def dg_second_moment(u, gauss_mean1, gauss_mean2, support1, support2):
"""
Missing documentation
Parameters
----------
u : Type
Description
gauss_mean1 : Type
Description
gauss_mean2 : Type
Description
support1 : Type
Description
support2 : Type
Description
Returns
-------
Value : Type
Description
"""
# subfunction DGSecondMoment: Calculate second Moment of the DG
# for a given correlation lambda
#a very, very inefficient function for calculating the second moments of a
#DG with specified gammas and supports and correlation lambda
from statsmodels.sandbox.distributions.multivariate import mvnormcdf
sig = np.array([[1, u], [u, 1]])
x, y = np.meshgrid(support2, support1)
xy = x * y
ps = np.zeros((len(support1), len(support2)))
for i in range(len(support1)):
for j in range(len(support2)):
ps[i, j] = mvnormcdf([gauss_mean1[i], gauss_mean2[j]], [0, 0], sig)
ps2 = ps.copy()
for i in range(len(support1)):
for j in range(len(support2)):
if i > 0 and j > 0:
ps2[i, j] = ps[i, j] + ps[i - 1, j - 1] - ps[i - 1,
j] - ps[i, j - 1]
elif j > 0 and i == 0:
ps2[i, j] = ps[i, j] - ps[i, j - 1]
elif i > 0 and j == 0:
ps2[i, j] = ps[i, j] - ps[i - 1, j]
elif i == 0 and j == 0:
ps2[i, j] = ps[i, j]
ps2 = np.clip(ps2, 0, ps2.max())
joint = ps2.copy()
ps2 = ps2 * xy
secmom = np.sum(ps2)
return secmom, joint
def dg_second_moment(u, gauss_mean1, gauss_mean2, support1, support2):
"""
Missing documentation
Parameters
----------
u : Type
Description
gauss_mean1 : Type
Description
gauss_mean2 : Type
Description
support1 : Type
Description
support2 : Type
Description
Returns
-------
Value : Type
Description
"""
# subfunction DGSecondMoment: Calculate second Moment of the DG
# for a given correlation lambda
#a very, very inefficient function for calculating the second moments of a
#DG with specified gammas and supports and correlation lambda
from statsmodels.sandbox.distributions.multivariate import mvnormcdf
sig = np.array([[1, u], [u, 1]])
x, y = np.meshgrid(support2, support1)
xy = x * y
ps = np.zeros((len(support1), len(support2)))
for i in range(len(support1)):
for j in range(len(support2)):
ps[i, j] = mvnormcdf([gauss_mean1[i], gauss_mean2[j]], [0, 0], sig)
ps2 = ps.copy()
for i in range(len(support1)):
for j in range(len(support2)):
if i > 0 and j > 0:
ps2[i, j] = ps[i, j] + ps[i - 1, j - 1] - ps[i - 1, j] - ps[i, j - 1]
elif j > 0 and i == 0:
ps2[i, j] = ps[i, j] - ps[i, j - 1]
elif i > 0 and j == 0:
ps2[i, j] = ps[i, j] - ps[i - 1, j]
elif i == 0 and j == 0:
ps2[i, j] = ps[i, j]
ps2 = np.clip(ps2, 0, ps2.max())
joint = ps2.copy()
ps2 = ps2 * xy
secmom = np.sum(ps2)
return secmom, joint
def maxpdf(x, mu, S):
s = np.zeros(x.shape[0])
d = mu.shape[0]
for i in xrange(d):
mu_i = mu[i]
S_ii = S[i, i]
mu_ni, S_nini = remove(mu, S, i)
S_ini = np.array(np.bmat([[S[:i, i], S[i+1:, i]]]))
mu_nii = mu_ni[:, None] + np.dot(S_ini.T, x[None, :] - mu_i) / S_ii
S_ninii = S_nini - np.dot(S_ini, S_ini.T) / S_ii
phi_i = norm.pdf(x, loc=mu_i, scale=np.sqrt(S_ii))
Phi_i = np.array([mvnormcdf(x[j], mu_nii[:, j], S_ninii)
for j in xrange(x.shape[0])])
s += phi_i * Phi_i
return s
def maxpdf(x, mu, S):
s = np.zeros(x.shape[0])
d = mu.shape[0]
for i in xrange(d):
mu_i = mu[i]
S_ii = S[i, i]
mu_ni, S_nini = remove(mu, S, i)
S_ini = np.array(np.bmat([[S[:i, i], S[i + 1:, i]]]))
mu_nii = mu_ni[:, None] + np.dot(S_ini.T, x[None, :] - mu_i) / S_ii
S_ninii = S_nini - np.dot(S_ini, S_ini.T) / S_ii
phi_i = norm.pdf(x, loc=mu_i, scale=np.sqrt(S_ii))
Phi_i = np.array([
mvnormcdf(x[j], mu_nii[:, j], S_ninii) for j in xrange(x.shape[0])
])
s += phi_i * Phi_i
return s
def cdf(self, x, **kwds):
'''cumulative distribution function
Parameters
----------
x : array_like
can be 1d or 2d, if 2d, then each row is taken as independent
multivariate random vector
kwds : dict
contains options for the numerical calculation of the cdf
Returns
-------
cdf : float or array
probability density value of each random vector
'''
#lower = -np.inf * np.ones_like(x)
#return mvstdnormcdf(lower, self.standardize(x), self.corr, **kwds)
return mvnormcdf(x, self.mean, self.cov, **kwds)
def cdf(self, x, **kwds):
'''cumulative distribution function
Parameters
----------
x : array_like
can be 1d or 2d, if 2d, then each row is taken as independent
multivariate random vector
kwds : dict
contains options for the numerical calculation of the cdf
Returns
-------
cdf : float or array
probability density value of each random vector
'''
#lower = -np.inf * np.ones_like(x)
#return mvstdnormcdf(lower, self.standardize(x), self.corr, **kwds)
return mvnormcdf(x, self.mean, self.cov, **kwds)
