Projection matrices about tornadox

[nathanaelbosch]

Just to make sure I'm thinking about the right thing here: For me it would be enough to implement a make_projmat(d, q, derivative_to_project_onto) that returns the actual projection matrix. Did you expect something different or is that fine?

[pnkraemer]

no that is fine. I think it would be useful to implement it as some linear-operator-thing, but I can make the exact refactoring I have in mind once things work :)

[pnkraemer]

along the lines of:

    def select_derivative(self, state, derivative):

        # Once we allow changed orderings, extend this functionality here.
        # Due to the behaviour in __init__,
        # non-coordinate-representation should be impossible
        assert self.state_ordering == "coordinate"

        derivative_indices = np.arange(
            start=derivative, stop=self.state_dimension, step=(self.num_derivatives + 1)
        )
        return np.take(state, indices=derivative_indices)

    def derivative_selection_operator(self, derivative):

        selection_unit_vector = np.eye(self.num_derivatives + 1)[:, derivative]
        selection_unit_vector_as_matrix = selection_unit_vector.reshape(
            (1, self.num_derivatives + 1)
        )
        selection_matrix = np.kron(
            np.eye(self.wiener_process_dimension), selection_unit_vector_as_matrix
        )
        return selection_matrix

[pnkraemer]

which I know realise is not an operator, my bad. I meant something like

class Projection2Derivative1d:
    def __init__(self, derivative):
        self._derivative = derivative

    def __matmul__(self, other):
        return np.take(other, axis=-2, indices=self.derivative)

and axis=-2 makes sure it behaves like numpy matmul. Non-1d projections are then fairly straightforward, but not really used for EK0, right?