def ctau(self, i=None, j=None):
"""Kendall's tau: 4*\int C(x,y) dC(x,y)-1
"""
if i is not None and j is not None:
var, c_var = self.prepare_var([i, j])
dij = self.eliminate(c_var)
if i == j:
c, e = 1, 0
else:
#c, e = integrate_iter(lambda x, y: x * y * dij.cpdf(x, y), 0.0, 1.0, 0.0, 1.0)
c, e = integrate_iter(lambda x, y: dij.ccdf(x, y) * dij.cpdf(x, y), 0.0, 1.0, 0.0, 1.0)
c = 4 * c - 1
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.ctau(i, j)
return c
def rho_s(self, i=None, j=None):
"""Spearmans rho: 12*\int x*y dC(x,y)-3 = 12 \int C(d,y)dxdy - 3
"""
if i is not None and j is not None:
var, c_var = self.prepare_var([i, j])
dij = self.eliminate(c_var)
if i == j:
c, e = 1, 0
else:
#c, e = integrate_iter(lambda x, y: x * y * dij.cpdf(x, y), 0.0, 1.0, 0.0, 1.0)
c, e = integrate_iter(lambda x, y: dij.ccdf(x, y), 0.0, 1.0, 0.0, 1.0)
c = 12 * c - 3
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.rho_s(i, j)
return c
def rho_s(self, i=None, j=None):
"""Spearmans rho: 12*\int x*y dC(x,y)-3 = 12 \int C(d,y)dxdy - 3
"""
if i is not None and j is not None:
var, c_var = self.prepare_var([i, j])
dij = self.eliminate(c_var)
if i == j:
c, e = 1, 0
else:
#c, e = integrate_iter(lambda x, y: x * y * dij.cpdf(x, y), 0.0, 1.0, 0.0, 1.0)
c, e = integrate_iter(lambda x, y: dij.ccdf(x, y), 0.0, 1.0,
0.0, 1.0)
c = 12 * c - 3
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.rho_s(i, j)
return c
def ctau(self, i=None, j=None):
"""Kendall's tau: 4*\int C(x,y) dC(x,y)-1
"""
if i is not None and j is not None:
var, c_var = self.prepare_var([i, j])
dij = self.eliminate(c_var)
if i == j:
c, e = 1, 0
else:
#c, e = integrate_iter(lambda x, y: x * y * dij.cpdf(x, y), 0.0, 1.0, 0.0, 1.0)
c, e = integrate_iter(
lambda x, y: dij.ccdf(x, y) * dij.cpdf(x, y), 0.0, 1.0,
0.0, 1.0)
c = 4 * c - 1
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.ctau(i, j)
return c
def tau(self, i=None, j=None):
"""Kendall's tau: 4*\int C(x,y) dC(x,y)-1
"""
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]
f0, f1 = f.get_piecewise_pdf().range()
g0, g1 = g.get_piecewise_pdf().range()
if i == j:
c, e = 1, 0
else:
c, e = integrate_iter(lambda x, y: dij.cdf(x, y) * dij.pdf(x, y), f0, f1, g0, g1)
c = 4 * c - 1
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.ctau(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 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.Vars[0], self.Vars[1]
fmean = 0 #f.mean()
gmean = 0 #g.mean()
f0, f1 = f.range()
g0, g1 = g.range()
if i == j:
c, e = 1, 0#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):
#print c[i,j]
#print self.cov(i,j)
c[i, j] = self.cov(i,j)
return c
def tau(self, i=None, j=None):
"""Kendall's tau: 4*\int C(x,y) dC(x,y)-1
"""
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]
f0, f1 = f.get_piecewise_pdf().range()
g0, g1 = g.get_piecewise_pdf().range()
if i == j:
c, e = 1, 0
else:
c, e = integrate_iter(
lambda x, y: dij.cdf(x, y) * dij.pdf(x, y), f0, f1, g0, g1)
c = 4 * c - 1
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.ctau(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
