orbithunter.EquilibriumOrbitKS.rmatvec

EquilibriumOrbitKS.rmatvec(other, **kwargs)

Matrix-vector product with the adjoint of the Jacobian

Parameters

otherOrbitKS

OrbitKS whose state represents the vector in the matrix-vector product.

Returns

orbit_rmatvecOrbitKS

OrbitKS with values representative of the adjoint-vector product

Notes

The adjoint vector product in this case is defined as J^T * v, where J is the jacobian matrix. Equivalent to evaluation of -v_t + v_xx + v_xxxx - (u .* v_x). In regards to preconditioning (which is very useful for certain numerical methods, right preconditioning and left preconditioning switch meanings when the jacobian is transposed. i.e. Right preconditi oning of the Jacobian can include preconditioning of the state parameters (which in this case are usually incremental corrections dt, dx, ds); this corresponds to LEFT preconditioning of the adjoint.

The derivatives always occur with respect to the parameters of u. therefore, the evaluation of _rmatvec_linear_component and _rnonlinear require the parameters from self.