text: #!/usr/bin/env python
  # -*- coding: utf-8 -*-
  #
  # Copyright (C) 2012 Jonathan Esterhazy <jonathan.esterhazy at gmail.com>
  # Licensed under the GNU LGPL v2.1 - http://www.gnu.org/licenses/lgpl.html
  #
  # HDP inference code is adapted from the onlinehdp.py script by
  # Chong Wang (chongw at cs.princeton.edu).
  # http://www.cs.princeton.edu/~chongw/software/onlinehdp.tar.gz
  #
  
  
  """Module for `online Hierarchical Dirichlet Processing
  <http://jmlr.csail.mit.edu/proceedings/papers/v15/wang11a/wang11a.pdf>`_.
  
  The core estimation code is directly adapted from the `blei-lab/online-hdp <https://github.com/blei-lab/online-hdp>`_
  from `Wang, Paisley, Blei: "Online Variational Inference for the Hierarchical Dirichlet Process",  JMLR (2011)
  <http://jmlr.csail.mit.edu/proceedings/papers/v15/wang11a/wang11a.pdf>`_.
  
  Examples
  --------
  
  Train :class:`~gensim.models.hdpmodel.HdpModel`
  
  .. sourcecode:: pycon
  
      >>> from gensim.test.utils import common_corpus, common_dictionary
      >>> from gensim.models import HdpModel
      >>>
      >>> hdp = HdpModel(common_corpus, common_dictionary)
  
  You can then infer topic distributions on new, unseen documents, with
  
  .. sourcecode:: pycon
  
      >>> unseen_document = [(1, 3.), (2, 4)]
      >>> doc_hdp = hdp[unseen_document]
  
  To print 20 topics with top 10 most probable words.
  
  .. sourcecode:: pycon
  
      >>> topic_info = hdp.print_topics(num_topics=20, num_words=10)
  
  The model can be updated (trained) with new documents via
  
  .. sourcecode:: pycon
  
      >>> hdp.update([[(1, 2)], [(1, 1), (4, 5)]])
  
  """
  
  import logging
  import time
  import warnings
  
  import numpy as np
  from scipy.special import gammaln, psi  # gamma function utils
  
  from gensim import interfaces, utils, matutils
  from gensim.matutils import dirichlet_expectation, mean_absolute_difference
  from gensim.models import basemodel, ldamodel
  from gensim.utils import deprecated
  
  
  logger = logging.getLogger(__name__)
  
  meanchangethresh = 0.00001
  rhot_bound = 0.0
  
  
  def expect_log_sticks(sticks):
      r"""For stick-breaking hdp, get the :math:`\mathbb{E}[log(sticks)]`.
  
      Parameters
      ----------
      sticks : numpy.ndarray
          Array of values for stick.
  
      Returns
      -------
      numpy.ndarray
          Computed :math:`\mathbb{E}[log(sticks)]`.
  
      """
      dig_sum = psi(np.sum(sticks, 0))
      ElogW = psi(sticks[0]) - dig_sum
      Elog1_W = psi(sticks[1]) - dig_sum
  
      n = len(sticks[0]) + 1
      Elogsticks = np.zeros(n)
      Elogsticks[0: n - 1] = ElogW
      Elogsticks[1:] = Elogsticks[1:] + np.cumsum(Elog1_W)
      return Elogsticks
  
  
  def lda_e_step(doc_word_ids, doc_word_counts, alpha, beta, max_iter=100):
      r"""Performs EM-iteration on a single document for calculation of likelihood for a maximum iteration of `max_iter`.
  
      Parameters
      ----------
      doc_word_ids : int
          Id of corresponding words in a document.
      doc_word_counts : int
          Count of words in a single document.
      alpha : numpy.ndarray
          Lda equivalent value of alpha.
      beta : numpy.ndarray
          Lda equivalent value of beta.
      max_iter : int, optional
          Maximum number of times the expectation will be maximised.
  
      Returns
      -------
      (numpy.ndarray, numpy.ndarray)
          Computed (:math:`likelihood`, :math:`\gamma`).
  
      """
      gamma = np.ones(len(alpha))
      expElogtheta = np.exp(dirichlet_expectation(gamma))
      betad = beta[:, doc_word_ids]
      phinorm = np.dot(expElogtheta, betad) + 1e-100
      counts = np.array(doc_word_counts)
      for _ in range(max_iter):
          lastgamma = gamma
  
          gamma = alpha + expElogtheta * np.dot(counts / phinorm, betad.T)
          Elogtheta = dirichlet_expectation(gamma)
          expElogtheta = np.exp(Elogtheta)
          phinorm = np.dot(expElogtheta, betad) + 1e-100
          meanchange = mean_absolute_difference(gamma, lastgamma)
          if meanchange < meanchangethresh:
              break
  
      likelihood = np.sum(counts * np.log(phinorm))
      likelihood += np.sum((alpha - gamma) * Elogtheta)
      likelihood += np.sum(gammaln(gamma) - gammaln(alpha))
      likelihood += gammaln(np.sum(alpha)) - gammaln(np.sum(gamma))
  
      return likelihood, gamma
  
  
  class SuffStats:
      """Stores sufficient statistics for the current chunk of document(s) whenever Hdp model is updated with new corpus.
      These stats are used when updating lambda and top level sticks. The statistics include number of documents in the
      chunk, length of words in the documents and top level truncation level.
  
      """
      def __init__(self, T, Wt, Dt):
          """
  
          Parameters
          ----------
          T : int
              Top level truncation level.
          Wt : int
              Length of words in the documents.
          Dt : int
              Chunk size.
  
