def test_lu_slogdet():
K = array([[2.76405235, 0.40015721], [0.97873798, 3.2408932]])
K = dot(K, K.T)
LU = lu_factor(K)
assert_allclose(lu_slogdet(LU), slogdet(K))
random = RandomState(6)
K = random.randn(3, 3)
K = dot(K, K.T)
LU = lu_factor(K)
assert_allclose(lu_slogdet(LU), slogdet(K))
def _logdetK(self):
from numpy_sugar.linalg import lu_slogdet
terms = self._terms
S = terms["S"]
Lz = terms["Lz"]
cov_logdet = lu_slogdet(Lz)[1]
cov_logdet -= 2 * log(S).sum() * self.nsamples
return cov_logdet
def lml(self):
from numpy_sugar.linalg import lu_slogdet
if self._cache["lml"] is not None:
return self._cache["lml"]
self._update()
LU = self._posterior.LU()
LQt = self._posterior.LQt()
cov = self._posterior.cov
Q = cov["QS"][0][0]
S = cov["QS"][1]
ttau = self._site.tau
teta = self._site.eta
ctau = self._cav["tau"]
ceta = self._cav["eta"]
m = self._posterior.mean
TS = ttau + ctau
s = cov["scale"]
d = cov["delta"]
A = self._posterior.A
dif = 2 * A * teta - A * ttau * m
lml = [
-0.5 * lu_slogdet(LU)[1],
-0.5 * sum(log(s * S)),
+0.5 * sum(log(A)),
# lml += 0.5 * sum(log(ttau)),
+0.5 * dot(teta * A, dot(Q, dot(LQt, teta * A))) * (1 - d),
-0.5 * dot(teta, teta / TS),
+dot(m, A * teta) - 0.5 * dot(m, A * ttau * m),
-0.5 * dot(m * A * ttau, dot(Q, dot(LQt, dif))) * (1 - d),
+sum(self._moments["log_zeroth"]),
+0.5 * sum(log(TS)),
# lml -= 0.5 * sum(log(ttau)),
-0.5 * sum(log(ctau)),
+0.5 * dot(ceta / TS, ttau * ceta / ctau - 2 * teta),
0.5 * s * d * sum(teta * A * teta),
]
lml = fsum(lml)
if not isfinite(lml):
raise ValueError("LML should not be %f." % lml)
self._cache["lml"] = lml
return lml
def lml(self):
from numpy_sugar.linalg import lu_slogdet
if self._cache["lml"] is not None:
return self._cache["lml"]
self._update()
LU = self._posterior.LU()
Q, S = self._posterior.cov["QS"]
Q = Q[0]
ttau = self._site.tau
teta = self._site.eta
ctau = self._cav["tau"]
ceta = self._cav["eta"]
m = self._posterior.mean
TS = ttau + ctau
lml = [
-0.5 * lu_slogdet(LU)[1],
-0.5 * sum(log(S)),
# lml += 0.5 * sum(log(ttau)),
+0.5 * dot(teta, dot(Q, lu_solve(LU, dot(Q.T, teta)))),
-0.5 * dot(teta, teta / TS),
+dot(m, teta) - 0.5 * dot(m, ttau * m),
-0.5 *
dot(m * ttau, dot(Q, lu_solve(LU, dot(Q.T, 2 * teta - ttau * m)))),
+sum(self._moments["log_zeroth"]),
+0.5 * sum(log(TS)),
# lml -= 0.5 * sum(log(ttau)),
-0.5 * sum(log(ctau)),
+0.5 * dot(ceta / TS, ttau * ceta / ctau - 2 * teta),
]
lml = fsum(lml)
if not isfinite(lml):
raise ValueError("LML should not be %f." % lml)
self._cache["lml"] = lml
return lml
def _terms(self):
from numpy_sugar.linalg import ddot, lu_slogdet, sum2diag
if self._cache["terms"] is not None:
return self._cache["terms"]
L0 = self._cov.C0.L
S, U = self._cov.C1.eigh()
W = ddot(U, 1 / S) @ U.T
S = 1 / sqrt(S)
Y = self._Y
A = self._mean.A
WL0 = W @ L0
YW = Y @ W
WA = W @ A
L0WA = L0.T @ WA
Z = kron(L0.T @ WL0, self._GG)
Z = sum2diag(Z, 1)
Lz = lu_factor(Z, check_finite=False)
# Юљ▓рхђRРЂ╗┬╣Юљ▓ = vec(YW)рхђЮљ▓
yRiy = (YW * self._Y).sum()
# MрхђRРЂ╗┬╣M = AрхђWA РіЌ XрхђX
MRiM = kron(A.T @ WA, self._XX)
# XрхђRРЂ╗┬╣Юљ▓ = vec(GрхђYWLРѓђ)
XRiy = vec(self._GY @ WL0)
# XрхђRРЂ╗┬╣M = (LРѓђрхђWA) РіЌ (GрхђX)
XRiM = kron(L0WA, self._GX)
# MрхђRРЂ╗┬╣Юљ▓ = vec(XрхђYWA)
MRiy = vec(self._XY @ WA)
ZiXRiM = lu_solve(Lz, XRiM)
ZiXRiy = lu_solve(Lz, XRiy)
MRiXZiXRiy = ZiXRiM.T @ XRiy
MRiXZiXRiM = XRiM.T @ ZiXRiM
yKiy = yRiy - XRiy @ ZiXRiy
MKiy = MRiy - MRiXZiXRiy
H = MRiM - MRiXZiXRiM
Lh = lu_factor(H, check_finite=False)
b = lu_solve(Lh, MKiy)
B = unvec(b, (self.ncovariates, -1))
self._mean.B = B
XRim = XRiM @ b
ZiXRim = ZiXRiM @ b
mRiy = b.T @ MRiy
mRim = b.T @ MRiM @ b
logdetK = lu_slogdet(Lz)[1]
logdetK -= 2 * log(S).sum() * self.nsamples
mKiy = mRiy - XRim.T @ ZiXRiy
mKim = mRim - XRim.T @ ZiXRim
self._cache["terms"] = {
"logdetK": logdetK,
"mKiy": mKiy,
"mKim": mKim,
"b": b,
"Z": Z,
"B": B,
"Lz": Lz,
"S": S,
"W": W,
"WA": WA,
"YW": YW,
"WL0": WL0,
"yRiy": yRiy,
"MRiM": MRiM,
"XRiy": XRiy,
"XRiM": XRiM,
"ZiXRiM": ZiXRiM,
"ZiXRiy": ZiXRiy,
"ZiXRim": ZiXRim,
"MRiy": MRiy,
"mRim": mRim,
"mRiy": mRiy,
"XRim": XRim,
"yKiy": yKiy,
"H": H,
"Lh": Lh,
"MRiXZiXRiy": MRiXZiXRiy,
"MRiXZiXRiM": MRiXZiXRiM,
}
return self._cache["terms"]