def test_nonperiodic_autocorrelation():
"""
test nonperiodic autocorrelation for spatial statistics
"""
from pymks import DiscreteIndicatorBasis
from pymks.stats import autocorrelate
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_auto = autocorrelate(X_)
X_result = np.array(
[
[
[0, 0, 0, 0],
[1.0 / 8, 1.0 / 12, 3.0 / 16, 1.0 / 12],
[0.2, 2.0 / 15, 0.3, 2.0 / 15],
[1.0 / 8, 1.0 / 12, 3.0 / 16, 1.0 / 12],
[0, 0, 0, 0],
]
]
)
assert np.allclose(X_result, X_auto[..., 1])
def test_mixperdic_mask():
from pymks import DiscreteIndicatorBasis
from pymks.stats import autocorrelate
from pymks.datasets import make_checkerboard_microstructure
X = make_checkerboard_microstructure(1, 3)
basis = DiscreteIndicatorBasis(n_states=2)
X_ = basis.discretize(X)
mask = np.ones((X.shape))
mask[0, 0, 0] = 0
X_auto_mixperiodic_mask = autocorrelate(X_, periodic_axes=[0], confidence_index=mask)
X_result_0 = np.array([[[1 / 5.0, 1 / 7.0, 2 / 5.0], [0, 0.5, 0], [2 / 5.0, 1 / 7.0, 1 / 5.0]]])
X_result_1 = np.array([[[2 / 5.0, 1 / 7.0, 2 / 5.0], [0, 0.5, 0.0], [2 / 5.0, 1 / 7.0, 2 / 5.0]]])
X_result = np.concatenate((X_result_0[..., None], X_result_1[..., None]), axis=-1)
assert np.allclose(X_auto_mixperiodic_mask, np.concatenate(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_nonperiodic_autocorrelation():
'''
test nonperiodic autocorrelation for spatial statistics
'''
from pymks import DiscreteIndicatorBasis
from pymks.stats import autocorrelate
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_auto = autocorrelate(X, basis)
X_result = np.array([[[0, 0, 0, 0], [1. / 8, 1. / 12, 3. / 16, 1. / 12],
[0.2, 2. / 15, 0.3, 2. / 15],
[1. / 8, 1. / 12, 3. / 16, 1. / 12], [0, 0, 0, 0]]])
assert (np.allclose(X_result, X_auto[..., 1]))
def test_periodic_autocorrelation():
'''
test periodic autocorrelation for spatial statistics
'''
from pymks import DiscreteIndicatorBasis
from pymks.stats import autocorrelate
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_auto = autocorrelate(X, basis, periodic_axes=(0, 1))
X_result = np.array([[[0, 0, 0, 0], [0.1, 0.1, 0.15, 0.1],
[0.2, 0.2, 0.3, 0.2], [0.1, 0.1, 0.15, 0.1],
[0, 0, 0, 0]]])
assert (np.allclose(X_result, X_auto[..., 1]))
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_autocorrelation():
"""
test periodic autocorrelation for spatial statistics
"""
from pymks import DiscreteIndicatorBasis
from pymks.stats import autocorrelate
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_auto = autocorrelate(X_, periodic_axes=(0, 1))
X_result = np.array(
[[[0, 0, 0, 0], [0.1, 0.1, 0.15, 0.1], [0.2, 0.2, 0.3, 0.2], [0.1, 0.1, 0.15, 0.1], [0, 0, 0, 0]]]
)
assert np.allclose(X_result, X_auto[..., 1])
def test_autocorrelate_with_specific_correlations():
from pymks.stats import autocorrelate
from pymks import PrimitiveBasis
X = np.array([[[1, 0, 1, 1], [1, 0, 1, 1], [0, 0, 2, 0], [0, 0, 0, 0],
[0, 0, 0, 0]]])
autocorrelations = [(0, 0), (2, 2)]
p_basis = PrimitiveBasis(n_states=3)
X_auto = autocorrelate(X, p_basis, autocorrelations=autocorrelations)
X_result_0 = np.array([[2 / 3., 1 / 3., 5 / 12., 4 / 9.],
[5 / 8., 5 / 12., 9 / 16., 1 / 2.],
[1 / 2., 7 / 15., 13 / 20., 7 / 15.],
[3 / 8., 1 / 2., 9 / 16., 5 / 12.],
[1 / 6., 4 / 9., 5 / 12., 1 / 3.]])
assert np.allclose(X_auto[0, ..., 0], X_result_0)
X_result_1 = np.array([[0., 0., 0., 0.], [0., 0., 0., 0.],
[0., 0., 0.05, 0.], [0., 0., 0., 0.],
[0., 0., 0., 0.]])
assert np.allclose(X_auto[0, ..., 1], X_result_1)
def test_nonperiodic_mask():
'''
test uncertainty masks for nonperiodic axes.
'''
from pymks import DiscreteIndicatorBasis
from pymks.stats import autocorrelate
from pymks.datasets import make_checkerboard_microstructure
X = make_checkerboard_microstructure(1, 3)
basis = DiscreteIndicatorBasis(n_states=2)
mask = np.ones((X.shape))
mask[0, 0, 0] = 0
X_auto_nonperiodic_mask = autocorrelate(X, basis, confidence_index=mask)
X_result_0 = np.array([[[1 / 3., 0, 0.5], [0, 0.5, 0.], [0.5, 0, 1 / 3.]]])
X_result_1 = np.array([[[2 / 3., 0, 0.5], [0, 0.5, 0.], [0.5, 0, 2 / 3.]]])
