def __matmul__(self, inp: CombT) -> RkhsObject:
if isinstance(inp, FiniteMap):
G = inner(self.inp_feat, inp.outp_feat)
if not inp.debias_outp:
matr = self.matr @ G @ inp.matr
inp_bias = (matr @ inp.bias.T).T
else:
matr = self.matr @ (G - G @ inp.bias.T) @ inp.matr
inp_bias = (self.matr @ G @ inp.bias.T).T
rval = FiniteMap(inp.inp_feat,
self.outp_feat,
matr,
outp_bias=self.bias + inp_bias)
rval.mean_center_inp = inp.mean_center_inp
return rval
else:
if isinstance(inp, DeviceArray):
inp = FiniteVec(self.inp_feat.k, np.atleast_2d(inp))
lin_map = (self.matr @ inner(self.inp_feat, inp)).T
if self.debias_outp:
r = [DecenterOutFeat(lin_map)]
else:
if self._normalize:
lin_map = lin_map / lin_map.sum(1, keepdims=True)
r = [LinearReduce(lin_map + self.bias)]
if len(inp) == 1:
r.append(Sum())
rval = self.outp_feat.extend_reduce(r)
return rval
def __init__(self,
inp_feat: Vec,
outp_feat: Vec,
ref_feat: Vec,
regul=0.01):
if True:
op = multiply(
CovOp(ref_feat, regul).inv(), Cmo(inp_feat, outp_feat, regul))
(self.inp_feat, self.outp_feat,
self.matr) = (op.inp_feat, op.outp_feat, op.matr)
else:
self.inp_feat = inp_feat
self.outp_feat = ref_feat
cmo_matr = np.linalg.inv(
inner(self.inp_feat) + regul * tf.eye(len(inp_feat)))
assert np.allclose(cmo_matr, Cmo(inp_feat, outp_feat, regul).matr)
inv_gram = np.linalg.inv(
inner(ref_feat) +
regul * np.eye(len(ref_feat), dtype=ref_feat.prefactors.dtype))
preimg_factor = (
np.diag(ref_feat.prefactors**2) @ inv_gram @ inv_gram)
#assert np.allclose(preimg_factor, CovOp(ref_feat, regul).inv().matr)
self.matr = preimg_factor @ inner(ref_feat, outp_feat) @ cmo_matr
def __init__(self,
start_feat: InpVecT,
timelagged_feat: InpVecT,
regul=0.01,
embedded=True,
koopman=False):
self.embedded = embedded
self.koopman = koopman
assert (start_feat.k == timelagged_feat.k)
if (embedded is True and koopman is False) or (embedded is False
and koopman is True):
self.matr = np.linalg.inv(
inner(start_feat) +
timelagged_feat * regul * np.eye(len(start_feat)))
else:
G_xy = inner(start_feat, timelagged_feat)
G_x = inner(start_feat)
matr = (np.linalg.pinv(G_xy)
@ np.linalg.pinv(G_x + len(timelagged_feat) * regul *
np.eye(len(timelagged_feat))) @ G_xy)
if koopman is True:
matr = self.matr.T
if koopman is False:
inp_feat = start_feat
outp_feat = timelagged_feat
else:
inp_feat = timelagged_feat
outp_feat = start_feat
super().__init__(inp_feat, outp_feat, matr)
def multiply(A:FiniteOp[IntermVecT, OutVecT], B:CombT) -> RkhsObject: # "T = TypeVar("T"); multiply(A:FiniteOp, B:T) -> T"
if isinstance(B, FiniteOp):
return FiniteOp(B.inp_feat, A.outp_feat, A.matr @ inner(A.inp_feat, B.outp_feat) @ B.matr)
else:
if len(B) == 1:
return FiniteVec.construct_RKHS_Elem(A.outp_feat.k, A.outp_feat.inspace_points, np.squeeze(A.matr @ inner(A.inp_feat, B)))
else:
pref = A.matr @ inner(A.inp_feat, B)
return FiniteVec(A.outp_feat.k, np.tile(A.outp_feat.inspace_points, (pref.shape[1], 1)), np.hstack(pref.T), points_per_split=pref.shape[0])
def inv(self, regul: float = None) -> "CovOp[InpVecT, InpVecT]":
"""Compute the inverse of this covariance operator with a certain regularization.
