def calc_probability_matrix(trains_a, trains_b, metric, tau, z):
""" Calculates the probability matrix that one spike train from stimulus X
will be classified as spike train from stimulus Y.
:param list trains_a: Spike trains of stimulus A.
:param list trains_b: Spike trains of stimulus B.
:param str metric: Metric to base the classification on. Has to be a key in
:const:`metrics.metrics`.
:param tau: Time scale parameter for the metric.
:type tau: Quantity scalar.
:param float z: Exponent parameter for the classifier.
"""
with warnings.catch_warnings():
warnings.filterwarnings("ignore", "divide by zero")
dist_mat = calc_single_metric(trains_a + trains_b, metric, tau) ** z
dist_mat[sp.diag_indices_from(dist_mat)] = 0.0
assert len(trains_a) == len(trains_b)
l = len(trains_a)
classification_of_a = sp.argmin(sp.vstack((
sp.sum(dist_mat[:l, :l], axis=0) / (l - 1),
sp.sum(dist_mat[l:, :l], axis=0) / l)) ** (1.0 / z), axis=0)
classification_of_b = sp.argmin(sp.vstack((
sp.sum(dist_mat[:l, l:], axis=0) / l,
sp.sum(dist_mat[l:, l:], axis=0) / (l - 1))) ** (1.0 / z), axis=0)
confusion = sp.empty((2, 2))
confusion[0, 0] = sp.sum(classification_of_a == 0)
confusion[1, 0] = sp.sum(classification_of_a == 1)
confusion[0, 1] = sp.sum(classification_of_b == 0)
confusion[1, 1] = sp.sum(classification_of_b == 1)
return confusion / 2.0 / l
def _get_yz(self, L, getcovar=True):
"""
Gets flux and error (y and z) near the line wavelengths, makes
sure everything is aligned.
"""
l = deepcopy(L)
#shift
l.wv -= self.p['shift']
m = (self.Lref.wv >= l.wv.min()) * (self.Lref.wv <= l.wv.max())
y, z = l.interp(self.Lref.wv[m])
#convolve
k = self._get_kernel(self.Lref.wv[m])
#have to make covar before smoothing z
if getcovar:
if self.kernelname == 'Delta':
covar = get_covarmatrix(l.wv, self.Lref.wv[m], l.ef, k, 2)
else:
covar = get_covarmatrix(l.wv, self.Lref.wv[m], l.ef, k,
5 * self.p['width'])
z = sp.sqrt(sp.convolve(z**2, k**2, mode='same'))
y = sp.convolve(y, k, mode='same')
#scale
z *= self.p['scale']
y *= self.p['scale']
if getcovar:
covar *= self.p['scale'] * self.p['scale']
#add reference errors now to simplify the chi2----these don't
#seem to matter much
covar[sp.diag_indices_from(covar)] += self.Lref.ef[m]**2
#trim 10% of data to help with edge effects and shifting the
#data. This number is hard-coded so that the degrees of
#freedom are fixed during the fit.
trim = int(round(0.05 * (self.Lref.wv[m].size)))
z = z[trim:-trim]
y = y[trim:-trim]
if getcovar:
covar = covar[:, trim:-trim]
covar = covar[trim:-trim, :]
#need a mask for reference when calculating chi^2
m2 = (self.Lref.wv >= self.Lref.wv[m][trim]) * (self.Lref.wv <
self.Lref.wv[m][-trim])
if getcovar:
# Note that z**2 (error spectrum) is slightly different
# than the diagonal of covar, because covariance was
# ignored for z
return y, z**2, m2, covar
else:
return y, z**2, m2
def probs(termList=termList):
probs = 1./(1+sp.exp(-1*sum(termList)))
probs[sp.diag_indices_from(probs)]= 0
return(probs)
def summed_dist_matrix(self, vectors, presorted=False):
