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// Geometric Tools, LLC
// Copyright (c) 1998-2014
// Distributed under the Boost Software License, Version 1.0.
// http://www.boost.org/LICENSE_1_0.txt
// http://www.geometrictools.com/License/Boost/LICENSE_1_0.txt
//
// File Version: 5.0.2 (2011/03/27)
#include "Wm5MathematicsPCH.h"
#include "Wm5Minimize1.h"
#include "Wm5Assert.h"
#include "Wm5Math.h"
namespace Wm5
{
//----------------------------------------------------------------------------
template <typename Real>
Minimize1<Real>::Minimize1 (Function function, int maxLevel, int maxBracket,
void* userData)
:
mFunction(function),
mMaxLevel(maxLevel),
mMaxBracket(maxBracket),
mUserData(userData)
{
}
//----------------------------------------------------------------------------
template <typename Real>
Minimize1<Real>::~Minimize1 ()
{
}
//----------------------------------------------------------------------------
template <typename Real>
void Minimize1<Real>::SetUserData (void* userData)
{
mUserData = userData;
}
//----------------------------------------------------------------------------
template <typename Real>
void* Minimize1<Real>::GetUserData () const
{
return mUserData;
}
//----------------------------------------------------------------------------
template <typename Real>
void Minimize1<Real>::GetMinimum (Real t0, Real t1, Real tInitial,
Real& tMin, Real& fMin)
{
assertion(t0 <= tInitial && tInitial <= t1, "Invalid initial t value\n");
mTMin = Math<Real>::MAX_REAL;
mFMin = Math<Real>::MAX_REAL;
Real f0 = mFunction(t0, mUserData);
if (f0 < mFMin)
{
mTMin = t0;
mFMin = f0;
}
Real fInitial = mFunction(tInitial, mUserData);
if (fInitial < mFMin)
{
mTMin = tInitial;
mFMin = fInitial;
}
Real f1 = mFunction(t1, mUserData);
if (f1 < mFMin)
{
mTMin = t1;
mFMin = f1;
}
GetMinimum(t0, f0, tInitial, fInitial, t1, f1, mMaxLevel);
tMin = mTMin;
fMin = mFMin;
}
//----------------------------------------------------------------------------
template <typename Real>
void Minimize1<Real>::GetMinimum (Real t0, Real f0, Real tm, Real fm, Real t1,
Real f1, int level)
{
if (level-- == 0)
{
return;
}
if ((t1 - tm)*(f0 - fm) > (tm - t0)*(fm - f1))
{
// The quadratic fit has positive second derivative at the midpoint.
if (f1 > f0)
{
if (fm >= f0)
{
// Increasing, repeat on [t0,tm].
GetMinimum(t0, f0, tm, fm, level);
}
else
{
// Not monotonic, have a bracket.
GetBracketedMinimum(t0, f0, tm, fm, t1, f1, level);
}
}
else if (f1 < f0)
{
if (fm >= f1)
{
// Decreasing, repeat on [tm,t1].
GetMinimum(tm, fm, t1, f1, level);
}
else
{
// Not monotonic, have a bracket.
GetBracketedMinimum(t0, f0, tm, fm, t1, f1, level);
}
}
else
{
// Constant, repeat on [t0,tm] and [tm,t1].
GetMinimum(t0, f0, tm, fm, level);
GetMinimum(tm, fm, t1, f1, level);
}
}
else
{
// The quadratic fit has a nonpositive second derivative at the
// midpoint.
if (f1 > f0)
{
// Repeat on [t0,tm].
GetMinimum(t0, f0, tm, fm, level);
}
else if ( f1 < f0 )
{
// Repeat on [tm,t1].
GetMinimum(tm, fm, t1, f1, level);
}
else
{
// Repeat on [t0,tm] and [tm,t1].
