def evaluate(self, values, use_pfun=True):
""" Evaluates value(s) belonging to the domain of the variable.
:param values: None, set of a single integer, array, or scalar.
:param use_pfun: boolean flag to make use of pfun if previously set.
:return: a NumPy array of the values (see Variable.evaluate()):
"""
use_pfun = use_pfun and self._pfun is not None and isunitsetint(values)
# If not using pfun while random sampling, we use sfun for booleans
if not use_pfun:
if self._vtype in VTYPES[bool] and hasattr(self._sfun, 'expr'):
if isunitsetint(values) and self._sfun.expr == bernoulli_sfun:
number = list(values)[0]
if not number or number < 0:
number = number if not number else -number
return Distribution(self._name,
{self.name: self._sfun[None](number)})
return super().evaluate(values)
# Evaluate values from inverse cdf bounded within cdf limits
number = list(values)[0]
assert self.isfinite, \
"Cannot evaluate {} values for bounds: {}".format(values, self._ulims)
lims = self.pfun[0](self._ulims)
values = uniform(
lims[0], lims[1], number,
isinstance(self._vset[0], tuple),
isinstance(self._vset[1], tuple)
)
return Distribution(self._name, {self.name: self.pfun[1](values)})
def interp(self, *args, cond_pdf=False):
# args in order of mean - one must be a unitsetint
idx = None
dmu = np.empty((self._n, 1), dtype=float)
vals = [arg for arg in args]
for i, arg in enumerate(args):
if isunitsetint(arg):
if idx is None:
idx = i
else:
raise ValueError(
"Only one argument can be interpolated at a time")
else:
dmu[i] = arg - self._mean[i]
assert idx is not None, "No variable specified for interpolation"
dmu = np.delete(dmu, (idx), axis=0)
lims = self._cdfs[idx]
number = list(args[idx])[0]
cdf = uniform(lims[0], lims[1], number)
mean = self._mean[idx] + float(self._coef[idx].dot(dmu))
stdv = self._stdv[idx]
vals = scipy.stats.norm.ppf(cdf, loc=mean, scale=stdv)
if not cond_pdf:
return vals
return vals, scipy.stats.norm.pdf(vals, loc=mean, scale=stdv)
def eval_step(self, pred_vals, succ_vals, reverse=False):
""" Returns adjusted succ_vals """
# Evaluate deltas if required
if succ_vals is None:
if self._delta is None:
pred_values = list(pred_vals.values())
if all([isscalar(pred_value) for pred_value in pred_values]):
raise ValueError(
"Stochastic step sampling not supported for Field; use RF"
)
else:
succ_vals = pred_vals
else:
succ_vals = self.eval_delta()
elif isinstance(succ_vals, Expression) or \
isinstance(succ_vals, (tuple, self._delta_type)):
succ_vals = self.eval_delta(succ_vals)
# Apply deltas
cond = None
if isinstance(succ_vals, self._delta_type):
succ_vals = self.apply_delta(pred_vals, succ_vals)
elif isunitsetint(succ_vals):
raise ValueError(
"Stochastic step sampling not supported for Field; use RF")
# Initialise outputs with predecessor values
dims = {}
kwargs = {'reverse': reverse}
if cond is not None:
kwargs = {'cond': cond}
vals = collections.OrderedDict()
for key in self._keylist:
vals.update({key: pred_vals[key]})
if succ_vals is None:
return vals, dims, kwargs
# If stepping, add successor values
for key in self._keylist:
mod_key = key + "'"
succ_key = key if mod_key not in succ_vals else mod_key
vals.update({key + "'": succ_vals[succ_key]})
return vals, dims, kwargs
def parse_args(self, *args, **kwds):
""" Returns (values, iid) from *args and **kwds """
pass_all = False if 'pass_all' not in kwds else kwds.pop('pass_all')
values = parse_as_str_dict(*args, **kwds)
seen_keys = []
for key, val in values.items():
count_comma = key.count(',')
if count_comma:
seen_keys.extend(key.split(','))
if isinstance(val, (tuple, list)):
assert len(val) == count_comma+1, \
"Mismatch in key specification {} and number of values {}".\
format(key, len(val))
else:
values.update({key: [val] * (count_comma + 1)})
else:
seen_keys.append(key)
if not pass_all:
assert seen_keys[-1] in self._keyset, \
"Unrecognised key {} among available Variables {}".format(
seen_keys[-1], self._keyset)
# Default values
def_val = None
if self._anyfloat:
if not len(values):
def_val = {0}
else:
def_val = {0}
for val in values.values():
if isunitsetint(val):
