def LQLEP_wBarrier( LQLEP = Th.dscalar(), ldet = Th.dscalar(), v1 = Th.dvector(),
N_spike = Th.dscalar(), ImM = Th.dmatrix(), U = Th.dmatrix(),
V2 = Th.dvector(), u = Th.dvector(), C = Th.dmatrix(),
**other):
'''
The actual Linear-Quadratic-Exponential-Poisson log-likelihood,
as a function of theta and M,
with a barrier on the log-det term and a prior.
'''
sq_nonlinearity = V2**2.*Th.sum( Th.dot(U,C)*U, axis=[1]) #Th.sum(U**2,axis=[1])
nonlinearity = V2 * Th.sqrt( Th.sum( Th.dot(U,C)*U, axis=[1])) #Th.sum(U**2,axis=[1]) )
if other.has_key('uc'):
LQLEP_wPrior = LQLEP + 0.5 * N_spike * ( 1./(ldet+250.)**2. \
- 0.000001 * Th.sum(Th.log(1.-4*sq_nonlinearity))) \
+ 10. * Th.sum( (u[2:]+u[:-2]-2*u[1:-1])**2. ) \
+ 10. * Th.sum( (other['uc'][2:]+other['uc'][:-2]-2*other['uc'][1:-1])**2. ) \
+ 0.000000001 * Th.sum( v1**2. )
# + 100. * Th.sum( v1 )
# + 0.0001*Th.sum( V2**2 )
else:
LQLEP_wPrior = LQLEP + 0.5 * N_spike * ( 1./(ldet+250.)**2. \
- 0.000001 * Th.sum(Th.log(1.-4*sq_nonlinearity))) \
+ 10. * Th.sum( (u[2:]+u[:-2]-2*u[1:-1])**2. ) \
+ 0.000000001 * Th.sum( v1**2. )
# + 100. * Th.sum( v1 )
# + 0.0001*Th.sum( V2**2 )
eigsImM,barrier = eig( ImM )
barrier = 1-(Th.sum(Th.log(eigsImM))>-250) * \
(Th.min(eigsImM)>0) * (Th.max(4*sq_nonlinearity)<1)
other.update(locals())
return named( **other )
def ldet( theta = Th.dvector('theta'), M = Th.dmatrix('M') ,
STA = Th.dvector('STA'), STC = Th.dmatrix('STC'), **other):
'''
Return log-det of I-sym(M), for display/debugging purposes.
'''
ImM = Th.identity_like(M)-(M+M.T)/2
w, v = eig(ImM)
return Th.sum(Th.log(w))
def eigs( theta = Th.dvector('theta'), M = Th.dmatrix('M') ,
STA = Th.dvector('STA') , STC = Th.dmatrix('STC'), **other):
'''
Return eigenvalues of I-sym(M), for display/debugging purposes.
'''
ImM = Th.identity_like(M)-(M+M.T)/2
w,v = eig( ImM )
return w
def eig_pos_barrier( theta = Th.dvector('theta'), M = Th.dmatrix('M') ,
STA = Th.dvector('STA'), STC = Th.dmatrix('STC'),
U = Th.dmatrix('U') , V1 = Th.dvector('V1'), **other):
'''
A barrier enforcing that the log-det of M should be > exp(-6),
and all the eigenvalues of M > 0. Returns true if barrier is violated.
'''
ImM = Th.identity_like(M)-(M+M.T)/2
w,v = eig( ImM )
return 1-(Th.sum(Th.log(w))>-250)*(Th.min(w)>0)*(Th.min(V1.flatten())>0) \
def eigsM( M = Th.dmatrix('M') , **result):
w,v = eig( Th.identity_like(M)-(M+M.T)/2 )
return w