def _forward(self, x, *args, **kwds):
d, n = 2 + 1, x.size
p = n
y = UTPM(np.zeros((d, p, n)))
y.data[0, :] = x.ravel()
y.data[1, :] = np.eye(n)
z0 = self.fun(y, *args, **kwds)
z = UTPM.as_utpm(z0)
H = z.data[2, ...] * 2
return H
def _forward(self, x, *args, **kwds):
x0 = np.asarray(x)
shape = x0.shape
P = 1
x = UTPM(np.zeros((self.n + 1, P) + shape))
x.data[0, 0] = x0
x.data[1, 0] = 1
z = self.f(x, *args, **kwds)
y = UTPM.as_utpm(z)
return y.data[self.n, 0] * misc.factorial(self.n)
def _forward(self, x, *args, **kwds):
x0 = np.asarray(x)
shape = x0.shape
P = 1
x = UTPM(np.zeros((self.n + 1, P) + shape))
x.data[0, 0] = x0
x.data[1, 0] = 1
z = self.fun(x, *args, **kwds)
y = UTPM.as_utpm(z)
return y.data[self.n, 0] * special.factorial(self.n)
def _forward(self, x, *args, **kwds):
d, n = 2+1, x.size
p = n
y = UTPM(np.zeros((d, p, n)))
y.data[0, :] = x.ravel()
y.data[1, :] = np.eye(n)
z0 = self.fun(y, *args, **kwds)
z = UTPM.as_utpm(z0)
H = z.data[2, ...] * 2
return H
def _forward(self, x, *args, **kwds):
# return np.diag(super(Hessdiag, self)._forward(x, *args, **kwds))
D, Nm = 2+1, x.size
P = Nm
y = UTPM(np.zeros((D, P, Nm)))
y.data[0, :] = x.ravel()
y.data[1, :] = np.eye(Nm)
z0 = self.f(y, *args, **kwds)
z = UTPM.as_utpm(z0)
H = z.data[2, ...] * 2
return H
def _forward(self, x, *args, **kwds):
# return np.diag(super(Hessdiag, self)._forward(x, *args, **kwds))
D, Nm = 2 + 1, x.size
P = Nm
y = UTPM(np.zeros((D, P, Nm)))
y.data[0, :] = x.ravel()
y.data[1, :] = np.eye(Nm)
z0 = self.f(y, *args, **kwds)
z = UTPM.as_utpm(z0)
H = z.data[2, ...] * 2
return H
def _jacobian_forward(self, x, *args, **kwds):
x = np.asarray(x, dtype=float)
# shape = x.shape
D, Nm = 2, x.size
P = Nm
y = UTPM(np.zeros((D, P, Nm)))
y.data[0, :] = x.ravel()
y.data[1, :] = np.eye(Nm)
z0 = self.f(y, *args, **kwds)
z = UTPM.as_utpm(z0)
J = z.data[1, :, :, 0]
return J
def hessian_forward():
def f(x, *args, **kwds):
return x[0] + x[1] ** 2 + x[2] ** 3
x = np.asarray([1, 2, 3], dtype=float)
# shape = x.shape
D, Nm = 2+1, x.size
P = Nm
y = UTPM(np.zeros((D, P, Nm)))
y.data[0, :] = x.ravel()
y.data[1, :] = np.eye(Nm)
z0 = f(y)
z = UTPM.as_utpm(z0)
J = z.data[2, ...] * 2
return J
