
      {
        v  = u;
        fv = fu;
      }
    }
  }
  Done = Standard_False;
  return;
}

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

void math_BrentMinimum::Dump(Standard_OStream& o) const
{
  o << "math_BrentMinimum ";
  if (Done)
  {
    o << " Status = Done \n";
    o << " Location value = " << x << "\n";
    o << " Minimum value = " << fx << "\n";
    o << " Number of iterations = " << iter << "\n";
  }
  else
  {
    o << " Status = not Done \n";
  }
}