text: #   Copyright 2020 The PyMC Developers
  #
  #   Licensed under the Apache License, Version 2.0 (the "License");
  #   you may not use this file except in compliance with the License.
  #   You may obtain a copy of the License at
  #
  #       http://www.apache.org/licenses/LICENSE-2.0
  #
  #   Unless required by applicable law or agreed to in writing, software
  #   distributed under the License is distributed on an "AS IS" BASIS,
  #   WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  #   See the License for the specific language governing permissions and
  #   limitations under the License.
  import warnings
  
  from typing import (
      Callable,
      Dict,
      Generator,
      Iterable,
      List,
      Optional,
      Sequence,
      Set,
      Tuple,
      Union,
  )
  
  import aesara
  import aesara.tensor as at
  import numpy as np
  import scipy.sparse as sps
  
  from aeppl.abstract import MeasurableVariable
  from aeppl.logprob import CheckParameterValue
  from aesara import config, scalar
  from aesara.compile.mode import Mode, get_mode
  from aesara.gradient import grad
  from aesara.graph import local_optimizer
  from aesara.graph.basic import (
      Apply,
      Constant,
      Variable,
      clone_get_equiv,
      graph_inputs,
      vars_between,
      walk,
  )
  from aesara.graph.fg import FunctionGraph
  from aesara.graph.op import Op, compute_test_value
  from aesara.sandbox.rng_mrg import MRG_RandomStream as RandomStream
  from aesara.scalar.basic import Cast
  from aesara.tensor.elemwise import Elemwise
  from aesara.tensor.random.op import RandomVariable
  from aesara.tensor.random.var import (
      RandomGeneratorSharedVariable,
      RandomStateSharedVariable,
  )
  from aesara.tensor.shape import SpecifyShape
  from aesara.tensor.sharedvar import SharedVariable
  from aesara.tensor.subtensor import AdvancedIncSubtensor, AdvancedIncSubtensor1
  from aesara.tensor.var import TensorConstant, TensorVariable
  
  from pymc.exceptions import ShapeError
  from pymc.vartypes import continuous_types, isgenerator, typefilter
  
  PotentialShapeType = Union[int, np.ndarray, Sequence[Union[int, Variable]], TensorVariable]
  
  
  __all__ = [
      "gradient",
      "hessian",
      "hessian_diag",
      "inputvars",
      "cont_inputs",
      "floatX",
      "intX",
      "smartfloatX",
      "jacobian",
      "CallableTensor",
      "join_nonshared_inputs",
      "make_shared_replacements",
      "generator",
      "set_at_rng",
      "at_rng",
      "convert_observed_data",
  ]
  
  
  def convert_observed_data(data):
      """Convert user provided dataset to accepted formats."""
  
      if hasattr(data, "to_numpy") and hasattr(data, "isnull"):
          # typically, but not limited to pandas objects
          vals = data.to_numpy()
          null_data = data.isnull()
          if hasattr(null_data, "to_numpy"):
              # pandas Series
              mask = null_data.to_numpy()
          else:
              # pandas Index
              mask = null_data
          if mask.any():
              # there are missing values
              ret = np.ma.MaskedArray(vals, mask)
          else:
              ret = vals
      elif isinstance(data, np.ndarray):
          if isinstance(data, np.ma.MaskedArray):
              if not data.mask.any():
                  # empty mask
                  ret = data.filled()
              else:
                  # already masked and rightly so
                  ret = data
          else:
              # already a ndarray, but not masked
              mask = np.isnan(data)
              if np.any(mask):
                  ret = np.ma.MaskedArray(data, mask)
              else:
                  # no masking required
                  ret = data
      elif isinstance(data, Variable):
          ret = data
      elif sps.issparse(data):
          ret = data
      elif isgenerator(data):
          ret = generator(data)
      else:
          ret = np.asarray(data)
  
      # type handling to enable index variables when data is int:
      if hasattr(data, "dtype"):
          if "int" in str(data.dtype):
              return intX(ret)
          # otherwise, assume float:
          else:
              return floatX(ret)
      # needed for uses of this function other than with pm.Data:
      else:
          return floatX(ret)
  
  
  def change_rv_size(
      rv: TensorVariable,
      new_size: PotentialShapeType,
      expand: Optional[bool] = False,
  ) -> TensorVariable:
      """Change or expand the size of a `RandomVariable`.
  
