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Model.py
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Model.py
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import numpy as np
import pylab as plt
import sys
plt.ion()
#plt.close('all')
#constants
TRAIN=0
TESTLOC=1
TESTHIC=2
D=10
a2str=['B','W','G','RS','RM','RL','S','M','L','XL']
a2data=np.array([[0,1,2,2,1,0,2,1,0,np.nan],
[2,1,0,2,1,0,2,1,0,np.nan],[np.nan,np.nan,np.nan,2,1,0,np.nan,2,1,0]])
data2a=np.zeros((3,D,3))
for i in range(3):
data2a[i,:,:] = np.int32(a2data==i).T
feedback=np.array([[1,0,0,0,0,1,0,0,1,np.nan],
[0,0,1,0,0,1,0,0,1,np.nan],[np.nan,np.nan,np.nan,0,0,1,0,0,0,1]])
w=np.array([1,1,1,0.5,0.5,0.5,0.5,0.5,0.5,0.5])
# functions
def getProb(a,d):
p=np.power(a,d)
p/=np.nansum(p)
return p
def chooseAction(p):
action=np.random.multinomial(1,p)
return action.nonzero()[0][0]
class Model():
def __init__(self,q0=0.5,u0=0.5,d=1,g=0.7,h=0.5,m=1):
''' q0 - prior preference of color over length (0,1)
u0 - prior preference of rel. over abs. length (0,1)
d - decision consistency (0,inf), 0=random, 1=deterministic
g - learning from positive feedback (0,1);
1=current evidence (fast shifting), 0= prior(slow shifing)
h - learning from negative feedback (0,1)
m - attentional focus (0, inf); 0= uniform distribution
'''
self.q0=q0; self.u0=u0; self.d=d
self.g=g; self.h=h; self.m=m
def exp1run(self):
T=20
#initialize
q=np.zeros(T+1); q[0]=self.q0
u=np.zeros(T+1); u[0]=self.u0
a=np.zeros((T+1,D));self.f=[]
p=np.zeros((T+1,D));dat=np.zeros(T)
a[0,:]=np.ones(10)/3.0
a[0,-1]=np.nan
a[0,:3]*=q[0]
a[0,3:6]*=(1-q[0])*u[0]
a[0,6:]*=(1-q[0])*(1-u[0])
b=np.zeros(T)# observed behavior
phase=0
#print a[0,:]
for t in range(T):
if t>10: phase=1
else: phase=0
p[t,:]=getProb(a[t,:],self.d)
b[t]=chooseAction(p[t,:])
dat[t]=a2data[phase,b[t]]
m=data2a[dat[t],:,phase]
f=feedback[phase,b[t]]
w=np.power(a[t,:],self.m)
self.f.append(f)
if f==1:
s=m*w
a[t+1,:]= self.g*s/np.nansum(s) + (1-self.g)*a[t,:]
else:
s=(1-m)*w
a[t+1,:]= self.h*s/np.nansum(s) + (1-self.h)*a[t,:]
u[t+1]= np.nansum(a[t+1,3:6])/np.nansum(a[t+1,3:])
q[t+1]= np.nansum(a[t+1,:3])/np.nansum(a[t+1,:])
#(np.nansum(a[t+1,:3])+(1-u[t+1])*np.nansum(a[t+1,6:])+u[t+1]*np.nansum(a[t+1,3:6])
self.a=a
self.b=b
self.dat=dat
self.f=np.array(self.f)
return self.dat,self.f
def exp1computeLL(self,dat,f):
T=20
#initialize
q=np.zeros(T+1); q[0]=self.q0
u=np.zeros(T+1); u[0]=self.u0
a=np.zeros((T+1,D));self.f=[]
p=np.zeros((T+1,D));
a[0,:]=np.ones(10)/3.0
a[0,-1]=np.nan
a[0,:3]*=q[0]
a[0,3:6]*=(1-q[0])*u[0]
a[0,6:]*=(1-q[0])*(1-u[0])
phase=0
LL=0
#print a[0,:]
for t in range(T):
if t>10: phase=1
else: phase=0
p[t,:]=getProb(a[t,:],self.d)
m=data2a[dat[t],:,phase]
w=np.power(a[t,:],self.m)
loglik= np.nansum(np.log(np.maximum(0.001,p[t,m==f[t]])))
if f[t]==1:
s=m*w
a[t+1,:]= self.g*s/np.nansum(s) + (1-self.g)*a[t,:]
else:
s=(1-m)*w
a[t+1,:]= self.h*s/np.nansum(s) + (1-self.h)*a[t,:]
#print t,dat[t],f[t],np.nansum(p[t,m==f[t]]),loglik
#print 'm= ',m
#print 'p= ',p
LL+=loglik
return LL
def plothistory(self):
a=self.a
