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functions.py~
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functions.py~
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import math
import numpy as np
import matplotlib.pylab as plt
import random
import copy
from scipy.signal import fftconvolve
def alpha_fun(tau_r,tau_d,dt,L,control='off'): #alpha functions for kernels.
x = np.arange(int(L/dt)) #abcsiss vector in timesteps.
tau_r_steps = tau_r/dt # in time steps.
tau_d_steps = tau_d/dt
y = np.exp(-x/tau_r_steps)-np.exp(-x/tau_d_steps)
y = y/np.sum(y*dt)
if control=='on':
plt.plot(x*dt,y) #x*dt is in ms.
plt.show()
return y
def exp_fun(tau,dt,L,control='off'): #exponential function for ASP.
x = np.arange(int(L/dt))
tau_steps = tau/dt
y = np.exp(-x/tau_steps)
if control=='on':
plt.plot(x*dt,y)
plt.show()
return y
def jitter(r,per=0.1): #add 10% of noise to r.
return r*(1+per*2*(random.random()-0.5))
def spike_train(neuron,gr,syn,string): #generate Poisson spike train.
spike_train = [0.]
dt = neuron.dt
for w in neuron.windows[string]:
tstart = w[0]
tstop = w[1]
cursor = 0.
while cursor < (tstop - tstart):
if syn=='exc':
cursor = cursor + np.random.exponential(1000./w[2+2*gr])
elif syn=='inh':
cursor = cursor + np.random.exponential(1000./w[3+2*gr])
if ((tstart + cursor) < tstop):
new_t = np.around((tstart + cursor)/dt)*dt
if new_t>(spike_train[-1]+dt):
spike_train = spike_train + [new_t]
return spike_train[1:]
def sigmoid(l,x):
y = l[0]/(1.+np.exp(-(x-l[1])/l[2]))
return y
def CosineBasis(K,T,dt,a=1.9,c=0.): #cosine function on logarithm scale. truncated.
F = np.zeros((K,T/dt),dtype='float')
I = np.arange(T/dt)*dt
for k in range(K):
lb = math.exp((k/2.-1)*math.pi/a) - c
ub = math.exp((k/2.+1)*math.pi/a) - c
cos_on_log = np.cos(a*np.log(I[(I>=lb)&(I<ub)]+c)-k*0.5*math.pi)
F[k,(I>=lb)&(I<ub)] = 0.5*(1 + cos_on_log)
return F
def NaturalSpline(knots,bnds,total_length):
dv = 0.00001*(bnds[1]-bnds[0])
F = np.zeros((len(knots),total_length),dtype='float')
c_knots = copy.copy(knots)
for i in range(len(c_knots)):
c_knots[i] = np.floor(((c_knots[i] - bnds[0])/(bnds[1]-bnds[0]))*total_length)
v = np.arange(total_length)
F[0,:] = 1.
F[1,:] = v
for i in range(2,len(c_knots)):
tmp1 = (v-c_knots[i-2])**3
tmp1[tmp1<0.] = 0.
tmp2 = (v-c_knots[-1])**3
tmp2[tmp2<0.] = 0.
tmp3 = (v-c_knots[-2])**3
tmp3[tmp3<0.] = 0.
dk = (tmp1 - tmp2)*(1./(c_knots[-1]-c_knots[i-2]))
dkm1 = (tmp3 - tmp2)*(1./(c_knots[-1]-c_knots[-2]))
F[i,:] = dk - dkm1
return F
def DerNaturalSpline(knots,bnds,total_length):
c_knots = copy.copy(knots)
dv = 0.00001*(bnds[1]-bnds[0])
F = np.zeros((len(c_knots),total_length),dtype='float')
for i in range(len(c_knots)):
c_knots[i] = np.floor(((c_knots[i] - bnds[0])/(bnds[1]-bnds[0]))*total_length)
v = np.arange(total_length)
F[0,:] = 0.
F[1,:] = 1./dv
for i in range(2,len(c_knots)):
tmp1 = 3*(v-c_knots[i-2])**2/dv
tmp1[tmp1<0.] = 0.
tmp2 = 3*(v-c_knots[-1])**2/dv
tmp2[tmp2<0.] = 0.
tmp3 = 3*(v-c_knots[-2])**2/dv
tmp3[tmp3<0.] = 0.
dk = (tmp1 - tmp2)*(1./(c_knots[-1]-c_knots[i-2]))
dkm1 = (tmp3 - tmp2)*(1./(c_knots[-1]-c_knots[-2]))
F[i,:] = dk - dkm1
return F
def SecDerNaturalSpline(knots,bnds,total_length):
c_knots = copy.copy(knots)
dv = 0.00001*(bnds[1]-bnds[0])
F = np.zeros((len(c_knots),total_length),dtype='float')
for i in range(len(c_knots)):
c_knots[i] = np.floor(((c_knots[i] - bnds[0])/(bnds[1]-bnds[0]))*total_length)
v = np.arange(total_length)
F[0,:] = 0.
