"""Generators to create vectors with specific properties."""
import numpy as np
[docs]def AxisAlignedVectors(d):
"""Generator for axis aligned vectors.
Can yield at most *d* vectors.
Note that while axis-aligned vectors can be useful for debugging,
they will not work well with most binding methods for Semantic Pointers.
Parameters
----------
d : int
Dimensionality of returned vectors.
Examples
--------
>>> for p in nengo_spa.vector_generation.AxisAlignedVectors(4):
... print(p)
[1. 0. 0. 0.]
[0. 1. 0. 0.]
[0. 0. 1. 0.]
[0. 0. 0. 1.]
"""
for v in np.eye(d):
yield v
[docs]class UnitLengthVectors:
"""Generator for uniformly distributed unit-length vectors.
Parameters
----------
d : int
Dimensionality of returned vectors.
rng : numpy.random.RandomState, optional
The random number generator to use to create new vectors.
"""
def __init__(self, d, rng=None):
if rng is None:
rng = np.random.RandomState()
self.d = d
self.rng = rng
def __iter__(self):
return self
def __next__(self):
v = self.rng.randn(self.d)
v /= np.linalg.norm(v)
return v
def next(self):
return self.__next__()
[docs]class UnitaryVectors:
"""Generator for unitary vectors (given some binding method).
Parameters
----------
d : int
Dimensionality of returned vectors.
algebra : AbstractAlgebra
Algebra that defines what vectors are unitary.
rng : numpy.random.RandomState, optional
The random number generator to use to create new vectors.
"""
def __init__(self, d, algebra, rng=None):
if rng is None:
rng = np.random.RandomState()
self.d = d
self.algebra = algebra
self.rng = rng
def __iter__(self):
return self
def __next__(self):
return self.algebra.make_unitary(self.rng.randn(self.d))
def next(self):
return self.__next__()
[docs]class OrthonormalVectors:
"""Generator for random orthonormal vectors.
Parameters
----------
d : int
Dimensionality of returned vectors.
rng : numpy.random.RandomState, optional
The random number generator to use to create new vectors.
"""
def __init__(self, d, rng=None):
if rng is None:
rng = np.random.RandomState()
self.d = d
self.rng = rng
self.vectors = []
def __iter__(self):
return self
def __next__(self):
v = self.rng.randn(self.d)
i = len(self.vectors)
if i >= self.d:
raise StopIteration()
elif i > 0:
vectors = np.asarray(self.vectors)
y = -np.dot(vectors[:, i:], v[i:])
A = vectors[:i, :i]
v[:i] = np.linalg.solve(A, y)
v /= np.linalg.norm(v)
self.vectors.append(v)
return v
def next(self):
return self.__next__()
[docs]class ExpectedUnitLengthVectors:
r"""Generator for vectors with expected unit-length.
The vectors will be uniformly distributed with an expected norm
of 1, but each specific pointer may have a length different than 1.
Specifically each vector component will be normal distributed with mean 0
and standard deviation :math:`1/\sqrt{d}`.
Parameters
----------
d : int
Dimensionality of returned vectors.
rng : numpy.random.RandomState, optional
The random number generator to use to create new vectors.
"""
def __init__(self, d, rng=None):
if rng is None:
rng = np.random.RandomState()
self.d = d
self.rng = rng
def __iter__(self):
return self
def __next__(self):
return self.rng.randn(self.d) / np.sqrt(self.d)
def next(self):
return self.__next__()
