def test_mask_two_samples():
from pymks import DiscreteIndicatorBasis
from pymks.stats import correlate
from pymks.datasets import make_microstructure
X = make_microstructure(n_samples=2, n_phases=2, size=(3, 3), grain_size=(2, 2), seed=99)
basis = DiscreteIndicatorBasis(n_states=2)
X_ = basis.discretize(X)
mask = np.ones(X.shape)
mask[:, 0, 0] = 0.0
X_corr = correlate(X_, confidence_index=mask)
X_result = np.array(
[
[
[[1 / 3.0, 1 / 3.0, 1 / 3.0], [1 / 5.0, 1 / 5.0, 1 / 5.0], [1 / 4.0, 1 / 4.0, 0]],
[[1 / 5.0, 1 / 5.0, 2 / 5.0], [1 / 2.0, 1 / 2.0, 0], [1 / 5.0, 1 / 5.0, 1 / 5.0]],
[[1 / 4.0, 1 / 4.0, 1 / 2.0], [1 / 5.0, 1 / 5.0, 2 / 5.0], [1 / 3.0, 1 / 3.0, 0]],
],
[
[[0.0, 0.0, 1 / 3.0], [2 / 5.0, 3 / 5.0, 0.0], [0.0, 0.0, 1 / 2.0]],
[[0.0, 0.0, 2 / 5.0], [3 / 8.0, 5 / 8.0, 0], [0.0, 0.0, 3 / 5.0]],
[[0.0, 0.0, 1 / 2.0], [2 / 5.0, 3 / 5.0, 0.0], [0.0, 0.0, 2 / 3.0]],
],
]
)
print np.round(X_corr, decimals=4)
print X_result
assert np.allclose(X_corr, X_result)
def test_mask_two_samples():
from pymks import DiscreteIndicatorBasis
from pymks.stats import correlate
from pymks.datasets import make_microstructure
X = make_microstructure(n_samples=2,
n_phases=2,
size=(3, 3),
grain_size=(2, 2),
seed=99)
basis = DiscreteIndicatorBasis(n_states=2)
X_ = basis.discretize(X)
mask = np.ones(X.shape)
mask[:, 0, 0] = 0.
X_corr = correlate(X_, confidence_index=mask)
X_result = np.array([[[[1 / 3., 1 / 3., 1 / 3.], [1 / 5., 1 / 5., 1 / 5.],
[1 / 4., 1 / 4., 0]],
[[1 / 5., 1 / 5., 2 / 5.], [1 / 2., 1 / 2., 0],
[1 / 5., 1 / 5., 1 / 5.]],
[[1 / 4., 1 / 4., 1 / 2.], [1 / 5., 1 / 5., 2 / 5.],
[1 / 3., 1 / 3., 0]]],
[[[0., 0., 1 / 3.], [2 / 5., 3 / 5., 0.],
[0., 0., 1 / 2.]],
[[0., 0., 2 / 5.], [3 / 8., 5 / 8., 0],
[0., 0., 3 / 5.]],
[[0., 0., 1 / 2.], [2 / 5., 3 / 5., 0.],
[0., 0., 2 / 3.]]]])
