def list_derivative(f, x, n, o=3, p=5):
"""
Returns the nth derivative of f with respect to x, where zip(x,f) are
datapoints, using curve-fit polynomials of order o to p points.
"""
assert p % 2 == 1 # should be odd imo
assert len(f) >= p # won't work otherwise
derivative = []
for i in xrange(len(f)):
start = i - (p - 1) / 2
if start < 0:
start = 0
end = start + p
if end >= len(f):
start = -1 - p
end = -1
spline = polyfit(x[start:end], f[start:end], o)
derivative.append(polyval(polyder(spline, n), x[i]))
print("diff in list lengths: " + str(len(f) - len(derivative)))
return array(derivative)
def analyze_olfaction_covariance(covariance, receptors):
''' Covariance: n x n covariance matrix.
Positions: list of n positions '''
positions = [pose.get_2d_position() for pose, sens in receptors] #@UnusedVariable
positions = array(positions).transpose().squeeze()
require_shape(square_shape(), covariance)
n = covariance.shape[0]
require_shape((2, n), positions)
distances = create_distance_matrix(positions)
correlation = cov2corr(covariance)
flat_distances = distances.reshape(n * n)
flat_correlation = correlation.reshape(n * n)
# let's fit a polynomial
deg = 4
poly = polyfit(flat_distances, flat_correlation, deg=deg)
knots = linspace(min(flat_distances), max(flat_distances), 2000)
poly_int = polyval(poly, knots)
poly_fder = polyder(poly)
fder = polyval(poly_fder, distances)
Ttheta = create_olfaction_Ttheta(positions, fder)
Tx, Ty = create_olfaction_Txy(positions, fder, distances)
report = Node('olfaction-theory')
report.data('flat_distances', flat_distances)
report.data('flat_correlation', flat_correlation)
with report.data_file('dist_vs_corr', 'image/png') as filename:
pylab.figure()
pylab.plot(flat_distances, flat_correlation, '.')
pylab.plot(knots, poly_int, 'r-')
pylab.xlabel('distance')
pylab.ylabel('correlation')
pylab.title('Correlation vs distance')
pylab.legend(['data', 'interpolation deg = %s' % deg])
pylab.savefig(filename)
pylab.close()
with report.data('fder', fder).data_file('fder', 'image/png') as filename:
pylab.figure()
pylab.plot(knots, polyval(poly_fder, knots), 'r-')
pylab.title('f der')
pylab.savefig(filename)
pylab.close()
report.data('distances', distances)
report.data('correlation', correlation)
report.data('covariance', covariance)
report.data('f', polyval(poly, distances))
f = report.figure(id='cor-vs-distnace', caption='Estimated kernels',
shape=(3, 3))
f.sub('dist_vs_corr')
f.sub('fder')
f.sub('f', display='scale')
f.sub('distances', display='scale')
f.sub('correlation', display='posneg')
f.sub('covariance', display='posneg')
T = numpy.zeros(shape=(3, Tx.shape[0], Tx.shape[1]))
T[0, :, :] = Tx
T[1, :, :] = Ty
T[2, :, :] = Ttheta
T_report = create_report_figure_tensors(T, report_id='tensors',
caption="Predicted learned tensors")
report.add_child(T_report)
return report