F[1,:] = 0.
for i in range(2,len(c_knots)):
tmp1 = 6*(v-c_knots[i-2])/dv**2
tmp1[tmp1<0.] = 0.
tmp2 = 6*(v-c_knots[-1])/dv**2
tmp2[tmp2<0.] = 0.
tmp3 = 6*(v-c_knots[-2])/dv**2
tmp3[tmp3<0.] = 0.
dk = (tmp1 - tmp2)*(1./(c_knots[-1]-c_knots[i-2]))
dkm1 = (tmp3 - tmp2)*(1./(c_knots[-1]-c_knots[-2]))
F[i,:] = dk - dkm1
return F
def Tents(knots,bnds,total_length):#uses knots and bnds to keep same syntax as splines
knots.sort()
dv = (bnds[1] - bnds[0])/total_length
knots = [bnds[0]] + knots + [bnds[1]]
for i in range(len(knots)):
knots[i] = int((knots[i]-bnds[0])/dv)
F = np.zeros((len(knots),total_length),dtype='float')
for i in range(1,len(knots)-1):
F[i,knots[i-1]:knots[i]] = np.arange(knots[i]-knots[i-1])
m = F[i,knots[i-1]:knots[i]].max()
d = knots[i+1]-knots[i]
F[i,knots[i]:knots[i+1]] = np.arange(d,0,-1.)*(float(m)/d)
F[0,:knots[1]] = np.arange(knots[1],0,-1)
F[-1,knots[-2]:] = np.arange(total_length-knots[-2])
return F
def DerTents(knots,bnds,total_length):#derivative of tent basis functions.for gradient
knots.sort()
dv = (bnds[1] - bnds[0])/total_length
knots = [bnds[0]] + knots + [bnds[1]]
for i in range(len(knots)):
knots[i] = int((knots[i]-bnds[0])/dv)
F = np.zeros((len(knots),total_length),dtype='float')
for i in range(1,len(knots)-1):
F[i,knots[i-1]:knots[i]] = 1./dv
m = float(knots[i]-knots[i-1])
d = knots[i+1]-knots[i]
F[i,knots[i]:knots[i+1]] = -(1./dv)*(float(m)/d)
F[0,:knots[1]] = -1./dv
F[-1,knots[-2]:] = 1./dv
return F
def SecDerTents(knots,bnds,total_length):
F = np.zeros((len(knots)+2,total_length),dtype='float')
return F
def Cst(knots,bnds,total_length):
F = np.zeros((len(knots)+2,total_length),dtype='float')
dv = (bnds[1] - bnds[0])/total_length
knots = [bnds[0]] + knots + [bnds[1]]
for i in range(len(knots)):
knots[i] = int((knots[i]-bnds[0])/dv)
for i in range(len(knots)-1):
F[i,knots[i]:knots[i+1]] = 1.
F[-1,knots[-2]:] = 1.
return F
def CstDer(knots,bnds,total_length):
F = np.zeros((len(knots)+2,total_length),dtype='float')
return F
def CstSecDer(knots,bnds,total_length):
F = np.zeros((len(knots)+2,total_length),dtype='float')
return F
def SplineParamsforId(knots,bnds):
F = NaturalSpline(knots,bnds)
dv = 0.00001*(bnds[1]-bnds[0])
v = np.arange(bnds[0],bnds[1],dv)
params = np.dot(np.linalg.inv(np.dot(F,F.transpose())),np.dot(F,v))
return params
def Ker2Param(ker,basis): #CRUCIAL.
B = basis
Nb = np.shape(B)[0]
Nparam = np.shape(ker)[0]*np.shape(B)[0]
paramKer = np.zeros((Nparam),dtype='float')
for i in range(np.shape(ker)[0]):
bbtm1 = np.linalg.inv(np.dot(B,B.transpose()))
yxt = np.dot(ker[i,:],B.transpose())
paramKer[i*Nb:(i+1)*Nb] = np.dot(yxt,bbtm1) #analytic formula of RSS minimum.
return paramKer
def SimMeas(out1,out2,model,delta):
conv1 = np.zeros((model.total_time_test/model.dt),dtype='float')
conv1_cvd = np.zeros((model.total_time_test/model.dt),dtype='float')
conv2 = np.zeros((model.total_time_test/model.dt),dtype='float')
conv2_cvd = np.zeros((model.total_time_test/model.dt),dtype='float')
for i in range(100):
outt1 = out1[i]
outt2 = out2[0]
outt1 = np.array(outt1)
outt1 = np.floor(outt1/model.dt)
outt1 = outt1.astype('int')
outt2 = np.array(outt2)
outt2 = np.floor(outt2/model.dt)
outt2 = outt2.astype('int')
conv1_tmp_c = np.zeros((model.total_time_test/model.dt),dtype='float')
conv1_tmp = np.zeros((model.total_time_test/model.dt),dtype='float')
conv2_tmp_c = np.zeros((model.total_time_test/model.dt),dtype='float')
conv2_tmp = np.zeros((model.total_time_test/model.dt),dtype='float')
conv1_tmp_c[outt1-int(delta/model.dt)] = 1.
conv1_tmp[outt1] = 1.
conv2_tmp_c[outt2-int(delta/model.dt)] = 1.
conv2_tmp[outt2] = 1.
conv1 = conv1 + 0.01*conv1_tmp
conv2 = conv2 + 0.01*conv2_tmp
conv1_cvd = conv1_cvd + 0.01*conv1_tmp_c
conv2_cvd = conv2_cvd + 0.01*conv2_tmp_c
ker = np.ones((int(2*delta/model.dt)),dtype='float')
figconv = plt.figure()
axc = figconv.add_subplot(111)
conv1_cvd = fftconvolve(conv1_cvd,ker)[:conv1.size]
conv2_cvd = fftconvolve(conv2_cvd,ker)[:conv2.size]
axc.plot(conv1)
axc.plot(conv2)
figconv.show()
SP = np.sum(conv1_cvd*conv2)
N1 = np.sum(conv1_cvd*conv1)
N2 = np.sum(conv2_cvd*conv2)
Md = 2*SP/(N1+N2)
print Md
return Md