X_result = np.concatenate((X_result_0[..., None], X_result_1[..., None]),
axis=-1)
assert np.allclose(X_auto_nonperiodic_mask, np.concatenate(X_result))
def test_mixperdic_mask():
from pymks import DiscreteIndicatorBasis
from pymks.stats import autocorrelate
from pymks.datasets import make_checkerboard_microstructure
X = make_checkerboard_microstructure(1, 3)
basis = DiscreteIndicatorBasis(n_states=2)
X_ = basis.discretize(X)
mask = np.ones((X.shape))
mask[0, 0, 0] = 0
X_auto_mixperiodic_mask = autocorrelate(X_,
periodic_axes=[0],
confidence_index=mask)
X_result_0 = np.array([[[1 / 5., 1 / 7., 2 / 5.], [0, 0.5, 0],
[2 / 5., 1 / 7., 1 / 5.]]])
X_result_1 = np.array([[[2 / 5., 1 / 7., 2 / 5.], [0, 0.5, 0.],
[2 / 5., 1 / 7., 2 / 5.]]])
X_result = np.concatenate((X_result_0[..., None], X_result_1[..., None]),
axis=-1)
assert np.allclose(X_auto_mixperiodic_mask, np.concatenate(X_result))
def test_nonperiodic_autocorrelation():
'''
test nonperiodic autocorrelation for spatial statistics
'''
from pymks import DiscreteIndicatorBasis
from pymks.stats import autocorrelate
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_auto = autocorrelate(X, basis)
X_result = np.array([[[0, 0, 0, 0],
[1. / 8, 1. / 12, 3. / 16, 1. / 12],
[0.2, 2. / 15, 0.3, 2. / 15],
[1. / 8, 1. / 12, 3. / 16, 1. / 12],
[0, 0, 0, 0]]])
assert(np.allclose(X_result, X_auto[..., 1]))
def test_nonperiodic_mask():
'''
test uncertainty masks for nonperiodic axes.
'''
from pymks import DiscreteIndicatorBasis
from pymks.stats import autocorrelate
from pymks.datasets import make_checkerboard_microstructure
X = make_checkerboard_microstructure(1, 3)
basis = DiscreteIndicatorBasis(n_states=2)
mask = np.ones((X.shape))
mask[0, 0, 0] = 0
X_auto_nonperiodic_mask = autocorrelate(X, basis, confidence_index=mask)
X_result_0 = np.array([[[1 / 3., 0, 0.5],
[0, 0.5, 0.],
[0.5, 0, 1 / 3.]]])
X_result_1 = np.array([[[2 / 3., 0, 0.5],
[0, 0.5, 0.],
[0.5, 0, 2 / 3.]]])
X_result = np.concatenate((X_result_0[..., None],
X_result_1[..., None]), axis=-1)
assert np.allclose(X_auto_nonperiodic_mask, np.concatenate(X_result))
def test_autocorrelate_with_specific_correlations():
from pymks.stats import autocorrelate
from pymks import PrimitiveBasis
X = np.array([[[1, 0, 1, 1],
[1, 0, 1, 1],
[0, 0, 2, 0],
[0, 0, 0, 0],
[0, 0, 0, 0]]])
autocorrelations = [(0, 0), (2, 2)]
p_basis = PrimitiveBasis(n_states=3)
X_auto = autocorrelate(X, p_basis, autocorrelations=autocorrelations)
X_result_0 = np.array([[2 / 3., 1 / 3., 5 / 12., 4 / 9.],
[5 / 8., 5 / 12., 9 / 16., 1 / 2.],
[1 / 2., 7 / 15., 13 / 20., 7 / 15.],
[3 / 8., 1 / 2., 9 / 16., 5 / 12.],
[1 / 6., 4 / 9., 5 / 12., 1 / 3.]])
assert np.allclose(X_auto[0, ..., 0], X_result_0)
X_result_1 = np.array([[0., 0., 0., 0.],
[0., 0., 0., 0.],
[0., 0., 0.05, 0.],
[0., 0., 0., 0.],
[0., 0., 0., 0.]])
assert np.allclose(X_auto[0, ..., 1], X_result_1)
import warnings
warnings.filterwarnings('ignore')
from pymks import PrimitiveBasis
from pymks.stats import autocorrelate
from pymks.tools import draw_autocorrelations
# Create list of autocorrelations corresponding to the binary image lists
two_point_correlations_precipitate = []
# Two states (black and white); using primitive basis for microstructure function
p_basis = PrimitiveBasis(n_states=2, domain=[0, 1])
for i in range(0, 144):
two_point_correlations_precipitate.append(
autocorrelate(binary_image_list_precipitate[i].reshape((1, 512, 512)),
p_basis,
periodic_axes=(0, 1),
autocorrelations=[(0, 0)]))
# assuming both axes are periodic and only calculating the black autocorrelations
two_point_correlations_bicontinuous = []
for i in range(0, 48):
two_point_correlations_bicontinuous.append(
autocorrelate(binary_image_list_bicontinuous[i].reshape((1, 512, 512)),
p_basis,
periodic_axes=(0, 1),
autocorrelations=[(0, 0)]))
two_point_correlations_unknown = []
for i in range(0, 52):
two_point_correlations_unknown.append(
autocorrelate(binary_image_list_unknown[i].reshape((1, 512, 512)),
from pymks.stats import crosscorrelate
from pymks.tools import draw_microstructures
from pymks.tools import draw_autocorrelations
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)
