def simulator( v2, N_filters, nonlinearity, N_cells , sigma_spatial , N_timebins ):
retina = simulate_retina.LNLNP_ring_model( nonlinearity = nonlinearity ,
N_cells = N_cells ,
sigma_spatial = sigma_spatial )
# stimulus = simulate_retina.white_gaussian_stimulus( dimension = N_cells[0] ,
# sigma = 1. )
stimulus = simulate_retina.Stimulus( simulate_retina.white_gaussian )
return simulate_retina.run_LNLNP( retina , stimulus = stimulus ,
N_timebins = N_timebins ,
average_me = {'features':lambda x: NL(np.dot(filters,x))} )
def phaseout( objective, true_run , stimulus , V2 , phase ):
iterations[0] = -1
model = copy.deepcopy( true_run['model'] )
model['U'] = retina.ring_weights( shape=true_run['model']['U'].shape,
offset_out=phase)
phase_objective = LL_with_U( objective , model['U'] , V2 )
true_objective = LL_with_U( objective , true_run['model']['U'] , V2 )
params = optimize_V1( phase_objective , true_run , model['U'], V2 )
opt_params = optimize_V1( true_objective , true_run , true_run['model']['V'], V2 )
model['V'] = params['V1']
dLopt = true_objective.LL(true_run['model']['V']) - true_objective.LL(opt_params)
dLL = phase_objective.LL(params) - true_objective.LL(opt_params)
seed = Rand.get_state()
true_100 = retina.run_LNLNP( true_model , stimulus = stimulus ,
keep=frozenset(['intensity']), N_timebins = 100000 )
Rand.set_state(seed)
this_100 = retina.run_LNLNP( model , stimulus = stimulus ,
keep=frozenset(['intensity']), N_timebins = 100000 )
intensities = np.vstack([true_100['intensity'].flatten(),this_100['intensity'].flatten()])
order = np.argsort( intensities[0,:] )
intensities = intensities[:,order[::20]]
p.close('all')
p.figure(1, figsize=(10,12))
ax0 = p.subplot(3,1,1)
p.plot( true_100['model']['V'].T )
#ax0.xaxis.set_label_text('subunits')
p.title('V filters')
ax1 = p.subplot(3,1,2)
p.plot( true_100['model']['U'].T )
#ax1.xaxis.set_label_text('cones')
p.title('True U filters , sigma = %.0f' % (sigma_spatial[0]))
ax2 = p.subplot(3,1,3)
p.semilogy( intensities.T )
ax2.xaxis.set_label_text('samples reordered by intensity of true model')
ax2.yaxis.set_label_text('intensities in spikes / bin')
p.title('Intensities of true vs. out-of-phase model (dLL=%.1e bits/spike, dLopt=%.1e) ' % \
(dLL/np.log(2.), dLopt/np.log(2.)) )
#p.subplot(2,1,2)
#p.plot( intensities.T )
p.savefig('/Users/kolia/Desktop/out-of-phase_sigma%d_phase%.1f.pdf' % \
(true_run['model']['sigma_spatial'][0], phase),format='pdf')
(dLL/np.log(2.), dLopt/np.log(2.)) )
#p.subplot(2,1,2)
#p.plot( intensities.T )
p.savefig('/Users/kolia/Desktop/out-of-phase_sigma%d_phase%.1f.pdf' % \
(true_run['model']['sigma_spatial'][0], phase),format='pdf')
N_cells = [ 20 , 13 , 7 ]
V2 = 0.5 * np.ones(N_cells[1])
def NL(x): return x + 0.5 * (V2 * ( x ** 2 ).T).T
for sigma_spatial in [[ 20., 3. ] , [ 10., 3. ] , [ 5., 3. ] , [ 2., 3. ] , [1.,3.]]:
true_model = retina.LNLNP_ring_model( nonlinearity = NL , N_cells = N_cells ,
sigma_spatial = sigma_spatial )
stimulus = retina.Stimulus( retina.white_gaussian )
true_run = retina.run_LNLNP( true_model , stimulus = stimulus ,
keep=frozenset(['intensity']), N_timebins = 1000000 )
obj_V1 = LL_V1( true_model['V'] )
phaseout( obj_V1, true_run , stimulus , V2 , 0.5 )
# candidate 'saturating' nonlinearities:
# exp(2.*x+1.) - exp(3.*(x-0.5)) + exp(3.5*(x-1.045))
# x = arange(-2.,3.1,0.1) ; plot( x, exp(3.*(x+1.)) - exp(3.001*(x+0.999)) + exp(4.*(x-1.718)))
import numpy as np
import pylab as p
# based on the taylor expansion of 1/(1+exp(x)) wrt exp(x) at exp(x0)
taylor = lambda x0,N,shift,constant,scale : lambda x : \
scale*( 1. - constant - np.sum( (-1)**(np.arange(N)[:,np.newaxis]) * \