print np.round(X_corr, decimals=4)
print X_result
assert np.allclose(X_corr, X_result)
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_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 test_n_components_change():
from pymks import MKSStructureAnalysis
from pymks import DiscreteIndicatorBasis
dbasis = DiscreteIndicatorBasis(n_states=2)
model = MKSStructureAnalysis(basis=dbasis)
model.n_components = 27
assert model.n_components == 27
def test_n_componets_from_reducer():
from pymks import MKSHomogenizationModel, DiscreteIndicatorBasis
from sklearn.manifold import LocallyLinearEmbedding
reducer = LocallyLinearEmbedding(n_components=7)
dbasis = DiscreteIndicatorBasis(n_states=3, domain=[0, 2])
model = MKSHomogenizationModel(dimension_reducer=reducer, basis=dbasis)
assert model.n_components == 7
def test_stress():
from pymks.datasets import make_elastic_stress_random
from pymks import MKSHomogenizationModel, DiscreteIndicatorBasis
sample_size = 200
grain_size = [(5, 5), (6, 4), (4, 6), (2, 2)]
n_samples = [sample_size] * len(grain_size)
elastic_modulus = (410, 200)
poissons_ratio = (0.28, 0.3)
macro_strain = 0.001
size = (21, 21)
X, y = make_elastic_stress_random(n_samples=n_samples,
size=size,
grain_size=grain_size,
elastic_modulus=elastic_modulus,
poissons_ratio=poissons_ratio,
macro_strain=macro_strain,
seed=0)
dbasis = DiscreteIndicatorBasis(n_states=2, domain=[0, 1])
model = MKSHomogenizationModel(basis=dbasis, n_components=3, degree=3)
model.fit(X, y)
test_sample_size = 1
n_samples = [test_sample_size] * len(grain_size)
X_new, y_new = make_elastic_stress_random(n_samples=n_samples,
size=size,
grain_size=grain_size,
elastic_modulus=elastic_modulus,
poissons_ratio=poissons_ratio,
macro_strain=macro_strain,
seed=3)
y_result = model.predict(X_new)
assert np.allclose(np.round(y_new, decimals=2),
np.round(y_result, decimals=2))
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., 0.1], [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_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_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_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. / 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_correlate():
'''
test corrleate for non-periodic microstructures
'''
from pymks import DiscreteIndicatorBasis
from pymks.stats import correlate
X = np.array([[[0, 0, 1, 0], [0, 0, 1, 0], [0, 0, 1, 0], [0, 0, 0, 0],
[0, 0, 1, 0]],
[[0, 1, 0, 0], [0, 1, 0, 0], [0, 1, 0, 0], [0, 0, 0, 0],
[0, 1, 0, 0]]])
basis = DiscreteIndicatorBasis(n_states=2)
X_ = basis.discretize(X)
X_corr = correlate(X_, periodic_axes=(0, 1))
X_result = [[0.6, 0.6, 0.75, 0.6], [0.6, 0.6, 0.75, 0.6],
[0.6, 0.6, 0.8, 0.6], [0.6, 0.6, 0.75, 0.6],
[0.6, 0.6, 0.75, 0.6]]
assert (np.allclose(X_result, X_corr[0, ..., 0]))
def test_nonperiodic_correlate():
'''
test corrleate for non-periodic microstructures
'''
from pymks import DiscreteIndicatorBasis
from pymks.stats import correlate
X = np.array([[[0, 0, 1, 0], [0, 0, 1, 0], [0, 0, 1, 0], [0, 0, 0, 0],
[0, 0, 1, 0]],
[[0, 1, 0, 0], [0, 1, 0, 0], [0, 1, 0, 0], [0, 0, 0, 0],
[0, 1, 0, 0]]])
basis = DiscreteIndicatorBasis(n_states=2)
X_ = basis.discretize(X)
X_corr = correlate(X_)
X_result = [[2 / 3., 4 / 9., 0.75, 4 / 9.], [5 / 8., 0.5, 0.75, 0.5],
[0.6, 7 / 15., 0.8, 7 / 15.], [5 / 8., 0.5, 0.75, 0.5],
[0.5, 4 / 9., 0.75, 4 / 9.]]
