Allow derivimplicit to use finite differences.
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In NOCMODL `derivimplicit` uses finite differences to compute each element of the Jacobian. In stead we try to use SymPy, however, if it fails, e.g. because it encounters an opaque function, we allow it to use a finite difference instead.
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In NOCMODL
derivimplicituses finite differences to compute eachelement of the Jacobian. In stead we try to use SymPy, however, if it
fails, e.g. because it encounters an opaque function, we allow it to use
a finite difference instead.
When SymPy can't compute a derivative analytically, it replaces it
with a
Derivative({func}, ({variable}, {n})), which represents thenth derivative offuncw.r.t.variable.In this PR we crawl SymPy's AST to find
Derivativeobjects, andreplace them with a finite difference. The step-with is the same
as used in NEURON for computing the elements of the Jacobian.
Additionally, there's some code to enable computing the
\Delta x.