GetMinimum(t0, f0, tm, fm, level);
GetMinimum(tm, fm, t1, f1, level);
}
}
}
//----------------------------------------------------------------------------
template <typename Real>
void Minimize1<Real>::GetMinimum (Real t0, Real f0, Real t1, Real f1,
int level)
{
if (level-- == 0)
{
return;
}
Real tm = ((Real)0.5)*(t0 + t1);
Real fm = mFunction(tm, mUserData);
if (fm < mFMin)
{
mTMin = tm;
mFMin = fm;
}
if (f0 - ((Real)2)*fm + f1 > (Real)0)
{
// The quadratic fit has positive second derivative at the midpoint.
if (f1 > f0)
{
if (fm >= f0)
{
// Increasing, repeat on [t0,tm].
GetMinimum(t0, f0, tm, fm, level);
}
else
{
// Not monotonic, have a bracket.
GetBracketedMinimum(t0, f0, tm, fm, t1, f1, level);
}
}
else if (f1 < f0)
{
if (fm >= f1)
{
// Decreasing, repeat on [tm,t1].
GetMinimum(tm, fm, t1, f1, level);
}
else
{
// Not monotonic, have a bracket.
GetBracketedMinimum(t0, f0, tm, fm, t1, f1, level);
}
}
else
{
// Constant, repeat on [t0,tm] and [tm,t1].
GetMinimum(t0, f0, tm, fm, level);
GetMinimum(tm, fm, t1, f1, level);
}
}
else
{
// The quadratic fit has nonpositive second derivative at the
// midpoint.
if (f1 > f0)
{
// Repeat on [t0,tm].
GetMinimum(t0, f0, tm, fm, level);
}
else if (f1 < f0)
{
// Repeat on [tm,t1].
GetMinimum(tm, fm, t1, f1, level);
}
else
{
// Repeat on [t0,tm] and [tm,t1].
GetMinimum(t0, f0, tm, fm, level);
GetMinimum(tm, fm, t1, f1, level);
}
}
}
//----------------------------------------------------------------------------
template <typename Real>
void Minimize1<Real>::GetBracketedMinimum (Real t0, Real f0, Real tm,
Real fm, Real t1, Real f1, int level)
{
for (int i = 0; i < mMaxBracket; ++i)
{
// Update minimum value.
if (fm < mFMin)
{
mTMin = tm;
mFMin = fm;
}
// Test for convergence.
const Real epsilon = (Real)1e-08;
const Real tolerance = (Real)1e-04;
if (Math<Real>::FAbs(t1-t0) <= ((Real)2)*tolerance*
Math<Real>::FAbs(tm) + epsilon )
{
break;
}
// Compute vertex of interpolating parabola.
Real dt0 = t0 - tm;
Real dt1 = t1 - tm;
Real df0 = f0 - fm;
Real df1 = f1 - fm;
Real tmp0 = dt0*df1;
Real tmp1 = dt1*df0;
Real denom = tmp1 - tmp0;
if (Math<Real>::FAbs(denom) < epsilon)
{
return;
}
Real tv = tm + ((Real)0.5)*(dt1*tmp1 - dt0*tmp0)/denom;
assertion(t0 <= tv && tv <= t1, "Vertex not in interval\n");
Real fv = mFunction(tv, mUserData);
if (fv < mFMin)
{
mTMin = tv;
mFMin = fv;
}
if (tv < tm)
{
if (fv < fm)
{
t1 = tm;
f1 = fm;
tm = tv;
fm = fv;
}
else
{
t0 = tv;
f0 = fv;
}
}
else if (tv > tm)
{
if (fv < fm)
{
t0 = tm;
f0 = fm;
tm = tv;
fm = fv;
}
else
{
t1 = tv;
f1 = fv;
}
}
else
{
// The vertex of parabola is already at middle sample point.
GetMinimum(t0, f0, tm, fm, level);
GetMinimum(tm, fm, t1, f1, level);
}
}
}
//----------------------------------------------------------------------------
//----------------------------------------------------------------------------
// Explicit instantiation.
//----------------------------------------------------------------------------
template WM5_MATHEMATICS_ITEM
class Minimize1<float>;
template WM5_MATHEMATICS_ITEM
class Minimize1<double>;
//----------------------------------------------------------------------------
}
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