code: def rebuild_collect_shared(
      outputs,
      inputs=None,
      replace=None,
      updates=None,
      rebuild_strict=True,
      copy_inputs_over=True,
      no_default_updates=False,
  ):
      """
      Function that allows replacing subgraphs of a computational graph.
  
      It returns a set of dictionaries and lists which collect (partial?)
      different information about shared variables. This info is required by
      `pfunc`.
  
      Parameters
      ----------
      outputs : list of Theano Variables (or Theano expressions)
          List of Theano variables or expressions representing the outputs of the
          computational graph.
      inputs : list of Theano Variables (or Theano expressions)
          List of Theano variables or expressions representing the inputs of the
          computational graph (or None).
      replace : dict
          Dictionary describing which subgraphs should be replaced by what.
          orig_value => new_value
      updates : dict
          Dictionary describing updates expressions for shared variables.
      rebuild_strict : bool
          Flag, if true the type of all inputs should be the same as the one for
          the current node.
      copy_inputs_over : bool
          Flag; if False it will clone inputs.
      no_default_updates : either bool or list of Variables
          If True, do not perform any automatic update on Variables.
          If False (default), perform them all.
          Else, perform automatic updates on all Variables that are neither in
          "updates" nor in "no_default_updates".
  
      """
  
      if isinstance(outputs, tuple):
          outputs = list(outputs)
  
      # This function implements similar functionality as graph.clone
      # and it should be merged with that
      clone_d = {}
      update_d = {}
      update_expr = []
      # list of shared inputs that are used as inputs of the graph
      shared_inputs = []
  
      def clone_v_get_shared_updates(v, copy_inputs_over):
          """
          Clones a variable and its inputs recursively until all are in clone_d.
          Also appends all shared variables met along the way to shared inputs,
          and their default_update (if applicable) to update_d and update_expr.
  
          v can have an fgraph attached to it, case in which we want to clone
          constants (to avoid having a constant belonging to two fgraphs).
  
          """
          # this co-recurses with clone_a
          assert v is not None
          if v in clone_d:
              return clone_d[v]
          if v.owner:
              owner = v.owner
              if owner not in clone_d:
                  for i in owner.inputs:
                      clone_v_get_shared_updates(i, copy_inputs_over)
  
                  clone_d[owner] = owner.clone_with_new_inputs(
                      [clone_d[i] for i in owner.inputs],
                      strict=rebuild_strict,
                  )
                  for old_o, new_o in zip(
                      owner.outputs, clone_d[owner].outputs
                  ):
                      clone_d.setdefault(old_o, new_o)
  
              return clone_d.setdefault(v, v)
          elif isinstance(v, SharedVariable):
              if v not in shared_inputs:
                  shared_inputs.append(v)
              if hasattr(v, "default_update"):
                  # Check that v should not be excluded from the default
                  # updates list
                  if no_default_updates is False or (
                      isinstance(no_default_updates, list)
                      and v not in no_default_updates
                  ):
                      # Do not use default_update if a "real" update was
                      # provided
                      if v not in update_d:
                          v_update = v.type.filter_variable(
                              v.default_update, allow_convert=False
                          )
                          if v_update.type != v.type:
                              raise TypeError(
                                  "an update must have the same type as "
                                  "the original shared variable",
                                  (v, v.type, v_update, v_update.type),
                              )
                          update_d[v] = v_update
                          update_expr.append((v, v_update))
          if not copy_inputs_over or (
              isinstance(v, Constant) and hasattr(v, "fgraph")
          ):
              # Cloning shared variables implies copying their underlying
              # memory buffer ?? No.
              return clone_d.setdefault(v, v.clone())
          else:
              return clone_d.setdefault(v, v)
  
      # intialize the clone_d mapping with the replace dictionary
      if replace is None:
          replace = []
      try:
          replace_pairs = list(replace.items())
      except Exception:
          replace_pairs = replace
  
      for v_orig, v_repl in replace_pairs:
          if not isinstance(v_orig, Variable):
              raise TypeError("given keys must be Variable", v_orig)
          if not isinstance(v_repl, Variable):
              v_repl = shared(v_repl)
  
          if v_orig in clone_d:
              raise AssertionError(
                  "When using 'givens' or 'replace' with several "
                  "(old_v, new_v) replacement pairs, you can not have a "
                  "new_v variable depend on an old_v one. For instance, "
                  "givens = {a:b, b:(a+1)} is not allowed. Here, the old_v "
                  "%s is used to compute other new_v's, but it is scheduled "
                  "to be replaced by %s." % (v_orig, v_repl)
              )
  
          clone_d[v_orig] = clone_v_get_shared_updates(
              v_repl, copy_inputs_over
          )
  
      if inputs is None:
          inputs = []
  
      def clone_inputs(i):
          if not copy_inputs_over:
              return clone_d.setdefault(i, i.clone())
          else:
              return clone_d.setdefault(i, i)
  
      input_variables = [clone_inputs(i) for i in inputs]
  
