# in a pylab environment
# >> execfile('demo.py')

import TypeX

ion()
figure()

I = 0.0
dt = 0.5

# plot nullclines

# v nullcline
null_v = lambda v,I: v - (v**3)/3 + I
v = arange(-3.0,3.0,0.1)

# w nullcline

Params = {'a': 1.25, 
          'tau': 15.6}

null_w = lambda v,I: Params['a']*(v+0.7)

subplot(211)
# non-changing plot
plot(v,null_w(v,I),'g:',lw=2,label='dw/dt=0')


axis([-2.5,2.5,-2.0,3.0])


# initial v,w
vw = (0.0,0.0)
vhist = [0.0]
whist = [0.0]
thist = [0.0]

# v,w at next time step
def iterate(vw,I):
    global Params,dt
    
    v = vw[0]
    w = vw[1]
    v_next = v + TypeX.dudt(v,w, I)*dt
    w_next = w + TypeX.dwdt(v, w, Params)*dt

    return (v_next,w_next)


l1, = plot(v,null_v(v,I),'r:',lw=2,label='dv/dt=0',scalex=False,scaley=False)
l2, = plot([vw[0]],[vw[1]],'ko',lw=2,scalex=False,scaley=False,label='v,w')

tex1 = figtext(0.5,0.8,'I=%.2f' % I,size=26)

legend()

l4, = plot(vhist,whist,'k-',lw=1,alpha=0.5,scalex=False,scaley=False)

xlabel('v')
ylabel('w')

subplot(212)

l3, = plot(thist,vhist,'b-',scalex=False,scaley=False,lw=2)

xlabel('t [ms]')
ylabel('v')

axis([0.0,200.0,-2.0,2.0])


for I in [0.0]*100+list(arange(0.0,0.5,0.01))+[0.5]*200:
    vw = iterate(vw,I)
    vhist.append(vw[0])
    whist.append(vw[1])
    thist.append(thist[-1]+dt)
    
    l2.set_data([vw[0]],[vw[1]])

    l4.set_data(vhist,whist)

    # recalc nullcline

    l1.set_ydata(null_v(v,I))

    tex1.set_text('I=%.2f' % I)

    l3.set_data(thist,vhist)

    draw()