def interp_f(self, *X):
ndfun = self.ndfun
arg = self.arg
c_var = self.c_var
v1 = self.v1
# print "======="
# print ndfun, arg, c_var, v1, X[0]
# print self.ndfun.a
# print self.ndfun.b
# print self.ndfun.a[v1]
# print self.ndfun.b[v1]
if isscalar(X[0]):
# TODO: fix integration bounds!!!!
if hasattr(self.ndfun, "f"):
y = integrate_fejer2(partial(self.integ_f, X), ndfun.f.a[v1], ndfun.f.b[v1])
else:
y = integrate_fejer2(partial(self.integ_f, X), ndfun.a[v1], ndfun.b[v1])
return y[0]
y = asfarray(zeros_like(X[0]))
for i in range(len(X[0])):
# TODO: fix integration bounds!!!!
if hasattr(self.ndfun, "f"):
y[i] = integrate_fejer2(partial(self.integ_f, [x[i] for x in X]), ndfun.f.a[v1], ndfun.f.b[v1])[0]
else:
y[i] = integrate_fejer2(partial(self.integ_f, [x[i] for x in X]), ndfun.a[v1], ndfun.b[v1])[0]
return y
def eliminate(self, var, a=None, b=None):
"""Integrate out var, i.e. return the marginal on all
remaining variables.
Optional integration limits are allowed, default being full
real line. var is an RV instance or dimension number"""
var, c_var = self.prepare_var(var)
# assume below var are dimension numbers
if len(var) == 0:
return self
v1 = var[-1]
c_var = list(sorted(set(range(self.d)) - set([v1])))
arg = zeros(self.d)
# def integ_f(f, arg, c_var, v1, X, x1):
# if isscalar(x1):
# arg[c_var] = X
# arg[v1] = x1
# y = f(*arg)
# else:
# Xcol = [None] * self.d
# for i, j in enumerate(c_var):
# Xcol[j] = zeros(len(x1)) + X[i]
# Xcol[v1] = x1
# return f(*Xcol)
# def interp_f(f, arg, c_var, v1, *X):
# if isscalar(X[0]):
# # TODO: fix integration bounds!!!!
# if hasattr(self, "f"):
# y = integrate_fejer2(partial(integ_f, self, arg, c_var, v1, X, self.d), self.f.a[v1], self.f.b[v1])
# else:
# y = integrate_fejer2(partial(integ_f, self, arg, c_var, v1, X, self.d), self.a[v1], self.b[v1])
# return y[0]
# y = asfarray(zeros_like(X[0]))
# for i in xrange(len(X[0])):
# # TODO: fix integration bounds!!!!
# if hasattr(self, "f"):
# y[i] = integrate_fejer2(partial(integ_f, self, arg, c_var, v1, [x[i] for x in X], self.d), self.f.a[v1], self.f.b[v1])[0]
# else:
# y[i] = integrate_fejer2(partial(integ_f, self, arg, c_var, v1, [x[i] for x in X], self.d), self.a[v1], self.b[v1])[0]
# return y
if self.d == 1:
X = []
# if hasattr(self, "f"):
# y = integrate_fejer2(partial(integ_f, self.fun, arg, c_var, v1, X), self.f.a[v1], self.f.b[v1])
# else:
# y = integrate_fejer2(partial(integ_f, self, arg, c_var, v1, X), self.a[v1], self.b[v1])
# return NDConstFactor(y[0])
if hasattr(self, "f"):
y = integrate_fejer2(partial(InterpRunner(self.fun, arg, c_var, v1).integ_f, X), self.f.a[v1], self.f.b[v1])
else:
y = integrate_fejer2(partial(InterpRunner(self, arg, c_var, v1).integ_f, X), self.a[v1], self.b[v1])
return NDConstFactor(y[0])
#m = NDInterpolatedDistr(self.d - 1, partial(self.interp_f, self, arg, c_var, v1), [self.Vars[i] for i in c_var])
m = NDInterpolatedDistr(self.d - 1, InterpRunner(self, arg, c_var, v1).interpxx, [self.Vars[i] for i in c_var])
if len(var) == 1:
return m
else:
# TODO: eliminate all vars at once using sparse grid integration
return m.eliminate(var[:-1])
def interp_fx(self, X):
ndfun = self.ndfun
arg = self.arg
c_var = self.c_var
v1 = self.v1
if hasattr(self.ndfun, "f"):
y = integrate_fejer2(partial(self.integ_f, X), ndfun.f.a[v1], ndfun.f.b[v1])[0]
else:
y = integrate_fejer2(partial(self.integ_f, X), ndfun.a[v1], ndfun.b[v1])[0]
return y
def interpxx(self, *X):
"""convolution of f and g
"""
ndfun = self.ndfun
v1 = self.v1
if isscalar(X[0]):
# TODO: fix integration bounds!!!!
if hasattr(self.ndfun, "f"):
y = integrate_fejer2(partial(self.integ_f, X), ndfun.f.a[v1], ndfun.f.b[v1])
else:
y = integrate_fejer2(partial(self.integ_f, X), ndfun.a[v1], ndfun.b[v1])
return y[0]
xx = transpose(array(X))
if isscalar(xx):
xx=asfarray([xx])
#print ">>>>>>>>", xx
p_map = get_parmap()
res = p_map(self.interp_fx, xx)
res = array(res)
return res
def cov(self, i=None, j=None):
if i is not None and j is not None:
var, c_var = self.prepare_var([i, j])
dij = self.eliminate(c_var)
f, g = dij.marginals[0], self.marginals[1]
fmean = f.mean()
gmean = g.mean()
f0, f1 = f.get_piecewise_pdf().range()
g0, g1 = g.get_piecewise_pdf().range()
print(fmean, gmean, var, c_var, f0, f1, g0, g1)
if i == j:
c, e = c, e = integrate_fejer2(lambda x: (x - fmean) ** 2 * f.pdf(x), f0, f1)
else:
c, e = integrate_iter(lambda x, y: (x - fmean) * (y - gmean) * dij.pdf(x, y), f0, f1, g0, g1)
return c
else:
c = zeros((self.d, self.d))
for i in range(self.d):
for j in range(self.d):
c[i, j] = self.cov(i, j)
return c
def cov(self, i=None, j=None):
if i is not None and j is not None:
var, c_var = self.prepare_var([i, j])
dij = self.eliminate(c_var)
f, g = dij.marginals[0], self.marginals[1]
fmean = f.mean()
gmean = g.mean()
f0, f1 = f.get_piecewise_pdf().range()
g0, g1 = g.get_piecewise_pdf().range()
print fmean, gmean, var, c_var, f0, f1, g0, g1
if i == j:
c, e = c, e = integrate_fejer2(
lambda x: (x - fmean)**2 * f.pdf(x), f0, f1)
else:
c, e = integrate_iter(
lambda x, y: (x - fmean) * (y - gmean) * dij.pdf(x, y), f0,
f1, g0, g1)
return c
else:
c = zeros((self.d, self.d))
for i in range(self.d):
for j in range(self.d):
c[i, j] = self.cov(i, j)
return c
def tau_c(self):
return 1 + 4 * integrate_fejer2(
lambda t: self.fi(t) / self.fi_deriv(t), 0, 1)[0]
def tau_c(self):
return 1 + 4 * integrate_fejer2(lambda t : self.fi(t) / self.fi_deriv(t), 0, 1)[0]