def Dfun(x):
Xs, ys, ts = destructure_x(x, return_ts=True)
aHs, omaHs, adHs = [], [], []
for i in xrange(N):
shard = Shard(Xs[i], k)
H, dX = shard(domain, return_dX=True, epsilon=epsilon)
aH = alpha * H
aHs.append(aH)
omaHs.append(1.0 - aH)
adHs.append(alpha * dX)
I = np.ones_like(aHs[0])
JXs, Jts = [], []
for l in xrange(N):
JXl = J0 * prod(I, omaHs, 0, l)[..., np.newaxis]
for i in xrange(l):
JXli = aHs[i] * prod(I, omaHs, i + 1, l)
JXl += ys[i] * JXli[..., np.newaxis]
prod_lp1 = prod(I, omaHs, l + 1)
JXl -= ys[l] * prod_lp1[..., np.newaxis]
JXl_T = adHs[l][..., np.newaxis] * JXl
JXs.append(JXl_T.reshape(X_size, -1))
neg_aH_prod_lp1 = -(aHs[l] * prod_lp1)
dy = sigmoid_dt(ts[l])
Jt = np.zeros(((y_size,) + I.shape + (y_size,)),
dtype=np.float64)
for i in xrange(y_size):
Jt[i, ..., i] = dy[i] * neg_aH_prod_lp1
Jts.append(Jt.reshape(y_size, -1))
return np.vstack(JXs + Jts).T
def Dfun(x):
X_, y_, t_ = destructure_x(x, return_t=True)
shard = Shard(X_, k)
H, dX = shard(domain, return_dX=True, epsilon=epsilon)
d = alpha * (J - y_)
JX = dX[..., np.newaxis] * d
aH = -alpha * H
dy = sigmoid_dt(t_)
n = y.size
Jy = np.zeros(((n,) + H.shape + (n,)), dtype=np.float64)
for i in xrange(n):
Jy[i, ..., i] = dy[i] * aH
return np.c_[JX.reshape(X.size, -1).T, Jy.reshape(n, -1).T]