          """
          self.m_chunksize = Dt
          self.m_var_sticks_ss = np.zeros(T)
          self.m_var_beta_ss = np.zeros((T, Wt))
  
      def set_zero(self):
          """Fill the sticks and beta array with 0 scalar value."""
          self.m_var_sticks_ss.fill(0.0)
          self.m_var_beta_ss.fill(0.0)
  
  
  class HdpModel(interfaces.TransformationABC, basemodel.BaseTopicModel):
      r"""`Hierarchical Dirichlet Process model <http://jmlr.csail.mit.edu/proceedings/papers/v15/wang11a/wang11a.pdf>`_
  
      Topic models promise to help summarize and organize large archives of texts that cannot be easily analyzed by hand.
      Hierarchical Dirichlet process (HDP) is a powerful mixed-membership model for the unsupervised analysis of grouped
      data. Unlike its finite counterpart, latent Dirichlet allocation, the HDP topic model infers the number of topics
      from the data. Here we have used Online HDP, which provides the speed of online variational Bayes with the modeling
      flexibility of the HDP. The idea behind Online variational Bayes in general is to optimize the variational
      objective function  with stochastic optimization.The challenge we face is that the existing coordinate ascent
      variational Bayes algorithms for the HDP require complicated approximation methods or numerical optimization. This
      model utilises stick breaking construction of Hdp which enables it to allow for coordinate-ascent variational Bayes
      without numerical approximation.
  
      **Stick breaking construction**
  
      To understand the HDP model we need to understand how it is modelled using the stick breaking construction. A very
      good analogy to understand the stick breaking construction is `chinese restaurant franchise
      <https://www.cs.princeton.edu/courses/archive/fall07/cos597C/scribe/20070921.pdf>`_.
  
  
      For this assume that there is a restaurant franchise (`corpus`) which has a large number of restaurants
      (`documents`, `j`) under it. They have a global menu of dishes (`topics`, :math:`\Phi_{k}`) which they serve.
      Also, a single dish (`topic`, :math:`\Phi_{k}`) is only served at a single table `t` for all the customers
      (`words`, :math:`\theta_{j,i}`) who sit at that table.
      So, when a customer enters the restaurant he/she has the choice to make where he/she wants to sit.
      He/she can choose to sit at a table where some customers are already sitting , or he/she can choose to sit
      at a new table. Here the probability of choosing each option is not same.
  
      Now, in this the global menu of dishes correspond to the global atoms  :math:`\Phi_{k}`, and each restaurant
      correspond to a single document `j`. So the number of dishes served in a particular restaurant correspond to the
      number of topics in a particular document. And the number of people sitting at each table correspond to the number
      of words belonging to each topic inside the document `j`.
  
      Now, coming on to the stick breaking construction, the concept understood from the chinese restaurant franchise is
      easily carried over to the stick breaking construction for hdp (`"Figure 1" from "Online Variational Inference
      for the Hierarchical Dirichlet Process" <http://proceedings.mlr.press/v15/wang11a/wang11a.pdf>`_).
  
      A two level hierarchical dirichlet process is a collection of dirichlet processes :math:`G_{j}` , one for each
      group, which share a base distribution :math:`G_{0}`, which is also a dirichlet process. Also, all :math:`G_{j}`
      share the same set of atoms, :math:`\Phi_{k}`, and only the atom weights :math:`\pi _{jt}` differs.
  
      There will be multiple document-level atoms :math:`\psi_{jt}` which map to the same corpus-level atom
      :math:`\Phi_{k}`. Here, the :math:`\beta` signify the weights given to each of the topics globally. Also, each
      factor :math:`\theta_{j,i}` is distributed according to :math:`G_{j}`, i.e., it takes on the value of
      :math:`\Phi_{k}` with probability :math:`\pi _{jt}`. :math:`C_{j,t}` is an indicator variable whose value `k`
      signifies the index of :math:`\Phi`. This helps to map :math:`\psi_{jt}` to :math:`\Phi_{k}`.
  
      The top level (`corpus` level) stick proportions correspond the values of :math:`\beta`,
      bottom level (`document` level) stick proportions correspond to the values of :math:`\pi`.
      The truncation level for the corpus (`K`) and document (`T`) corresponds to the number of :math:`\beta`
      and :math:`\pi` which are in existence.
  
      Now, whenever coordinate ascent updates are to be performed, they happen at two level. The document level as well
      as corpus level.
  
      At document level, we update the following:
  
      #. The parameters to the document level sticks, i.e, a and b parameters of :math:`\beta` distribution of the
         variable :math:`\pi _{jt}`.
      #. The parameters to per word topic indicators, :math:`Z_{j,n}`. Here :math:`Z_{j,n}` selects topic parameter
         :math:`\psi_{jt}`.
      #. The parameters to per document topic indices :math:`\Phi_{jtk}`.
  
      At corpus level, we update the following:
  
      #. The parameters to the top level sticks, i.e., the parameters of the :math:`\beta` distribution for the
         corpus level :math:`\beta`, which signify the topic distribution at corpus level.
      #. The parameters to the topics :math:`\Phi_{k}`.
  
      Now coming on to the steps involved, procedure for online variational inference for the Hdp model is as follows:
  
      1. We initialise the corpus level parameters, topic parameters randomly and set current time to 1.
      2. Fetch a random document j from the corpus.
      3. Compute all the parameters required for document level updates.
      4. Compute natural gradients of corpus level parameters.
      5. Initialise the learning rate as a function of kappa, tau and current time. Also, increment current time by 1
         each time it reaches this step.
      6. Update corpus level parameters.
  
      Repeat 2 to 6 until stopping condition is not met.
  
