test_alpham_Taylor.py
73851d6ac128master

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: 2018-09-28 14:14:11


			''' 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()