assert (np.allclose(X_result, X_corr[0, ..., 0]))
def test_n_components_with_reducer():
from pymks import MKSHomogenizationModel, DiscreteIndicatorBasis
from sklearn.manifold import Isomap
reducer = Isomap(n_components=7)
dbasis = DiscreteIndicatorBasis(n_states=3, domain=[0, 2])
model = MKSHomogenizationModel(dimension_reducer=reducer,
basis=dbasis,
n_components=9)
assert model.n_components == 9
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)
X_ = basis.discretize(X)
mask = np.ones((X.shape))
mask[0, 0, 0] = 0
X_auto_nonperiodic_mask = autocorrelate(X_, 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_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.,
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_correlate():
"""
test corrleate for non-periodic microstructures
"""
from pymks import DiscreteIndicatorBasis
from pymks.stats import correlate
X = np.array(
[
[[0, 0, 1, 0], [0, 0, 1, 0], [0, 0, 1, 0], [0, 0, 0, 0], [0, 0, 1, 0]],
[[0, 1, 0, 0], [0, 1, 0, 0], [0, 1, 0, 0], [0, 0, 0, 0], [0, 1, 0, 0]],
]
)
basis = DiscreteIndicatorBasis(n_states=2)
X_ = basis.discretize(X)
X_corr = correlate(X_, periodic_axes=(0, 1))
X_result = [
[0.6, 0.6, 0.75, 0.6],
[0.6, 0.6, 0.75, 0.6],
[0.6, 0.6, 0.8, 0.6],
[0.6, 0.6, 0.75, 0.6],
[0.6, 0.6, 0.75, 0.6],
]
assert np.allclose(X_result, X_corr[0, ..., 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])
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)
mask = np.ones((X.shape))
mask[0, 0, 0] = 0
X_auto_mixperiodic_mask = autocorrelate(X,
basis,
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 make_elastic_stress_random(n_samples=[10, 10], elastic_modulus=(100, 150),
poissons_ratio=(0.3, 0.3), size=(21, 21),
macro_strain=0.01, grain_size=[(3, 3), (9, 9)],
seed=10):
"""
Generates microstructures and their macroscopic stress values for an
applied macroscopic strain.
Args:
n_samples (int, optional): number of samples
elastic_modulus (tuple, optional): list of elastic moduli for the
different phases.
poissons_ratio (tuple, optional): list of poisson's ratio values for
the phases.
size (tuple, optional): size of the microstructures
macro_strain (tuple, optional): macroscopic strain applied to the
sample.
grain_size (tuple, optional): effective dimensions of grains
seed (int, optional): seed for random number generator
Returns:
array of microstructures with dimensions (n_samples, n_x, ...) and
effective stress values
Example
>>> X, y = make_elastic_stress_random(n_samples=1, elastic_modulus=(1, 1),
... poissons_ratio=(1, 1),
... grain_size=(3, 3), macro_strain=1.0)
>>> assert np.allclose(y, np.ones(y.shape))
>>> X, y = make_elastic_stress_random(n_samples=1, grain_size=(1, 1),
... elastic_modulus=(100, 200),
... size=(2, 2), poissons_ratio=(1, 3),
... macro_strain=1., seed=3)
>>> X_result = np.array([[[1, 1],
... [0, 1]]])
>>> assert np.allclose(X, X_result)
>>> assert float(np.round(y, decimals=5)[0]) == 228.74696
>>> X, y = make_elastic_stress_random(n_samples=1, grain_size=(1, 1, 1),
... elastic_modulus=(100, 200),
... poissons_ratio=(1, 3), seed=3,
... macro_strain=1., size=(2, 2, 2))
>>> X_result = np.array([[[1, 1],
... [0, 0]],
... [[1, 1],
... [0, 0]]])
>>> assert np.allclose(X, X_result)
>>> assert np.round(y[0]).astype(int) == 150
"""
if not isinstance(grain_size[0], (list, tuple, np.ndarray)):
grain_size = (grain_size,)
if not isinstance(n_samples, (list, tuple, np.ndarray)):
n_samples = (n_samples,)
if not isinstance(size, (list, tuple, np.ndarray)) or len(size) > 3:
raise RuntimeError('size must have length of 2 or 3')
[RuntimeError('dimensions of size and grain_size are not the same.')
for grains in grain_size if len(size) != len(grains)]
if len(elastic_modulus) != len(poissons_ratio):
raise RuntimeError('length of elastic_modulus and poissons_ratio are \
not the same.')
