Fix epsilon according to dtype in LdaModel (#1770)

* add type check + adopt eps for different dtypes

* fix typo

* improve readability

* move mapping to module level, remove duplication

* fix typo + remove duplication

gensim/models/ldamodel.py

@@ -50,6 +50,12 @@
 
 logger = logging.getLogger('gensim.models.ldamodel')
 
+DTYPE_TO_EPS = {
+    np.float16: 1e-5,
+    np.float32: 1e-35,
+    np.float64: 1e-100,
+}
+
 
 def logsumexp(x):
     """Log of sum of exponentials
@@ -275,6 +281,7 @@ def __init__(self, corpus=None, num_topics=100, id2word=None,
         `callbacks` a list of metric callbacks to log/visualize evaluation metrics of topic model during training.
 
         `dtype` is data-type to use during calculations inside model. All inputs are also converted to this dtype.
+        Available types: `numpy.float16`, `numpy.float32`, `numpy.float64`.
 
         Example:
 
@@ -286,6 +293,11 @@ def __init__(self, corpus=None, num_topics=100, id2word=None,
         >>> lda = LdaModel(corpus, num_topics=50, alpha='auto', eval_every=5)  # train asymmetric alpha from data
 
         """
+        if dtype not in DTYPE_TO_EPS:
+            raise ValueError(
+                "Incorrect 'dtype', please choose one of {}".format(
+                    ", ".join("numpy.{}".format(tp.__name__) for tp in sorted(DTYPE_TO_EPS))))
+
         self.dtype = dtype
 
         # store user-supplied parameters
@@ -497,8 +509,9 @@ def inference(self, chunk, collect_sstats=False):
 
             # The optimal phi_{dwk} is proportional to expElogthetad_k * expElogbetad_w.
             # phinorm is the normalizer.
-            # TODO treat zeros explicitly, instead of adding 1e-100?
-            phinorm = np.dot(expElogthetad, expElogbetad) + 1e-100
+            # TODO treat zeros explicitly, instead of adding epsilon?
+            eps = DTYPE_TO_EPS[self.dtype]
+            phinorm = np.dot(expElogthetad, expElogbetad) + eps
 
             # Iterate between gamma and phi until convergence
             for _ in xrange(self.iterations):
@@ -509,7 +522,7 @@ def inference(self, chunk, collect_sstats=False):
                 gammad = self.alpha + expElogthetad * np.dot(cts / phinorm, expElogbetad.T)
                 Elogthetad = dirichlet_expectation(gammad)
                 expElogthetad = np.exp(Elogthetad)
-                phinorm = np.dot(expElogthetad, expElogbetad) + 1e-100
+                phinorm = np.dot(expElogthetad, expElogbetad) + eps
                 # If gamma hasn't changed much, we're done.
                 meanchange = np.mean(abs(gammad - lastgamma))
                 if meanchange < self.gamma_threshold: