Source code for pyNN.space

# encoding: utf-8
"""
Tools for performing spatial/topographical calculations.

Classes:

  Space           - representation of a Cartesian space for use in calculating
                    distances

  Line            - represents a structure with neurons distributed evenly on a
                    straight line.
  Grid2D          - represents a structure with neurons distributed on a 2D grid.
  Grid3D          - represents a structure with neurons distributed on a 3D grid.
  RandomStructure - represents a structure with neurons distributed randomly
                    within a given volume.

  Cuboid          - representation of a cuboidal volume, for use with RandomStructure.
  Sphere          - representation of a spherical volume, for use with RandomStructure.

:copyright: Copyright 2006-2020 by the PyNN team, see AUTHORS.
:license: CeCILL, see LICENSE for details.
"""

# There must be some Python package out there that provides most of this stuff.
# Distance computations are provided by scipy.spatial, but scipy is a fairly heavy dependency.

try:
    reduce
except NameError:
    from functools import reduce
import numpy
import math
from operator import and_
from pyNN.random import NumpyRNG
from pyNN import descriptions
import logging

logger = logging.getLogger("PyNN")


def distance(src, tgt, mask=None, scale_factor=1.0, offset=0.0,
             periodic_boundaries=None):  # may need to add an offset parameter
    """
    Return the Euclidian distance between two cells.
    `mask` allows only certain dimensions to be considered, e.g.::
      * to ignore the z-dimension, use `mask=array([0,1])`
      * to ignore y, `mask=array([0,2])`
      * to just consider z-distance, `mask=array([2])`
    `scale_factor` allows for different units in the pre- and post- position
    (the post-synaptic position is multipied by this quantity).
    """
    d = src.position - scale_factor * (tgt.position + offset)

    if periodic_boundaries is not None:
        d = numpy.minimum(abs(d), periodic_boundaries - abs(d))
    if mask is not None:
        d = d[mask]
    return numpy.sqrt(numpy.dot(d, d))


