bool TShapeOrientB1::evaluate_with_hess( const MsqMatrix<2,2>& T,
double& result,
MsqMatrix<2,2>& deriv_wrt_T,
MsqMatrix<2,2> second_wrt_T[3],
MsqError& err )
{
const double norm = Frobenius(T);
const double invroot = 1.0/MSQ_SQRT_TWO;
const double tau = det(T);
if (TMetric::invalid_determinant(tau)) { // barrier
MSQ_SETERR(err)( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
return false;
}
const double inv_tau = 1.0/tau;
const double invnorm = 1.0/norm;
const double f = norm - invroot * trace(T);
result = 0.5 * inv_tau * f;
const MsqMatrix<2,2> adjt = transpose_adj(T);
deriv_wrt_T = invnorm * T;
pluseq_scaled_I( deriv_wrt_T, -invroot );
deriv_wrt_T *= 0.5;
deriv_wrt_T -= result * adjt;
deriv_wrt_T *= inv_tau;
const double a = 0.5 * inv_tau * invnorm;
set_scaled_outer_product( second_wrt_T, -a*invnorm*invnorm, T );
pluseq_scaled_I( second_wrt_T, a );
pluseq_scaled_outer_product( second_wrt_T, f*inv_tau*inv_tau*inv_tau, adjt );
pluseq_scaled_2nd_deriv_of_det( second_wrt_T, -0.5*f*inv_tau*inv_tau, T );
pluseq_scaled_sum_outer_product( second_wrt_T, -0.5*inv_tau*inv_tau*invnorm, T, adjt );
pluseq_scaled_sum_outer_product_I( second_wrt_T, 0.5*inv_tau*inv_tau*invroot, adjt );
return true;
}
template <unsigned DIM> static inline
bool hess( const MsqMatrix<DIM,DIM>& T,
double& result,
MsqMatrix<DIM,DIM>& deriv,
MsqMatrix<DIM,DIM>* second )
{
const double norm = Frobenius(T);
const double invroot = 1.0/DimConst<DIM>::sqrt();
const double tau = det(T);
if (TMetric::invalid_determinant(tau)) { // barrier
result = 0.0;
return false;
}
const double inv_tau = 1.0/tau;
const double invnorm = 1.0/norm;
const double f = norm - invroot * trace(T);
result = 0.5 * inv_tau * f;
const MsqMatrix<DIM,DIM> adjt = transpose_adj(T);
deriv = invnorm * T;
pluseq_scaled_I( deriv, -invroot );
deriv *= 0.5;
deriv -= result * adjt;
deriv *= inv_tau;
const double a = 0.5 * inv_tau * invnorm;
set_scaled_outer_product( second, -a*invnorm*invnorm, T );
pluseq_scaled_I( second, a );
pluseq_scaled_outer_product( second, f*inv_tau*inv_tau*inv_tau, adjt );
pluseq_scaled_2nd_deriv_of_det( second, -0.5*f*inv_tau*inv_tau, T );
pluseq_scaled_sum_outer_product( second, -0.5*inv_tau*inv_tau*invnorm, T, adjt );
pluseq_scaled_sum_outer_product_I( second, 0.5*inv_tau*inv_tau*invroot, adjt );
return true;
}
bool Target2DShapeOrientBarrier::evaluate_with_hess( const MsqMatrix<2,2>& A,
const MsqMatrix<2,2>& W,
double& result,
MsqMatrix<2,2>& deriv,
MsqMatrix<2,2> second[3],
MsqError& err )
{
const MsqMatrix<2,2> Winv = inverse(W);
const MsqMatrix<2,2> T = A * Winv;
const double norm = Frobenius(T);
const double invroot = 1.0/MSQ_SQRT_TWO;
const double tau = det(T);
if (invalid_determinant(tau)) { // barrier
result = 0.0;
return false;
}
const double inv_tau = 1.0/tau;
const double invnorm = 1.0/norm;
const double f = norm - invroot * trace(T);
result = 0.5 * inv_tau * f;
const MsqMatrix<2,2> adjt = transpose_adj(T);
deriv = invnorm * T;
deriv(0,0) -= invroot;
deriv(1,1) -= invroot;
deriv *= 0.5;
deriv -= result * adjt;
deriv *= inv_tau;
deriv = deriv * transpose(Winv);
const double a = 0.5 * inv_tau * invnorm;
set_scaled_outer_product( second, -a*invnorm*invnorm, T );
pluseq_scaled_I( second, a );
pluseq_scaled_outer_product( second, f*inv_tau*inv_tau*inv_tau, adjt );
pluseq_scaled_2nd_deriv_of_det( second, -0.5*f*inv_tau*inv_tau );
pluseq_scaled_sum_outer_product( second, -0.5*inv_tau*inv_tau*invnorm, T, adjt );
pluseq_scaled_sum_outer_product_I( second, 0.5*inv_tau*inv_tau*invroot, adjt );
second_deriv_wrt_product_factor( second, Winv );
return true;
}