      Parameters
      ==========
      rv
          The old `RandomVariable` output.
      new_size
          The new size.
      expand:
          Expand the existing size by `new_size`.
  
      """
      # Check the dimensionality of the `new_size` kwarg
      new_size_ndim = np.ndim(new_size)
      if new_size_ndim > 1:
          raise ShapeError("The `new_size` must be ≤1-dimensional.", actual=new_size_ndim)
      elif new_size_ndim == 0:
          new_size = (new_size,)
  
      # Extract the RV node that is to be resized, together with its inputs, name and tag
      assert rv.owner.op is not None
      if isinstance(rv.owner.op, SpecifyShape):
          rv = rv.owner.inputs[0]
      rv_node = rv.owner
      rng, size, dtype, *dist_params = rv_node.inputs
      name = rv.name
      tag = rv.tag
  
      if expand:
          shape = tuple(rv_node.op._infer_shape(size, dist_params))
          size = shape[: len(shape) - rv_node.op.ndim_supp]
          new_size = tuple(new_size) + tuple(size)
  
      # Make sure the new size is a tensor. This dtype-aware conversion helps
      # to not unnecessarily pick up a `Cast` in some cases (see #4652).
      new_size = at.as_tensor(new_size, ndim=1, dtype="int64")
  
      new_rv_node = rv_node.op.make_node(rng, new_size, dtype, *dist_params)
      new_rv = new_rv_node.outputs[-1]
      new_rv.name = name
      for k, v in tag.__dict__.items():
          new_rv.tag.__dict__.setdefault(k, v)
  
      # Update "traditional" rng default_update, if that was set for old RV
      default_update = getattr(rng, "default_update", None)
      if default_update is not None and default_update is rv_node.outputs[0]:
          rng.default_update = new_rv_node.outputs[0]
  
      if config.compute_test_value != "off":
          compute_test_value(new_rv_node)
  
      return new_rv
  
  
  def extract_rv_and_value_vars(
      var: TensorVariable,
  ) -> Tuple[TensorVariable, TensorVariable]:
      """Return a random variable and it's observations or value variable, or ``None``.
  
      Parameters
      ==========
      var
          A variable corresponding to a ``RandomVariable``.
  
      Returns
      =======
      The first value in the tuple is the ``RandomVariable``, and the second is the
      measure/log-likelihood value variable that corresponds with the latter.
  
      """
      if not var.owner:
          return None, None
  
      if isinstance(var.owner.op, RandomVariable):
          rv_value = getattr(var.tag, "observations", getattr(var.tag, "value_var", None))
          return var, rv_value
  
      return None, None
  
  
  def extract_obs_data(x: TensorVariable) -> np.ndarray:
      """Extract data from observed symbolic variables.
  
      Raises
      ------
      TypeError
  
      """
      if isinstance(x, Constant):
          return x.data
      if isinstance(x, SharedVariable):
          return x.get_value()
      if x.owner and isinstance(x.owner.op, Elemwise) and isinstance(x.owner.op.scalar_op, Cast):
          array_data = extract_obs_data(x.owner.inputs[0])
          return array_data.astype(x.type.dtype)
      if x.owner and isinstance(x.owner.op, (AdvancedIncSubtensor, AdvancedIncSubtensor1)):
          array_data = extract_obs_data(x.owner.inputs[0])
          mask_idx = tuple(extract_obs_data(i) for i in x.owner.inputs[2:])
          mask = np.zeros_like(array_data)
          mask[mask_idx] = 1
          return np.ma.MaskedArray(array_data, mask)
  
