template.class_template.SymmetryOrbitEQN.hess

SymmetryOrbitEQN.hess(**kwargs)

Matrix of second derivatives of the governing equations.

Returns

np.ndarray :

The tensor of second derivatives of the governing equations. Will typically have dimensions equal to (self.orbit_vector.size, self.orbit_vector.size, self.size).

Notes

The components of the tensor \(H_{kj}\) is the vector of derivatives with respect to \(x_k, x_j\) of equation component \(F_i\). The governing equations will typically have vector valued output; in general the matrix of second derivatives of each component is a tensor.

What is returned is the rank 3 tensor with correct shape for a vector valued equation F(x) where x has N degrees of freedom but F only has d dimensions.