Affine Pattern Matching¶

is_affine
(fn)[source]¶ A sound but incomplete test to determine whether a funsor is affine with respect to all of its real inputs.
Parameters: fn (Funsor) – A funsor. Return type: bool

affine_inputs
(fn)[source]¶ Returns a [sound sub]set of real inputs of
fn
wrt whichfn
is known to be affine.Parameters: fn (Funsor) – A funsor. Returns: A set of input names wrt which fn
is affine.Return type: frozenset

extract_affine
(fn)[source]¶ Extracts an affine representation of a funsor, satisfying:
x = ... const, coeffs = extract_affine(x) y = sum(Einsum(eqn, coeff, Variable(var, coeff.output)) for var, (coeff, eqn) in coeffs.items()) assert_close(y, x) assert frozenset(coeffs) == affine_inputs(x)
The
coeffs
will have one key per input wrt whichfn
is known to be affine (viaaffine_inputs()
), andconst
andcoeffs.values
will all be constant wrt these inputs.The affine approximation is computed by ev evaluating
fn
at zero and each basis vector. To improve performance, users may want to run under theMemoize()
interpretation.Parameters: fn (Funsor) – A funsor that is affine wrt the (add,mul) semiring in some subset of its inputs. Returns: A pair (const, coeffs)
where const is a funsor with no real inputs andcoeffs
is an OrderedDict mapping input name to a(coefficient, eqn)
pair in einsum form.Return type: tuple