[docs]class Space(object): """ Class representing a space within distances can be calculated. The space is Cartesian, may be 1-, 2- or 3-dimensional, and may have periodic boundaries in any of the dimensions. Arguments: axes: if not supplied, then the 3D distance is calculated. If supplied, axes should be a string containing the axes to be used, e.g. 'x', or 'yz'. axes='xyz' is the same as axes=None. scale_factor: it may be that the pre and post populations use different units for position, e.g. degrees and ┬Ám. In this case, `scale_factor` can be specified, which is applied to the positions in the post-synaptic population. offset: if the origins of the coordinate systems of the pre- and post- synaptic populations are different, `offset` can be used to adjust for this difference. The offset is applied before any scaling. periodic_boundaries: either `None`, or a tuple giving the boundaries for each dimension, e.g. `((x_min, x_max), None, (z_min, z_max))`. """ AXES = {'x': [0], 'y': [1], 'z': [2], 'xy': [0, 1], 'yz': [1, 2], 'xz': [0, 2], 'xyz': range(3), None: range(3)} def __init__(self, axes=None, scale_factor=1.0, offset=0.0, periodic_boundaries=None): """ """ self.periodic_boundaries = periodic_boundaries self.axes = numpy.array(Space.AXES[axes]) self.scale_factor = scale_factor self.offset = offset
[docs] def distances(self, A, B, expand=False): """ Calculate the distance matrix between two sets of coordinates, given the topology of the current space. From http://projects.scipy.org/pipermail/numpy-discussion/2007-April/027203.html """ #logger.debug("Calculating distance between A (shape=%s) and B (shape=%s)" % (A.shape, B.shape)) assert A.ndim <= 2 assert B.ndim <= 2 assert A.shape[-1] == 3 if len(A.shape) == 1: A = A.reshape(1, 3) if len(B.shape) == 1: B = B.reshape(1, 3) B = self.scale_factor * (B + self.offset) d = numpy.zeros((len(self.axes), A.shape[0], B.shape[0]), dtype=A.dtype) for i, axis in enumerate(self.axes): diff2 = A[:, None, axis] - B[:, axis] if self.periodic_boundaries is not None: boundaries = self.periodic_boundaries[axis] if boundaries is not None: range = boundaries[1] - boundaries[0] ad2 = abs(diff2) diff2 = numpy.minimum(ad2, range - ad2) diff2 **= 2 d[i] = diff2 if not expand: d = numpy.sum(d, 0) numpy.sqrt(d, d) return d.flatten()
[docs] def distance_generator(self, f, g): def distance_map(i, j): shape = [] if isinstance(i, numpy.ndarray) and i.ndim == 2: i = i[:, 0] shape.append(i.size) if isinstance(j, numpy.ndarray) and j.ndim == 2: j = j[0, :] shape.append(j.size) d = self.distances(f(i), g(j)) if shape: return d.reshape(shape) else: return d return distance_map
class BaseStructure(object): def __repr__(self): return "%s(%s)" % (self.__class__.__name__, ", ".join("%s=%r" % item for item in self.get_parameters().items())) def __eq__(self, other): return reduce(and_, (getattr(self, attr) == getattr(other, attr) for attr in self.parameter_names)) def get_parameters(self): """Return a dict containing the parameters of the :class:`Structure`.""" P = {} for name in self.parameter_names: P[name] = getattr(self, name) return P def describe(self, template='structure_default.txt', engine='default'): """ Returns a human-readable description of the network structure. The output may be customized by specifying a different template togther with an associated template engine (see ``pyNN.descriptions``). If template is None, then a dictionary containing the template context will be returned. """ context = {'name': self.__class__.__name__, 'parameters': self.get_parameters()} return descriptions.render(engine, template, context) def generate_positions(self, n): """ Calculate and return the positions of `n` neurons positioned according to this structure. """ raise NotImplementedError
[docs]class Line(BaseStructure): """ Represents a structure with neurons distributed evenly on a straight line. Arguments: `dx`: distance between points in the line. `y`, `z`,: y- and z-coordinates of all points in the line. `x0`: x-coordinate of the first point in the line. """ parameter_names = ("dx", "x0", "y", "z") def __init__(self, dx=1.0, x0=0.0, y=0.0, z=0.0): self.dx = dx self.x0 = x0 self.y = y self.z = z
[docs] def generate_positions(self, n): x = self.dx * numpy.arange(n, dtype=float) + self.x0 y = numpy.zeros(n) + self.y z = numpy.zeros(n) + self.z return numpy.array((x, y, z))
generate_positions.__doc__ = BaseStructure.generate_positions.__doc__
[docs]class Grid2D(BaseStructure): """ Represents a structure with neurons distributed on a 2D grid. Arguments: `dx`, `dy`: distances between points in the x, y directions. `x0`, `y0`: coordinates of the starting corner of the grid. `z`: the z-coordinate of all points in the grid. `aspect_ratio`: ratio of the number of grid points per side (not the ratio of the side lengths, unless ``dx == dy``) `fill_order`: may be 'sequential' or 'random' """ parameter_names = ("aspect_ratio", "dx", "dy", "x0", "y0", "z", "fill_order") def __init__(self, aspect_ratio=1.0, dx=1.0, dy=1.0, x0=0.0, y0=0.0, z=0, fill_order="sequential", rng=None): self.aspect_ratio = aspect_ratio assert fill_order in ('sequential', 'random') self.fill_order = fill_order self.rng = rng self.dx = dx; self.dy = dy; self.x0 = x0; self.y0 = y0; self.z = z
