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;
}
bool Target3DShapeSizeBarrierAlt1::evaluate_with_hess( const MsqMatrix<3,3>& A,
const MsqMatrix<3,3>& W,
double& result,
MsqMatrix<3,3>& wrt_A,
MsqMatrix<3,3> second[6],
MsqError& err )
{
const MsqMatrix<3,3> Winv = inverse(W);
const MsqMatrix<3,3> T = A * Winv;
const double tau = det(T);
if (invalid_determinant(tau)) { // barrier
result = 0.0;
return false;
}
const double f = sqr_Frobenius(T);
const double g = sqr_Frobenius(adj(T));
result = (f + g)/(6 * tau);
MsqMatrix<3,3> dtau = transpose_adj(T);
MsqMatrix<3,3> dg = -transpose(T) * T;
dg(0,0) += f;
dg(1,1) += f;
dg(2,2) += f;
dg = T * dg;
dg *= 2;
wrt_A = T;
wrt_A += 0.5*dg;
wrt_A *= 1.0/3.0;
wrt_A -= result * dtau;
wrt_A *= 1.0/tau;
wrt_A = wrt_A * transpose(Winv);
set_scaled_2nd_deriv_norm_sqr_adj( second, 1.0/6.0, T );
pluseq_scaled_I( second, 1.0/3.0 );
pluseq_scaled_sum_outer_product( second, -1./3./tau, T, dtau );
pluseq_scaled_sum_outer_product( second, -1./6./tau, dg, dtau );
pluseq_scaled_outer_product( second, 2*result/tau, dtau );
pluseq_scaled_2nd_deriv_of_det( second, -result, T );
hess_scale( second, 1.0/tau );
second_deriv_wrt_product_factor( second, Winv );
result -= 1.0;
return true;
}
bool TShapeSize3DB2::evaluate_with_hess( const MsqMatrix<3,3>& T,
double& result,
MsqMatrix<3,3>& wrt_T,
MsqMatrix<3,3> second[6],
MsqError& err )
{
const double tau = det(T);
if (invalid_determinant(tau)) { // barrier
result = 0.0;
return false;
}
const double f = sqr_Frobenius(T);
const double g = sqr_Frobenius(adj(T));
result = (f + g)/(6 * tau);
MsqMatrix<3,3> dtau = transpose_adj(T);
MsqMatrix<3,3> dg = -transpose(T) * T;
dg(0,0) += f;
dg(1,1) += f;
dg(2,2) += f;
dg = T * dg;
dg *= 2;
wrt_T = T;
wrt_T += 0.5*dg;
wrt_T *= 1.0/3.0;
wrt_T -= result * dtau;
wrt_T *= 1.0/tau;
set_scaled_2nd_deriv_norm_sqr_adj( second, 1.0/6.0, T );
pluseq_scaled_I( second, 1.0/3.0 );
pluseq_scaled_sum_outer_product( second, -1./3./tau, T, dtau );
pluseq_scaled_sum_outer_product( second, -1./6./tau, dg, dtau );
pluseq_scaled_outer_product( second, 2*result/tau, dtau );
pluseq_scaled_2nd_deriv_of_det( second, -result, T );
hess_scale( second, 1.0/tau );
result -= 1.0;
return true;
}
