def test_periodic_crosscorrelation():
"""
test nonperiodic crosscorrelation
"""
from pymks import DiscreteIndicatorBasis
from pymks.stats import crosscorrelate
X = np.array([[[1, 0, 1, 1], [1, 0, 1, 1], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]])
basis = DiscreteIndicatorBasis(n_states=2)
X_ = basis.discretize(X)
X_cross = crosscorrelate(X_, periodic_axes=(0, 1))
X_result = np.array(
[
[
[0.3, 0.3, 0.3, 0.3],
[0.2, 0.2, 0.15, 0.2],
[0.1, 0.1, 0.0, 0.1],
[0.2, 0.2, 0.15, 0.2],
[0.3, 0.3, 0.3, 0.3],
]
]
)
assert np.allclose(X_result, X_cross[..., 0])
def test_crosscorrelate_with_specific_correlations():
from pymks.stats import crosscorrelate
from pymks import PrimitiveBasis
X = np.array([[[0, 0, 0, 0], [0, 1, 0, 0], [0, 0, 2, 0], [0, 0, 0, 0],
[0, 0, 0, 0]]])
crosscorrelations = [(1, 2)]
p_basis = PrimitiveBasis(n_states=3)
X_cross = crosscorrelate(X, p_basis, crosscorrelations=crosscorrelations)
X_result = np.array([[0., 0., 0., 0.], [0., 0., 0., 0.], [0., 0., 0., 0.],
[0., 0., 0., 1 / 12.], [0., 0., 0., 0.]])
assert np.allclose(X_cross[0, ..., 0], X_result)
def _get_spatial_correlations(self, X):
"""
Generates spatial correlations for a microstructure X.
Args:
X: The microstructure, an `(n_samples, N, ...)` shaped
array where `n_samples` is the number of samples and `N`
is the spatial discretization.
Returns:
Autocorrelations and crosscorrelations.
"""
X_ = self.basis.discretize(X)
X_auto = autocorrelate(X_)
X_cross = crosscorrelate(X_)
return np.concatenate((X_auto, X_cross), axis=-1)
def test_periodic_crosscorrelation():
'''
test periodic crosscorrelation
'''
from pymks import DiscreteIndicatorBasis
from pymks.stats import crosscorrelate
X = np.array([[[1, 0, 1, 1], [1, 0, 1, 1], [0, 0, 0, 0], [0, 0, 0, 0],
[0, 0, 0, 0]]])
basis = DiscreteIndicatorBasis(n_states=2)
X_cross = crosscorrelate(X, basis, periodic_axes=(0, 1))
X_result = np.array([[[0.3, 0.3, 0.3, 0.3], [0.2, 0.2, 0.15, 0.2],
[0.1, 0.1, 0., 0.1], [0.2, 0.2, 0.15, 0.2],
[0.3, 0.3, 0.3, 0.3]]])
assert (np.allclose(X_result, X_cross[..., 0]))
def _get_spatial_correlations(self, X):
"""
Generates spatial correlations for a microstructure X.
Args:
X: The microstructure, an `(n_samples, N, ...)` shaped
array where `n_samples` is the number of samples and `N`
is the spatial discretization.
Returns:
Autocorrelations and crosscorrelations.
"""
X_ = self.basis.discretize(X)
X_auto = autocorrelate(X_)
X_cross = crosscorrelate(X_)
return np.concatenate((X_auto, X_cross), axis=-1)
def test_crosscorrelate_with_specific_correlations():
from pymks.stats import crosscorrelate
from pymks import PrimitiveBasis
X = np.array([[[0, 0, 0, 0],
[0, 1, 0, 0],
[0, 0, 2, 0],
[0, 0, 0, 0],
[0, 0, 0, 0]]])
crosscorrelations = [(1, 2)]
p_basis = PrimitiveBasis(n_states=3)
X_cross = crosscorrelate(X, p_basis, crosscorrelations=crosscorrelations)
X_result = np.array([[0., 0., 0., 0.],
[0., 0., 0., 0.],
[0., 0., 0., 0.],
[0., 0., 0., 1 / 12.],
[0., 0., 0., 0.]])
