import nef
net = nef.Network('Recurrent Test 1')
net.make('A', neurons=1000, dimensions=1)
def feedback(x):
    return x[0]+1
net.connect('A', 'A', func=feedback, pstc=0.1)
net.add_to_nengo()
net.view()

import nef
net = nef.Network('Recurrent Test 1')
net.make('A', neurons=100, dimensions=1)
def feedback(x):
    return -x[0]
net.connect('A', 'A', func=feedback)
net.add_to_nengo()
net.view()

import nef
net = nef.Network('Recurrent Test 1')
net.make('A', neurons=100, dimensions=1)
def feedback(x):
    return -x[0]
net.connect('A', 'A', func=feedback)

net.make_input('input', [0])
net.connect('input', 'A')

net.add_to_nengo()
net.view()

import nef
net = nef.Network('Recurrent Test 1')
net.make('A', neurons=100, dimensions=1)
def feedback(x):
    return x[0]*x[0]
net.connect('A', 'A', func=feedback)

net.make_input('input', [0])
net.connect('input', 'A')

net.add_to_nengo()
net.view()

import syde556

dt = 0.001

t = numpy.arange(1000)*dt
x = numpy.zeros(1000)
x[300:]=1

A = syde556.Ensemble(neurons=80, dimensions=1, max_rate=(50,100))

decoder = A.compute_decoder(x, x, noise=0.2)

spikes_A, xhat = A.simulate_spikes(x, decoder, tau=0.1)

import pylab
pylab.plot(t, x, label='$x$')
pylab.plot(t, xhat, label='$\hat{x}$')
pylab.legend(loc='best')
pylab.ylim(-0.2, 1.2)
pylab.show()


import syde556

dt = 0.001

t = numpy.arange(1000)*dt
x = numpy.zeros(1000)
x[300:]=1

A = syde556.Ensemble(neurons=80, dimensions=1, max_rate=(50,100))

decoder = A.compute_decoder(x, x, noise=0.2)

spikes_A, xhat = A.simulate_spikes(x, decoder, tau=0.03)

import pylab
pylab.plot(t, x, label='$x$')
pylab.plot(t, xhat, label='$\hat{x}$')
pylab.legend(loc='best')
pylab.ylim(-0.2, 1.2)
pylab.show()


import syde556

dt = 0.001

t = numpy.arange(1000)*dt
x = numpy.zeros(1000)
x[300:]=1

h = syde556.psc_filter(t-0.5, 0.1)
fx = syde556.apply_filter(numpy.array(x)[:,None], h)*dt

A = syde556.Ensemble(neurons=80, dimensions=1, max_rate=(50,100))

decoder = A.compute_decoder(x, x, noise=0.2)

spikes_A, xhat = A.simulate_spikes(x, decoder, tau=0.1)

import pylab
pylab.plot(t, x, label='$x(t)$')
pylab.plot(t, xhat, label='$\hat{x}(t)$')
pylab.plot(t, fx, label='$x(t)*h(t)$')
pylab.legend(loc='lower right')
pylab.ylim(-0.2, 1.2)
pylab.show()


import nef

tau=0.1

net = nef.Network('Neural Integrator')
net.make('velocity', neurons=100, dimensions=1)
net.make('position', neurons=100, dimensions=1)
def recurrent(x):
    return x[0]
net.connect('position', 'position', func=recurrent, pstc=tau)
net.connect('velocity', 'position', transform=[[tau]])

net.make_input('input', [0])
net.connect('input', 'velocity')

net.add_to_nengo()
net.view()

import syde556
reload(syde556)

x = numpy.linspace(-1, 1, 100)

