def jacob(lam, n_eq, I, WS):
"""Log-Jacobian for SUR Error model
Parameters
----------
lam : array
n_eq by 1 array of spatial autoregressive parameters
n_eq : int
number of equations
I : sparse matrix
sparse Identity matrix
WS : sparse matrix
sparse spatial weights matrix
Returns
-------
logjac : float
the log Jacobian
"""
logjac = 0.0
for r in range(n_eq):
lami = lam[r]
lamWS = WS.multiply(lami)
B = (I - lamWS).tocsc()
LU = SuperLU(B)
jj = np.sum(np.log(np.abs(LU.U.diagonal())))
logjac += jj
return logjac
def lag_c_loglik_sp(rho, n, e0, e1, I, Wsp):
# concentrated log-lik for lag model, sparse algebra
if isinstance(rho, np.ndarray):
if rho.shape == (1,1):
rho = rho[0][0] #why does the interior value change?
er = e0 - rho * e1
sig2 = spdot(er.T, er) / n
nlsig2 = (n / 2.0) * np.log(sig2)
a = I - rho * Wsp
LU = SuperLU(a.tocsc())
jacob = np.sum(np.log(np.abs(LU.U.diagonal())))
clike = nlsig2 - jacob
return clike
def err_c_loglik_sp(lam, n, y, ylag, x, xlag, I, Wsp):
# concentrated log-lik for error model, no constants, LU
if isinstance(lam, np.ndarray):
if lam.shape == (1, 1):
lam = lam[0][0] #why does the interior value change?
ys = y - lam * ylag
xs = x - lam * xlag
ysys = np.dot(ys.T, ys)
xsxs = np.dot(xs.T, xs)
xsxsi = np.linalg.inv(xsxs)
xsys = np.dot(xs.T, ys)
x1 = np.dot(xsxsi, xsys)
x2 = np.dot(xsys.T, x1)
ee = ysys - x2
sig2 = ee[0][0] / n
nlsig2 = (n / 2.0) * np.log(sig2)
a = I - lam * Wsp
LU = SuperLU(a.tocsc())
jacob = np.sum(np.log(np.abs(LU.U.diagonal())))
# this is the negative of the concentrated log lik for minimization
clik = nlsig2 - jacob
return clik