b=self.b
plt.figure(figsize=(12,6))
I=np.concatenate([a.T,np.array(np.nansum(a[:,:3],1),ndmin=2),
np.array(np.nansum(a[:,3:6],1),ndmin=2),np.array(np.nansum(a[:,6:],1),ndmin=2)],axis=0)
plt.plot(range(b.size),b,'rx',ms=8,mew=2)
plt.plot([10.5,10.5],[-1,I.shape[1]],'r',lw=2)
plt.imshow(I,interpolation='nearest',cmap='winter')
plt.colorbar()
ax=plt.gca()
ax.set_yticks(range(I.shape[0]))
ax.set_yticklabels(['']*a.shape[0]+['color','rel len','abs len'])
c1=plt.Circle((-1.5,0),radius=0.4,color='blue',clip_on=False)
c2=plt.Circle((-1.5,1),radius=0.4,color='white',clip_on=False)
c3=plt.Circle((-1.5,2),radius=0.4,color='yellow',clip_on=False)
ax.add_patch(c1);ax.add_patch(c2);ax.add_patch(c3);
c1=plt.Rectangle((-2,3),1,0.2,color='white',clip_on=False)
c2=plt.Rectangle((-2.5,4),1.5,0.2,color='white',clip_on=False)
c3=plt.Rectangle((-3,5),2,0.2,color='white',clip_on=False)
ax.add_patch(c1);ax.add_patch(c2);ax.add_patch(c3);
c1=plt.Rectangle((-2,6),1,0.2,color='gray',clip_on=False)
c2=plt.Rectangle((-2.5,7),1.5,0.2,color='gray',clip_on=False)
c3=plt.Rectangle((-3,8),2,0.2,color='gray',clip_on=False)
c4=plt.Rectangle((-3.5,9),2.5,0.2,color='gray',clip_on=False)
ax.add_patch(c1);ax.add_patch(c2);ax.add_patch(c3);ax.add_patch(c4);
print I[-3,-1]
def LLsample(M,Y):
LL=0
for y in Y:
LL+= M.exp1computeLL(y[0],y[1])
return LL
def checkLL(M,n=50):
np.random.seed(4)
fname='LLq%.2fu%.2fh%.2fg%.2fm%.2fd%.2f'%(M.q0,M.u0,M.h,M.g,M.m,M.d)
Y=[]
for i in range(n):
dat,f=M.exp1run()
Y.append([dat,f])
return Y
#M.plothistory()
h= np.linspace(0,1,21)#np.array([1])
g= np.linspace(0,1,21)
m=np.linspace(0,2,21)
d=np.linspace(0,2,21)
import time
t0=time.time()
out=np.ones((h.size,g.size,m.size,d.size))
for hh in range(h.size):
print np.round(hh/float(h.size),2)
for gg in range(g.size):
for mm in range(m.size):
for dd in range(d.size):
M.h=h[hh];M.g=g[gg]
M.m=m[mm];M.d=d[dd]
out[hh,gg,mm,dd]=LLsample(M,Y)
print time.time()-t0
np.save(fname,out)
def plotLL(fname='out4.npy'):
plt.figure()
h= np.linspace(0,1,21)
g= np.linspace(0,1,21)
m=np.linspace(0,2,21)
d=np.linspace(0,2,21)
out=np.load(fname)
print np.nanmax(out),np.nanmin(out)
rang=np.nanmax(out)-np.nanmin(out)
maxloc= np.squeeze(np.array((np.nanmax(out)==out).nonzero()))
H,G=np.meshgrid(h,g)
print maxloc
for mm in range(m.size/2):
for dd in range(d.size/2):
plt.subplot(10,10,(9-mm)*10+dd+1)
plt.pcolormesh(h,g,out[:,:,mm*2,dd*2].T,
vmax=np.nanmax(out),vmin=np.nanmax(out)-rang/4.)
plt.gca().set_xticks([])
plt.gca().set_yticks([])
if mm==maxloc[2]/2 and dd==maxloc[3]/2:
plt.plot(h[maxloc[0]],g[maxloc[1]],'ow',ms=8)
if dd==0:
print mm,dd
plt.ylabel('%.1f'%m[mm*2])
if mm==0: plt.xlabel('%.1f'%d[dd*2])
plt.title(fname[:6])
if __name__ == '__main__':
## ags=[]
## for i in range(1,len(sys.argv)): ags.append(float(sys.argv[i]))
## M=Model(q0=ags[0],u0=ags[1],h=ags[2],
## g=ags[3],m=ags[4],d=ags[5])
## checkLL(M)
Y=checkLL(Model())
plotLL(fname='LLq0.20u0.50h0.50g0.50m1.00d1.00.npy')
plotLL(fname='LLq0.50u0.50h0.50g0.50m1.00d1.00.npy')
plotLL(fname='LLq0.80u0.50h0.50g0.50m1.00d1.00.npy')