Args:
regul (float, optional): Regularization parameter to be used. Defaults to self.regul.
Returns:
CovOp[InpVecT, InpVecT]: The inverse operator
"""
set_inv = False
rval = self._inv
if regul is None:
set_inv = True
regul = self.regul
print("regul=", regul)
if self._inv is None or set_inv:
inv_gram = np.linalg.inv(
inner(self.inp_feat) +
regul * np.eye(len(self.inp_feat), dtype=self.matr.dtype))
matr = (self.matr @ self.matr @ inv_gram @ inv_gram)
rval = CovOp(self.inp_feat, regul)
rval.matr = matr
rval._inv = self
if set_inv:
self._inv = rval
return rval
def inv(self):
if self._inv is None:
inv_gram = np.linalg.inv(inner(self.inp_feat) + self.regul * np.eye(len(self.inp_feat), dtype = self.matr.dtype))
matr = (self.matr**2 @ inv_gram @ inv_gram)
self._inv = CovOp(self.inp_feat, self.regul)
self._inv.matr = matr
self._inv._inv = self
return self._inv
def solve(self, result: FiniteVec):
if np.all(self.outp_feat.inspace_points == result.inspace_points):
s = np.linalg.solve(
self.matr @ inner(self.inp_feat, self.inp_feat),
result.prefactors)
return FiniteVec.construct_RKHS_Elem(result.k,
result.inspace_points, s)
else:
assert ()
def __init__(self, inp_feat:InpVecT, outp_feat:OutVecT, regul = 0.01):
self.inp_feat = inp_feat
self.outp_feat = outp_feat
regul = np.array(regul, dtype=np.float32)
if False:
op = multiply(CrossCovOp(inp_feat, outp_feat), CovOp(inp_feat, regul).inv())
(self.inp_feat, self.outp_feat, self.matr) = (op.inp_feat,
op.outp_feat,
op.matr)
else:
self.matr = np.linalg.inv(inner(self.inp_feat) + regul * np.eye(len(inp_feat)))
def multiply(
A: FiniteOp,
B: RkhsObject,
copy_tensors=True
) -> RkhsObject: # "T = TypeVar("T"); multiply(A:FiniteOp, B:T) -> T"
assert (copy_tensors is False,
"copy_tensors == True is not implemented yet")
try:
return FiniteOp(B.inp_feat, A.outp_feat,
A.matr @ inner(A.inp_feat, B.outp_feat) @ B.matr)
except AttributeError:
if len(B) == 1:
#print("len 1")
return FiniteVec.construct_RKHS_Elem(
A.outp_feat.k, A.outp_feat.inspace_points,
np.squeeze(A.matr @ inner(A.inp_feat, B)))
else:
# print("len "+str(len(B)))
pref = A.matr @ inner(A.inp_feat, B)
return FiniteVec(A.outp_feat.k,
np.tile(A.outp_feat.inspace_points,
(pref.shape[1], 1)),
np.hstack(pref.T),
points_per_split=pref.shape[0])
def __init__(self,
inp_feat: InpVecT,
outp_feat: OutVecT,
regul: float = 0.01,
center=False,
regul_func=None):
regul = np.array(regul, dtype=np.float32)
#we do not center the output features - this still leads to the correct results in the output of the CME
c_inp_feat = inp_feat.centered() if center else inp_feat
G = inner(c_inp_feat)
if regul_func is None:
assert regul.squeeze().size == 1 or regul.squeeze(
).shape[0] == len(inp_feat)
matr = np.linalg.inv(G + regul * np.eye(len(inp_feat)))
else:
matr = regul_func(G)
super().__init__(inp_feat,
outp_feat,
matr,
mean_center_inp=center,
decenter_outp=center)