      Here the stopping condition corresponds to
  
      * time limit expired
      * chunk limit reached
      * whole corpus processed
  
      Attributes
      ----------
      lda_alpha : numpy.ndarray
          Same as :math:`\alpha` from :class:`gensim.models.ldamodel.LdaModel`.
      lda_beta : numpy.ndarray
          Same as :math:`\beta` from from :class:`gensim.models.ldamodel.LdaModel`.
      m_D : int
          Number of documents in the corpus.
      m_Elogbeta : numpy.ndarray:
          Stores value of dirichlet expectation, i.e., compute :math:`E[log \theta]` for a vector
          :math:`\theta \sim Dir(\alpha)`.
      m_lambda : {numpy.ndarray, float}
          Drawn samples from the parameterized gamma distribution.
      m_lambda_sum : {numpy.ndarray, float}
          An array with the same shape as `m_lambda`, with the specified axis (1) removed.
      m_num_docs_processed : int
          Number of documents finished processing.This is incremented in size of chunks.
      m_r : list
          Acts as normaliser in lazy updating of `m_lambda` attribute.
      m_rhot : float
          Assigns weight to the information obtained from the mini-chunk and its value it between 0 and 1.
      m_status_up_to_date : bool
          Flag to indicate whether `lambda `and :math:`E[log \theta]` have been updated if True, otherwise - not.
      m_timestamp : numpy.ndarray
          Helps to keep track and perform lazy updates on lambda.
      m_updatect : int
          Keeps track of current time and is incremented every time :meth:`~gensim.models.hdpmodel.HdpModel.update_lambda`
          is called.
      m_var_sticks : numpy.ndarray
          Array of values for stick.
      m_varphi_ss : numpy.ndarray
          Used to update top level sticks.
      m_W : int
          Length of dictionary for the input corpus.
  
      """
      def __init__(self, corpus, id2word, max_chunks=None, max_time=None,
                   chunksize=256, kappa=1.0, tau=64.0, K=15, T=150, alpha=1,
                   gamma=1, eta=0.01, scale=1.0, var_converge=0.0001,
                   outputdir=None, random_state=None):
          """
  
          Parameters
          ----------
          corpus : iterable of list of (int, float)
              Corpus in BoW format.
          id2word : :class:`~gensim.corpora.dictionary.Dictionary`
              Dictionary for the input corpus.
          max_chunks : int, optional
              Upper bound on how many chunks to process. It wraps around corpus beginning in another corpus pass,
              if there are not enough chunks in the corpus.
          max_time : int, optional
              Upper bound on time (in seconds) for which model will be trained.
          chunksize : int, optional
              Number of documents in one chuck.
          kappa: float,optional
              Learning parameter which acts as exponential decay factor to influence extent of learning from each batch.
          tau: float, optional
              Learning parameter which down-weights early iterations of documents.
          K : int, optional
              Second level truncation level
          T : int, optional
              Top level truncation level
          alpha : int, optional
              Second level concentration
          gamma : int, optional
              First level concentration
          eta : float, optional
              The topic Dirichlet
          scale : float, optional
              Weights information from the mini-chunk of corpus to calculate rhot.
          var_converge : float, optional
              Lower bound on the right side of convergence. Used when updating variational parameters for a
              single document.
          outputdir : str, optional
              Stores topic and options information in the specified directory.
          random_state : {None, int, array_like, :class:`~np.random.RandomState`, optional}
              Adds a little random jitter to randomize results around same alpha when trying to fetch a closest
              corresponding lda model from :meth:`~gensim.models.hdpmodel.HdpModel.suggested_lda_model`
  
          """
          self.corpus = corpus
          self.id2word = id2word
          self.chunksize = chunksize
          self.max_chunks = max_chunks
          self.max_time = max_time
          self.outputdir = outputdir
  
          self.random_state = utils.get_random_state(random_state)
  
          self.lda_alpha = None
          self.lda_beta = None
  
          self.m_W = len(id2word)
          self.m_D = 0
          if corpus:
              self.m_D = len(corpus)
  
          self.m_T = T
          self.m_K = K
          self.m_alpha = alpha
          self.m_gamma = gamma
  
          self.m_var_sticks = np.zeros((2, T - 1))
          self.m_var_sticks[0] = 1.0
          self.m_var_sticks[1] = range(T - 1, 0, -1)
          self.m_varphi_ss = np.zeros(T)
  
          self.m_lambda = self.random_state.gamma(1.0, 1.0, (T, self.m_W)) * self.m_D * 100 / (T * self.m_W) - eta
          self.m_eta = eta
          self.m_Elogbeta = dirichlet_expectation(self.m_eta + self.m_lambda)
  
          self.m_tau = tau + 1
          self.m_kappa = kappa
          self.m_scale = scale
          self.m_updatect = 0
          self.m_status_up_to_date = True
          self.m_num_docs_processed = 0
  
          self.m_timestamp = np.zeros(self.m_W, dtype=int)
          self.m_r = [0]
          self.m_lambda_sum = np.sum(self.m_lambda, axis=1)
  
          self.m_var_converge = var_converge
  
          if self.outputdir:
              self.save_options()
  
          # if a training corpus was provided, start estimating the model right away
          if corpus is not None:
              self.update(corpus)
  
      def inference(self, chunk):
          """Infers the gamma value based for `chunk`.
  
          Parameters
          ----------
          chunk : iterable of list of (int, float)
              Corpus in BoW format.
  
          Returns
          -------
          numpy.ndarray
              First level concentration, i.e., Gamma value.
  
          Raises
          ------
          RuntimeError
              If model doesn't trained yet.
  
