template <unsigned DIM> inline
bool TUntangleMu::hess( const MsqMatrix<DIM,DIM>& T,
double& result,
MsqMatrix<DIM,DIM>& deriv_wrt_T,
MsqMatrix<DIM,DIM>* second_wrt_T,
MsqError& err )
{
bool valid = mBaseMetric->evaluate_with_hess( T, result, deriv_wrt_T, second_wrt_T, err );
if (MSQ_CHKERR(err) || !valid)
return false;
if (mConstant < result) {
const double s = result - mConstant;
result = s*s*s;
hess_scale( second_wrt_T, 3*s*s );
pluseq_scaled_outer_product( second_wrt_T, 6*s, deriv_wrt_T );
deriv_wrt_T *= 3*s*s;
}
else {
result = 0;
deriv_wrt_T = MsqMatrix<DIM,DIM>(0.0);
set_scaled_I( second_wrt_T, 0.0 ); // zero everything
}
return true;
}
template <unsigned DIM> static inline
bool hess( const MsqMatrix<DIM,DIM>& T, double& result,
MsqMatrix<DIM,DIM>& deriv_wrt_T, MsqMatrix<DIM,DIM>* second_wrt_T )
{
result = sqr_Frobenius( T );
deriv_wrt_T = 2 * T;
set_scaled_I( second_wrt_T, 2.0 );
return true;
}
template <unsigned DIM> static inline
bool hess( const MsqMatrix<DIM,DIM>& A,
const MsqMatrix<DIM,DIM>& W,
double& result,
MsqMatrix<DIM,DIM>& deriv,
MsqMatrix<DIM,DIM>* second )
{
deriv = A - W;
result = sqr_Frobenius( deriv );
deriv *= 2.0;
set_scaled_I( second, 2.0 );
return true;
}
template <unsigned DIM> static inline
bool hess( const MsqMatrix<DIM,DIM>& T,
double& result,
MsqMatrix<DIM,DIM>& deriv_wrt_T,
MsqMatrix<DIM,DIM>* second_wrt_T )
{
const double tr = trace(T);
const double f = DimConst<DIM>::inv() * fabs(tr);
result = sqr_Frobenius( T ) - f * tr;
deriv_wrt_T = T;
pluseq_scaled_I( deriv_wrt_T, -f );
deriv_wrt_T *= 2;
set_scaled_I( second_wrt_T, 2.0 );
pluseq_scaled_outer_product_I_I( second_wrt_T, DimConst<DIM>::inv() * (tr < 0 ? 2 : -2) );
return true;
}