      raise TypeError(f"Data cannot be extracted from {x}")
  
  
  def walk_model(
      graphs: Iterable[TensorVariable],
      walk_past_rvs: bool = False,
      stop_at_vars: Optional[Set[TensorVariable]] = None,
      expand_fn: Callable[[TensorVariable], Iterable[TensorVariable]] = lambda var: [],
  ) -> Generator[TensorVariable, None, None]:
      """Walk model graphs and yield their nodes.
  
      By default, these walks will not go past ``RandomVariable`` nodes.
  
      Parameters
      ==========
      graphs
          The graphs to walk.
      walk_past_rvs
          If ``True``, the walk will not terminate at ``RandomVariable``s.
      stop_at_vars
          A list of variables at which the walk will terminate.
      expand_fn
          A function that returns the next variable(s) to be traversed.
      """
      if stop_at_vars is None:
          stop_at_vars = set()
  
      def expand(var):
          new_vars = expand_fn(var)
  
          if (
              var.owner
              and (walk_past_rvs or not isinstance(var.owner.op, RandomVariable))
              and (var not in stop_at_vars)
          ):
              new_vars.extend(reversed(var.owner.inputs))
  
          return new_vars
  
      yield from walk(graphs, expand, False)
  
  
  def replace_rvs_in_graphs(
      graphs: Iterable[TensorVariable],
      replacement_fn: Callable[[TensorVariable], Dict[TensorVariable, TensorVariable]],
      initial_replacements: Optional[Dict[TensorVariable, TensorVariable]] = None,
      **kwargs,
  ) -> Tuple[TensorVariable, Dict[TensorVariable, TensorVariable]]:
      """Replace random variables in graphs
  
      This will *not* recompute test values.
  
      Parameters
      ==========
      graphs
          The graphs in which random variables are to be replaced.
  
      Returns
      =======
      Tuple containing the transformed graphs and a ``dict`` of the replacements
      that were made.
      """
      replacements = {}
      if initial_replacements:
          replacements.update(initial_replacements)
  
      def expand_replace(var):
          new_nodes = []
          if var.owner and isinstance(var.owner.op, RandomVariable):
              new_nodes.extend(replacement_fn(var, replacements))
          return new_nodes
  
      for var in walk_model(graphs, expand_fn=expand_replace, **kwargs):
          pass
  
      if replacements:
          inputs = [i for i in graph_inputs(graphs) if not isinstance(i, Constant)]
          equiv = {k: k for k in replacements.keys()}
          equiv = clone_get_equiv(inputs, graphs, False, False, equiv)
  
          fg = FunctionGraph(
              [equiv[i] for i in inputs],
              [equiv[o] for o in graphs],
              clone=False,
          )
  
          fg.replace_all(replacements.items(), import_missing=True)
  
          graphs = list(fg.outputs)
  
      return graphs, replacements
  
  
  def rvs_to_value_vars(
      graphs: Iterable[TensorVariable],
      apply_transforms: bool = False,
      initial_replacements: Optional[Dict[TensorVariable, TensorVariable]] = None,
      **kwargs,
  ) -> Tuple[TensorVariable, Dict[TensorVariable, TensorVariable]]:
      """Clone and replace random variables in graphs with their value variables.
  
      This will *not* recompute test values in the resulting graphs.
  
      Parameters
      ==========
      graphs
          The graphs in which to perform the replacements.
      apply_transforms
          If ``True``, apply each value variable's transform.
      initial_replacements
          A ``dict`` containing the initial replacements to be made.
  