# This implementation is based on
#
# Houghton, C., & Kreuz, T. (2012). On the efficient calculation of van
# Rossum distances. Network: Computation in Neural Systems, 23(1-2),
# 48-58.
#
# Note that the cited paper contains some errors: In formula (9) the
# left side of the equation should be divided by two and in the last
# sum in this equation it should say `j|v_i >= u_i` instead of
# `j|v_i > u_i`. Also, in equation (11) it should say `j|u_i >= v_i`
# instead of `j|u_i > v_i`.
#
# Given N vectors with n entries on average the run-time complexity is
# O(N^2 * n). O(N^2 + N * n) memory will be needed.
if len(vectors) <= 0:
return sp.zeros((0, 0))
if not presorted:
vectors = [v.copy() for v in vectors]
for v in vectors:
v.sort()
sizes = sp.asarray([v.size for v in vectors])
values = sp.empty((len(vectors), max(1, sizes.max())))
values.fill(sp.nan)
for i, v in enumerate(vectors):
if v.size > 0:
values[i, :v.size] = \
(v / self.kernel_size * pq.dimensionless).simplified
exp_diffs = sp.exp(values[:, :-1] - values[:, 1:])
markage = sp.zeros(values.shape)
for u in xrange(len(vectors)):
markage[u, 0] = 0
for i in xrange(sizes[u] - 1):
markage[u, i + 1] = (markage[u, i] + 1.0) * exp_diffs[u, i]
# Same vector terms
D = sp.empty((len(vectors), len(vectors)))
D[sp.diag_indices_from(D)] = sizes + 2.0 * sp.sum(markage, axis=1)
# Cross vector terms
for u in xrange(D.shape[0]):
all_ks = sp.searchsorted(values[u], values, 'left') - 1
for v in xrange(u):
js = sp.searchsorted(values[v], values[u], 'right') - 1
ks = all_ks[v]
slice_j = sp.s_[sp.searchsorted(js, 0):sizes[u]]
slice_k = sp.s_[sp.searchsorted(ks, 0):sizes[v]]
D[u, v] = sp.sum(
sp.exp(values[v][js[slice_j]] - values[u][slice_j]) *
(1.0 + markage[v][js[slice_j]]))
D[u, v] += sp.sum(
sp.exp(values[u][ks[slice_k]] - values[v][slice_k]) *
(1.0 + markage[u][ks[slice_k]]))
D[v, u] = D[u, v]
if self.normalize:
normalization = self.normalization_factor(self.kernel_size)
else:
normalization = 1.0
return normalization * D
def get_covarmatrix(x, xinterp, z, k, breakwidth):
"""
Calculates the covariance matrix when needed. Assumes both an
interpolation and a smoothing----for now, only linear
interpolation will work (only does one diagonal, but propagates
the error correctly).
"""
isort = sp.searchsorted(x, xinterp)
f = (xinterp - x[isort - 1]) / (x[isort] - x[isort - 1])
z2 = sp.sqrt((f**2) * (z[isort]**2) + ((1 - f)**2) * (z[isort - 1]**2))
#for a delta function
if k.size == 1:
return sp.diag(z2**2)
covar1 = sp.zeros((z2.size, z2.size))
covar2 = sp.zeros((z2.size, z2.size))
#the part from interpolation---searchsorted has thrown out the
#first index, the last index won't be selected because of the slice
covar1[sp.diag_indices_from(covar1)] = z2**2
# print sp.shape(f), sp.shape(z[isort.min():isort.max()-1]),sp.shape(z)
diag1 = f[0:-1] * (1 - f[0:-1]) * (z[isort.min():isort.max()]**2)
#linear interpolation only has one diagonal
covar1 += sp.diag(diag1, 1)
covar1 += sp.diag(diag1, -1)
covar1 = sp.matrix(covar1)
#the part from convolution
#make kernel match size of input
if k.size == z2.size - 2:
k = sp.r_[0, k, 0]
elif k.size == z2.size - 1:
k = sp.r_[0, k]
#force it to wrap around
cent = k.size // 2
k = sp.r_[k[cent::], k[0:cent]]