if val == {0}:
def_val = None
for key in self._keylist:
if key not in seen_keys:
values.update({key: def_val})
if pass_all:
list_keys = list(values.keys())
for key in list_keys:
if key not in self._keylist:
values.pop(key)
return values
def eval_step(self, pred_vals, succ_vals, reverse=False):
""" Returns adjusted succ_vals """
if succ_vals is None:
if self._delta is None:
if all([isscalar(pred_value) for pred_value in pred_vals]):
succ_vals = {0}
# If not sampling succeeding values, use deterministic call
if not isunitsetint(succ_vals):
return super().eval_step(pred_vals, succ_vals, reverse=reverse)
if self._tfun is not None and self._tfun.callable:
succ_vals = self.eval_tfun(pred_vals)
elif self._nvars == 1:
var = self._varlist[0]
tran = var.tran
tfun = var.tfun
if (tran is not None and not tran.callable) or \
(tfun is not None and tfun.callable):
vals, dims, kwargs = var.eval_step(pred_vals[var.name],
succ_vals,
reverse=reverse)
return vals, dims, kwargs
raise ValueError("Transitional CDF calling requires callable tfun")
else:
raise ValueError("Transitional CDF calling requires callable tfun")
# Initialise outputs with predecessor values
dims = {}
kwargs = {'reverse': reverse}
vals = collections.OrderedDict()
for key in self._keylist:
vals.update({key: pred_vals[key]})
if succ_vals is None and self._tran is None:
return vals, dims, kwargs
# If stepping or have a transition function, add successor values
for key in self._keylist:
mod_key = key + "'"
succ_key = key if mod_key not in succ_vals else mod_key
vals.update({key + "'": succ_vals[succ_key]})
return vals, dims, kwargs
def product(*args, **kwds):
""" Multiplies two or more PDs subject to the following:
1. They must not share the same marginal variables.
2. Conditional variables must be identical unless contained as marginal from
another distribution.
"""
from probayes.pd import PD
# Check pscales, scalars, possible fasttrack
if not len(args):
return None
kwds = dict(kwds)
pscales = [arg.pscale for arg in args]
pscale = kwds.get('pscale', None) or prod_pscale(pscales)
aresingleton = [arg.issingleton for arg in args]
maybe_fasttrack = all(aresingleton) and \
np.all(pscale == np.array(pscales)) and \
pscale in [0, 1.]
# Collate vals, probs, marg_names, and cond_names as lists
vals = [collections.OrderedDict(arg) for arg in args]
probs = [arg.prob for arg in args]
marg_names = [list(arg.marg.values()) for arg in args]
cond_names = [list(arg.cond.values()) for arg in args]
# Detect uniqueness in marginal keys and identical conditionals
all_marg_keys = []
for arg in args:
all_marg_keys.extend(list(arg.marg.keys()))
marg_sets = None
if len(all_marg_keys) != len(set(all_marg_keys)):
marg_keys, cond_keys, marg_sets, = None, None, None
for arg in args:
if marg_keys is None:
marg_keys = list(arg.marg.keys())
elif marg_keys != list(arg.marg.keys()):
marg_keys = None
break
if cond_keys is None:
cond_keys = list(arg.cond.keys())
elif cond_keys != list(arg.cond.keys()):
marg_keys = None
break
if marg_keys:
are_marg_sets = np.array([isunitsetint(arg[marg_key]) for
marg_key in marg_keys])
if marg_sets is None:
if np.any(are_marg_sets):
marg_sets = are_marg_sets
else:
marg_keys = None
break
elif not np.all(marg_sets == are_marg_sets):
marg_keys = None
break
assert marg_keys is not None and marg_sets is not None, \
"Non-unique marginal variables for currently not supported: {}".\
format(all_marg_keys)
maybe_fasttrack = True
# Maybe fast-track identical conditionals
if maybe_fasttrack:
marg_same = True
cond_same = True
if marg_sets is None: # no need to recheck if not None (I think)
marg_same = True
for name in marg_names[1:]:
if marg_names[0] != name:
marg_same = False
break
cond_same = not any(cond_names)
if not cond_same:
cond_same = True
for name in cond_names[1:]:
if cond_names[0] != name:
cond_same = False
break
if marg_same and cond_same:
marg_names = marg_names[0]
cond_names = cond_names[0]
prod_marg_name = ','.join(marg_names)
prod_cond_name = ','.join(cond_names)
prod_name = '|'.join([prod_marg_name, prod_cond_name])
prod_vals = collections.OrderedDict()