          """
          if self.lda_alpha is None or self.lda_beta is None:
              raise RuntimeError("model must be trained to perform inference")
          chunk = list(chunk)
          if len(chunk) > 1:
              logger.debug("performing inference on a chunk of %i documents", len(chunk))
  
          gamma = np.zeros((len(chunk), self.lda_beta.shape[0]))
          for d, doc in enumerate(chunk):
              if not doc:  # leave gamma at zero for empty documents
                  continue
              ids, counts = zip(*doc)
              _, gammad = lda_e_step(ids, counts, self.lda_alpha, self.lda_beta)
              gamma[d, :] = gammad
          return gamma
  
      def __getitem__(self, bow, eps=0.01):
          """Accessor method for generating topic distribution of given document.
  
          Parameters
          ----------
          bow : {iterable of list of (int, float), list of (int, float)
              BoW representation of the document/corpus to get topics for.
          eps : float, optional
              Ignore topics with probability below `eps`.
  
          Returns
          -------
          list of (int, float) **or** :class:`gensim.interfaces.TransformedCorpus`
              Topic distribution for the given document/corpus `bow`, as a list of `(topic_id, topic_probability)` or
              transformed corpus
  
          """
          is_corpus, corpus = utils.is_corpus(bow)
          if is_corpus:
              return self._apply(corpus)
  
          gamma = self.inference([bow])[0]
          topic_dist = gamma / sum(gamma) if sum(gamma) != 0 else []
          return [(topicid, topicvalue) for topicid, topicvalue in enumerate(topic_dist) if topicvalue >= eps]
  
      def update(self, corpus):
          """Train the model with new documents, by EM-iterating over `corpus` until any of the conditions is satisfied.
  
          * time limit expired
          * chunk limit reached
          * whole corpus processed
  
          Parameters
          ----------
          corpus : iterable of list of (int, float)
              Corpus in BoW format.
  
          """
          save_freq = max(1, int(10000 / self.chunksize))  # save every 10k docs, roughly
          chunks_processed = 0
          start_time = time.perf_counter()
  
          while True:
              for chunk in utils.grouper(corpus, self.chunksize):
                  self.update_chunk(chunk)
                  self.m_num_docs_processed += len(chunk)
                  chunks_processed += 1
  
                  if self.update_finished(start_time, chunks_processed, self.m_num_docs_processed):
                      self.update_expectations()
                      alpha, beta = self.hdp_to_lda()
                      self.lda_alpha = alpha
                      self.lda_beta = beta
                      self.print_topics(20)
                      if self.outputdir:
                          self.save_topics()
                      return
  
                  elif chunks_processed % save_freq == 0:
                      self.update_expectations()
                      # self.save_topics(self.m_num_docs_processed)
                      self.print_topics(20)
                      logger.info('PROGRESS: finished document %i of %i', self.m_num_docs_processed, self.m_D)
  
      def update_finished(self, start_time, chunks_processed, docs_processed):
          """Flag to determine whether the model has been updated with the new corpus or not.
  
          Parameters
          ----------
          start_time : float
              Indicates the current processor time as a floating point number expressed in seconds.
              The resolution is typically better on Windows than on Unix by one microsecond due to differing
              implementation of underlying function calls.
          chunks_processed : int
              Indicates progress of the update in terms of the number of chunks processed.
          docs_processed : int
              Indicates number of documents finished processing.This is incremented in size of chunks.
  
          Returns
          -------
          bool
              If True - model is updated, False otherwise.
  
          """
          return (
              # chunk limit reached
              (self.max_chunks and chunks_processed == self.max_chunks)
  
              # time limit reached
              or (self.max_time and time.perf_counter() - start_time > self.max_time)
  
              # no limits and whole corpus has been processed once
              or (not self.max_chunks and not self.max_time and docs_processed >= self.m_D))
  
      def update_chunk(self, chunk, update=True, opt_o=True):
          """Performs lazy update on necessary columns of lambda and variational inference for documents in the chunk.
  
          Parameters
          ----------
          chunk : iterable of list of (int, float)
              Corpus in BoW format.
          update : bool, optional
              If True - call :meth:`~gensim.models.hdpmodel.HdpModel.update_lambda`.
          opt_o : bool, optional
              Passed as argument to :meth:`~gensim.models.hdpmodel.HdpModel.update_lambda`.
              If True then the topics will be ordered, False otherwise.
  
          Returns
          -------
          (float, int)
              A tuple of likelihood and sum of all the word counts from each document in the corpus.
  
          """
          # Find the unique words in this chunk...
          unique_words = dict()
          word_list = []
          for doc in chunk:
              for word_id, _ in doc:
                  if word_id not in unique_words:
                      unique_words[word_id] = len(unique_words)
                      word_list.append(word_id)
  
          wt = len(word_list)  # length of words in these documents
  
          # ...and do the lazy updates on the necessary columns of lambda
          rw = np.array([self.m_r[t] for t in self.m_timestamp[word_list]])
          self.m_lambda[:, word_list] *= np.exp(self.m_r[-1] - rw)
          self.m_Elogbeta[:, word_list] = \
              psi(self.m_eta + self.m_lambda[:, word_list]) - \
              psi(self.m_W * self.m_eta + self.m_lambda_sum[:, np.newaxis])
  
          ss = SuffStats(self.m_T, wt, len(chunk))
  
          Elogsticks_1st = expect_log_sticks(self.m_var_sticks)  # global sticks
  
          # run variational inference on some new docs
          score = 0.0
          count = 0
          for doc in chunk:
              if len(doc) > 0:
                  doc_word_ids, doc_word_counts = zip(*doc)
                  doc_score = self.doc_e_step(
                      ss, Elogsticks_1st,
                      unique_words, doc_word_ids,
                      doc_word_counts, self.m_var_converge
                  )
                  count += sum(doc_word_counts)
                  score += doc_score
  
          if update:
              self.update_lambda(ss, word_list, opt_o)
  
          return score, count
  
      def doc_e_step(self, ss, Elogsticks_1st, unique_words, doc_word_ids, doc_word_counts, var_converge):
          """Performs E step for a single doc.
  