#for matrix equation, see Gardner 2003, Uncertainties in
#Interpolated Spectral Data; equation 6
# seems like there is a better way than a double loop....
for i in range(z2.size):
for n in range(int(breakwidth)):
#can shorten the loop because most of the matrix is
#zero:the idea is that kernels that are far apart
#should have zero overlap. If k2 gets shifted
#relative to k1 more than 5x the kernel width, assume
#no overlap
j = i + n
if j > z2.size - 1: j = z2.size - 1
k1 = sp.matrix(sp.roll(k, i))
k2 = sp.matrix(sp.roll(k, j))
trim1 = cent + i
if trim1 <= k1.size:
k1[:, trim1::] = 0
else:
k1[:, 0:trim1 - k1.size] = 0
trim2 = cent + j
if trim2 <= k2.size:
k2[:, trim2::] = 0
else:
k2[:, 0:(trim2 - k2.size)] = 0
covar2[i, j] = k1 * covar1 * k2.T
#matrix is symmetric
covar2 += covar2.T
covar2[sp.diag_indices_from(covar2)] /= 2.
return covar2
def summed_dist_matrix(self, vectors, presorted=False):
# This implementation is based on
#
# Houghton, C., & Kreuz, T. (2012). On the efficient calculation of van
# Rossum distances. Network: Computation in Neural Systems, 23(1-2),
# 48-58.
#
# Note that the cited paper contains some errors: In formula (9) the
# left side of the equation should be divided by two and in the last
# sum in this equation it should say `j|v_i >= u_i` instead of
# `j|v_i > u_i`. Also, in equation (11) it should say `j|u_i >= v_i`
# instead of `j|u_i > v_i`.
#
# Given N vectors with n entries on average the run-time complexity is
# O(N^2 * n). O(N^2 + N * n) memory will be needed.
if len(vectors) <= 0:
return sp.zeros((0, 0))
if not presorted:
vectors = [v.copy() for v in vectors]
for v in vectors:
v.sort()
sizes = sp.asarray([v.size for v in vectors])
values = sp.empty((len(vectors), max(1, sizes.max())))
values.fill(sp.nan)
for i, v in enumerate(vectors):
if v.size > 0:
values[i, :v.size] = \
(v / self.kernel_size * pq.dimensionless).simplified
exp_diffs = sp.exp(values[:, :-1] - values[:, 1:])
markage = sp.zeros(values.shape)
for u in xrange(len(vectors)):
markage[u, 0] = 0
for i in xrange(sizes[u] - 1):
markage[u, i + 1] = (markage[u, i] + 1.0) * exp_diffs[u, i]
# Same vector terms
D = sp.empty((len(vectors), len(vectors)))
D[sp.diag_indices_from(D)] = sizes + 2.0 * sp.sum(markage, axis=1)
# Cross vector terms
for u in xrange(D.shape[0]):
all_ks = sp.searchsorted(values[u], values, 'left') - 1
for v in xrange(u):
js = sp.searchsorted(values[v], values[u], 'right') - 1
ks = all_ks[v]
slice_j = sp.s_[sp.searchsorted(js, 0):sizes[u]]
slice_k = sp.s_[sp.searchsorted(ks, 0):sizes[v]]
D[u, v] = sp.sum(
sp.exp(values[v][js[slice_j]] - values[u][slice_j]) *
(1.0 + markage[v][js[slice_j]]))
D[u, v] += sp.sum(
sp.exp(values[u][ks[slice_k]] - values[v][slice_k]) *
(1.0 + markage[u][ks[slice_k]]))
D[v, u] = D[u, v]
if self.normalize:
normalization = self.normalization_factor(self.kernel_size)
else:
normalization = 1.0
return normalization * D