      """
  
      # Avoid circular dependency
      from pymc.distributions import NoDistribution
  
      def transform_replacements(var, replacements):
          rv_var, rv_value_var = extract_rv_and_value_vars(var)
  
          if rv_value_var is None:
              # If RandomVariable does not have a value_var and corresponds to
              # a NoDistribution, we allow further replacements in upstream graph
              if isinstance(rv_var.owner.op, NoDistribution):
                  return rv_var.owner.inputs
  
              else:
                  warnings.warn(
                      f"No value variable found for {rv_var}; "
                      "the random variable will not be replaced."
                  )
                  return []
  
          transform = getattr(rv_value_var.tag, "transform", None)
  
          if transform is None or not apply_transforms:
              replacements[var] = rv_value_var
              # In case the value variable is itself a graph, we walk it for
              # potential replacements
              return [rv_value_var]
  
          trans_rv_value = transform.backward(rv_value_var, *rv_var.owner.inputs)
          replacements[var] = trans_rv_value
  
          # Walk the transformed variable and make replacements
          return [trans_rv_value]
  
      # Clone original graphs
      inputs = [i for i in graph_inputs(graphs) if not isinstance(i, Constant)]
      equiv = clone_get_equiv(inputs, graphs, False, False, {})
      graphs = [equiv[n] for n in graphs]
  
      if initial_replacements:
          initial_replacements = {
              equiv.get(k, k): equiv.get(v, v) for k, v in initial_replacements.items()
          }
  
      return replace_rvs_in_graphs(graphs, transform_replacements, initial_replacements, **kwargs)
  
  
  def inputvars(a):
      """
      Get the inputs into Aesara variables
  
      Parameters
      ----------
          a: Aesara variable
  
      Returns
      -------
          r: list of tensor variables that are inputs
      """
      return [
          v
          for v in graph_inputs(makeiter(a))
          if isinstance(v, TensorVariable) and not isinstance(v, TensorConstant)
      ]
  
  
  def cont_inputs(a):
      """
      Get the continuous inputs into Aesara variables
  
      Parameters
      ----------
          a: Aesara variable
  
      Returns
      -------
          r: list of tensor variables that are continuous inputs
      """
      return typefilter(inputvars(a), continuous_types)
  
  
  def floatX(X):
      """
      Convert an Aesara tensor or numpy array to aesara.config.floatX type.
      """
      try:
          return X.astype(aesara.config.floatX)
      except AttributeError:
          # Scalar passed
          return np.asarray(X, dtype=aesara.config.floatX)
  
  
  _conversion_map = {"float64": "int32", "float32": "int16", "float16": "int8", "float8": "int8"}
  
  
  def intX(X):
      """
      Convert a aesara tensor or numpy array to aesara.tensor.int32 type.
      """
      intX = _conversion_map[aesara.config.floatX]
      try:
          return X.astype(intX)
      except AttributeError:
          # Scalar passed
          return np.asarray(X, dtype=intX)
  
  
  def smartfloatX(x):
      """
      Converts numpy float values to floatX and leaves values of other types unchanged.
      """
      if str(x.dtype).startswith("float"):
          x = floatX(x)
      return x
  
  
  """
  Aesara derivative functions
  """
  
  
  def gradient1(f, v):
      """flat gradient of f wrt v"""
      return at.flatten(grad(f, v, disconnected_inputs="warn"))
  
  
  empty_gradient = at.zeros(0, dtype="float32")
  
  
  def gradient(f, vars=None):
      if vars is None:
          vars = cont_inputs(f)
  
      if vars:
          return at.concatenate([gradient1(f, v) for v in vars], axis=0)
      else:
          return empty_gradient
  
  
  def jacobian1(f, v):
      """jacobian of f wrt v"""
      f = at.flatten(f)
      idx = at.arange(f.shape[0], dtype="int32")
  
      def grad_i(i):
          return gradient1(f[i], v)
  
      return aesara.map(grad_i, idx)[0]
  
  
  def jacobian(f, vars=None):
      if vars is None:
          vars = cont_inputs(f)
  
      if vars:
          return at.concatenate([jacobian1(f, v) for v in vars], axis=1)
      else:
          return empty_gradient
  
  
  def jacobian_diag(f, x):
      idx = at.arange(f.shape[0], dtype="int32")
  
      def grad_ii(i, f, x):
          return grad(f[i], x)[i]
  
      return aesara.scan(
          grad_ii, sequences=[idx], n_steps=f.shape[0], non_sequences=[f, x], name="jacobian_diag"
      )[0]
  