      # It was decided, as a first step, to prevent shared variables from
      # being used as function inputs. Although it is technically possible,
      # it is also not clear when/how to use the value of that shared
      # variable (is it a default? ignored?, if the shared variable changes,
      # does that function default also change?).
      for v in input_variables:
          if isinstance(v, SharedVariable):
              raise TypeError(
                  (
                      "Cannot use a shared variable (%s) as explicit "
                      "input. Consider substituting a non-shared"
                      " variable via the `givens` parameter"
                  )
                  % v
              )
  
      # Fill update_d and update_expr with provided updates
      if updates is None:
          updates = []
      for store_into, update_val in iter_over_pairs(updates):
          if not isinstance(store_into, SharedVariable):
              raise TypeError(
                  "update target must be a SharedVariable", store_into
              )
          if store_into in update_d:
              raise ValueError(
                  "this shared variable already has an update "
                  "expression",
                  (store_into, update_d[store_into]),
              )
  
          # filter_variable ensure smooth conversion of cpu/gpu Types
          try:
              update_val = store_into.type.filter_variable(
                  update_val, allow_convert=False
              )
          except TypeError:
              err_msg = (
                  "An update must have the same type as the"
                  " original shared variable (shared_var=%s,"
                  " shared_var.type=%s,"
                  " update_val=%s, update_val.type=%s)."
                  % (
                      store_into,
                      store_into.type,
                      update_val,
                      getattr(update_val, "type", None),
                  )
              )
              err_sug = (
                  "If the difference is related to the broadcast pattern,"
                  " you can call the"
                  " tensor.unbroadcast(var, axis_to_unbroadcast[, ...])"
                  " function to remove broadcastable dimensions."
              )
  
              raise TypeError(err_msg, err_sug)
          assert update_val.type == store_into.type
  
          update_d[store_into] = update_val
          update_expr.append((store_into, update_val))
  
      # Elements of "outputs" are here cloned to "cloned_outputs"
      if isinstance(outputs, list):
          cloned_outputs = []
          for v in outputs:
              if isinstance(v, Variable):
                  cloned_v = clone_v_get_shared_updates(
                      v, copy_inputs_over
                  )
                  cloned_outputs.append(cloned_v)
              elif isinstance(v, Out):
                  cloned_v = clone_v_get_shared_updates(
                      v.variable, copy_inputs_over
                  )
                  cloned_outputs.append(Out(cloned_v, borrow=v.borrow))
              else:
                  raise TypeError(
                      "Outputs must be theano Variable or "
                      "Out instances. Received "
                      + str(v)
                      + " of type "
                      + str(type(v))
                  )
              # computed_list.append(cloned_v)
      else:
          if isinstance(outputs, Variable):
              cloned_v = clone_v_get_shared_updates(
                  outputs, copy_inputs_over
              )
              cloned_outputs = cloned_v
              # computed_list.append(cloned_v)
          elif isinstance(outputs, Out):
              cloned_v = clone_v_get_shared_updates(
                  outputs.variable, copy_inputs_over
              )
              cloned_outputs = Out(cloned_v, borrow=outputs.borrow)
              # computed_list.append(cloned_v)
          elif outputs is None:
              cloned_outputs = (
                  []
              )  # TODO: get Function.__call__ to return None
          else:
              raise TypeError(
                  "output must be a theano Variable or Out "
                  "instance (or list of them)",
                  outputs,
              )
  
      # Iterate over update_expr, cloning its elements, and updating
      # shared_inputs, update_d and update_expr from the SharedVariables
      # we discover.
      # If the variable to be updated is a shared variable not already
      # in shared_inputs, add it.
      # Note: we extend update_expr while iterating over it.
  
      i = 0
      while i < len(update_expr):
          v, v_update = update_expr[i]
          cloned_v_update = clone_v_get_shared_updates(
              v_update, copy_inputs_over
          )
          update_d[v] = cloned_v_update
          if isinstance(v, SharedVariable) and v not in shared_inputs:
              shared_inputs.append(v)
          i += 1
  
      return (
          input_variables,
          cloned_outputs,
          [clone_d, update_d, update_expr, shared_inputs],
      )
  
file_path: Theano/theano/compile/pfunc.py
imports: from __future__ import absolute_import, print_function, division
  import warnings
  from theano import config
  from six import iteritems
  from theano.compile import orig_function, In, Out
  from theano.compile import UnusedInputError
  from theano.compile.sharedvalue import SharedVariable, shared
  from theano.compile.profiling import ProfileStats
  from theano.gof import Variable, Constant
  import logging
label_desc: Use image node_id 1 for calling a global function with example usage: rebuild_collect_shared(outputs, inputs, replace, updates, rebuild_strict, copy_inputs_over, no_default_updates) and returns: input_variables,  cloned_outputs,  list, clone_d, clone_d, clone_d, clone_d, clone_d, clone_d