test_alpham_Taylor.py
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	#!/usr/bin/env python
	# -- coding: utf-8 --
	# @Author: Theo Lemaire
	# @Date: 2017-03-21 11:38:56
	# @Email: theo.lemaire@epfl.ch
	# @Last Modified by: Theo Lemaire
	# @Last Modified time: 2017-03-29 19:12:27


	""" Taylor expansions of the alpha_m function around different potential values. """

	import numpy as np
	from scipy.special import factorial
	import matplotlib.pyplot as plt
	from utils import bilinearExp

	# Vm vector
	nVm = 100
	Vm = np.linspace(-80.0, 50.0, nVm) # mV

	# alpha_m vector
	am_params = (-43.2, -0.32, 0.25)
	alpham = bilinearExp(Vm, am_params, 0)

	# alpha_m Taylor expansion
	npoints = 10
	norder = 4
	Vm0 = np.linspace(-80.0, 50.0, npoints) # mV
	Vmdiff = Vm - np.tile(Vm0, (nVm, 1)).transpose()
	Talpham = np.empty((npoints, nVm))
	for i in range(npoints):
	T = np.zeros(nVm)
	for j in range(norder + 1):
	T[:] += bilinearExp(Vm0[i], am_params, j) * Vmdiff[i, :]**j / factorial(j)
	Talpham[i, :] = T

	# Plot standard alpha_m vs. Taylor reconstruction around Vm0
	_, ax = plt.subplots(figsize=(22, 10))
	ax.set_xlabel('$V_m\ [mV]$', fontsize=20)
	ax.set_ylabel('$[ms^{-1}]$', fontsize=20)
	ax.plot(Vm, alpham, linewidth=2, label='$\\alpha_m$')
	for i in range(npoints):
	ax.plot(Vm, Talpham[i, :], linewidth=2, label='$T_{}\\alpha_m({:.1f})$'.format(norder, Vm0[i]))
	ax.legend(fontsize=20)

	plt.show()