  
  @aesara.config.change_flags(compute_test_value="ignore")
  def hessian(f, vars=None):
      return -jacobian(gradient(f, vars), vars)
  
  
  @aesara.config.change_flags(compute_test_value="ignore")
  def hessian_diag1(f, v):
      g = gradient1(f, v)
      idx = at.arange(g.shape[0], dtype="int32")
  
      def hess_ii(i):
          return gradient1(g[i], v)[i]
  
      return aesara.map(hess_ii, idx)[0]
  
  
  @aesara.config.change_flags(compute_test_value="ignore")
  def hessian_diag(f, vars=None):
      if vars is None:
          vars = cont_inputs(f)
  
      if vars:
          return -at.concatenate([hessian_diag1(f, v) for v in vars], axis=0)
      else:
          return empty_gradient
  
  
  def makeiter(a):
      if isinstance(a, (tuple, list)):
          return a
      else:
          return [a]
  
  
  class IdentityOp(scalar.UnaryScalarOp):
      @staticmethod
      def st_impl(x):
          return x
  
      def impl(self, x):
          return x
  
      def grad(self, inp, grads):
          return grads
  
      def c_code(self, node, name, inp, out, sub):
          return f"{out[0]} = {inp[0]};"
  
      def __eq__(self, other):
          return isinstance(self, type(other))
  
      def __hash__(self):
          return hash(type(self))
  
  
  scalar_identity = IdentityOp(scalar.upgrade_to_float, name="scalar_identity")
  identity = Elemwise(scalar_identity, name="identity")
  
  
  def make_shared_replacements(point, vars, model):
      """
      Makes shared replacements for all *other* variables than the ones passed.
  
      This way functions can be called many times without setting unchanging variables. Allows us
      to use func.trust_input by removing the need for DictToArrayBijection and kwargs.
  
      Parameters
      ----------
      point: dictionary mapping variable names to sample values
      vars: list of variables not to make shared
      model: model
  
      Returns
      -------
      Dict of variable -> new shared variable
      """
      othervars = set(model.value_vars) - set(vars)
      return {
          var: aesara.shared(point[var.name], var.name + "_shared", broadcastable=var.broadcastable)
          for var in othervars
      }
  
  
  def join_nonshared_inputs(
      point: Dict[str, np.ndarray],
      xs: List[TensorVariable],
      vars: List[TensorVariable],
      shared,
      make_shared: bool = False,
  ):
      """
      Takes a list of Aesara Variables and joins their non shared inputs into a single input.
  
      Parameters
      ----------
      point: a sample point
      xs: list of Aesara tensors
      vars: list of variables to join
  
      Returns
      -------
      tensors, inarray
      tensors: list of same tensors but with inarray as input
      inarray: vector of inputs
      """
      if not vars:
          raise ValueError("Empty list of variables.")
  
