def test_poly_phi(n, d, deg):
X = randn(n,d)
Phi = phi(X,deg)
polydeg = lambda x,y: dotp(x,y)**deg
(K , _, _) = bhatta.kernel_matrix(X, polydeg)
(Kp, _, _) = bhatta.kernel_matrix(Phi, dotp)
return sum(abs(K-Kp))
def eig_poly(X1, X2, deg, eta, r):
# Not tested in the slightest ... probably all broken
# Make Kc1, Kc2
# U1.T * S1 * U1
kernel = bhatta.polyk(deg)
(n1, d1) = X1.shape
(n2, d) = X2.shape
assert d1==d
n = n1+n2
X = bmat("X1;X2")
#Let's get this shit forreal now:
Xp = phi(X,deg)
(n, pd) = Xp.shape
X1p = Xp[0:n1, :]
X2p = Xp[n1:n, :]
mu1p = sum(X1p,0) / n1
mu2p = sum(X2p,0) / n2
X1cp = X1p - tile(mu1p, (n1,1))
X2cp = X2p - tile(mu2p, (n2,1))
Xcp = bmat('X1cp; X2cp')
Etap = eye(pd) * eta
S1p = Etap + X1cp.T * X1cp / n1
S2p = Etap + X2cp.T * X2cp / n2
mu3p = .5 * (S1p.I * mu1p.T + S2p.I * mu2p.T).T
S3p = 2 * (S1p.I + S2p.I).I
dt1p = det(S1p) ** -.25
dt2p = det(S2p) ** -.25
dt3p = det(S3p) ** .5
dterm = dt1p * dt2p * dt3p
e1p = -.25 * mu1p * S1p.I * mu1p.T
e2p = -.25 * mu2p * S2p.I * mu2p.T
e3p = .5 * mu3p * S3p * mu3p.T
eterm = math.exp(e1p + e2p + e3p)
(Lam1p, Alpha1p) = eigsh(S1p, r)
(Lam2p, Alpha2p) = eigsh(S2p, r)
Alpha1p = matrix(Alpha1p)
Alpha2p = matrix(Alpha2p)
(K, Kuc, Kc) = bhatta.kernel_matrix(X, kernel, n1, n2)
Kc1 = Kc[0:n1, 0:n1]
Kc2 = Kc[n1:n, n1:n]
(Lam1, Alpha1) = eigsh(Kc1, r)
(Lam2, Alpha2) = eigsh(Kc2, r)
Alpha1 = matrix(Alpha1)
Alpha2 = matrix(Alpha2)
Lam1 = Lam1 / n1
Lam2 = Lam2 / n2
Lam1 += eta
Lam2 += eta
Beta1 = zeros((n,r))
Beta2 = zeros((n,r))
for i in xrange(r):
Beta1[0:n1, i] = Alpha1[:,i] / (n1 * Lam1[i])**.5
Beta2[n1:n, i] = Alpha2[:,i] / (n2 * Lam2[i])**.5
#Eta = eye((gamma, gamma)) * eta
Beta = bmat('Beta1, Beta2')
Gamma = eig_ortho(Kc, Beta)
Omega = Beta * Gamma
V = Xcp.T * Beta #RKHS representation of eigenvectors
#V[0:r] is orthonormal, V[r:2r] is orthonormal
W = Xcp.T * Omega # RKHS representation of orthogonalized eigenvectors
mu1_v = sum(Kuc[0:n1, :] * Beta1, 0) / n1
mu2_v = sum(Kuc[n1:n, :] * Beta2, 0) / n2
mu1_w = sum(Kuc[0:n1, :] * Omega, 0) / n1
mu2_w = sum(Kuc[n1:n, :] * Omega, 0) / n2
Eta_v = 0 * eye(r)
Eta_w = 0 * eye(2*r)
S1_v = makediag(Lam1) + Eta_v
S2_v = makediag(Lam2) + Eta_v
#d1 = (product(Lam1 + eta) * eta ** n2) ** -.25
#d2 = product(Lam2 + eta) ** -.25
S1_w = Omega.T * Kc[:,0:n1] * Kc[0:n1,:] * Omega / n1
S2_w = Omega.T * Kc[:,n1:n] * Kc[n1:n,:] * Omega / n2
S1_w += Eta_w
S2_w += Eta_w
mu3_w = .5 * (S1_w.I * mu1_w.T + S2_w.I * mu2_w.T).T
S3_w = 2 * (S1_w.I + S2_w.I).I
d1 = det(S1_w) ** -.25
d2 = det(S2_w) ** -.25
e1 = exp(-mu1_w * S1_w.I * mu1_w.T / 4)
e2 = exp(-mu2_w * S2_w.I * mu2_w.T / 4)
d3 = det(S3_w) ** .5
e3 = exp(mu3_w * S3_w * mu3_w.T / 2)
try:
assert not(isnan(d1*d2*d3*e1*e2*e3))
rval = float(d1*d2*d3*e1*e2*e3)
except AssertionError:
rval = -1
ebhatta = eterm*dterm
#print "Explicit: {} Eigen: {}".format(ebhatta,rval)
#print "Diff: {} Ratio: {}".format(ebhatta-rval, ebhatta/rval)
#print "---"
return (rval)
