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stats.py
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stats.py
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import numpy as np
import numpy.linalg as la
from numpy.random import randn
import gnuplot.gnuplot as gp
def cov(X):
"""
Covariance matrix
note: specifically for mean-centered data
note: numpy's `cov` uses N-1 as normalization
"""
return np.dot(X.T, X) / X.shape[0]
def pca(data, fraction=0.8, n_comp=None):
"""
Principal component analysis using eigenvalues
note: this mean-centers and auto-scales the data (in-place)
"""
data -= np.mean(data, 0)
data /= np.std(data, 0)
C = cov(data)
E, V = la.eigh(C)
print(E)
if n_comp is not None:
key = np.argsort(E)[::-1][:n_comp]
E, V = E[key], V[:, key]
else:
sumvariance = np.cumsum(E)
sumvariance /= sumvariance[-1]
key = data.shape[1] - np.searchsorted(sumvariance, fraction) + 1
print(key)
E, V = E[-key:], V[:, -key:]
U = np.dot(data, V)
return U, E, V
def hmean(array, **kwargs):
return 1 / np.nanmean(1 / array, **kwargs)
def gmean(array, axis=0, **kwargs):
return np.power(np.nanprod(array, axis=axis, **kwargs), -array.shape[axis])
def skewness(array, **kwargs):
mean = np.nanmean(array, **kwargs)
std = np.sqrt(np.nanmean(np.abs(array - mean)**2, **kwargs))
return 3 * (mean - np.nanmedian(array, **kwargs)) / std
def normal(x, mean, std):
std2 = std ** 2
return np.exp(-0.5 * ((x - mean)**2) / std2) / np.sqrt(2 * np.pi * std2)
def lognormal(x, mean, std):
std2 = std ** 2
return np.exp(-0.5 * ((np.log(x) - mean)**2) / std2) \
/ (x * np.sqrt(2 * np.pi * std2))
class Distro(object):
def __init__(self, area=None, mean=None, std=None, var=None):
self._area, self._mean, self._std, self._var = \
area, mean, std, var
def calc_attribute(self, attr, fun, **kwargs):
attr = getattr(self, attr)
if attr is None or kwargs.get("update", False):
attr = fun(*args, **kwargs)
return attr
class PDF(Distro):
def __init__(self, x, pdf):
self.x = x
self.pdf = pdf
Distro.__init__(self)
def area(self, **kwargs):
return Distro.calc_attribute(self, "area", np.trapz,
(self.pdf, self.x), **kwargs)
def mean(self, **kwargs):
return Distro.calc_attribute(self, "mean", np.trapz,
(self.x * self.pdf, self.x), **kwargs)
def var(self, **kwargs):
return Distro.calc_attribute(self, "var", np.trapz,
(self.x * self.pdf, self.x), **kwargs)
def mean(self, **kwargs):
#Distro.mean(np.trapz, (self.pdf, self.x),
if self._mean is None or kwargs.get("update", False):
self._mean = np.trapz(self.x * self.pdf, self.x, **kwargs)
return self._mean
def var(self, **kwargs):
if self._var is None or kwargs.get("update", False):
arg = self.pdf * (self.x - self.mean(**kwargs))**2
self._var = np.trapz(arg, self.x)
return self._var
def std(self, **kwargs):
if self._std is None or kwargs.get("update", False):
self._std = np.sqrt(self.var(**kwargs))
return self._std
def skewness(self, **kwargs):
return 3 * (self.mean(**kwargs) - np.nanmedian(array, **kwargs)) \
/ self.std(**kwargs)
class Histo(Distro):
def __init__(self, x, **kwargs):
self.histo, self.edges = np.histogram(x, **kwargs)
Distro.__init__(self)
self.cedges = None, None, None, None
def cent_edges(self, update=False):
if self.cedges is None or update:
self.cedges = self.edges[:-1] + (self.edges[1] - self.edges[0]) / 2.0
return self.cedges
def area(self, **kwargs):
if self._area is None or kwargs.get("update", False):
self._area = np.sum(self.histo, **kwargs)
return self._area
def mean(self, **kwargs):
if self._mean is None or kwargs.get("update", False):
self._mean = np.nanmean(self.histo, **kwargs)
return self._mean
def var(self, **kwargs):
if self._var is None or kwargs.get("update", False):
self._var = np.sum((self.histo - self.mean())**2)
return self._var
def std(self, **kwargs):
if self._std is None or kwargs.get("update", False):
self._std = np.sqrt(self.var(**kwargs))
return self._std
def hmean(self, **kwargs):
return 1 / np.nanmean(1 / self.histo, **kwargs)
def gmean(self, axis=0, **kwargs):
return np.power(np.nanprod(self.histo, axis=axis, **kwargs),
-array.shape[axis])
def skewness(self, **kwargs):
return 3 * (self.mean(**kwargs) - np.nanmedian(self.histo, **kwargs)) \
/ self.std(**kwargs)
def main():
""" test data """
data = np.array([randn(8) for k in range(150)])
data[:50, 2:4] += 10
data[50:, 2:5] += 10
""" visualize """
gp.output("pca.png", term="pngcairo", size=(1000,800))
gp.multiplot(4, nrows=2)
gp.title("Original")
gp.plot_data(data[:50, 0], data[:50, 1], ptype="points", pt="o")
gp.plot_data(data[50:, 0], data[50:, 1], ptype="points", pt="x")
gp.plot()
gp.title("PCA Fraction 0.2")
trans = pca(data, fraction=0.2)[0]
gp.plot_data(trans[:50, 0], trans[:50, 1], ptype="points", pt="o")
gp.plot_data(trans[50:, 0], trans[50:, 1], ptype="points", pt="x")
gp.plot()
gp.title("PCA Fraction 0.8")
trans = pca(data, fraction=0.8)[0]
gp.plot_data(trans[:50, 0], trans[:50, 1], ptype="points", pt="o")
gp.plot_data(trans[50:, 0], trans[50:, 1], ptype="points", pt="x")
gp.plot()
gp.title("PCA first 2 components")
trans = pca(data, n_comp=2)[0]
gp.plot_data(trans[:50, 0], trans[:50, 1], ptype="points", pt="o")
gp.plot_data(trans[50:, 0], trans[50:, 1], ptype="points", pt="x")
gp.plot()
if __name__ == "__main__":
main()