X_cal, y_cal = make_elastic_FE_strain_delta(elastic_modulus,
poissons_ratio, size,
macro_strain)
n_states = len(elastic_modulus)
basis = DiscreteIndicatorBasis(n_states)
model = MKSRegressionModel(basis=basis)
model.fit(X_cal, y_cal)
X = np.concatenate([make_microstructure(n_samples=sample, size=size,
n_phases=n_states,
grain_size=gs, seed=seed) for gs,
sample in zip(grain_size, n_samples)])
X_ = basis.discretize(X)
index = tuple([None for i in range(len(size) + 1)]) + (slice(None),)
modulus = np.sum(X_ * np.array(elastic_modulus)[index], axis=-1)
y_stress = model.predict(X) * modulus
return X, np.average(y_stress.reshape(np.sum(n_samples), y_stress[0].size),
axis=1)
def test_default_n_components():
from pymks import MKSHomogenizationModel, DiscreteIndicatorBasis
dbasis = DiscreteIndicatorBasis(n_states=2)
model = MKSHomogenizationModel(basis=dbasis)
assert model.n_components == 5
def test_degree_change():
from pymks import MKSHomogenizationModel, DiscreteIndicatorBasis
dbasis = DiscreteIndicatorBasis(n_states=2)
model = MKSHomogenizationModel(basis=dbasis)
model.degree = 4
assert model.degree == 4
def make_elastic_stress_random(n_samples=[10, 10], elastic_modulus=(100, 150),
poissons_ratio=(0.3, 0.3), size=(21, 21),
macro_strain=0.01, grain_size=[(3, 3), (9, 9)],
seed=10, volume_fraction=None,
percent_variance=None):
"""
Generates microstructures and their macroscopic stress values for an
applied macroscopic strain.
Args:
n_samples (int, optional): number of samples
elastic_modulus (tuple, optional): list of elastic moduli for the
different phases.
poissons_ratio (tuple, optional): list of poisson's ratio values for
the phases.
size (tuple, optional): size of the microstructures
macro_strain (tuple, optional): macroscopic strain applied to the
sample.
grain_size (tuple, optional): effective dimensions of grains
seed (int, optional): seed for random number generator
volume_fraction(tuple, optional): specify the volume fraction of
each phase
percent_variance(int, optional): Only used if volume_fraction is
specified. Randomly varies the volume fraction of the
microstructure.
Returns:
array of microstructures with dimensions (n_samples, n_x, ...) and
effective stress values
Example
>>> X, y = make_elastic_stress_random(n_samples=1, elastic_modulus=(1, 1),
... poissons_ratio=(1, 1),
... grain_size=(3, 3), macro_strain=1.0)
>>> assert np.allclose(y, np.ones(y.shape))
>>> X, y = make_elastic_stress_random(n_samples=1, grain_size=(1, 1),
... elastic_modulus=(100, 200),
... size=(2, 2), poissons_ratio=(1, 3),
... macro_strain=1., seed=3)
>>> X_result = np.array([[[1, 1],
... [0, 1]]])
>>> assert np.allclose(X, X_result)
>>> assert float(np.round(y, decimals=5)[0]) == 228.74696
>>> X, y = make_elastic_stress_random(n_samples=1, grain_size=(1, 1, 1),
... elastic_modulus=(100, 200),
... poissons_ratio=(1, 3), seed=3,
... macro_strain=1., size=(2, 2, 2))
>>> X_result = np.array([[[1, 1],
... [0, 0]],
... [[1, 1],
... [0, 0]]])
>>> assert np.allclose(X, X_result)
>>> assert np.round(y[0]).astype(int) == 150
"""
if not isinstance(grain_size[0], (list, tuple, np.ndarray)):
grain_size = (grain_size,)
if not isinstance(n_samples, (list, tuple, np.ndarray)):
n_samples = (n_samples,)
if volume_fraction is None:
volume_fraction = (None,) * len(n_samples)
vf_0 = volume_fraction[0]
if not isinstance(vf_0, (list, tuple, np.ndarray)) and vf_0 is not None:
volume_fraction = (volume_fraction,)
if not isinstance(size, (list, tuple, np.ndarray)) or len(size) > 3:
raise RuntimeError('size must have length of 2 or 3')
[RuntimeError('dimensions of size and grain_size are not the same.')
for grains in grain_size if len(size) != len(grains)]
if vf_0 is not None:
[RuntimeError('dimensions of size and grain_size are not the same.')
for volume_frac in volume_fraction
if len(elastic_modulus) != len(volume_frac)]
if len(elastic_modulus) != len(poissons_ratio):
raise RuntimeError('length of elastic_modulus and poissons_ratio are \
not the same.')