      joined = at.concatenate([var.ravel() for var in vars])
  
      if not make_shared:
          tensor_type = joined.type
          inarray = tensor_type("inarray")
      else:
          if point is None:
              raise ValueError("A point is required when `make_shared` is True")
          joined_values = np.concatenate([point[var.name].ravel() for var in vars])
          inarray = aesara.shared(joined_values, "inarray")
  
      if aesara.config.compute_test_value != "off":
          inarray.tag.test_value = joined.tag.test_value
  
      replace = {}
      last_idx = 0
      for var in vars:
          shape = point[var.name].shape
          arr_len = np.prod(shape, dtype=int)
          replace[var] = reshape_t(inarray[last_idx : last_idx + arr_len], shape).astype(var.dtype)
          last_idx += arr_len
  
      replace.update(shared)
  
      xs_special = [aesara.clone_replace(x, replace, rebuild_strict=False) for x in xs]
      return xs_special, inarray
  
  
  def reshape_t(x, shape):
      """Work around fact that x.reshape(()) doesn't work"""
      if shape != ():
          return x.reshape(shape)
      else:
          return x[0]
  
  
  class CallableTensor:
      """Turns a symbolic variable with one input into a function that returns symbolic arguments
      with the one variable replaced with the input.
      """
  
      def __init__(self, tensor):
          self.tensor = tensor
  
      def __call__(self, input):
          """Replaces the single input of symbolic variable to be the passed argument.
  
          Parameters
          ----------
          input: TensorVariable
          """
          (oldinput,) = inputvars(self.tensor)
          return aesara.clone_replace(self.tensor, {oldinput: input}, rebuild_strict=False)
  
  
  class GeneratorOp(Op):
      """
      Generator Op is designed for storing python generators inside aesara graph.
  
      __call__ creates TensorVariable
          It has 2 new methods
          - var.set_gen(gen): sets new generator
          - var.set_default(value): sets new default value (None erases default value)
  
      If generator is exhausted, variable will produce default value if it is not None,
      else raises `StopIteration` exception that can be caught on runtime.
  
      Parameters
      ----------
      gen: generator that implements __next__ (py3) or next (py2) method
          and yields np.arrays with same types
      default: np.array with the same type as generator produces
      """
  
      __props__ = ("generator",)
  
      def __init__(self, gen, default=None):
          from pymc.data import GeneratorAdapter
  
          super().__init__()
          if not isinstance(gen, GeneratorAdapter):
              gen = GeneratorAdapter(gen)
          self.generator = gen
          self.set_default(default)
  
      def make_node(self, *inputs):
          gen_var = self.generator.make_variable(self)
          return Apply(self, [], [gen_var])
  
      def perform(self, node, inputs, output_storage, params=None):
          if self.default is not None:
              output_storage[0][0] = next(self.generator, self.default)
          else:
              output_storage[0][0] = next(self.generator)
  
      def do_constant_folding(self, fgraph, node):
          return False
  
      __call__ = aesara.config.change_flags(compute_test_value="off")(Op.__call__)
  
      def set_gen(self, gen):
          from pymc.data import GeneratorAdapter
  
          if not isinstance(gen, GeneratorAdapter):
              gen = GeneratorAdapter(gen)
          if not gen.tensortype == self.generator.tensortype:
              raise ValueError("New generator should yield the same type")
          self.generator = gen
  
      def set_default(self, value):
          if value is None:
              self.default = None
          else:
              value = np.asarray(value, self.generator.tensortype.dtype)
              t1 = (False,) * value.ndim
              t2 = self.generator.tensortype.broadcastable
              if not t1 == t2:
                  raise ValueError("Default value should have the same type as generator")
              self.default = value
  
  
  def generator(gen, default=None):
      """
      Generator variable with possibility to set default value and new generator.
      If generator is exhausted variable will produce default value if it is not None,
      else raises `StopIteration` exception that can be caught on runtime.
  
      Parameters
      ----------
      gen: generator that implements __next__ (py3) or next (py2) method
          and yields np.arrays with same types
      default: np.array with the same type as generator produces
  
      Returns
      -------
      TensorVariable
          It has 2 new methods
          - var.set_gen(gen): sets new generator
          - var.set_default(value): sets new default value (None erases default value)
      """
      return GeneratorOp(gen, default)()
  
  
  _at_rng = RandomStream()
  
  
  def at_rng(random_seed=None):
      """
      Get the package-level random number generator or new with specified seed.
  
