solprop.backends.multistep_general

The general Adams path: the comparison variants SEP 13 did not select.

PECE, explicit Adams-Bashforth and the matched predictor-corrector pairs controlled by Milne’s estimate (ComparisonMultistep) combine a list of host arrays one product at a time rather than handing a store of history rows to an engine. AdamsMarch hands their trials to GeneralPath, which keeps their arithmetic and shares the march’s controller, history, ledger and lifecycle (SEP 39 phase 0, Q7). The selected method and the one-order-higher PEC variants never reach it.

Classes

GeneralPath(march)

The trials of the general Adams path, on the march they belong to.

class solprop.backends.multistep_general.GeneralPath(march)

Bases: object

The trials of the general Adams path, on the march they belong to.

Parameters:

marchsolprop.backends.multistep.AdamsMarch

The march whose history, order, ledger and controller the trials use.

attempt(dz, *, fixed=False, landing=None)

Try one step of length dz on the general path; commit it if accepted.

Parameters:

dzfloat

The step, m.

fixedbool, optional

Whether the step is a prescribed schedule’s, accepted whatever its norm.

landingtuple or None, optional

Where an accepted step ends, m, and whether that is a hard kink, which restarts the history; None ends it at z + dz and restarts nothing.

Returns:

tuple

Whether the step was accepted, and its scaled error norm.

commit(trial, advanced, source, norm, formula, landing=None)

Adopt an accepted step: the state, the re-anchored history and the proposal.

Parameters:

trial_Trial

The accepted step.

advancednumpy.ndarray

The state at its end, before the boundary treatments.

sourcenumpy.ndarray

The source at the predicted field, in the step’s anchor frame.

normfloat

The step’s scaled error norm.

formulatuple

The nodes and anchor-frame derivatives of the accepted formula.

landingtuple or None, optional

Where the step ends and whether it is a hard kink (attempt()).

correct(trial, source)

Return the accepted increment and its local-defect estimate.

Parameters:

trial_Trial

The step being tried.

sourcenumpy.ndarray

The source at the predicted field, in the anchor’s frame.

Returns:

tuple

The increment v - a_n the step would accept and the estimate of its local defect, both in the anchor’s frame, and the nodes and derivatives of the formula that produced the increment, for dense observation.

next_order(trial, source, norm)

Choose the next step’s order from neighbouring estimates; no extra call.

For the one-order-higher PEC/PECE family the defect of order k is the difference between the k + 1-derivative corrector through the new source and the k-derivative predictor, so orders q - 1 and q + 1 are estimated from the same history and source as the step itself (SEP 13 section 4.4). The order maximising the predicted step wins if it beats the current one by ORDER_HYSTERESIS; the order never rises straight after a rejection.

Parameters:

trial_Trial

The accepted step.

sourcenumpy.ndarray

Its predicted-state source, in the step’s anchor frame.

normfloat

Its scaled defect at its own order.

Returns:

tuple

The next order and the norm it is controlled with.