class DiscreteDistr(Distr):
"""Discrete distribution"""
def __init__(self, xi=[0.0, 1.0], pi=[0.5, 0.5]):
super(DiscreteDistr, self).__init__([])
assert(len(xi) == len(pi))
px = zip(xi, pi)
px.sort()
self.px = px
self.xi = [p[0] for p in px]
self.pi = [p[1] for p in px]
self.cumP = cumsum(self.pi)
def pdf(self, x):
x = array(x)
"""it override pdf() method to obtain discrete probabilities"""
yy = zeros_like(x, dtype=float)
for i in range(len(self.pi)):
yy[x==self.xi[i]] += float(self.pi[i])
return yy
def init_piecewise_pdf(self):
self.piecewise_pdf = PiecewiseDistribution([])
for i in xrange(len(self.xi)):
self.piecewise_pdf.addSegment(DiracSegment(self.xi[i], self.pi[i]))
for i in xrange(len(self.xi)-1):
self.piecewise_pdf.addSegment(ConstSegment(self.xi[i], self.xi[i+1], 0))
def rand_raw(self, n):
u = uniform(0, 1, n)
i = searchsorted(self.cumP, u)
i[i > len(self.xi)] = len(self.xi)
return array(self.xi)[i]
def __str__(self):
pstr = ", ".join("{0}:{1}".format(x, p) for x, p in self.px)
return "Discrete({0})#{1}".format(pstr, self.id())
def getName(self):
return "Di({0})".format(len(self.xi))
def convmodel(self):
"""Probabilistic operation defined by model
"""
op = self.symop #d.getSym()
x = self.symvars[0]
y = self.symvars[1]
lop = my_lambdify([x, y], op, "numpy")
F = self.vars[0]
G = self.vars[1]
#self.nddistr.setMarginals(F, G)
f = self.vars[0].get_piecewise_pdf()
g = self.vars[1].get_piecewise_pdf()
bf = f.getBreaks()
bg = g.getBreaks()
bi = zeros(len(bf) * len(bg))
k = 0
for xi in bf:
for yi in bg:
if not isnan(lop(xi, yi)):
bi[k] = lop(xi, yi)
else:
pass
#print "not a number, xi=", xi, "yi=", yi, "result=", lop(xi,yi)
k += 1
ub = array(unique(bi))
fun = lambda x: self.convmodelx(segList, x)
fg = PiecewiseDistribution([])
if isinf(ub[0]):
segList = _findSegList(f, g, ub[1] - 1, lop)
seg = MInfSegment(ub[1], fun)
segint = seg.toInterpolatedSegment()
fg.addSegment(segint)
ub = ub[1:]
if isinf(ub[-1]):
segList = _findSegList(f, g, ub[-2] + 1, lop)
seg = PInfSegment(ub[-2], fun)
segint = seg.toInterpolatedSegment()
fg.addSegment(segint)
ub = ub[0:-1]
for i in range(len(ub) - 1):
segList = _findSegList(f, g, (ub[i] + ub[i + 1]) / 2, lop)
seg = Segment(ub[i], ub[i + 1], partial(self.convmodelx, segList))
#seg = Segment(ub[i],ub[i+1], fun)
segint = seg.toInterpolatedSegment()
fg.addSegment(segint)
# Discrete parts of distributions
#fg_discr = convdiracs(f, g, fun = lambda x,y : x * p + y * q)
#for seg in fg_discr.getDiracs():
# fg.addSegment(seg)
return fg
def convmean(F, G, p=0.5, q=0.5, theta=1.0):
"""Probabilistic weighted mean of f and g
"""
f = F.get_piecewise_pdf()
g = G.get_piecewise_pdf()
if p + q <> 1.0:
p1 = abs(p) / (abs(p) + abs(q))
q = abs(q) / (abs(p) + abs(q))
p = p1
if q == 0:
return f
bf = f.getBreaks()
bg = g.getBreaks()
b = add.outer(bf * p, bg * q)
fun = lambda x: convmeanx(F, G, segList, x, p, q, theta=theta)
ub = epsunique(b)
fg = PiecewiseDistribution([])
op = lambda x, y: p * x + q * y
if isinf(ub[0]):
segList = _findSegList(f, g, ub[1] - 1, op)
seg = MInfSegment(ub[1], fun)
segint = seg.toInterpolatedSegment()
fg.addSegment(segint)
ub = ub[1:]
if isinf(ub[-1]):
segList = _findSegList(f, g, ub[-2] + 1, op)
seg = PInfSegment(ub[-2], fun)
segint = seg.toInterpolatedSegment()
fg.addSegment(segint)
ub = ub[0:-1]
for i in range(len(ub) - 1):
segList = _findSegList(f, g, (ub[i] + ub[i + 1]) / 2, op)
seg = Segment(ub[i], ub[i + 1], fun)
segint = seg.toInterpolatedSegment()
fg.addSegment(segint)
# Discrete parts of distributions
fg_discr = convdiracs(f, g, fun=lambda x, y: x * p + y * q)
for seg in fg_discr.getDiracs():
fg.addSegment(seg)
return fg
def convmodel(self):
"""Probabilistic operation defined by model
"""
op = self.symop#d.getSym()
x = self.symvars[0]
y = self.symvars[1]
lop = my_lambdify([x, y], op, "numpy")
F = self.vars[0]
G = self.vars[1]
#self.nddistr.setMarginals(F, G)
f = self.vars[0].get_piecewise_pdf()
g = self.vars[1].get_piecewise_pdf()
bf = f.getBreaks()
bg = g.getBreaks()
bi = zeros(len(bf) * len(bg))
k = 0;
for xi in bf:
for yi in bg:
if not isnan(lop(xi, yi)):
bi[k] = lop(xi, yi)
else:
pass
#print "not a number, xi=", xi, "yi=", yi, "result=", lop(xi,yi)