for i, val in enumerate(vals):
areunitsetints = np.array([isunitsetint(_val)
for _val in val.values()])
if not np.any(areunitsetints):
prod_vals.update(val)
else:
assert marg_sets is not None, "Variable mismatch"
assert np.all(marg_sets == areunitsetints[:len(marg_sets)]), \
"Variable mismatch"
if not len(prod_vals):
prod_vals.update(collections.OrderedDict(val))
else:
for j, key in enumerate(prod_vals.keys()):
if areunitsetints[j]:
prod_vals.update({key: {list(prod_vals[key])[0] + \
list(val[key])[0]}})
if marg_sets is not None:
prob, pscale = prod_rule(*tuple(probs), pscales=pscales, pscale=pscale)
return PD(prod_name, prod_vals, dims=args[0].dims, prob=prob, pscale=pscale)
else:
prod_prob = float(sum(probs)) if iscomplex(pscale) else float(np.prod(probs))
return PD(prod_name, prod_vals, prob=prod_prob, pscale=pscale)
# Check cond->marg accounts for all differences between conditionals
prod_marg = [name for dist_marg_names in marg_names \
for name in dist_marg_names]
prod_marg_name = ','.join(prod_marg)
flat_cond_names = [name for dist_cond_names in cond_names \
for name in dist_cond_names]
cond2marg = [cond_name for cond_name in flat_cond_names \
if cond_name in prod_marg]
prod_cond = [cond_name for cond_name in flat_cond_names \
if cond_name not in cond2marg]
cond2marg_set = set(cond2marg)
# Check conditionals compatible
prod_cond_set = set(prod_cond)
cond2marg_dict = {name: None for name in cond2marg}
for i, arg in enumerate(args):
cond_set = set(cond_names[i]) - cond2marg_set
if cond_set:
assert prod_cond_set == cond_set, \
"Incompatible product conditional {} for conditional set {}: ".format(
prod_cond_set, cond_set)
for name in cond2marg:
if name in arg.keys():
values = arg[name]
if not isscalar(values):
values = np.ravel(values)
if cond2marg_dict[name] is None:
cond2marg_dict[name] = values
elif not np.allclose(cond2marg_dict[name], values):
raise ValueError("Mismatch in values for condition {}".format(name))
# Establish product name, values, and dimensions
prod_keys = str2key(prod_marg + prod_cond)
prod_nkeys = len(prod_keys)
prod_aresingleton = np.zeros(prod_nkeys, dtype=bool)
prod_areunitsetints = np.zeros(prod_nkeys, dtype=bool)
prod_cond_name = ','.join(prod_cond)
prod_name = prod_marg_name if not len(prod_cond_name) \
else '|'.join([prod_marg_name, prod_cond_name])
prod_vals = collections.OrderedDict()
for i, key in enumerate(prod_keys):
values = None
for val in vals:
if key in val.keys():
values = val[key]
prod_areunitsetints[i] = isunitsetint(val[key])
if prod_areunitsetints[i]:
values = {0}
break
assert values is not None, "Values for key {} not found".format(key)
prod_aresingleton[i] = issingleton(values)
prod_vals.update({key: values})
if np.any(prod_areunitsetints):
for i, key in enumerate(prod_keys):
if prod_areunitsetints[i]:
for val in vals:
if key in val:
assert isunitsetint(val[key]), "Mismatch in variables {} vs {}".\
format(prod_vals, val)
prod_vals.update({key: {list(prod_vals[key])[0] + list(val[key])[0]}})
prod_newdims = np.array(np.logical_not(prod_aresingleton))
dims_shared = False
for arg in args:
argdims = [dim for dim in arg.dims.values() if dim is not None]
if len(argdims) != len(set(argdims)):
dims_shared = True
# Shared dimensions limit product dimensionality
if dims_shared:
seen_keys = set()
for i, key in enumerate(prod_keys):
if prod_newdims[i] and key not in seen_keys:
for arg in args:
if key in arg.dims:
dim = arg.dims[key]
seen_keys.add(key)
for argkey, argdim in arg.dims.items():
seen_keys.add(argkey)
if argkey != key and argdim is not None:
if dim == argdim:
index = prod_keys.index(argkey)
prod_newdims[index] = False
prod_cdims = np.cumsum(prod_newdims)
prod_ndims = prod_cdims[-1]
# Fast-track scalar products
if maybe_fasttrack and prod_ndims == 0:
prob = float(sum(probs)) if iscomplex(pscale) else float(np.prod(probs))
return PD(prod_name, prod_vals, prob=prob, pscale=pscale)
# Reshape values - they require no axes swapping
ones_ndims = np.ones(prod_ndims, dtype=int)
prod_shape = np.ones(prod_ndims, dtype=int)
scalarset = set()
prod_dims = collections.OrderedDict()