[docs] def calculate_size(self, n): """docstring goes here""" nx = math.sqrt(n * self.aspect_ratio) if n % nx != 0: raise Exception("Invalid size: n=%g, nx=%d" % (n, nx)) nx = int(round(nx)) ny = n // nx return nx, ny
[docs] def generate_positions(self, n): nx, ny = self.calculate_size(n) x, y, z = numpy.indices((nx, ny, 1), dtype=float) x = self.x0 + self.dx * x.flatten() y = self.y0 + self.dy * y.flatten() z = self.z + z.flatten() positions = numpy.array((x, y, z)) # use column_stack, if we decide to switch from (3,n) to (n,3) if self.fill_order == 'sequential': return positions else: # random if self.rng is None: self.rng = NumpyRNG() return self.rng.permutation(positions.T).T
generate_positions.__doc__ = BaseStructure.generate_positions.__doc__
[docs]class Grid3D(BaseStructure): """ Represents a structure with neurons distributed on a 3D grid. Arguments: `dx`, `dy`, `dz`: distances between points in the x, y, z directions. `x0`, `y0`. `z0`: coordinates of the starting corner of the grid. `aspect_ratioXY`, `aspect_ratioXZ`: ratios of the number of grid points per side (not the ratio of the side lengths, unless ``dx == dy == dz``) `fill_order`: may be 'sequential' or 'random'. If `fill_order` is 'sequential', the z-index will be filled first, then y then x, i.e. the first cell will be at (0,0,0) (given default values for the other arguments), the second at (0,0,1), etc. """ parameter_names = ("aspect_ratios", "dx", "dy", "dz", "x0", "y0", "z0", "fill_order") def __init__(self, aspect_ratioXY=1.0, aspect_ratioXZ=1.0, dx=1.0, dy=1.0, dz=1.0, x0=0.0, y0=0.0, z0=0, fill_order="sequential", rng=None): self.aspect_ratios = (aspect_ratioXY, aspect_ratioXZ) assert fill_order in ('sequential', 'random') self.fill_order = fill_order self.rng = rng self.dx = dx; self.dy = dy; self.dz = dz self.x0 = x0; self.y0 = y0; self.z0 = z0
[docs] def calculate_size(self, n): """docstring goes here""" a, b = self.aspect_ratios nx = int(round(math.pow(n * a * b, 1 / 3.0))) ny = int(round(nx / a)) nz = int(round(nx / b)) assert nx * ny * nz == n, str((nx, ny, nz, nx * ny * nz, n, a, b)) return nx, ny, nz
[docs] def generate_positions(self, n): nx, ny, nz = self.calculate_size(n) x, y, z = numpy.indices((nx, ny, nz), dtype=float) x = self.x0 + self.dx * x.flatten() y = self.y0 + self.dy * y.flatten() z = self.z0 + self.dz * z.flatten() positions = numpy.array((x, y, z)) if self.fill_order == 'sequential': return positions else: if self.rng is None: self.rng = NumpyRNG() return self.rng.permutation(positions.T).T
generate_positions.__doc__ = BaseStructure.generate_positions.__doc__
class Shape(object): pass
[docs]class Cuboid(Shape): """ Represents a cuboidal volume within which neurons may be distributed. Arguments: height: extent in y direction width: extent in x direction depth: extent in z direction """ def __init__(self, width, height, depth): self.height = height self.width = width self.depth = depth def __repr__(self): return "Cuboid(width=%r, height=%r, depth=%r)" % (self.width, self.height, self.depth)
[docs] def sample(self, n, rng): """Return `n` points distributed randomly with uniform density within the cuboid.""" return 0.5 * rng.uniform(-1, 1, size=(n, 3)) * (self.width, self.height, self.depth)
[docs]class Sphere(Shape): """ Represents a spherical volume within which neurons may be distributed. """ def __init__(self, radius): Shape.__init__(self) self.radius = radius def __repr__(self): return "Sphere(radius=%r)" % self.radius
[docs] def sample(self, n, rng): """Return `n` points distributed randomly with uniform density within the sphere.""" # this implementation is wasteful, as it throws away a lot of numbers, # but simple. More efficient implementations welcome. positions = numpy.empty((n, 3)) i = 0 while i < n: candidate = rng.uniform(-1, 1, size=(1, 3)) if (candidate**2).sum() < 1: positions[i] = candidate i += 1 return self.radius * positions
[docs]class RandomStructure(BaseStructure): """ Represents a structure with neurons distributed randomly within a given volume. Arguments: `boundary` - a subclass of :class:`Shape`. `origin` - the coordinates (x,y,z) of the centre of the volume. """ parameter_names = ('boundary', 'origin', 'rng') def __init__(self, boundary, origin=(0.0, 0.0, 0.0), rng=None): assert isinstance(boundary, Shape) assert len(origin) == 3 self.boundary = boundary self.origin = origin self.rng = rng or NumpyRNG()
[docs] def generate_positions(self, n): return (numpy.array(self.origin) + self.boundary.sample(n, self.rng)).T
generate_positions.__doc__ = BaseStructure.generate_positions.__doc__
# what about rotations?