X_cal, y_cal = make_elastic_FE_strain_delta(elastic_modulus,
poissons_ratio, size,
macro_strain)
n_states = len(elastic_modulus)
basis = DiscreteIndicatorBasis(n_states)
model = MKSRegressionModel(basis=basis)
model.fit(X_cal, y_cal)
X = np.concatenate([make_microstructure(n_samples=sample, size=size,
n_phases=n_states,
grain_size=gs, seed=seed,
volume_fraction=vf,
percent_variance=percent_variance)
for vf, gs, sample in zip(volume_fraction,
grain_size, n_samples)])
X_ = basis.discretize(X)
index = tuple([None for i in range(len(size) + 1)]) + (slice(None),)
modulus = np.sum(X_ * np.array(elastic_modulus)[index], axis=-1)
y_stress = model.predict(X) * modulus
return X, np.average(y_stress.reshape(len(y_stress), -1), axis=1)
def make_elastic_stress_random(n_samples=[10, 10],
elastic_modulus=(100, 150),
poissons_ratio=(0.3, 0.3),
size=(21, 21),
macro_strain=0.01,
grain_size=[(3, 3), (9, 9)],
seed=10,
volume_fraction=None,
percent_variance=None):
"""
Generates microstructures and their macroscopic stress values for an
applied macroscopic strain.
Args:
n_samples (int, optional): number of samples
elastic_modulus (tuple, optional): list of elastic moduli for the
different phases.
poissons_ratio (tuple, optional): list of poisson's ratio values for
the phases.
size (tuple, optional): size of the microstructures
macro_strain (tuple, optional): macroscopic strain applied to the
sample.
grain_size (tuple, optional): effective dimensions of grains
seed (int, optional): seed for random number generator
volume_fraction(tuple, optional): specify the volume fraction of
each phase
percent_variance(int, optional): Only used if volume_fraction is
specified. Randomly varies the volume fraction of the
microstructure.
Returns:
array of microstructures with dimensions (n_samples, n_x, ...) and
effective stress values
"""
if not isinstance(grain_size[0], (list, tuple, np.ndarray)):
grain_size = (grain_size, )
if not isinstance(n_samples, (list, tuple, np.ndarray)):
n_samples = (n_samples, )
if volume_fraction is None:
volume_fraction = (None, ) * len(n_samples)
vf_0 = volume_fraction[0]
if not isinstance(vf_0, (list, tuple, np.ndarray)) and vf_0 is not None:
volume_fraction = (volume_fraction, )
np.random.seed(seed)
if not isinstance(size, (list, tuple, np.ndarray)) or len(size) > 3:
raise RuntimeError('size must have length of 2 or 3')
[
RuntimeError('dimensions of size and grain_size are not the same.')
for grains in grain_size if len(size) != len(grains)
]
if vf_0 is not None:
[
RuntimeError('dimensions of size and grain_size are not the same.')
for volume_frac in volume_fraction
if len(elastic_modulus) != len(volume_frac)
]
if len(elastic_modulus) != len(poissons_ratio):
raise RuntimeError('length of elastic_modulus and poissons_ratio are' \
'not the same.')
np.random.seed(seed)
seed = np.random.randint(100, size=(len(volume_fraction), ))
X_cal, y_cal = make_elastic_FE_strain_delta(elastic_modulus,
poissons_ratio, size,
macro_strain)
n_states = len(elastic_modulus)
basis = DiscreteIndicatorBasis(n_states)
model = MKSRegressionModel(basis=basis)
model.fit(X_cal, y_cal)
X = np.concatenate([
make_microstructure(n_samples=sample,
size=size,
n_phases=n_states,
grain_size=gs,
seed=s,
volume_fraction=vf,
percent_variance=percent_variance) for vf, s, gs,
sample in zip(volume_fraction, seed, grain_size, n_samples)
])
X_ = basis.discretize(X)
index = tuple([None for i in range(len(size) + 1)]) + (slice(None), )
modulus = np.sum(X_ * np.array(elastic_modulus)[index], axis=-1)
y_stress = model.predict(X) * modulus
return X, np.average(y_stress.reshape(len(y_stress), -1), axis=1)
