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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 (2011/03/09)
#include "Wm5MathematicsPCH.h"
#include "Wm5MinimizeN.h"
#include "Wm5Math.h"
#include "Wm5Memory.h"
namespace Wm5
{
//----------------------------------------------------------------------------
template <typename Real>
MinimizeN<Real>::MinimizeN (int dimensions, Function function,
int maxLevel, int maxBracket, int maxIterations, void* userData)
:
mDimensions(dimensions),
mFunction(function),
mMaxIterations(maxIterations),
mUserData(userData),
mMinimizer(LineFunction, maxLevel, maxBracket)
{
assertion(mDimensions >= 1 && mFunction, "Invalid inputs\n");
mTCurr = new1<Real>(mDimensions);
mTSave = new1<Real>(mDimensions);
mDirectionStorage = new1<Real>(mDimensions*(mDimensions + 1));
mDirection = new1<Real*>(mDimensions + 1);
for (int i = 0; i <= mDimensions; ++i)
{
mDirection[i] = &mDirectionStorage[i*mDimensions];
}
mDConj = mDirection[mDimensions];
mLineArg = new1<Real>(mDimensions);
}
//----------------------------------------------------------------------------
template <typename Real>
MinimizeN<Real>::~MinimizeN ()
{
delete1(mTCurr);
delete1(mTSave);
delete1(mDirectionStorage);
delete1(mDirection);
delete1(mLineArg);
}
//----------------------------------------------------------------------------
template <typename Real>
void MinimizeN<Real>::GetMinimum (const Real* t0, const Real* t1,
const Real* tInitial, Real* tMin, Real& fMin)
{
// For 1D function callback.
mMinimizer.SetUserData(this);
// The initial guess.
size_t numBytes = mDimensions*sizeof(Real);
mFCurr = mFunction(tInitial, mUserData);
memcpy(mTSave, tInitial, numBytes);
memcpy(mTCurr, tInitial, numBytes);
// Initialize the direction set to the standard Euclidean basis.
size_t numBasisBytes = numBytes*(mDimensions + 1);
memset(mDirectionStorage, 0, numBasisBytes);
int i;
for (i = 0; i < mDimensions; ++i)
{
mDirection[i][i] = (Real)1;
}
Real ell0, ell1, ellMin;
for (int iter = 0; iter < mMaxIterations; iter++)
{
// Find minimum in each direction and update current location.
for (i = 0; i < mDimensions; ++i)
{
mDCurr = mDirection[i];
ComputeDomain(t0, t1, ell0, ell1);
mMinimizer.GetMinimum(ell0, ell1, (Real)0, ellMin, mFCurr);
for (int j = 0; j < mDimensions; ++j)
{
mTCurr[j] += ellMin*mDCurr[j];
}
}
// Estimate a unit-length conjugate direction.
Real length = (Real)0;
for (i = 0; i < mDimensions; ++i)
{
mDConj[i] = mTCurr[i] - mTSave[i];
length += mDConj[i]*mDConj[i];
}
const Real epsilon = (Real)1e-06;
length = Math<Real>::Sqrt(length);
if (length < epsilon)
{
// New position did not change significantly from old one.
// Should there be a better convergence criterion here?
break;
}
Real invlength = ((Real)1)/length;
for (i = 0; i < mDimensions; ++i)
{
mDConj[i] *= invlength;
}
// Minimize in conjugate direction.
mDCurr = mDConj;
ComputeDomain(t0, t1, ell0, ell1);
mMinimizer.GetMinimum(ell0, ell1, (Real)0, ellMin, mFCurr);
for (i = 0; i < mDimensions; ++i)
{
mTCurr[i] += ellMin*mDCurr[i];
}
// Cycle the directions and add conjugate direction to set.
mDConj = mDirection[0];
for (i = 0; i < mDimensions; ++i)
{
mDirection[i] = mDirection[i+1];
}
// Set parameters for next pass.
memcpy(mTSave, mTCurr, numBytes);
}
memcpy(tMin, mTCurr, numBytes);
fMin = mFCurr;
}
//----------------------------------------------------------------------------
template <typename Real>
void MinimizeN<Real>::ComputeDomain (const Real* t0, const Real* t1,
Real& ell0, Real& ell1)
{
ell0 = -Math<Real>::MAX_REAL;
ell1 = +Math<Real>::MAX_REAL;
for (int i = 0; i < mDimensions; ++i)
{
Real b0 = t0[i] - mTCurr[i];
Real b1 = t1[i] - mTCurr[i];
Real inv;
if (mDCurr[i] > (Real)0)
{
// The valid t-interval is [b0,b1].
inv = ((Real)1)/mDCurr[i];
b0 *= inv;
if (b0 > ell0)
{
ell0 = b0;
}
b1 *= inv;
if (b1 < ell1)
{
ell1 = b1;
}
}
else if (mDCurr[i] < (Real)0)
{
// The valid t-interval is [b1,b0].
inv = ((Real)1)/mDCurr[i];
b0 *= inv;
if (b0 < ell1)
{
ell1 = b0;
}
b1 *= inv;
if (b1 > ell0)
{
ell0 = b1;
}
}
}
// Correction if numerical errors lead to values nearly zero.
if (ell0 > (Real)0)
{
ell0 = (Real)0;
}
if (ell1 < (Real)0)
{
ell1 = (Real)0;
}
}
//----------------------------------------------------------------------------
template <typename Real>
Real MinimizeN<Real>::LineFunction (Real t, void* userData)
{
MinimizeN& self = *(MinimizeN*)userData;
for (int i = 0; i < self.mDimensions; ++i)
{
self.mLineArg[i] = self.mTCurr[i] + t*self.mDCurr[i];
}
Real result = self.mFunction(self.mLineArg, self.mUserData);
return result;
}
//----------------------------------------------------------------------------
//----------------------------------------------------------------------------
// Explicit instantiation.
//----------------------------------------------------------------------------
template WM5_MATHEMATICS_ITEM
class MinimizeN<float>;
template WM5_MATHEMATICS_ITEM
class MinimizeN<double>;
//----------------------------------------------------------------------------
}
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