for i, key in enumerate(prod_keys):
if prod_aresingleton[i]:
scalarset.add(key)
else:
values = prod_vals[key]
re_shape = np.copy(ones_ndims)
dim = prod_cdims[i]-1
prod_dims.update({key: dim})
re_shape[dim] = values.size
prod_shape[dim] = values.size
prod_vals.update({key: values.reshape(re_shape)})
# Match probability axes and shapes with axes swapping then reshaping
for i in range(len(args)):
prob = probs[i]
if not isscalar(prob):
dims = collections.OrderedDict()
for key, val in args[i].dims.items():
if val is not None:
dims.update({val: prod_dims[key]})
old_dims = []
new_dims = []
for key, val in dims.items():
if key not in old_dims:
old_dims.append(key)
new_dims.append(val)
if len(old_dims) > 1 and not old_dims == new_dims:
max_dims_inc = max(new_dims) + 1
while prob.ndim < max_dims_inc:
prob = np.expand_dims(prob, -1)
prob = np.moveaxis(prob, old_dims, new_dims)
re_shape = np.copy(ones_ndims)
for dim in new_dims:
re_shape[dim] = prod_shape[dim]
probs[i] = prob.reshape(re_shape)
# Multiply the probabilities and output the result as a distribution instance
prob, pscale = prod_rule(*tuple(probs), pscales=pscales, pscale=pscale)
return PD(prod_name, prod_vals, dims=prod_dims, prob=prob, pscale=pscale)
def summate(*args):
""" Quick and dirty concatenation """
from probayes.pd import PD
if not len(args):
return None
pscales = [arg.pscale for arg in args]
vals = [dict(arg) for arg in args]
probs = [arg.prob for arg in args]
# Check pscales are the same
pscale = pscales[0]
for _pscale in pscales[1:]:
assert pscale == _pscale, \
"Cannot summate distributions with different pscales"
# Check marginal and conditional keys
marg_keys = list(args[0].marg.keys())
cond_keys = list(args[0].cond.keys())
for arg in args[1:]:
assert marg_keys == list(arg.marg.keys()), \
"Marginal variable names not identical across distributions: {}"
assert cond_keys == list(arg.cond.keys()), \
"Conditional variable names not identical across distributions: {}"
sum_keys = marg_keys + cond_keys
sum_name = ','.join(marg_keys)
if cond_keys:
sum_name += '|' + ','.join(cond_keys)
# If all singleton, concatenate in dimension 0
if all([arg.issingleton for arg in args]):
unitsets = {key: isunitsetint(args[0][key]) for key in sum_keys}
sum_dims = {key: None if unitsets[key] else 0 for key in sum_keys}
sum_vals = {key: 0 if unitsets[key] else [] for key in sum_keys}
sum_prob = []
for arg in args:
for key, val in arg.items():
if unitsets[key]:
assert isunitsetint(val), \
"Cannot mix unspecified set and specified values"
sum_vals[key] += list(val)[0]
else:
assert not isunitsetint(val), \
"Cannot mix unspecified set and specified values"
sum_vals[key].append(val)
sum_prob.append(arg.prob)
for key in sum_keys:
if unitsets[key]:
sum_vals[key] = {sum_vals[key]}
else:
sum_vals[key] = np.ravel(sum_vals[key])
sum_prob = np.ravel(sum_prob)
return PD(sum_name, sum_vals, dims=sum_dims, prob=sum_prob, pscale=pscale)
# 2. all identical but in one dimension: concatenate in that dimension
# TODO: fix the remaining code of this function below
sum_vals = collections.OrderedDict(args[0])
sum_dims = [None] * (len(args) - 1)
for i, arg in enumerate(args):
if i == 0:
continue
for key in marg_keys:
if sum_dims[i-1] is not None:
continue
elif not arg.singleton(key):
key_vals = arg[key]
if key_vals.size == sum_vals[key].size:
if np.allclose(key_vals, sum_vals[key]):
continue
sum_dims[i-1] = arg.dims[key]
assert len(set(sum_dims)) > 1, "Cannot find unique concatenation axis"
sum_dim = sum_dims[0]
sum_dims = args[0].dims
key = marg_keys[sum_dim]
sum_prob = np.copy(probs[0])
for i, val in enumerate(vals):
if i == 0:
continue
sum_vals[key] = np.concatenate([sum_vals[key], val[key]], axis=sum_dim)
sum_prob = np.concatenate([sum_prob, probs[i]], axis=sum_dim)
return PD(sum_name, sum_vals, dims=sum_dims, prob=sum_prob, pscale=pscale)
def eval_step(self, pred_vals, succ_vals, reverse=False):
""" Evaluates a successive values from previous values with an optional
direction reversal flag, outputting a three-length tuple that includes the
successive values in the first argument.
