def simplex_grid(length, subdivisions, using=None, inplace=False):
"""Returns a generator over distributions, determined by a grid.
The grid is "triangular" in Euclidean space.
The total number of points on the grid is::
(subdivisions + length - 1)! / (subdivisions)! / (length-1)!
and is equivalent to the total number of ways ``n`` indistinguishable items
can be placed into ``k`` distinguishable slots, where n=`subdivisions` and
k=`length`.
Parameters
----------
length : int
The number of elements in each distribution. The dimensionality
of the simplex is length-1.
subdivisions : int
The number of subdivisions for the interval [0, 1]. Each component
will take on values at the boundaries of the subdivisions. For example,
one subdivision means each component can take the values 0 or 1 only.
Two subdivisions corresponds to :math:`[[0, 1/2], [1/2, 1]]` and thus,
each component can take the values 0, 1/2, or 1. A common use case is
to exponentially increase the number of subdivisions at each level.
That is, subdivisions would be: 2**0, 2**1, 2**2, 2**3, ...
using : None, callable, or distribution
If None, then scalar distributions on integers are yielded. If `using`
is a distribution, then each yielded distribution is a copy of `using`
with its pmf set appropriately. For other callables, a tuple of the
pmf is passed to the callable and then yielded.
inplace : bool
If `True`, then each yielded distribution is the same Python object,
but with a new probability mass function. If `False`, then each yielded
distribution is a unique Python object and can be safely stored for
other calculations after the generator has finished. This keyword has
an effect only when `using` is None or some distribution.
Examples
--------
>>> list(dit.simplex_grid(2, 2, using=tuple))
[(0.0, 1.0), (0.25, 0.75), (0.5, 0.5), (0.75, 0.25), (1.0, 0.0)]
"""
from dit.math.combinatorics import slots
if subdivisions < 1:
raise ditException('`subdivisions` must be greater than or equal to 1')
elif length < 1:
raise ditException('`length` must be greater than or equal to 1')
gen = slots(int(subdivisions), int(length), normalized=True)
if using is None:
using = random_scalar_distribution(length)
if using is tuple:
for pmf in gen:
yield pmf
elif not isinstance(using, BaseDistribution):
for pmf in gen:
yield using(pmf)
else:
if length != len(using.pmf):
raise Exception('`length` must match the length of pmf')
if inplace:
d = using
for pmf in gen:
d.pmf[:] = pmf
yield d
else:
for pmf in gen:
d = using.copy()
d.pmf[:] = pmf
yield d
def test_slots1():
x = list(slots(3, 2))
x_ = [(0, 3), (1, 2), (2, 1), (3, 0)]
assert x == x_
def test_slots2():
x = np.asarray(list(slots(3, 2, normalized=True)))
x_ = np.asarray([(0, 1), (1 / 3, 2 / 3), (2 / 3, 1 / 3), (1, 0)])
assert np.allclose(x, x_)
def test_slots2():
x = np.asarray(list(slots(3, 2, normalized=True)))
x_ = np.asarray([(0, 1), (1/3, 2/3), (2/3, 1/3), (1, 0)])
assert np.allclose(x, x_)
def test_slots1():
x = list(slots(3, 2))
x_ = [(0, 3), (1, 2), (2, 1), (3, 0)]
assert x == x_
def test_slots1():
x = list(slots(3, 2))
x_ = [(0, 3), (1, 2), (2, 1), (3, 0)]
assert_equal(x, x_)
def simplex_grid(length, subdivisions, using=None, inplace=False):
"""Returns a generator over distributions, determined by a grid.
The grid is "triangular" in Euclidean space.
The total number of points on the grid is::
(subdivisions + length - 1)! / (subdivisions)! / (length-1)!
and is equivalent to the total number of ways ``n`` indistinguishable items
can be placed into ``k`` distinguishable slots, where n=`subdivisions` and
k=`length`.
Parameters
----------
length : int
The number of elements in each distribution. The dimensionality
of the simplex is length-1.
subdivisions : int
The number of subdivisions for the interval [0, 1]. Each component
will take on values at the boundaries of the subdivisions. For example,
one subdivision means each component can take the values 0 or 1 only.
Two subdivisions corresponds to :math:`[[0, 1/2], [1/2, 1]]` and thus,
each component can take the values 0, 1/2, or 1. A common use case is
to exponentially increase the number of subdivisions at each level.
That is, subdivisions would be: 2**0, 2**1, 2**2, 2**3, ...
using : None, callable, or distribution
If None, then scalar distributions on integers are yielded. If `using`
is a distribution, then each yielded distribution is a copy of `using`
with its pmf set appropriately. For other callables, a tuple of the
pmf is passed to the callable and then yielded.
inplace : bool
If `True`, then each yielded distribution is the same Python object,
but with a new probability mass function. If `False`, then each yielded
distribution is a unique Python object and can be safely stored for
other calculations after the generator has finished. This keyword has
an effect only when `using` is None or some distribution.
Examples
--------
>>> list(dit.simplex_grid(2, 2, using=tuple))
[(0.0, 1.0), (0.25, 0.75), (0.5, 0.5), (0.75, 0.25), (1.0, 0.0)]
"""
from dit.math.combinatorics import slots
if subdivisions < 1:
raise ditException('`subdivisions` must be greater than or equal to 1')
elif length < 1:
raise ditException('`length` must be greater than or equal to 1')
gen = slots(int(subdivisions), int(length), normalized=True)
if using is None:
using = random_scalar_distribution(length)
if using is tuple:
for pmf in gen:
yield pmf
elif not isinstance(using, BaseDistribution):
for pmf in gen:
yield using(pmf)
else:
if length != len(using.pmf):
raise Exception('`length` must match the length of pmf')
if inplace:
d = using
for pmf in gen:
d.pmf[:] = pmf
yield d
else:
for pmf in gen:
d = using.copy()
d.pmf[:] = pmf
yield d
def test_slots1():
x = list(slots(3, 2))
x_ = [(0, 3), (1, 2), (2, 1), (3, 0)]
assert_equal(x, x_)