      Parameters
      ----------
      random_seed: int
          If not None
          returns *new* aesara random generator without replacing package global one
  
      Returns
      -------
      `aesara.tensor.random.utils.RandomStream` instance
          `aesara.tensor.random.utils.RandomStream`
          instance passed to the most recent call of `set_at_rng`
      """
      if random_seed is None:
          return _at_rng
      else:
          ret = RandomStream(random_seed)
          return ret
  
  
  def set_at_rng(new_rng):
      """
      Set the package-level random number generator.
  
      Parameters
      ----------
      new_rng: `aesara.tensor.random.utils.RandomStream` instance
          The random number generator to use.
      """
      # pylint: disable=global-statement
      global _at_rng
      # pylint: enable=global-statement
      if isinstance(new_rng, int):
          new_rng = RandomStream(new_rng)
      _at_rng = new_rng
  
  
  def floatX_array(x):
      return floatX(np.array(x))
  
  
  def ix_(*args):
      """
      Aesara np.ix_ analog
  
      See numpy.lib.index_tricks.ix_ for reference
      """
      out = []
      nd = len(args)
      for k, new in enumerate(args):
          if new is None:
              out.append(slice(None))
          new = at.as_tensor(new)
          if new.ndim != 1:
              raise ValueError("Cross index must be 1 dimensional")
          new = new.reshape((1,) * k + (new.size,) + (1,) * (nd - k - 1))
          out.append(new)
      return tuple(out)
  
  
  def largest_common_dtype(tensors):
      dtypes = {
          str(t.dtype) if hasattr(t, "dtype") else smartfloatX(np.asarray(t)).dtype for t in tensors
      }
      return np.stack([np.ones((), dtype=dtype) for dtype in dtypes]).dtype
  
  
  @local_optimizer(tracks=[CheckParameterValue])
  def local_remove_check_parameter(fgraph, node):
      """Rewrite that removes Aeppl's CheckParameterValue
  
      This is used when compile_rv_inplace
      """
      if isinstance(node.op, CheckParameterValue):
          return [node.inputs[0]]
  
  
  @local_optimizer(tracks=[CheckParameterValue])
  def local_check_parameter_to_ninf_switch(fgraph, node):
      if isinstance(node.op, CheckParameterValue):
          logp_expr, *logp_conds = node.inputs
          if len(logp_conds) > 1:
              logp_cond = at.all(logp_conds)
          else:
              (logp_cond,) = logp_conds
          out = at.switch(logp_cond, logp_expr, -np.inf)
          out.name = node.op.msg
  
          if out.dtype != node.outputs[0].dtype:
              out = at.cast(out, node.outputs[0].dtype)
  
          return [out]
  
  
  aesara.compile.optdb["canonicalize"].register(
      "local_remove_check_parameter",
      local_remove_check_parameter,
      use_db_name_as_tag=False,
  )
  
  aesara.compile.optdb["canonicalize"].register(
      "local_check_parameter_to_ninf_switch",
      local_check_parameter_to_ninf_switch,
      use_db_name_as_tag=False,
  )
  
  
  def find_rng_nodes(
      variables: Iterable[Variable],
  ) -> List[Union[RandomStateSharedVariable, RandomGeneratorSharedVariable]]:
      """Return RNG variables in a graph"""
      return [
          node
          for node in graph_inputs(variables)
          if isinstance(node, (RandomStateSharedVariable, RandomGeneratorSharedVariable))
      ]
  
