template.class_template.SymmetryOrbitEQN.hessp

SymmetryOrbitEQN.hessp(left_other, right_other, **kwargs)

Tensor product u * H * v where H is the matrix of second derivatives of governing equations.

Parameters

left_otherOrbit

Orbit whose state is to be multiplied with the Hessian on the LEFT

right_otherOrbit

Orbit whose orbit_vector is to be multiplied with the Hessian on the RIGHT

kwargsdict

Any keywords relevant for the tensor-free evaluation of the Hessian product.

Returns

Orbit :

Orbit whose state and parameters are the product of orbit_vector() with matrix of second derivatives.

Notes

Requires an equation to define, just like rmatvec and matvec; return zeros because no equation here. Tensor multiplication can be written u * d^2 F * v, dimensions of each component are: u=(N,) d^2F = (N, N+d-c, N+d-c), v = (N+d-c, 1); therefore it returns a vector of dimension (N+d-c, 1) this orbit_vector is then returned as an Orbit instance. N=number of state variables, p=parameters, c=constants