def transform_Dlt_on_Moments(dlt_tfm, moments):
'''Transform the Moments using an affine transformation.
Parameters
----------
dlt_tfm : Dlt
general dilatation
moments : Moments
general moments
Returns
-------
Moments
affined-transformed moments
'''
a = dlt_tfm.scale
A = np.diag(a)
old_m0 = moments.m0
old_mean = moments.mean
old_cov = moments.cov
new_mean = a*old_mean + dlt_tfm.offset
new_cov = A @ old_cov @ A.T
new_m0 = old_m0*abs(np.prod(a))
new_m1 = new_m0*new_mean
new_m2 = new_m0*(np.outer(new_mean, new_mean) + new_cov)
return Moments(new_m0, new_m1, new_m2)
def __init__(self, aff_tfm, make_normalised=True):
'''Initialises a hyperellipsoid with an affine transformation.'''
if not isinstance(aff_tfm, Aff):
raise ValueError("Only an instance of class `Aff` is accepted.")
if make_normalised:
U, S, VT = np.linalg.svd(aff_tfm.weight, full_matrices=False)
aff_tfm = Aff(bias=aff_tfm.bias, weight=U @ np.diag(S))
self.aff_tfm = aff_tfm
def __init__(self, aff_tfm, make_normalised=True):
'''Initialises an ellipse with an affine transformation.'''
if not isinstance(aff_tfm, Aff2d):
raise ValueError("Only an instance of class `Aff2d` is accepted.")
if make_normalised:
U, S, VT = np.linalg.svd(aff_tfm.weight, full_matrices=False)
aff_tfm = Aff2d(offset=aff_tfm.offset,
linear=Lin2d.from_matrix(U @ np.diag(S)))
self.aff_tfm = aff_tfm
def approx_Moments2d_to_Ellipse(obj):
'''Approximates a Moments2d instance with a normalised Ellipse that has the same mean and covariance as the mean and covariance of the instance.'''
# A
AAT = obj.cov * 4
w, v = np.linalg.eig(AAT)
A = v @ np.diag(np.sqrt(w))
# aff_tfm
aff_tfm = Aff2d(offset=obj.mean, linear=Lin2d.from_matrix(A))
return Ellipse(aff_tfm)
def weight(self):
return np.diag(self.scale)
if not isinstance(other, Dlt):
return super(Dlt, self).multiply(other)
return Dlt(self << other.offset, self.scale*other.scale)
multiply.__doc__ = Aff.multiply.__doc__
def invert(self):
return Dlt(-self.offset/self.scale, 1/self.scale)
invert.__doc__ = Aff.invert.__doc__
# ----- casting -----
_bc.register_cast(Dlt, Aff, lambda x: Aff(weight=x.weight, bias=x.bias, check_shapes=False))
_bc.register_cast(Aff, Dlt, lambda x: Dlt(offset=x.bias, scale=np.diagonal(x.weight)))
_bc.register_castable(Aff, Dlt, lambda x: np.count_nonzero(x.weight - np.diag(np._diagonal(x.weight))) > 0)
# ----- transform functions -----
def transform_Dlt_on_Moments(dlt_tfm, moments):
'''Transform the Moments using an affine transformation.
Parameters
----------
dlt_tfm : Dlt
general dilatation
moments : Moments
general moments
return Dltra(offset=t, scale=s)
def pow(self, k: float):
"""Raises the Dltra to a scalar power."""
u, v = self.logm()
return Dltra.expm(u * k, v * k)
# ----- casting -----
_bc.register_cast(Dltra, Dliso,
lambda x: Dliso(offset=x.offset, scale=x.scale))
_bc.register_cast(
Dltra,
Dlt,
lambda x: Dlt(offset=x.offset, scale=np.diag(x.scale), check_shapes=False),
)
# ----- approximation ------
def approx_Dliso_to_Dltra(obj):
"""Approximates an Dliso instance with a Dltra by ignoring the unitary part."""
return Dltra(offset=obj.offset, scale=obj.scale)
register_approx(Dliso, Dltra, approx_Dliso_to_Dltra)
def approx_Dlt_to_Dltra(dlt):
"""Approximates a Dlt instance with a Dltra.