          Parameters
          ----------
          ss : :class:`~gensim.models.hdpmodel.SuffStats`
              Stats for all document(s) in the chunk.
          Elogsticks_1st : numpy.ndarray
              Computed Elogsticks value by stick-breaking process.
          unique_words : dict of (int, int)
              Number of unique words in the chunk.
          doc_word_ids : iterable of int
              Word ids of for a single document.
          doc_word_counts : iterable of int
              Word counts of all words in a single document.
          var_converge : float
              Lower bound on the right side of convergence. Used when updating variational parameters for a single
              document.
  
          Returns
          -------
          float
              Computed value of likelihood for a single document.
  
          """
          chunkids = [unique_words[id] for id in doc_word_ids]
  
          Elogbeta_doc = self.m_Elogbeta[:, doc_word_ids]
          # very similar to the hdp equations
          v = np.zeros((2, self.m_K - 1))
          v[0] = 1.0
          v[1] = self.m_alpha
  
          # back to the uniform
          phi = np.ones((len(doc_word_ids), self.m_K)) * 1.0 / self.m_K
  
          likelihood = 0.0
          old_likelihood = -1e200
          converge = 1.0
  
          iter = 0
          max_iter = 100
          # not yet support second level optimization yet, to be done in the future
          while iter < max_iter and (converge < 0.0 or converge > var_converge):
              # update variational parameters
  
              # var_phi
              if iter < 3:
                  var_phi = np.dot(phi.T, (Elogbeta_doc * doc_word_counts).T)
                  (log_var_phi, log_norm) = matutils.ret_log_normalize_vec(var_phi)
                  var_phi = np.exp(log_var_phi)
              else:
                  var_phi = np.dot(phi.T, (Elogbeta_doc * doc_word_counts).T) + Elogsticks_1st
                  (log_var_phi, log_norm) = matutils.ret_log_normalize_vec(var_phi)
                  var_phi = np.exp(log_var_phi)
  
              # phi
              if iter < 3:
                  phi = np.dot(var_phi, Elogbeta_doc).T
                  (log_phi, log_norm) = matutils.ret_log_normalize_vec(phi)
                  phi = np.exp(log_phi)
              else:
                  phi = np.dot(var_phi, Elogbeta_doc).T + Elogsticks_2nd  # noqa:F821
                  (log_phi, log_norm) = matutils.ret_log_normalize_vec(phi)
                  phi = np.exp(log_phi)
  
              # v
              phi_all = phi * np.array(doc_word_counts)[:, np.newaxis]
              v[0] = 1.0 + np.sum(phi_all[:, :self.m_K - 1], 0)
              phi_cum = np.flipud(np.sum(phi_all[:, 1:], 0))
              v[1] = self.m_alpha + np.flipud(np.cumsum(phi_cum))
              Elogsticks_2nd = expect_log_sticks(v)
  
              likelihood = 0.0
              # compute likelihood
              # var_phi part/ C in john's notation
              likelihood += np.sum((Elogsticks_1st - log_var_phi) * var_phi)
  
              # v part/ v in john's notation, john's beta is alpha here
              log_alpha = np.log(self.m_alpha)
              likelihood += (self.m_K - 1) * log_alpha
              dig_sum = psi(np.sum(v, 0))
              likelihood += np.sum((np.array([1.0, self.m_alpha])[:, np.newaxis] - v) * (psi(v) - dig_sum))
              likelihood -= np.sum(gammaln(np.sum(v, 0))) - np.sum(gammaln(v))
  
              # Z part
              likelihood += np.sum((Elogsticks_2nd - log_phi) * phi)
  
              # X part, the data part
              likelihood += np.sum(phi.T * np.dot(var_phi, Elogbeta_doc * doc_word_counts))
  
              converge = (likelihood - old_likelihood) / abs(old_likelihood)
              old_likelihood = likelihood
  
              if converge < -0.000001:
                  logger.warning('likelihood is decreasing!')
  
              iter += 1
  
          # update the suff_stat ss
          # this time it only contains information from one doc
          ss.m_var_sticks_ss += np.sum(var_phi, 0)
          ss.m_var_beta_ss[:, chunkids] += np.dot(var_phi.T, phi.T * doc_word_counts)
  
          return likelihood
  
      def update_lambda(self, sstats, word_list, opt_o):
          """Update appropriate columns of lambda and top level sticks based on documents.
  
          Parameters
          ----------
          sstats : :class:`~gensim.models.hdpmodel.SuffStats`
              Statistic for all document(s) in the chunk.
          word_list : list of int
              Contains word id of all the unique words in the chunk of documents on which update is being performed.
          opt_o : bool, optional
              If True - invokes a call to :meth:`~gensim.models.hdpmodel.HdpModel.optimal_ordering` to order the topics.
  
