def _contour_t(mu, Cov, nu, axes=None, scale=4, transpose=False, colors='k'):
"""
"""
if axes is None:
axes = plt.gca()
if np.shape(mu) != (2, ) or np.shape(Cov) != (2, 2) or np.shape(nu) != ():
print(np.shape(mu), np.shape(Cov), np.shape(nu))
raise ValueError("Only 2-d t-distribution allowed")
if transpose:
mu = mu[[1, 0]]
Cov = Cov[np.ix_([1, 0], [1, 0])]
s = np.sqrt(np.diag(Cov))
x0 = np.linspace(mu[0] - scale * s[0], mu[0] + scale * s[0], num=100)
x1 = np.linspace(mu[1] - scale * s[1], mu[1] + scale * s[1], num=100)
X0X1 = misc.grid(x0, x1)
Y = X0X1 - mu
L = linalg.chol(Cov)
logdet_Cov = linalg.chol_logdet(L)
Z = linalg.chol_solve(L, Y)
Z = linalg.inner(Y, Z, ndim=1)
lpdf = random.t_logpdf(Z, logdet_Cov, nu, 2)
p = np.exp(lpdf)
shape = (np.size(x0), np.size(x1))
X0 = np.reshape(X0X1[:, 0], shape)
X1 = np.reshape(X0X1[:, 1], shape)
P = np.reshape(p, shape)
return axes.contour(X0, X1, P, colors=colors)
def _contour_t(mu, Cov, nu, axes=None, scale=4, transpose=False, colors='k'):
"""
"""
if axes is None:
axes = plt.gca()
if np.shape(mu) != (2,) or np.shape(Cov) != (2,2) or np.shape(nu) != ():
print(np.shape(mu), np.shape(Cov), np.shape(nu))
raise ValueError("Only 2-d t-distribution allowed")
if transpose:
mu = mu[[1,0]]
Cov = Cov[np.ix_([1,0],[1,0])]
s = np.sqrt(np.diag(Cov))
x0 = np.linspace(mu[0]-scale*s[0], mu[0]+scale*s[0], num=100)
x1 = np.linspace(mu[1]-scale*s[1], mu[1]+scale*s[1], num=100)
X0X1 = misc.grid(x0, x1)
Y = X0X1 - mu
L = linalg.chol(Cov)
logdet_Cov = linalg.chol_logdet(L)
Z = linalg.chol_solve(L, Y)
Z = linalg.inner(Y, Z, ndim=1)
lpdf = random.t_logpdf(Z, logdet_Cov, nu, 2)
p = np.exp(lpdf)
shape = (np.size(x0), np.size(x1))
X0 = np.reshape(X0X1[:,0], shape)
X1 = np.reshape(X0X1[:,1], shape)
P = np.reshape(p, shape)
return axes.contour(X0, X1, P, colors=colors)
def _pdf_t(mu, s2, nu, axes=None, scale=4, color='k'):
"""
"""
s = np.sqrt(s2)
x = np.linspace(mu-scale*s, mu+scale*s, num=100)
y2 = (x-mu)**2 / s2
lpdf = random.t_logpdf(y2, np.log(s2), nu, 1)
p = np.exp(lpdf)
if axes is None:
axes = plt
return axes.plot(x, p, color=color)
def _pdf_t(mu, s2, nu, axes=None, scale=4, color='k'):
"""
"""
if axes is None:
axes = plt.gca()
s = np.sqrt(s2)
x = np.linspace(mu - scale * s, mu + scale * s, num=100)
y2 = (x - mu)**2 / s2
lpdf = random.t_logpdf(y2, np.log(s2), nu, 1)
p = np.exp(lpdf)
return axes.plot(x, p, color=color)