def check_simple(self):
a = [[8,2,3],[2,9,3],[3,3,6]]
c = cholesky(a)
assert_array_almost_equal(dot(transpose(c),c),a)
c = transpose(c)
a = dot(c,transpose(c))
assert_array_almost_equal(cholesky(a,lower=1),c)
def check_simple_complex(self):
m = array([[3+1j,3+4j,5],[0,2+2j,2+7j],[0,0,7+4j]])
a = dot(transpose(conjugate(m)),m)
c = cholesky(a)
a1 = dot(transpose(conjugate(c)),c)
assert_array_almost_equal(a,a1)
c = transpose(c)
a = dot(c,transpose(conjugate(c)))
assert_array_almost_equal(cholesky(a,lower=1),c)
def check_random_complex(self):
n = 20
for k in range(2):
m = random([n,n])+1j*random([n,n])
for i in range(n):
m[i,i] = 20*(.1+abs(m[i,i]))
a = dot(transpose(conjugate(m)),m)
c = cholesky(a)
a1 = dot(transpose(conjugate(c)),c)
assert_array_almost_equal(a,a1)
c = transpose(c)
a = dot(c,transpose(conjugate(c)))
assert_array_almost_equal(cholesky(a,lower=1),c)
def check_random(self):
n = 20
for k in range(2):
m = random([n,n])
for i in range(n):
m[i,i] = 20*(.1+m[i,i])
a = dot(transpose(m),m)
c = cholesky(a)
a1 = dot(transpose(c),c)
assert_array_almost_equal(a,a1)
c = transpose(c)
a = dot(c,transpose(c))
assert_array_almost_equal(cholesky(a,lower=1),c)
def __new__(subtype, eval_fun, base_mesh, obs_mesh, obs_taus, withsigma = False, withtau = False, lintrans = None, **params): # You may need to reshape these so f2py doesn't puke. subtype.base_mesh = base_mesh subtype.obs_mesh = obs_mesh subtype.obs_taus = obs_taus subtype.withsigma = withsigma subtype.withtau = withtau subtype.lintrans = lintrans subtype.params = params subtype.eval_fun = eval_fun # Call the covariance evaluation function length = (base_mesh.shape)[0] subtype.data = zeros((length,length), dtype=float) eval_fun(subtype.data, base_mesh, base_mesh, symm=True, **params) # Condition condition(subtype.data, eval_fun, base_mesh, obs_mesh, **params) if withsigma: # Try Cholesky factorization try: subtype.sigma = cholesky(subtype.data) # If there's a small eigenvalue, diagonalize except linalg.linalg.LinAlgError: subtype.eigval, subtype.eigvec = eigh(subtype.data) subtype.sigma = subtype.eigvec * sqrt(subtype.eigval) if withtau: # Make this faster. subtype.tau = inv(subtype.data) # Return the data return subtype.data.view(subtype) def __array__(self): return self.data def __call__(self, point_1, point_2): value = zeros((1,1),dtype=float) # Evaluate the covariance self.eval_fun(value,point_1,point_2,**self.params) if not obs_mesh: return value[0,0] # Condition on the observed values nobs = shape(obs_mesh)[0] ndim = shape(obs_mesh)[1] Q = zeros((1,1),dtype=float) RF = zeros((2,1),dtype=float) base_mesh = vstack([point_1,point_2]) for i in range(len(obs_mesh)): om_now = reshape(obs_mesh[i,:],(1,ndim)) eval_fun(Q,om_now,om_now,**params) eval_fun(RF,base_mesh,om_now,**params) value -= RF[0]*RF[1]/Q return value[0,0]
