def point_sample(comp_count, pdof=10):
"""
Sample 'pdof * (sum(comp_count) - len(comp_count))' points in
composition space for the sublattice configuration specified
by 'comp_count'. Points are sampled quasi-randomly from a Halton sequence.
A Halton sequence is like a uniform random distribution, but the
result will always be the same for a given 'comp_count' and 'pdof'.
Note: For systems with only one component, only one point will be
returned, regardless of 'pdof'. This is because the degrees of freedom
are zero for that case.
Parameters
----------
comp_count : list
Number of components in each sublattice.
pdof : int
Number of points to sample per degree of freedom.
Returns
-------
ndarray of generated points satisfying the mass balance.
Examples
--------
>>> comps = [8,1] # 8 components in sublattice 1; only 1 in sublattice 2
>>> pts = point_sample(comps, pdof=20) # 7 d.o.f, returns a 140x7 ndarray
"""
# Generate Halton sequence with appropriate dimensions and size
pts = halton(sum(comp_count),
pdof * (sum(comp_count) - len(comp_count)),
scramble=True)
# Convert low-discrepancy sequence to normalized exponential
# This will be uniformly distributed over the simplices
pts = -np.log(pts)
cur_idx = 0
for ctx in comp_count:
end_idx = cur_idx + ctx
pts[:, cur_idx:end_idx] /= pts[:, cur_idx:end_idx].sum(axis=1)[:, None]
cur_idx = end_idx
if len(pts) == 0:
pts = np.atleast_2d([1] * len(comp_count))
return pts
def point_sample(comp_count, pdof=10):
"""
Sample 'pdof * (sum(comp_count) - len(comp_count))' points in
composition space for the sublattice configuration specified
by 'comp_count'. Points are sampled quasi-randomly from a Halton sequence.
A Halton sequence is like a uniform random distribution, but the
result will always be the same for a given 'comp_count' and 'pdof'.
Note: For systems with only one component, only one point will be
returned, regardless of 'pdof'. This is because the degrees of freedom
are zero for that case.
Parameters
----------
comp_count : list
Number of components in each sublattice.
pdof : int
Number of points to sample per degree of freedom.
Returns
-------
ndarray of generated points satisfying the mass balance.
Examples
--------
>>> comps = [8,1] # 8 components in sublattice 1; only 1 in sublattice 2
>>> pts = point_sample(comps, pdof=20) # 7 d.o.f, returns a 140x7 ndarray
"""
# Generate Halton sequence with appropriate dimensions and size
pts = halton(sum(comp_count),
pdof * (sum(comp_count) - len(comp_count)), scramble=True)
# Convert low-discrepancy sequence to normalized exponential
# This will be uniformly distributed over the simplices
pts = -np.log(pts)
cur_idx = 0
for ctx in comp_count:
end_idx = cur_idx + ctx
pts[:, cur_idx:end_idx] /= pts[:, cur_idx:end_idx].sum(axis=1)[:, None]
cur_idx = end_idx
if len(pts) == 0:
pts = np.atleast_2d([1] * len(comp_count))
return pts
def time_halton(dim, pts):
halton(dim, pts)
def time_halton(dim, pts):
halton(dim, pts)