k += 1
ub = array(unique(bi))
fun = lambda x : self.convmodelx(segList, x)
fg = PiecewiseDistribution([]);
if isinf(ub[0]):
segList = _findSegList(f, g, ub[1] -1, lop)
seg = MInfSegment(ub[1], fun)
segint = seg.toInterpolatedSegment()
fg.addSegment(segint)
ub=ub[1:]
if isinf(ub[-1]):
segList = _findSegList(f, g, ub[-2] + 1, lop)
seg = PInfSegment(ub[-2], fun)
segint = seg.toInterpolatedSegment()
fg.addSegment(segint)
ub=ub[0:-1]
for i in range(len(ub) - 1) :
segList = _findSegList(f, g, (ub[i] + ub[i + 1]) / 2, lop)
seg = Segment(ub[i], ub[i + 1], partial(self.convmodelx, segList))
#seg = Segment(ub[i],ub[i+1], fun)
segint = seg.toInterpolatedSegment()
fg.addSegment(segint)
# Discrete parts of distributions
#fg_discr = convdiracs(f, g, fun = lambda x,y : x * p + y * q)
#for seg in fg_discr.getDiracs():
# fg.addSegment(seg)
return fg
def convmean(F, G, p=0.5, q=0.5, theta=1.0):
"""Probabilistic weighted mean of f and g
"""
f = F.get_piecewise_pdf()
g = G.get_piecewise_pdf()
if p + q != 1.0 :
p1 = abs(p) / (abs(p) + abs(q))
q = abs(q) / (abs(p) + abs(q))
p = p1;
if q == 0:
return f;
bf = f.getBreaks()
bg = g.getBreaks()
b = add.outer(bf * p, bg * q)
fun = lambda x : convmeanx(F, G, segList, x, p, q, theta=theta)
ub = epsunique(b)
fg = PiecewiseDistribution([]);
op = lambda x, y : p * x + q * y;
if isinf(ub[0]):
segList = _findSegList(f, g, ub[1] - 1, op)
seg = MInfSegment(ub[1], fun)
segint = seg.toInterpolatedSegment()
fg.addSegment(segint)
ub = ub[1:]
if isinf(ub[-1]):
segList = _findSegList(f, g, ub[-2] + 1, op)
seg = PInfSegment(ub[-2], fun)
segint = seg.toInterpolatedSegment()
fg.addSegment(segint)
ub = ub[0:-1]
for i in range(len(ub) - 1) :
segList = _findSegList(f, g, (ub[i] + ub[i + 1]) / 2, op)
seg = Segment(ub[i], ub[i + 1], fun)
segint = seg.toInterpolatedSegment()
fg.addSegment(segint)
# Discrete parts of distributions
fg_discr = convdiracs(f, g, fun=lambda x, y : x * p + y * q)
for seg in fg_discr.getDiracs():
fg.addSegment(seg)
return fg
def init_piecewise_pdf(self):
self.piecewise_pdf = PiecewiseDistribution([])
for i in xrange(len(self.xi)):
self.piecewise_pdf.addSegment(DiracSegment(self.xi[i], self.pi[i]))
for i in xrange(len(self.xi)-1):
self.piecewise_pdf.addSegment(ConstSegment(self.xi[i], self.xi[i+1], 0))
#! How to use PaCal
#! ================
from pacal import *
from pacal.segments import PiecewiseDistribution, Segment
from pacal.standard_distr import PDistr
from pylab import figure, show
if __name__ == "__main__":
#! User defined piecewise distribution
#! -----------------------------------
#! Let consider triangular distribution, it consists two smooth segments.
fun = PiecewiseDistribution([])
fun.addSegment(Segment(0, 1, lambda x: x))
fun.addSegment(Segment(1, 2, lambda x: 2 - x))
distr = PDistr(fun)
#! Here we have summary statistics and accuracies
distr.summary()
#! Another way to do it:
distr = FunDistr(fun=lambda x: 1 - abs(1 - x), breakPoints=[0, 1, 2])
distr.summary()
#$ Notice that we set the break point at point 1 and User have to care
#$ about $L_1$ nor of distribution.
#! The same one obtain using sum of two uniform distributions
u = UniformDistr(0, 1)
tri = u + u
tri.summary()
#! Users API for distr object:
#! How to use PaCal
#! ================
from __future__ import print_function
from pacal import *
from pacal.segments import PiecewiseDistribution, Segment
from pacal.standard_distr import PDistr
from pylab import figure, show
if __name__ == "__main__":
#! User defined piecewise distribution
#! -----------------------------------
#! Let consider triangular distribution, it consists two smooth segments.
fun = PiecewiseDistribution([])
fun.addSegment(Segment(0, 1, lambda x:x))
fun.addSegment(Segment(1, 2, lambda x:2 - x))
distr = PDistr(fun)
#! Here we have summary statistics and accuracies
distr.summary()
#! Another way to do it:
distr = FunDistr(fun=lambda x: 1 - abs(1 - x), breakPoints=[0, 1, 2])
distr.summary()
#$ Notice that we set the break point at point 1 and User have to care
#$ about $L_1$ nor of distribution.
#! The same one obtain using sum of two uniform distributions
u = UniformDistr(0, 1)
tri = u + u
