def pux_sampling(x, A, C, invC, sampleNr):
h = size(x, 0)
w = size(x, 1)
s2 = 0.5; # sigma squared
x = x.reshape(h*w)
zarr = zeros(size(x))
ident = identity(size(x))
c = zeros(sampleNr)
m = zeros((sampleNr, h*w))
s = zeros((sampleNr, h*w, h*w))
zsum = 0
nsum = 0
acat = dot(A, dot(C, A.T))
ata = dot(A.T, A)
for i in range(0, sampleNr):
z = random.gammavariate(2,2)
c[i] = multi_norm(x, zarr, s2*ident + z**2*acat)
zsum += z*c[i]
nsum += c[i]
s[i] = linalg.inv(invC + z/s2*ata)
m[i] = z/s2*dot(s[i]*A.T,x)
c = c/sum(c); # normalization
return [c, m, s, zsum/nsum]
def pux_integration(x, sat, icorr, s, s2, start, end, pointNr):
# see example usage in posterior_covariance.py
# s[i] = linalg.inv(invC + z_a[i]/s2*ata)
# icorr[i] = linalg.inv(s2*ident + z_a[i]**2*acat)
# sat[i] = s[i]*A.T
h = size(x, 0)
w = size(x, 1)
x = x.reshape(h*w)
zarr = zeros(size(x))
c = zeros(pointNr)
m = zeros((pointNr, size(sat,1)))
zsum = 0
nsum = 0
z_a = linspace(start, end, pointNr)
g_dist = stats.gamma(2., loc = 0., scale = 2.)
for i in range(0,pointNr):
z = z_a[i]
c[i] = g_dist.pdf(z)*multi_norm(x, zarr, icorr[i], inverted=True)
zsum += z*c[i]
nsum += c[i]
# s[i] = linalg.inv(invC + z/s2*ata)
m[i] = z/s2*dot(sat[i],x)
print (sum(c))
c = c/sum(c); # normalization
return [c, m, zsum/nsum]