  
  SeedSequenceSeed = Optional[Union[int, Sequence[int], np.ndarray, np.random.SeedSequence]]
  
  
  def reseed_rngs(
      rngs: Sequence[SharedVariable],
      seed: SeedSequenceSeed,
  ) -> None:
      """Create a new set of RandomState/Generator for each rng based on a seed"""
      bit_generators = [
          np.random.PCG64(sub_seed) for sub_seed in np.random.SeedSequence(seed).spawn(len(rngs))
      ]
      for rng, bit_generator in zip(rngs, bit_generators):
          new_rng: Union[np.random.RandomState, np.random.Generator]
          if isinstance(rng, at.random.var.RandomStateSharedVariable):
              new_rng = np.random.RandomState(bit_generator)
          else:
              new_rng = np.random.Generator(bit_generator)
          rng.set_value(new_rng, borrow=True)
  
  
  def compile_pymc(
      inputs,
      outputs,
      random_seed: SeedSequenceSeed = None,
      mode=None,
      **kwargs,
  ) -> Callable[..., Union[np.ndarray, List[np.ndarray]]]:
      """Use ``aesara.function`` with specialized pymc rewrites always enabled.
  
      This function also ensures shared RandomState/Generator used by RandomVariables
      in the graph are updated across calls, to ensure independent draws.
  
      Parameters
      ----------
      inputs: list of TensorVariables, optional
          Inputs of the compiled Aesara function
      outputs: list of TensorVariables, optional
          Outputs of the compiled Aesara function
      random_seed: int, array-like of int or SeedSequence, optional
          Seed used to override any RandomState/Generator shared variables in the graph.
          If not specified, the value of original shared variables will still be overwritten.
      mode: optional
          Aesara mode used to compile the function
  
      Included rewrites
      -----------------
      random_make_inplace
          Ensures that compiled functions containing random variables will produce new
          samples on each call.
      local_check_parameter_to_ninf_switch
          Replaces Aeppl's CheckParameterValue assertions is logp expressions with Switches
          that return -inf in place of the assert.
  
      Optional rewrites
      -----------------
      local_remove_check_parameter
          Replaces Aeppl's CheckParameterValue assertions is logp expressions. This is used
          as an alteranative to the default local_check_parameter_to_ninf_switch whenenver
          this function is called within a model context and the model `check_bounds` flag
          is set to False.
      """
      # Create an update mapping of RandomVariable's RNG so that it is automatically
      # updated after every function call
      rng_updates = {}
      output_to_list = outputs if isinstance(outputs, (list, tuple)) else [outputs]
      for random_var in (
          var
          for var in vars_between(inputs, output_to_list)
          if var.owner
          and isinstance(var.owner.op, (RandomVariable, MeasurableVariable))
          and var not in inputs
      ):
          # All nodes in `vars_between(inputs, outputs)` have owners.
          # But mypy doesn't know, so we just assert it:
          assert random_var.owner.op is not None
          if isinstance(random_var.owner.op, RandomVariable):
              rng = random_var.owner.inputs[0]
              if not hasattr(rng, "default_update"):
                  rng_updates[rng] = random_var.owner.outputs[0]
              else:
                  rng_updates[rng] = rng.default_update
          else:
              update_fn = getattr(random_var.owner.op, "update", None)
              if update_fn is not None:
                  rng_updates.update(update_fn(random_var.owner))
  
      # We always reseed random variables as this provides RNGs with no chances of collision
      if rng_updates:
          reseed_rngs(rng_updates.keys(), random_seed)
  
      # If called inside a model context, see if check_bounds flag is set to False
      try:
          from pymc.model import modelcontext
  
          model = modelcontext(None)
          check_bounds = model.check_bounds
      except TypeError:
          check_bounds = True
      check_parameter_opt = (
          "local_check_parameter_to_ninf_switch" if check_bounds else "local_remove_check_parameter"
      )
  
      mode = get_mode(mode)
      opt_qry = mode.provided_optimizer.including("random_make_inplace", check_parameter_opt)
      mode = Mode(linker=mode.linker, optimizer=opt_qry)
      aesara_function = aesara.function(
          inputs,
          outputs,
          updates={**rng_updates, **kwargs.pop("updates", {})},
          mode=mode,
          **kwargs,
      )
      return aesara_function
  