bool Target3DShapeOrientBarrierAlt1::evaluate_with_Hess( const MsqMatrix<3,3>& A,
const MsqMatrix<3,3>& W,
double& result,
MsqMatrix<3,3>& deriv_wrt_A,
MsqMatrix<3,3> second_wrt_A[6],
MsqError& err )
{
MsqMatrix<3,3> Winv = inverse(W);
MsqMatrix<3,3> T = A * Winv;
double tau = det(T);
if (invalid_determinant(tau)) {
result = 0.0;
return false;
}
const double b = 0.5/tau;
// calculate non-barrier value (ShapeOrientAlt1)
const double tr = trace(T);
const double f = MSQ_ONE_THIRD * fabs(tr);
result = sqr_Frobenius( T ) - f * tr;
// calculate non-barrier first derivatives
deriv_wrt_A = T;
deriv_wrt_A(0,0) -= f;
deriv_wrt_A(1,1) -= f;
deriv_wrt_A(2,2) -= f;
deriv_wrt_A *= 2;
// calculate barrier second derivs
const MsqMatrix<3,3> adjt = transpose_adj(T);
set_scaled_sum_outer_product( second_wrt_A, -b/tau, deriv_wrt_A, adjt );
pluseq_scaled_outer_product( second_wrt_A, result/(tau*tau*tau), adjt );
pluseq_scaled_2nd_deriv_of_det( second_wrt_A, -result * b / tau, T );
// calculate non-barrier barrier portion of second derivs
pluseq_scaled_I( second_wrt_A, 1/tau );
pluseq_scaled_outer_product_I_I( second_wrt_A, MSQ_ONE_THIRD/tau * (tr < 0 ? 1 : -1) );
// calculate barrier derivs from non-barrier
deriv_wrt_A *= tau;
deriv_wrt_A -= result * adjt;
deriv_wrt_A *= b/tau;
// barrier value from non-barrier
result *= b;
// convert from derivs wrt T to derivs wrt A
deriv_wrt_A = deriv_wrt_A * transpose(Winv);
second_deriv_wrt_product_factor( second_wrt_A, Winv );
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;
}
bool TShapeOrientB2::evaluate_with_hess( const MsqMatrix<3,3>& T,
double& result,
MsqMatrix<3,3>& deriv_wrt_T,
MsqMatrix<3,3> second_wrt_T[6],
MsqError& err )
{
double tau = det(T);
if (TMetric::invalid_determinant(tau)) {
MSQ_SETERR(err)( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
result = 0.0;
return false;
}
const double b = 0.5/tau;
// calculate non-barrier value (ShapeOrientAlt1)
const double tr = trace(T);
const double f = MSQ_ONE_THIRD * fabs(tr);
result = sqr_Frobenius( T ) - f * tr;
// calculate non-barrier first derivatives
deriv_wrt_T = T;
pluseq_scaled_I( deriv_wrt_T, -f );
deriv_wrt_T *= 2;
// calculate barrier second derivs
const MsqMatrix<3,3> adjt = transpose_adj(T);
set_scaled_sum_outer_product( second_wrt_T, -b/tau, deriv_wrt_T, adjt );
pluseq_scaled_outer_product( second_wrt_T, result/(tau*tau*tau), adjt );
pluseq_scaled_2nd_deriv_of_det( second_wrt_T, -result * b / tau, T );
// calculate non-barrier barrier portion of second derivs
pluseq_scaled_I( second_wrt_T, 1/tau );
pluseq_scaled_outer_product_I_I( second_wrt_T, MSQ_ONE_THIRD/tau * (tr < 0 ? 1 : -1) );
// calculate barrier derivs from non-barrier
deriv_wrt_T *= tau;
deriv_wrt_T -= result * adjt;
deriv_wrt_T *= b/tau;
// barrier value from non-barrier
result *= b;
return true;
}
