code: def sample_chain(
      kernel,
      num_results,
      current_state,
      previous_kernel_results=None,
      reducer=(),
      previous_reducer_state=None,
      trace_fn=_trace_everything,
      parallel_iterations=10,
      seed=None,
      name=None,
  ):
      """Runs a Markov chain defined by the given `TransitionKernel`.
  
      This is meant as a (more) helpful frontend to the low-level
      `TransitionKernel`-based MCMC API, supporting several main features:
  
      - Running a batch of multiple independent chains using SIMD parallelism
      - Tracing the history of the chains, or not tracing it to save memory
      - Computing reductions over chain history, whether it is also traced or not
      - Warm (re-)start, including auxiliary state
  
      This function samples from a Markov chain at `current_state` whose
      stationary distribution is governed by the supplied `TransitionKernel`
      instance (`kernel`).
  
      The `current_state` can be represented as a single `Tensor` or a `list` of
      `Tensors` which collectively represent the current state.
  
      This function can sample from multiple chains, in parallel.  Whether or not
      there are multiple chains is dictated by how the `kernel` treats its inputs.
      Typically, the shape of the independent chains is shape of the result of the
      `target_log_prob_fn` used by the `kernel` when applied to the given
      `current_state`.
  
      This function can compute reductions over the samples in tandem with sampling,
      for example to return summary statistics without materializing all the
      samples.  To request reductions, pass a `Reducer` object, or a nested
      structure of `Reducer` objects, as the `reducer=` argument.
  
      In addition to the chain state, this function supports tracing of auxiliary
      variables used by the kernel, as well as intermediate values of any supplied
      reductions. The traced values are selected by specifying `trace_fn`.  The
      `trace_fn` must be a callable accepting three arguments: the chain state, the
      kernel_results of the `kernel`, and the current results of the reductions, if
      any are supplied.  The return value of `trace_fn` (which may be a `Tensor` or
      a nested structure of `Tensor`s) is accumulated, such that each `Tensor` gains
      a new outmost dimension representing time in the chain history.
  
      Since MCMC states are correlated, it is sometimes desirable to produce
      additional intermediate states, and then discard them, ending up with a set of
      states with decreased autocorrelation.  See [Owen (2017)][1]. Such 'thinning'
      is made possible by setting `num_steps_between_results > 0`. The chain then
      takes `num_steps_between_results` extra steps between the steps that make it
      into the results, or are shown to any supplied reductions. The extra steps
      are never materialized, and thus do not increase memory requirements.
  
      Args:
        kernel: An instance of `tfp.mcmc.TransitionKernel` which implements one step
          of the Markov chain.
        num_results: Integer number of (non-discarded) Markov chain draws to
          compute.
        current_state: `Tensor` or Python `list` of `Tensor`s representing the
          initial state(s) of the Markov chain(s).
        previous_kernel_results: A `Tensor` or a nested collection of `Tensor`s
          representing internal calculations made within the previous call to this
          function (or as returned by `bootstrap_results`).
        reducer: A (possibly nested) structure of `Reducer`s to be evaluated
          on the `kernel`'s samples. If no reducers are given (`reducer=None`),
          their states will not be passed to any supplied `trace_fn`.
        previous_reducer_state: A (possibly nested) structure of running states
          corresponding to the structure in `reducer`.  For resuming streaming
          reduction computations begun in a previous run.
        trace_fn: A callable that takes in the current chain state, the current
          auxiliary kernel state, and the current result of any reducers, and
          returns a `Tensor` or a nested collection of `Tensor`s that is then
          traced.  If `None`, nothing is traced.
        parallel_iterations: The number of iterations allowed to run in parallel. It
          must be a positive integer. See `tf.while_loop` for more details.
        seed: PRNG seed; see `tfp.random.sanitize_seed` for details.
        name: Python `str` name prefixed to Ops created by this function.
          Default value: `None` (i.e., 'mcmc_sample_chain').
  
