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pdf.py
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import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from numpy import exp, sqrt, pi
class PDF(object):
def __init__(self, series, start=None, stop=None, bw=1):
if not type(series) == pd.Series:
series = pd.Series(series)
series = series[series.notnull()]
self.name = series.name
self.size = series.count()
self.values = series.unique()
self.bw = bw
def _estimate(self):
NotImplemented
def plot(self):
x = np.linspace(self.ends[0], self.ends[1], len(self.pdf))
y = list(self.pdf)
plt.plot(x, y)
plt.show()
def prob(self, li):
NotImplemented
def verify_slice(self, li):
NotImplemented
@classmethod
def make(cls, series, pdf_type=None, start=None, stop=None):
if pdf_type:
if pdf_type == 'continuous':
obj = ContinuousPDF(series, start, stop)
elif pdf_type == 'discrete':
obj = DiscretePDF(series, start, stop)
elif pdf_type == 'indexed':
obj = IndexedPDF(series)
else:
raise Exception('%s unrecognized distribution type' % pdf_type)
else:
if 'float' in str(series.dtype):
obj = ContinuousPDF(series, start, stop)
elif 'int' in str(series.dtype):
obj = DiscretePDF(series, start, stop)
else:
obj = IndexedPDF(series)
return obj
class ContinuousPDF(PDF):
def __init__(self, series, start=None, stop=None):
super(ContinuousPDF, self).__init__(series)
if not type(series) == pd.Series:
series = pd.Series(series)
series = series[series.notnull()]
if start is not None and stop is not None:
self.ends = np.array((start, stop))
else:
self.ends = np.array((self.values.min(), self.values.max()))
self.width = 200
self.step = float((self.ends[1] - self.ends[0]) / float(self.width))
self.pdf = self._estimate(series)
def _estimate(self, series):
def kde(xv, vect, d, bw):
return sum(exp(-0.5 * ((xv - vect) / bw) ** 2)
/ d)
d = sqrt(2 * pi * self.bw ** 2)
r = np.linspace(*self.ends, num=self.width)
a = np.array([kde(xv, series, d, self.bw) for xv in r])
return a * (1 / a.sum())
def prob(self, li):
li = np.array([li])
self.verify_slice(li)
if li.size == 1:
li = np.array([li[0] - .5 * self.step, li[0] + .5 * self.step])
left = max(int((li.min() - self.ends[0]) / self.step) - 1, 0)
right = min(int((li.max() - self.ends[0]) / self.step) + 1, self.width)
return self.pdf[range(left, right)].sum()
def verify_slice(self, li):
try:
assert li.min() >= self.ends[0] and li.max() <= self.ends[1]
except:
s = '%s has range %s but %s provided'
s = s % (self.name, self.ends, li)
raise Exception(s)
class DiscretePDF(PDF):
def __init__(self, series, start=None, stop=None):
super(DiscretePDF, self).__init__(series)
if not type(series) == pd.Series:
series = pd.Series(series)
series = series[series.notnull()]
if start is not None and stop is not None:
self.ends = np.array((start, stop))
else:
self.ends = np.array((self.values.min(), self. values.max() + 1))
self.pdf = self._estimate(series)
def _estimate(self, series):
def kde(xv, vect, d, bw):
return sum(exp(-0.5 * ((xv - vect) / bw) ** 2)
/ d)
d = sqrt(2 * pi * self.bw ** 2)
r = range(*self.ends)
a = np.array([kde(xv, series, d, self.bw) for xv in r])
return a * (1 / a.sum())
def prob(self, li):
li = np.array(li)
self.verify_slice(li)
li = li - self.ends.min()
return self.pdf[li].sum()
def verify_slice(self, li):
try:
assert all(np.intersect1d(li, np.array(range(*self.ends))) == li)
except:
s = '%s has range %s but %s provided'
s = s % (self.name, self.ends, li)
raise Exception(s)
class IndexedPDF(PDF):
def __init__(self, series):
super(IndexedPDF, self).__init__(series)
if not type(series) == pd.Series:
series = pd.Series(series)
series = series[series.notnull()]
self.ends = self.values
self.pdf = self._estimate(series)
def _estimate(self, series):
a = np.array([(series == k).sum() for k in self.values])
return a / float(series.count())
def prob(self, li):
li = np.array(li)
self.verify_slice(li)
p = 0
for k in self.values:
if k in li:
p += self.pdf[np.argmax(self.values == k)]
return p
def plot(self):
x = np.array(range(-1, self.values.count() + 1))
y = [0] + list(self.pdf) + [0]
plt.step(x, y)
plt.xticks(np.array(range(0, self.values.count())) - .5, self.values)
plt.show()
def verify_slice(self, li):
try:
assert all([v in self.values for v in li])
except:
s = '%s has range %s but %s provided'
s = s % (self.name, self.ends, li)
raise Exception(s)