def get_DisplacementGradientMap(strained_vectors, unstrained_vectors):
"""
Calculates the displacement gradient by comparing vectors with linear algebra
Parameters
----------
strained_vectors : Signal2D
unstrained_vectors : numpy.array with shape (2,2)
For two vectors: V and U measured in x and y the components should fill the array as
>>> array([[Vx, Vy],
[Ux, Uy]])
Returns
-------
D : DisplacementGradientMap
The 3x3 displacement gradient tensor (measured in reciprocal space)
at every navigation position
See Also
--------
get_single_DisplacementGradientTensor()
Notes
-----
This function does not currently support keyword arguments to the underlying map function.
"""
D = strained_vectors.map(get_single_DisplacementGradientTensor,
Vu=unstrained_vectors,
inplace=False)
return DisplacementGradientMap(D)
def get_DisplacementGradientMap(strained_vectors,
unstrained_vectors,
weights=None):
r"""Calculates the displacement gradient tensor at each navigation position in a map.
Compares vectors to determine the 2 x 2 matrix,
:math:`\\mathbf(L)`, that maps unstrained vectors, Vu, to strained vectors,
Vs, using the np.lingalg.inv() function to find L that satisfies
:math:`Vs = \\mathbf(L) Vu`.
The transformation is returned as a 3 x 3 displacement gradient tensor.
Parameters
----------
strained_vectors : hyperspy.Signal2D
Signal2D with a 2 x n array at each navigation position containing the
Cartesian components of two strained basis vectors, V and U, defined as
row vectors.
unstrained_vectors : numpy.array
A 2 x n array containing the Cartesian components of two unstrained
basis vectors, V and U, defined as row vectors.
weights : list
of weights to be passed to the least squares optimiser, not used for n=2
Returns
-------
D : DisplacementGradientMap
The 3 x 3 displacement gradient tensor (measured in reciprocal space) at
every navigation position.
Notes
-----
n=2 now behaves the same as the n>2 case; see Release Notes for 0.10.0 for details.
See Also
--------
get_single_DisplacementGradientTensor()
"""
# Calculate displacement gradient tensor across map.
D = strained_vectors.map(
get_single_DisplacementGradientTensor,
Vu=unstrained_vectors,
weights=weights,
inplace=False,
output_signal_size=(3, 3),
output_dtype=np.float64,
)
return DisplacementGradientMap(D)
def get_DisplacementGradientMap(strained_vectors, unstrained_vectors):
"""Calculates the displacement gradient tensor at each navigation position
in a map by comparing vectors to determine the 2 x 2 matrix,
:math:`\\mathbf(L)`, that maps unstrained vectors, Vu, to strained vectors,
Vs, using the np.lingalg.inv() function to find L that satisfies
:math:`Vs = \\mathbf(L) Vu`.
The transformation is returned as a 3 x 3 displacement gradient tensor.
Parameters
----------
strained_vectors : hyperspy.Signal2D
Signal2D with a 2 x 2 array at each navigation position containing the
Cartesian components of two strained basis vectors, V and U, defined as
row vectors.
unstrained_vectors : numpy.array
A 2 x 2 array containing the Cartesian components of two unstrained
basis vectors, V and U, defined as row vectors.
Returns
-------
D : DisplacementGradientMap
The 3 x 3 displacement gradient tensor (measured in reciprocal space) at
every navigation position.
See Also
--------
get_single_DisplacementGradientTensor()
"""
# Calculate displacement gradient tensor across map.
D = strained_vectors.map(get_single_DisplacementGradientTensor,
Vu=unstrained_vectors,
inplace=False)
return DisplacementGradientMap(D)
def construct_displacement_gradient(self):
"""Construct a map of the displacement gradient tensor at each
navigation position as determined by fitting an affine transformed
reference pattern.
Returns
-------
D : DisplacementGradientMap
Signal containing the displacement gradient tensor at each
navigation postion.
"""
D = DisplacementGradientMap(
np.ones(np.append(self.d11.map.shape, (3, 3))))
D.data[:, :, 0, 0] = self.d11.map["values"]
D.data[:, :, 1, 0] = self.d12.map["values"]
D.data[:, :, 2, 0] = 0.0
D.data[:, :, 0, 1] = self.d21.map["values"]
D.data[:, :, 1, 1] = self.d22.map["values"]
D.data[:, :, 2, 1] = 0.0
D.data[:, :, 0, 2] = 0.0
D.data[:, :, 1, 2] = 0.0
D.data[:, :, 2, 2] = 1.0
return D
[0.25881905, 0.96592583, 0.],
[0., 0., 1.]]),
-0.2617993877991494),
])
def test_get_rotation_angle(R, theta):
tc = _get_rotation_angle(R)
np.testing.assert_almost_equal(tc, theta)
@pytest.mark.parametrize('dgm, rotation_map, distortion_map', [
(DisplacementGradientMap(np.array([[[[0.98860899, -0.2661997, 0.],
[0.2514384, 0.94324267, 0.],
[0., 0., 1.]],
[[0.98860899, -0.2661997, 0.],
[0.2514384, 0.94324267, 0.],
[0., 0., 1.]]],
[[[0.98860899, -0.2661997, 0.],
[0.2514384, 0.94324267, 0.],
[0., 0., 1.]],
[[0.98860899, -0.2661997, 0.],
[0.2514384, 0.94324267, 0.],
[0., 0., 1.]]]])),
np.array([[[[0.96592583, -0.25881905, 0.],
[0.25881905, 0.96592583, 0.],
[0., 0., 1.]],
[[0.96592583, -0.25881905, 0.],
[0.25881905, 0.96592583, 0.],
[0., 0., 1.]]],
[[[0.96592583, -0.25881905, 0.],
[0.25881905, 0.96592583, 0.],
[0., 0., 1.]],
[[0.96592583, -0.25881905, 0.],
[
(
DisplacementGradientMap(
np.array([
[
[
[0.98860899, -0.2661997, 0.0],
[0.2514384, 0.94324267, 0.0],
[0.0, 0.0, 1.0],
],
[
[0.98860899, -0.2661997, 0.0],
[0.2514384, 0.94324267, 0.0],
[0.0, 0.0, 1.0],
],
],
[
[
[0.98860899, -0.2661997, 0.0],
[0.2514384, 0.94324267, 0.0],
[0.0, 0.0, 1.0],
],
[
[0.98860899, -0.2661997, 0.0],
[0.2514384, 0.94324267, 0.0],
[0.0, 0.0, 1.0],
],
],
])),
np.array([
[