:param pred_vals: predecessor values (NumPy array).
:param succ_vals: succecessor values (see step()).
:param reverse: boolean flag (default False) to reverse direction.
:return vals: a dictionary including both predecessor and successor values.
:return dims: a dictionary with dimension indices for the values in vals.
:return kwargs: a dictionary that includes optional keywords for eval_tran()
"""
if succ_vals is None:
assert self._tran is not None, "No transitional function specified"
if isinstance(pred_vals, dict):
pred_vals = pred_vals[self.name]
kwargs = dict() # to pass over to eval_tran()
if succ_vals is None:
if self._delta is None:
succ_vals = {0} if isscalar(pred_vals) else pred_vals
else:
delta = self.eval_delta()
succ_vals = self.apply_delta(pred_vals, delta)
#---------------------------------------------------------------------------
def _reshape_vals(pred, succ):
dims = {}
ndim = 0
# Now reshape the values according to succ > prev dimensionality
if issingleton(succ):
dims.update({self._name+"'": None})
else:
dims.update({self._name+"'": ndim})
ndim += 1
if issingleton(pred):
dims.update({self._name: None})
else:
dims.update({self._name: ndim})
ndim += 1
if ndim == 2: # pred_vals distributed along inner dimension:
pred = pred.reshape([1, pred.size])
succ = succ.reshape([succ.size, 1])
return pred, succ, dims
#---------------------------------------------------------------------------
# Scalar treatment is the most trivial and ignores reverse
if self._tran is None or self._tran.isscalar:
if isunitsetint(succ_vals):
succ_vals = self.evaluate(succ_vals, use_pfun=False)[self._name]
elif isunitsetfloat(succ_vals):
assert self._vtype in VTYPES[float], \
"Inverse CDF sampling for scalar probabilities unavailable for " + \
"{} data type".format(self._vtype)
cdf_val = list(succ_vals)[0]
lo, hi = min(self._limits), max(self._limits)
succ_val = lo*(1.-cdf_val) + hi*cdf_val
if self._ufun is not None:
succ_val = self.ufun[-1](succ_val)
prob = self._tran() if self._tran is not None else None
pred_vals, succ_vals, dims = _reshape_vals(pred_vals, succ_vals)
# Handle discrete non-callables
elif not self._tran.callable:
if reverse and not self._tran.ismulti and not self.__sym_tran:
warnings.warn("Reverse direction called from asymmetric transitional")
prob = self._tran() if not self._tran.ismulti else \
self._tran[int(reverse)]()
if isunitset(succ_vals):
succ_vals, pred_idx, succ_idx = matrix_cond_sample(pred_vals,
succ_vals,
prob=prob,
vset=self._vset)
kwargs.update({'pred_idx': pred_idx, 'succ_idx': succ_idx})
pred_vals, succ_vals, dims = _reshape_vals(pred_vals, succ_vals)
# That just leaves callables
else:
kwds = {self._name: pred_vals}
if isunitset(succ_vals):
assert self._tfun is not None, \
"Conditional sampling requires setting CDF and ICDF " + \
"conditional functions using rv.set.tfun()"
assert isscalar(pred_vals), \
"Successor sampling only possible with scalar predecessors"
succ_vals = list(succ_vals)[0]
if type(succ_vals) in VTYPES[int] or type(succ_vals) in VTYPES[np.uint]:
lo, hi = min(self._ulims), max(self._ulims)
kwds.update({self._name+"'": np.array([lo, hi], dtype=float)})
lohi = self._tfun[0](**kwds)
lo, hi = float(min(lohi)), float(max(lohi))
succ_vals = uniform(lo, hi, succ_vals,
isinstance(self._vset[0], tuple),
isinstance(self._vset[1], tuple))
else:
succ_vals = np.atleast_1d(succ_vals)
kwds.update({self._name: pred_vals,
self._name+"'": succ_vals})
succ_vals = self._tfun[1](**kwds)
elif not isscalar(succ_vals):
succ_vals = np.atleast_1d(succ_vals)
pred_vals, succ_vals, dims = _reshape_vals(pred_vals, succ_vals)
vals = collections.OrderedDict({self._name+"'": succ_vals,
self._name: pred_vals})
kwargs.update({'reverse': reverse})
return vals, dims, kwargs