import math
from collections import OrderedDict
from functools import reduce
from typing import Tuple, Union
import torch
from multipledispatch import dispatch
from multipledispatch.variadic import Variadic
import funsor.ops as ops
from funsor.cnf import Contraction, GaussianMixture
from funsor.delta import Delta
from funsor.domains import bint
from funsor.gaussian import Gaussian, align_gaussian, cholesky, cholesky_inverse
from funsor.ops import AssociativeOp
from funsor.terms import Funsor, Independent, Number, Reduce, Unary, eager, moment_matching, normalize
from funsor.torch import Tensor, align_tensor
@dispatch(str, str, Variadic[(Gaussian, GaussianMixture)])
def eager_cat_homogeneous(name, part_name, *parts):
assert parts
output = parts[0].output
inputs = OrderedDict([(part_name, None)])
for part in parts:
assert part.output == output
assert part_name in part.inputs
inputs.update(part.inputs)
int_inputs = OrderedDict((k, v) for k, v in inputs.items() if v.dtype != "real")
real_inputs = OrderedDict((k, v) for k, v in inputs.items() if v.dtype == "real")
inputs = int_inputs.copy()
inputs.update(real_inputs)
discretes = []
info_vecs = []
precisions = []
for part in parts:
inputs[part_name] = part.inputs[part_name]
int_inputs[part_name] = inputs[part_name]
shape = tuple(d.size for d in int_inputs.values())
if isinstance(part, Gaussian):
discrete = None
gaussian = part
elif issubclass(type(part), GaussianMixture): # TODO figure out why isinstance isn't working
discrete, gaussian = part.terms[0], part.terms[1]
discrete = align_tensor(int_inputs, discrete).expand(shape)
else:
raise NotImplementedError("TODO")
discretes.append(discrete)
info_vec, precision = align_gaussian(inputs, gaussian)
info_vecs.append(info_vec.expand(shape + (-1,)))
precisions.append(precision.expand(shape + (-1, -1)))
if part_name != name:
del inputs[part_name]
del int_inputs[part_name]
dim = 0
info_vec = torch.cat(info_vecs, dim=dim)
precision = torch.cat(precisions, dim=dim)
inputs[name] = bint(info_vec.size(dim))
int_inputs[name] = inputs[name]
result = Gaussian(info_vec, precision, inputs)
if any(d is not None for d in discretes):
for i, d in enumerate(discretes):
if d is None:
discretes[i] = info_vecs[i].new_zeros(info_vecs[i].shape[:-1])
discrete = torch.cat(discretes, dim=dim)
result += Tensor(discrete, int_inputs)
return result
#################################
# patterns for moment-matching
#################################
[docs]@moment_matching.register(Contraction, AssociativeOp, AssociativeOp, frozenset, Variadic[object])
def moment_matching_contract_default(*args):
return None
[docs]@moment_matching.register(Contraction, ops.LogAddExpOp, ops.AddOp, frozenset, (Number, Tensor), Gaussian)
def moment_matching_contract_joint(red_op, bin_op, reduced_vars, discrete, gaussian):
approx_vars = frozenset(k for k in reduced_vars if k in gaussian.inputs
and gaussian.inputs[k].dtype != 'real')
exact_vars = reduced_vars - approx_vars
if exact_vars and approx_vars:
return Contraction(red_op, bin_op, exact_vars, discrete, gaussian).reduce(red_op, approx_vars)
if approx_vars and not exact_vars:
discrete += gaussian.log_normalizer
new_discrete = discrete.reduce(ops.logaddexp, approx_vars.intersection(discrete.inputs))
new_discrete = discrete.reduce(ops.logaddexp, approx_vars.intersection(discrete.inputs))
num_elements = reduce(ops.mul, [
gaussian.inputs[k].num_elements for k in approx_vars.difference(discrete.inputs)], 1)
if num_elements != 1:
new_discrete -= math.log(num_elements)
int_inputs = OrderedDict((k, d) for k, d in gaussian.inputs.items() if d.dtype != 'real')
probs = (discrete - new_discrete.clamp_finite()).exp()
old_loc = Tensor(gaussian.info_vec.unsqueeze(-1).cholesky_solve(gaussian._precision_chol).squeeze(-1),
int_inputs)
new_loc = (probs * old_loc).reduce(ops.add, approx_vars)
old_cov = Tensor(cholesky_inverse(gaussian._precision_chol), int_inputs)
diff = old_loc - new_loc
outers = Tensor(diff.data.unsqueeze(-1) * diff.data.unsqueeze(-2), diff.inputs)
new_cov = ((probs * old_cov).reduce(ops.add, approx_vars) +
(probs * outers).reduce(ops.add, approx_vars))
# Numerically stabilize by adding bogus precision to empty components.
total = probs.reduce(ops.add, approx_vars)
mask = (total.data == 0).to(total.data.dtype).unsqueeze(-1).unsqueeze(-1)
new_cov.data += mask * torch.eye(new_cov.data.size(-1))
new_precision = Tensor(cholesky_inverse(cholesky(new_cov.data)), new_cov.inputs)
new_info_vec = new_precision.data.matmul(new_loc.data.unsqueeze(-1)).squeeze(-1)
new_inputs = new_loc.inputs.copy()
new_inputs.update((k, d) for k, d in gaussian.inputs.items() if d.dtype == 'real')
new_gaussian = Gaussian(new_info_vec, new_precision.data, new_inputs)
new_discrete -= new_gaussian.log_normalizer
return new_discrete + new_gaussian
return None
####################################################
# Patterns for normalizing
####################################################
[docs]@eager.register(Reduce, ops.AddOp, Unary[ops.ExpOp, Funsor], frozenset)
def eager_reduce_exp(op, arg, reduced_vars):
# x.exp().reduce(ops.add) == x.reduce(ops.logaddexp).exp()
log_result = arg.arg.reduce(ops.logaddexp, reduced_vars)
if log_result is not normalize(Reduce, ops.logaddexp, arg.arg, reduced_vars):
return log_result.exp()
return None
[docs]@eager.register(Independent,
(Contraction[ops.NullOp, ops.AddOp, frozenset, Tuple[Delta, Union[Number, Tensor], Gaussian]],
Contraction[ops.NullOp, ops.AddOp, frozenset, Tuple[Delta, Union[Number, Tensor, Gaussian]]]),
str, str, str)
def eager_independent_joint(joint, reals_var, bint_var, diag_var):
if diag_var not in joint.terms[0].fresh:
return None
delta = Independent(joint.terms[0], reals_var, bint_var, diag_var)
new_terms = (delta,) + tuple(t.reduce(ops.add, bint_var) for t in joint.terms[1:])
return reduce(joint.bin_op, new_terms)