# -*- coding: utf-8 -*-
"""
Kernel generating functions.
AUTHORS:
- THOMAS MCTAVISH (2010-02-05): initial version
- THOMAS MCTAVISH (2011-01-12): Fixed bug where kernels did not normalize with dt.
"""
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# McTavish, T.S. NeuronPy library, version 0.1, http://bitbucket.org/tommctavish/neuronpy
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import numpy
[docs]def gauss_1d(sigma=1., dt=1., limit=.01, normalize=True):
"""
Get a Gaussian distribution that sums to 1 along 1 dimension,
quantized by discrete steps.
"""
tail=[]
x=0.
val=1.
two_times_sigma_squared=2*sigma*sigma
scale_factor = 1./numpy.sqrt(two_times_sigma_squared*numpy.pi)
while val > limit:
val = float(numpy.exp(-(x*x)/two_times_sigma_squared)*scale_factor)
tail.append(val)
x+=dt
k=tail[::-1] # Make a copy of the reversed tail
k.extend(tail[1:]) # Reflect
# Normalize
if normalize:
k = numpy.divide(k,numpy.sum(k)/dt)
return k
[docs]def triangle(dt=.1, normalize=True):
"""
Make a ramp from 0 to 1 back to 0 again by dt.
:param dt: timestep interval. Kernel will be of length 2/dt - 1 with
peak at 1/dt.
:param normalize: If True, the kernel sums to 1. Otherwise, each point
on the ramp is quantized by an integer.
"""
k = numpy.arange(dt, 1, dt)
k = numpy.concatenate((k, numpy.arange(1, 0, -dt)))
# Normalize
if normalize:
k = numpy.divide(k,numpy.sum(k)/dt)
return k
[docs]def rectangle_window(window=0, dt=.1, normalize=True):
"""
Make a rectangle (really a vector) that has a particular length.
:param window: Length of the kernel, in ms. A value of zero (default), will
still make a kernel of len == 1, corresponding to 1 time interval value,
and filtering with such a kernel will yield the input.
.. Note:: A time window of 5 ms, say, will be different depending on the value
of dt. If dt == 1, then the kernel will range from [-2,2] across 5 values.
If dt == 0.1, then the kernel will range from [-2.5, 2.5] across 51 values.
"""
the_len = int(window/dt)
if the_len % 2 != 1:
the_len += 1 # Make sure odd
k = numpy.ones(the_len)
# Normalize
if normalize:
k = numpy.divide(k,float(the_len))
return k