//----------------------------------------------------------------------------
void Minimize1D::GetMinimum (float fT0, float fT1, float fTInitial,
float& rfTMin, float& rfFMin)
{
VERIFY( fT0 <= fTInitial && fTInitial <= fT1 );
m_fTMin = flt_max;
m_fFMin = flt_max;
float fF0 = m_oF(fT0,m_pvUserData);
float fFInitial = m_oF(fTInitial,m_pvUserData);
float fF1 = m_oF(fT1,m_pvUserData);
GetMinimum(fT0,fF0,fTInitial,fFInitial,fT1,fF1,m_iMaxLevel);
rfTMin = m_fTMin;
rfFMin = m_fFMin;
}
bool Bisect1<Real>::Bisect (Real fX0, Real fX1, Real& rfRoot)
{
// test two endpoints
Real fF0 = m_oF(fX0);
if (Math<Real>::FAbs(fF0) <= m_fTolerance)
{
rfRoot = fX0;
return true;
}
Real fF1 = m_oF(fX1);
if (Math<Real>::FAbs(fF1) <= m_fTolerance)
{
rfRoot = fX1;
return true;
}
if (fF0*fF1 > (Real)0.0)
return false;
for (int iLevel = 0; iLevel < m_iMaxLevel; iLevel++)
{
Real fXm = ((Real)0.5)*(fX0+fX1);
Real fFm = m_oF(fXm);
if (Math<Real>::FAbs(fFm) <= m_fTolerance)
{
rfRoot = fXm;
return true;
}
if (fF0*fFm < (Real)0.0)
{
fX1 = fXm;
fF1 = fFm;
}
else if (fF1*fFm < (Real)0.0)
{
fX0 = fXm;
fF0 = fFm;
}
}
return false;
}
//----------------------------------------------------------------------------
void Minimize1D::GetBracketedMinimum (float fT0, float fF0, float fTm,
float fFm, float fT1, float fF1, int iLevel)
{
for (int i = 0; i < m_iMaxBracket; i++)
{
// update minimum value
if ( fFm < m_fFMin )
{
m_fTMin = fTm;
m_fFMin = fFm;
}
// test for convergence
const float fEps = 1e-08f, fTol = 1e-04f;
if ( _abs(fT1-fT0) <= 2.0f*fTol*_abs(fTm) + fEps )
break;
// compute vertex of interpolating parabola
float fDT0 = fT0 - fTm, fDT1 = fT1 - fTm;
float fDF0 = fF0 - fFm, fDF1 = fF1 - fFm;
float fTmp0 = fDT0*fDF1, fTmp1 = fDT1*fDF0;
float fDenom = fTmp1 - fTmp0;
if ( _abs(fDenom) < fEps )
return;
float fTv = fTm + 0.5f*(fDT1*fTmp1-fDT0*fTmp0)/fDenom;
VERIFY( fT0 <= fTv && fTv <= fT1 );
float fFv = m_oF(fTv,m_pvUserData);
if ( fTv < fTm )
{
if ( fFv < fFm )
{
fT1 = fTm;
fF1 = fFm;
fTm = fTv;
fFm = fFv;
}
else
{
fT0 = fTv;
fF0 = fFv;
}
}
else if ( fTv > fTm )
{
if ( fFv < fFm )
{
fT0 = fTm;
fF0 = fFm;
fTm = fTv;
fFm = fFv;
}
else
{
fT1 = fTv;
fF1 = fFv;
}
}
else
{
// vertex of parabola is already at middle sample point
GetMinimum(fT0,fF0,fTm,fFm,iLevel);
GetMinimum(fTm,fFm,fT1,fF1,iLevel);
}
}
}
//----------------------------------------------------------------------------
void Minimize1D::GetMinimum (float fT0, float fF0, float fT1, float fF1,
int iLevel)
{
if ( fF0 < m_fFMin )
{
m_fTMin = fT0;
m_fFMin = fF0;
}
if ( fF1 < m_fFMin )
{
m_fTMin = fT1;
m_fFMin = fF1;
}
if ( iLevel-- == 0 )
return;
float fTm = 0.5f*(fT0+fT1);
float fFm = m_oF(fTm,m_pvUserData);
if ( fF0 - 2.0f*fFm + fF1 > 0.0f )
{
// quadratic fit has positive second derivative at midpoint
if ( fF1 > fF0 )
{
if ( fFm >= fF0 )
{
// increasing, repeat on [t0,tm]
GetMinimum(fT0,fF0,fTm,fFm,iLevel);
}
else
{
// not monotonic, have a bracket
GetBracketedMinimum(fT0,fF0,fTm,fFm,fT1,fF1,iLevel);
}
}
else if ( fF1 < fF0 )
{
if ( fFm >= fF1 )
{
// decreasing, repeat on [tm,t1]
GetMinimum(fTm,fFm,fT1,fF1,iLevel);
}
else
{
// not monotonic, have a bracket
GetBracketedMinimum(fT0,fF0,fTm,fFm,fT1,fF1,iLevel);
}
}
else
{
// constant, repeat on [t0,tm] and [tm,t1]
GetMinimum(fT0,fF0,fTm,fFm,iLevel);
GetMinimum(fTm,fFm,fT1,fF1,iLevel);
}
}
else
{
// quadratic fit has nonpositive second derivative at midpoint
if ( fF1 > fF0 )
{
// repeat on [t0,tm]
GetMinimum(fT0,fF0,fTm,fFm,iLevel);
}
else if ( fF1 < fF0 )
{
// repeat on [tm,t1]
GetMinimum(fTm,fFm,fT1,fF1,iLevel);
}
else
{
// repeat on [t0,tm] and [tm,t1]
GetMinimum(fT0,fF0,fTm,fFm,iLevel);
GetMinimum(fTm,fFm,fT1,fF1,iLevel);
}
}
}