assert np.allclose(X_cross[0, ..., 0], X_result)
def test_nonperiodic_crosscorrelation():
'''
test nonperiodic crosscorrelation
'''
from pymks import DiscreteIndicatorBasis
from pymks.stats import crosscorrelate
X = np.array([[[1, 0, 1, 1], [1, 0, 1, 1], [0, 0, 0, 0], [0, 0, 0, 0],
[0, 0, 0, 0]]])
basis = DiscreteIndicatorBasis(n_states=2)
X_cross = crosscorrelate(X, basis)
X_result = np.array([[[
1 / 3.,
4 / 9.,
0.5,
4 / 9.,
], [1 / 8., 0.25, 3 / 16., 0.25], [0., 2 / 15., 0., 2 / 15.],
[0., 1 / 12., 0, 1 / 12.], [0, 0, 0, 0]]])
assert (np.allclose(X_result, X_cross[..., 0]))
def test_nonperiodic_crosscorrelation():
'''
test nonperiodic crosscorrelation
'''
from pymks import DiscreteIndicatorBasis
from pymks.stats import crosscorrelate
X = np.array([[[1, 0, 1, 1],
[1, 0, 1, 1],
[0, 0, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 0]]])
basis = DiscreteIndicatorBasis(n_states=2)
X_cross = crosscorrelate(X, basis)
X_result = np.array([[[1 / 3., 4 / 9., 0.5, 4 / 9., ],
[1 / 8., 0.25, 3 / 16., 0.25],
[0., 2 / 15., 0., 2 / 15.],
[0., 1 / 12., 0, 1 / 12.],
[0, 0, 0, 0]]])
assert(np.allclose(X_result, X_cross[..., 0]))
def test_periodic_crosscorrelation():
'''
test periodic crosscorrelation
'''
from pymks import DiscreteIndicatorBasis
from pymks.stats import crosscorrelate
X = np.array([[[1, 0, 1, 1],
[1, 0, 1, 1],
[0, 0, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 0]]])
basis = DiscreteIndicatorBasis(n_states=2)
X_cross = crosscorrelate(X, basis, periodic_axes=(0, 1))
X_result = np.array([[[0.3, 0.3, 0.3, 0.3],
[0.2, 0.2, 0.15, 0.2],
[0.1, 0.1, 0., 0.1],
[0.2, 0.2, 0.15, 0.2],
[0.3, 0.3, 0.3, 0.3]]])
assert(np.allclose(X_result, X_cross[..., 0]))
def test_nonperiodic_crosscorrelation():
"""
test nonperiodic crosscorrelation
"""
from pymks import DiscreteIndicatorBasis
from pymks.stats import crosscorrelate
X = np.array([[[1, 0, 1, 1], [1, 0, 1, 1], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]])
basis = DiscreteIndicatorBasis(n_states=2)
X_ = basis.discretize(X)
X_cross = crosscorrelate(X_)
X_result = np.array(
[
[
[1 / 3.0, 4 / 9.0, 0.5, 4 / 9.0],
[1 / 8.0, 0.25, 3 / 16.0, 0.25],
[0.0, 2 / 15.0, 0.0, 2 / 15.0],
[0.0, 1 / 12.0, 0, 1 / 12.0],
[0, 0, 0, 0],
]
]
)
assert np.allclose(X_result, X_cross[..., 0])
from pymks.tools import draw_crosscorrelations
# Make checkerboard microstructure and observe it.
X = make_checkerboard_microstructure(square_size=10, n_squares=6)
draw_microstructures(X)
# Define the basis for 2-point statistics
prim_basis = PrimitiveBasis(n_states=2)
X_ = prim_basis.discretize(X)
# Computing auto-correlatiions of the microstructure function and drawing the same
X_auto = autocorrelate(X,
basis=PrimitiveBasis(n_states=2),
periodic_axes=(0, 1))
correlations = [('white', 'white'), ('black', 'black')]
draw_autocorrelations(X_auto[0], autocorrelations=correlations)
# Checking the volume fraction of both the phases i.e. (0,0) value of auto-correlations
centre = (X_auto.shape[1] + 1) / 2
print('Volume fraction of black phase', X_auto[0, centre, centre, 0])
print('Volume fraction of black phase', X_auto[0, centre, centre, 1])
# Computing the cross correlation of the microstructure function and drawing the same
X_cross = crosscorrelate(X,
basis=PrimitiveBasis(n_states=2),
periodic_axes=(0, 1))
correlations = [('black', 'white')]
draw_crosscorrelations(X_cross[0], crosscorrelations=correlations)
# Crosscorrelation at (0,0) should be zero
print('Center value : ', X_cross[0, centre, centre, 0])