          """
          self.m_status_up_to_date = False
          # rhot will be between 0 and 1, and says how much to weight
          # the information we got from this mini-chunk.
          rhot = self.m_scale * pow(self.m_tau + self.m_updatect, -self.m_kappa)
          if rhot < rhot_bound:
              rhot = rhot_bound
          self.m_rhot = rhot
  
          # Update appropriate columns of lambda based on documents.
          self.m_lambda[:, word_list] = \
              self.m_lambda[:, word_list] * (1 - rhot) + rhot * self.m_D * sstats.m_var_beta_ss / sstats.m_chunksize
          self.m_lambda_sum = (1 - rhot) * self.m_lambda_sum + \
              rhot * self.m_D * np.sum(sstats.m_var_beta_ss, axis=1) / sstats.m_chunksize
  
          self.m_updatect += 1
          self.m_timestamp[word_list] = self.m_updatect
          self.m_r.append(self.m_r[-1] + np.log(1 - rhot))
  
          self.m_varphi_ss = \
              (1.0 - rhot) * self.m_varphi_ss + rhot * sstats.m_var_sticks_ss * self.m_D / sstats.m_chunksize
  
          if opt_o:
              self.optimal_ordering()
  
          # update top level sticks
          self.m_var_sticks[0] = self.m_varphi_ss[:self.m_T - 1] + 1.0
          var_phi_sum = np.flipud(self.m_varphi_ss[1:])
          self.m_var_sticks[1] = np.flipud(np.cumsum(var_phi_sum)) + self.m_gamma
  
      def optimal_ordering(self):
          """Performs ordering on the topics."""
          idx = matutils.argsort(self.m_lambda_sum, reverse=True)
          self.m_varphi_ss = self.m_varphi_ss[idx]
          self.m_lambda = self.m_lambda[idx, :]
          self.m_lambda_sum = self.m_lambda_sum[idx]
          self.m_Elogbeta = self.m_Elogbeta[idx, :]
  
      def update_expectations(self):
          """Since we're doing lazy updates on lambda, at any given moment the current state of lambda may not be
          accurate. This function updates all of the elements of lambda and Elogbeta so that if (for example) we want to
          print out the topics we've learned we'll get the correct behavior.
  
          """
          for w in range(self.m_W):
              self.m_lambda[:, w] *= np.exp(self.m_r[-1] - self.m_r[self.m_timestamp[w]])
          self.m_Elogbeta = \
              psi(self.m_eta + self.m_lambda) - psi(self.m_W * self.m_eta + self.m_lambda_sum[:, np.newaxis])
  
          self.m_timestamp[:] = self.m_updatect
          self.m_status_up_to_date = True
  
      def show_topic(self, topic_id, topn=20, log=False, formatted=False, num_words=None):
          """Print the `num_words` most probable words for topic `topic_id`.
  
          Parameters
          ----------
          topic_id : int
              Acts as a representative index for a particular topic.
          topn : int, optional
              Number of most probable words to show from given `topic_id`.
          log : bool, optional
              If True - logs a message with level INFO on the logger object.
          formatted : bool, optional
              If True - get the topics as a list of strings, otherwise - get the topics as lists of (weight, word) pairs.
          num_words : int, optional
              DEPRECATED, USE `topn` INSTEAD.
  
          Warnings
          --------
          The parameter `num_words` is deprecated, will be removed in 4.0.0, please use `topn` instead.
  
          Returns
          -------
          list of (str, numpy.float) **or** list of str
              Topic terms output displayed whose format depends on `formatted` parameter.
  
          """
          if num_words is not None:  # deprecated num_words is used
              warnings.warn(
                  "The parameter `num_words` is deprecated, will be removed in 4.0.0, please use `topn` instead."
              )
              topn = num_words
  
          if not self.m_status_up_to_date:
              self.update_expectations()
          betas = self.m_lambda + self.m_eta
          hdp_formatter = HdpTopicFormatter(self.id2word, betas)
          return hdp_formatter.show_topic(topic_id, topn, log, formatted)
  
      def get_topics(self):
          """Get the term topic matrix learned during inference.
  
          Returns
          -------
          np.ndarray
              `num_topics` x `vocabulary_size` array of floats
  
          """
          topics = self.m_lambda + self.m_eta
          return topics / topics.sum(axis=1)[:, None]
  
      def show_topics(self, num_topics=20, num_words=20, log=False, formatted=True):
          """Print the `num_words` most probable words for `num_topics` number of topics.
  
          Parameters
          ----------
          num_topics : int, optional
              Number of topics for which most probable `num_words` words will be fetched, if -1 - print all topics.
          num_words :  int, optional
              Number of most probable words to show from `num_topics` number of topics.
          log : bool, optional
              If True - log a message with level INFO on the logger object.
          formatted : bool, optional
              If True - get the topics as a list of strings, otherwise - get the topics as lists of (weight, word) pairs.
  
          Returns
          -------
          list of (str, numpy.float) **or** list of str
              Output format for topic terms depends on the value of `formatted` parameter.
  
          """
          if not self.m_status_up_to_date:
              self.update_expectations()
          betas = self.m_lambda + self.m_eta
          hdp_formatter = HdpTopicFormatter(self.id2word, betas)
          return hdp_formatter.show_topics(num_topics, num_words, log, formatted)
  
      @deprecated("This method will be removed in 4.0.0, use `save` instead.")
      def save_topics(self, doc_count=None):
          """Save discovered topics.
  
          Warnings
          --------
          This method is deprecated, use :meth:`~gensim.models.hdpmodel.HdpModel.save` instead.
  
          Parameters
          ----------
          doc_count : int, optional
              Indicates number of documents finished processing and are to be saved.
  
          """
          if not self.outputdir:
              logger.error("cannot store topics without having specified an output directory")
  
          if doc_count is None:
              fname = 'final'
          else:
              fname = 'doc-%i' % doc_count
          fname = '%s/%s.topics' % (self.outputdir, fname)
          logger.info("saving topics to %s", fname)
          betas = self.m_lambda + self.m_eta
          np.savetxt(fname, betas)
  
      @deprecated("This method will be removed in 4.0.0, use `save` instead.")
      def save_options(self):
          """Writes all the values of the attributes for the current model in "options.dat" file.
  
          Warnings
          --------
          This method is deprecated, use :meth:`~gensim.models.hdpmodel.HdpModel.save` instead.
  