A = syde556.Ensemble(neurons=200, dimensions=1, seed=1, tau_rc=0.02)
decoder = A.compute_decoder(x, x, noise=0.1)
activity, xhat = A.simulate_rate(x, decoder)

import pylab
pylab.axhline(0, color='k')
pylab.plot(x, x-xhat, label='$x-\hat{x}$')
pylab.legend(loc='best')
pylab.xlabel('$x$')
pylab.show()


import nef

tau=0.1
tau_centre=1.0
net = nef.Network('Neural Integrator')
net.make('velocity', neurons=100, dimensions=1)
net.make('position', neurons=100, dimensions=1)
def recurrent(x):
    return (1-tau/tau_centre)*x[0]
net.connect('position', 'position', func=recurrent, pstc=tau)
net.connect('velocity', 'position', transform=[[tau]])

net.make_input('input', [0])
net.connect('input', 'velocity')

net.add_to_nengo()
net.view()

import nef

tau=0.1
tau_centre=1.0
net = nef.Network('Controlled Neural Integrator')
net.make('decay', neurons=100, dimensions=1)
net.make('velocity', neurons=100, dimensions=1)
net.make('position', neurons=200, dimensions=2)
def recurrent(x):
    return x[0]-x[1]*x[0], 0
net.connect('position', 'position', func=recurrent, pstc=tau)
net.connect('velocity', 'position', transform=[tau, 0])
net.connect('decay', 'position', transform=[0, 1])

net.make_input('input', [0])
net.connect('input', 'velocity')

net.make_input('input_decay', [0])
net.connect('input_decay', 'decay')

net.add_to_nengo()
net.view()

import nef
net = nef.Network('Linear Oscillator')
net.make('A', neurons=100, dimensions=2)
def feedback(x):
    return x[0]+x[1], -x[0]+x[1]
net.connect('A', 'A', func=feedback, pstc=0.01)

net.make_input('input', [0])
net.connect('input', 'A')

net.add_to_nengo()
net.view()

tau = 0.1
sigma = 10
beta = 8.0/3
rho = 28

import nef
net = nef.Network('Lorenz attractor', seed=6)
net.make('A', 2000, 3, radius=60)

def feedback(x):
    dx0 = -sigma * x[0] + sigma * x[1]
    dx1 = -x[0] * x[2] - x[1]
    dx2 = x[0] * x[1] - beta * (x[2] + rho) - rho
    return [dx0 * tau + x[0], 
            dx1 * tau + x[1], 
            dx2 * tau + x[2]]
net.connect('A', 'A', func=feedback, pstc=tau)

net.view()

import nef
net = nef.Network('Square Oscillator')
net.make('A', neurons=1000, dimensions=2)

tau = 0.02
r=4
def feedback(x):    
    if abs(x[1])>abs(x[0]):
        if x[1]>0: dx=[r, 0]
        else: dx=[-r, 0]
    else:
        if x[0]>0: dx=[0, -r]
        else: dx=[0, r]
    return [tau*dx[0]+x[0], tau*dx[1]+x[1]]        
net.connect('A', 'A', func=feedback, pstc=tau)

net.make_input('input', [0,0])
net.connect('input', 'A')

net.add_to_nengo()
net.view()

import nef
net = nef.Network('Heart Oscillator')
net.make('A', neurons=1000, dimensions=2)

tau = 0.02
r=4
def feedback(x):    
    return [-tau*r*x[1]+x[0], tau*r*x[0]+x[1]]
net.connect('A', 'A', func=feedback, pstc=tau)

from math import atan2, sin, cos, sqrt
def heart(x):
    theta = atan2(x[1], x[0])
    r = 2 - 2 * sin(theta) + sin(theta)*sqrt(abs(cos(theta)))/(sin(theta)+1.4)
    return [-r*cos(theta), r*sin(theta)]

net.make('B', neurons=10, dimensions=2)
net.connect('A', 'B', func=heart, pstc=tau)
net.make_input('input', [0,0])
net.connect('input', 'A')

net.add_to_nengo()
net.view()

import nef
net = nef.Network('Controlled Oscillator')
net.make('A', neurons=500, dimensions=3, radius=1.7)

tau = 0.1
scale = 10
def feedback(x):
    return x[1]*x[2]*scale*tau+1.1*x[0], -x[0]*x[2]*scale*tau+1.1*x[1], 0
net.connect('A', 'A', func=feedback, pstc=tau)

net.make_input('input', [0,0,0])
net.connect('input', 'A')

net.add_to_nengo()
net.view()