add jitter to fast_kde (#1629)

* add jitter to fast_kde, prevents errors when input values are all the same

* remove unnecessary print

pymc3/plots.py

@@ -1,6 +1,5 @@
 import numpy as np
 from scipy.stats import kde, mode
-from numpy.linalg import LinAlgError
 import matplotlib.pyplot as plt
 import pymc3 as pm
 from .stats import quantiles, hpd
@@ -122,26 +121,18 @@ def histplot_op(ax, data, alpha=.35):
 
 
 def kdeplot_op(ax, data, prior=None, prior_alpha=1, prior_style='--'):
-    errored = []
     for i in range(data.shape[1]):
         d = data[:, i]
-        try:
-            density, l, u = fast_kde(d)
-            x = np.linspace(l, u, len(density))
-
-            if prior is not None:
-                p = prior.logp(x).eval()
-                ax.plot(x, np.exp(p), alpha=prior_alpha, ls=prior_style)
+        density, l, u = fast_kde(d)
+        x = np.linspace(l, u, len(density))
 
-            ax.plot(x, density)
+        if prior is not None:
+            p = prior.logp(x).eval()
+            ax.plot(x, np.exp(p), alpha=prior_alpha, ls=prior_style)
 
-        except LinAlgError:
-            errored.append(i)
+        ax.plot(x, density)
 
     ax.set_ylim(ymin=0)
-    if errored:
-        ax.text(.27, .47, 'WARNING: KDE plot failed for: ' + str(errored), style='italic',
-                bbox={'facecolor': 'red', 'alpha': 0.5, 'pad': 10})
 
 
 def make_2d(a):
@@ -793,6 +784,7 @@ def get_trace_dict(tr, varnames):
 
         fig.tight_layout()
     return ax
+
 
 def fast_kde(x):
     """
@@ -813,14 +805,16 @@ def fast_kde(x):
     xmax: maximum value of x
     
     """
+    # add small jitter in case input values are the same
+    x = np.random.normal(x, 1e-12)
 
     xmin, xmax = x.min(), x.max()
 
     n = len(x)
     nx = 256
 
     # compute histogram
-    bins = np.linspace(x.min(), x.max(), nx)
+    bins = np.linspace(xmin, xmax, nx)
     xyi = np.digitize(x, bins)
     dx = (xmax - xmin) / (nx - 1)
     grid = np.histogram(x, bins=nx)[0]