          """
          if not self.outputdir:
              logger.error("cannot store options without having specified an output directory")
              return
          fname = '%s/options.dat' % self.outputdir
          with utils.open(fname, 'wb') as fout:
              fout.write('tau: %s\n' % str(self.m_tau - 1))
              fout.write('chunksize: %s\n' % str(self.chunksize))
              fout.write('var_converge: %s\n' % str(self.m_var_converge))
              fout.write('D: %s\n' % str(self.m_D))
              fout.write('K: %s\n' % str(self.m_K))
              fout.write('T: %s\n' % str(self.m_T))
              fout.write('W: %s\n' % str(self.m_W))
              fout.write('alpha: %s\n' % str(self.m_alpha))
              fout.write('kappa: %s\n' % str(self.m_kappa))
              fout.write('eta: %s\n' % str(self.m_eta))
              fout.write('gamma: %s\n' % str(self.m_gamma))
  
      def hdp_to_lda(self):
          """Get corresponding alpha and beta values of a LDA almost equivalent to current HDP.
  
          Returns
          -------
          (numpy.ndarray, numpy.ndarray)
              Alpha and Beta arrays.
  
          """
          # alpha
          sticks = self.m_var_sticks[0] / (self.m_var_sticks[0] + self.m_var_sticks[1])
          alpha = np.zeros(self.m_T)
          left = 1.0
          for i in range(0, self.m_T - 1):
              alpha[i] = sticks[i] * left
              left = left - alpha[i]
          alpha[self.m_T - 1] = left
          alpha *= self.m_alpha
  
          # beta
          beta = (self.m_lambda + self.m_eta) / (self.m_W * self.m_eta + self.m_lambda_sum[:, np.newaxis])
  
          return alpha, beta
  
      def suggested_lda_model(self):
          """Get a trained ldamodel object which is closest to the current hdp model.
  
          The `num_topics=m_T`, so as to preserve the matrices shapes when we assign alpha and beta.
  
          Returns
          -------
          :class:`~gensim.models.ldamodel.LdaModel`
              Closest corresponding LdaModel to current HdpModel.
  
          """
          alpha, beta = self.hdp_to_lda()
          ldam = ldamodel.LdaModel(
              num_topics=self.m_T, alpha=alpha, id2word=self.id2word, random_state=self.random_state, dtype=np.float64
          )
          ldam.expElogbeta[:] = beta
          return ldam
  
      def evaluate_test_corpus(self, corpus):
          """Evaluates the model on test corpus.
  
          Parameters
          ----------
          corpus : iterable of list of (int, float)
              Test corpus in BoW format.
  
          Returns
          -------
          float
              The value of total likelihood obtained by evaluating the model for all documents in the test corpus.
  
          """
          logger.info('TEST: evaluating test corpus')
          if self.lda_alpha is None or self.lda_beta is None:
              self.lda_alpha, self.lda_beta = self.hdp_to_lda()
          score = 0.0
          total_words = 0
          for i, doc in enumerate(corpus):
              if len(doc) > 0:
                  doc_word_ids, doc_word_counts = zip(*doc)
                  likelihood, gamma = lda_e_step(doc_word_ids, doc_word_counts, self.lda_alpha, self.lda_beta)
                  theta = gamma / np.sum(gamma)
                  lda_betad = self.lda_beta[:, doc_word_ids]
                  log_predicts = np.log(np.dot(theta, lda_betad))
                  doc_score = sum(log_predicts) / len(doc)
                  logger.info('TEST: %6d    %.5f', i, doc_score)
                  score += likelihood
                  total_words += sum(doc_word_counts)
          logger.info(
              "TEST: average score: %.5f, total score: %.5f,  test docs: %d",
              score / total_words, score, len(corpus)
          )
          return score
  
  
  class HdpTopicFormatter:
      """Helper class for :class:`gensim.models.hdpmodel.HdpModel` to format the output of topics."""
      (STYLE_GENSIM, STYLE_PRETTY) = (1, 2)
  
      def __init__(self, dictionary=None, topic_data=None, topic_file=None, style=None):
          """Initialise the :class:`gensim.models.hdpmodel.HdpTopicFormatter` and store topic data in sorted order.
  
          Parameters
          ----------
          dictionary : :class:`~gensim.corpora.dictionary.Dictionary`,optional
              Dictionary for the input corpus.
          topic_data : numpy.ndarray, optional
              The term topic matrix.
          topic_file : {file-like object, str, pathlib.Path}
              File, filename, or generator to read. If the filename extension is .gz or .bz2, the file is first
              decompressed. Note that generators should return byte strings for Python 3k.
          style : bool, optional
              If True - get the topics as a list of strings, otherwise - get the topics as lists of (word, weight) pairs.
  
          Raises
          ------
          ValueError
              Either dictionary is None or both `topic_data` and `topic_file` is None.
  
          """
          if dictionary is None:
              raise ValueError('no dictionary!')
  
          if topic_data is not None:
              topics = topic_data
          elif topic_file is not None:
              topics = np.loadtxt('%s' % topic_file)
          else:
              raise ValueError('no topic data!')
  
          # sort topics
          topics_sums = np.sum(topics, axis=1)
          idx = matutils.argsort(topics_sums, reverse=True)
          self.data = topics[idx]
  
          self.dictionary = dictionary
  
          if style is None:
              style = self.STYLE_GENSIM
  
          self.style = style
  
      def print_topics(self, num_topics=10, num_words=10):
          """Give the most probable `num_words` words from `num_topics` topics.
          Alias for :meth:`~gensim.models.hdpmodel.HdpTopicFormatter.show_topics`.
  