      Returns:
        result: A `SampleChainResults` instance containing information about the
          sampling run.  Main fields are `trace`, the history of outputs of
          `trace_fn`, and `reduction_results`, the final outputs of all supplied
          `Reducer`s.  See `SampleChainResults` for contents of other fields.
      """
      # Features omitted for simplicity:
      # - Can only warm start either all the reducers or none of them, not
      #   piecemeal.
      #
      # Defects admitted for simplicity:
      # - All reducers are finalized internally at every step, whether the user
      #   wished to trace them or not.  We expect graph mode TF to avoid that unused
      #   computation, but eager mode will not.
      # - The user is not given the opportunity to trace the running state of
      #   reducers.  For example, the user cannot trace the sum and count of a
      #   running mean, only the running mean itself.  Arguably this is a feature,
      #   because the sum and count can be considered implementation details, the
      #   hiding of which is the purpose of the `finalize` method.
      with tf.name_scope(name or "mcmc_sample_chain"):
          if not kernel.is_calibrated:
              warnings.warn(
                  "supplied `TransitionKernel` is not calibrated. Markov "
                  "chain may not converge to intended target distribution."
              )
  
          if trace_fn is None:
              trace_fn = lambda *args: ()
  
          # Form kernel onion
          reduction_kernel = with_reductions.WithReductions(
              inner_kernel=kernel, reducer=reducer
          )
  
          # User trace function should be called with
          # - current chain state
          # - kernel results structure of the passed-in kernel
          # - if there were any reducers, their intermediate results
          #
          # `WithReductions` will show the TracingReducer the intermediate state as
          # the kernel results of the onion named `reduction_kernel` above.  This
          # wrapper converts from that to what the user-supplied trace function needs
          # to see.
          def internal_trace_fn(curr_state, kr):
              if reducer:
  
                  def fin(reducer, red_state):
                      return reducer.finalize(red_state)
  
                  # Extra level of list will be unwrapped by *reduction_args, below.
                  reduction_args = [
                      nest.map_structure_up_to(
                          reducer, fin, reducer, kr.reduction_results
                      )
                  ]
              else:
                  reduction_args = []
              return trace_fn(
                  curr_state, kr.inner_results, *reduction_args
              )
  
          trace_reducer = tracing_reducer.TracingReducer(
              trace_fn=internal_trace_fn, size=num_results
          )
          tracing_kernel = with_reductions.WithReductions(
              inner_kernel=reduction_kernel,
              reducer=trace_reducer,
          )
  
          # Bootstrap corresponding warm start
          if previous_kernel_results is None:
              previous_kernel_results = kernel.bootstrap_results(
                  current_state
              )
          reduction_pkr = reduction_kernel.bootstrap_results(
              current_state,
              previous_kernel_results,
              previous_reducer_state,
          )
          tracing_pkr = tracing_kernel.bootstrap_results(
              current_state, reduction_pkr
          )
  
          # pylint: disable=unbalanced-tuple-unpacking
          final_state, tracing_kernel_results = step.step_kernel(
              num_steps=num_results,
              current_state=current_state,
              previous_kernel_results=tracing_pkr,
              kernel=tracing_kernel,
              return_final_kernel_results=True,
              parallel_iterations=parallel_iterations,
              seed=seed,
              name=name,
          )
  
          trace = trace_reducer.finalize(
              tracing_kernel_results.reduction_results
          )
  
          reduction_kernel_results = (
              tracing_kernel_results.inner_results
          )
          reduction_results = nest.map_structure_up_to(
              reducer,
              lambda r, s: r.finalize(s),
              reducer,
              reduction_kernel_results.reduction_results,
              check_types=False,
          )
  
          user_kernel_results = reduction_kernel_results.inner_results
  
          resume_kwargs = {
              "current_state": final_state,
              "previous_kernel_results": user_kernel_results,
              "kernel": kernel,
              "reducer": reducer,
              "previous_reducer_state": reduction_kernel_results.reduction_results,
          }
  
          return SampleChainResults(
              trace=trace,
              reduction_results=reduction_results,
              final_state=final_state,
              final_kernel_results=user_kernel_results,
              resume_kwargs=resume_kwargs,
          )
  
file_path: probability/tensorflow_probability/python/experimental/mcmc/sample.py
imports: import collections
  import warnings
  import tensorflow.compat.v2
  from tensorflow_probability.python.experimental.mcmc import step
  from tensorflow_probability.python.experimental.mcmc import tracing_reducer
  from tensorflow_probability.python.experimental.mcmc import with_reductions
  from tensorflow.python.util import nest
label_desc: Use image node_id 2 for calling a global function with example usage: sample_chain(kernel, num_results, current_state, previous_kernel_results, reducer, previous_reducer_state, trace_fn, parallel_iterations, seed, name) and returns: SampleChainResults, trace_fn, reducer