Source code for funsor.affine

# Copyright Contributors to the Pyro project.
# SPDX-License-Identifier: Apache-2.0

from collections import OrderedDict
from functools import reduce, singledispatch

import opt_einsum

from funsor.interpreter import gensym
from funsor.tensor import Einsum, Tensor, get_default_prototype
from funsor.terms import Binary, Funsor, Lambda, Reduce, Unary, Variable, Bint

from . import ops

[docs]def is_affine(fn): """ A sound but incomplete test to determine whether a funsor is affine with respect to all of its real inputs. :param Funsor fn: A funsor. :rtype: bool """ return affine_inputs(fn) == _real_inputs(fn)
def _real_inputs(fn): return frozenset(k for k, d in fn.inputs.items() if d.dtype == "real")
[docs]def affine_inputs(fn): """ Returns a [sound sub]set of real inputs of ``fn`` wrt which ``fn`` is known to be affine. :param Funsor fn: A funsor. :return: A set of input names wrt which ``fn`` is affine. :rtype: frozenset """ result = getattr(fn, '_affine_inputs', None) if result is None: result = fn._affine_inputs = _affine_inputs(fn) return result
@singledispatch def _affine_inputs(fn): assert isinstance(fn, Funsor) return frozenset() # Make registration public. affine_inputs.register = _affine_inputs.register @affine_inputs.register(Variable) def _(fn): return _real_inputs(fn) @affine_inputs.register(Unary) def _(fn): if fn.op in (ops.neg, ops.add) or isinstance(fn.op, ops.ReshapeOp): return affine_inputs(fn.arg) return frozenset() @affine_inputs.register(Binary) def _(fn): if fn.op in (ops.add, ops.sub): return affine_inputs(fn.lhs) | affine_inputs(fn.rhs) if fn.op is ops.truediv: return affine_inputs(fn.lhs) - _real_inputs(fn.rhs) if isinstance(fn.op, ops.GetitemOp): return affine_inputs(fn.lhs) if fn.op in (ops.mul, ops.matmul): lhs_affine = affine_inputs(fn.lhs) - _real_inputs(fn.rhs) rhs_affine = affine_inputs(fn.rhs) - _real_inputs(fn.lhs) if not lhs_affine: return rhs_affine if not rhs_affine: return lhs_affine # This multilinear case introduces incompleteness, since some vars # could later be reduced, making remaining vars affine. return frozenset() return frozenset() @affine_inputs.register(Reduce) def _(fn): return affine_inputs(fn.arg) - fn.reduced_vars @affine_inputs.register(Einsum) def _(fn): # This is simply a multiary version of the above Binary(ops.mul, ...) case. results = [] for i, x in enumerate(fn.operands): others = fn.operands[:i] + fn.operands[i+1:] other_inputs = reduce(ops.or_, map(_real_inputs, others), frozenset()) results.append(affine_inputs(x) - other_inputs) # This multilinear case introduces incompleteness, since some vars # could later be reduced, making remaining vars affine. if sum(map(bool, results)) == 1: for result in results: if result: return result return frozenset()
[docs]def extract_affine(fn): """ 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 which ``fn`` is known to be affine (via :func:`affine_inputs` ), and ``const`` and ``coeffs.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 the :func:`~funsor.memoize.memoize` interpretation. :param Funsor fn: A funsor that is affine wrt the (add,mul) semiring in some subset of its inputs. :return: A pair ``(const, coeffs)`` where const is a funsor with no real inputs and ``coeffs`` is an OrderedDict mapping input name to a ``(coefficient, eqn)`` pair in einsum form. :rtype: tuple """ # NB: this depends on the global default backend. prototype = get_default_prototype() # Determine constant part by evaluating fn at zero. inputs = affine_inputs(fn) inputs = OrderedDict((k, v) for k, v in fn.inputs.items() if k in inputs) zeros = {k: Tensor(ops.new_zeros(prototype, v.shape)) for k, v in inputs.items()} const = fn(**zeros) # Determine linear coefficients by evaluating fn on basis vectors. name = gensym('probe') coeffs = OrderedDict() for k, v in inputs.items(): dim = v.num_elements var = Variable(name, Bint[dim]) subs = zeros.copy() subs[k] = Tensor(ops.new_eye(prototype, (dim,)).reshape((dim,) + v.shape))[var] coeff = Lambda(var, fn(**subs) - const).reshape(v.shape + const.shape) inputs1 = ''.join(map(opt_einsum.get_symbol, range(len(coeff.shape)))) inputs2 = inputs1[:len(v.shape)] output = inputs1[len(v.shape):] eqn = '{},{}->{}'.format(inputs1, inputs2, output) coeffs[k] = coeff, eqn return const, coeffs
__all__ = [ "affine_inputs", "extract_affine", "is_affine", ]