          Parameters
          ----------
          num_topics : int, optional
              Top `num_topics` to be printed.
          num_words : int, optional
              Top `num_words` most probable words to be printed from each topic.
  
          Returns
          -------
          list of (str, numpy.float) **or** list of str
              Output format for `num_words` words from `num_topics` topics depends on the value of `self.style` attribute.
  
          """
          return self.show_topics(num_topics, num_words, True)
  
      def show_topics(self, num_topics=10, num_words=10, log=False, formatted=True):
          """Give the most probable `num_words` words from `num_topics` topics.
  
          Parameters
          ----------
          num_topics : int, optional
              Top `num_topics` to be printed.
          num_words : int, optional
              Top `num_words` most probable words to be printed from each topic.
          log : bool, optional
              If True - log a message with level INFO on the logger object.
          formatted : bool, optional
              If True - get the topics as a list of strings, otherwise as lists of (word, weight) pairs.
  
          Returns
          -------
          list of (int, list of (str, numpy.float) **or** list of str)
              Output format for terms from `num_topics` topics depends on the value of `self.style` attribute.
  
          """
          shown = []
          num_topics = max(num_topics, 0)
          num_topics = min(num_topics, len(self.data))
  
          for k in range(num_topics):
              lambdak = self.data[k, :]
              lambdak = lambdak / lambdak.sum()
  
              temp = zip(lambdak, range(len(lambdak)))
              temp = sorted(temp, key=lambda x: x[0], reverse=True)
  
              topic_terms = self.show_topic_terms(temp, num_words)
  
              if formatted:
                  topic = self.format_topic(k, topic_terms)
  
                  # assuming we only output formatted topics
                  if log:
                      logger.info(topic)
              else:
                  topic = (k, topic_terms)
              shown.append(topic)
  
          return shown
  
      def print_topic(self, topic_id, topn=None, num_words=None):
          """Print the `topn` most probable words from topic id `topic_id`.
  
          Warnings
          --------
          The parameter `num_words` is deprecated, will be removed in 4.0.0, please use `topn` instead.
  
          Parameters
          ----------
          topic_id : int
              Acts as a representative index for a particular topic.
          topn : int, optional
              Number of most probable words to show from given `topic_id`.
          num_words : int, optional
              DEPRECATED, USE `topn` INSTEAD.
  
          Returns
          -------
          list of (str, numpy.float) **or** list of str
              Output format for terms from a single topic depends on the value of `formatted` parameter.
  
          """
          if num_words is not None:  # deprecated num_words is used
              warnings.warn(
                  "The parameter `num_words` is deprecated, will be removed in 4.0.0, please use `topn` instead."
              )
              topn = num_words
  
          return self.show_topic(topic_id, topn, formatted=True)
  
      def show_topic(self, topic_id, topn=20, log=False, formatted=False, num_words=None,):
          """Give the most probable `num_words` words for the id `topic_id`.
  
          Warnings
          --------
          The parameter `num_words` is deprecated, will be removed in 4.0.0, please use `topn` instead.
  
          Parameters
          ----------
          topic_id : int
              Acts as a representative index for a particular topic.
          topn : int, optional
              Number of most probable words to show from given `topic_id`.
          log : bool, optional
              If True logs a message with level INFO on the logger object, False otherwise.
          formatted : bool, optional
              If True return the topics as a list of strings, False as lists of
              (word, weight) pairs.
          num_words : int, optional
              DEPRECATED, USE `topn` INSTEAD.
  
          Returns
          -------
          list of (str, numpy.float) **or** list of str
              Output format for terms from a single topic depends on the value of `self.style` attribute.
  
          """
          if num_words is not None:  # deprecated num_words is used
              warnings.warn(
                  "The parameter `num_words` is deprecated, will be removed in 4.0.0, please use `topn` instead."
              )
              topn = num_words
  
          lambdak = self.data[topic_id, :]
          lambdak = lambdak / lambdak.sum()
  
          temp = zip(lambdak, range(len(lambdak)))
          temp = sorted(temp, key=lambda x: x[0], reverse=True)
  
          topic_terms = self.show_topic_terms(temp, topn)
  
          if formatted:
              topic = self.format_topic(topic_id, topic_terms)
  
              # assuming we only output formatted topics
              if log:
                  logger.info(topic)
          else:
              topic = (topic_id, topic_terms)
  
          # we only return the topic_terms
          return topic[1]
  
      def show_topic_terms(self, topic_data, num_words):
          """Give the topic terms along with their probabilities for a single topic data.
  
          Parameters
          ----------
          topic_data : list of (str, numpy.float)
              Contains probabilities for each word id belonging to a single topic.
          num_words : int
              Number of words for which probabilities are to be extracted from the given single topic data.
  
          Returns
          -------
          list of (str, numpy.float)
              A sequence of topic terms and their probabilities.
  
          """
          return [(self.dictionary[wid], weight) for (weight, wid) in topic_data[:num_words]]
  
      def format_topic(self, topic_id, topic_terms):
          """Format the display for a single topic in two different ways.
  
          Parameters
          ----------
          topic_id : int
              Acts as a representative index for a particular topic.
          topic_terms : list of (str, numpy.float)
              Contains the most probable words from a single topic.
  
          Returns
          -------
          list of (str, numpy.float) **or** list of str
              Output format for topic terms depends on the value of `self.style` attribute.
  
          """
          if self.STYLE_GENSIM == self.style:
              fmt = ' + '.join('%.3f*%s' % (weight, word) for (word, weight) in topic_terms)
          else:
              fmt = '\n'.join('    %20s    %.8f' % (word, weight) for (word, weight) in topic_terms)
  
          fmt = (topic_id, fmt)
          return fmt
  