def normal(self, mean, covariance, x=None): """ sample from a normal distribution or specify `x` for the likelihood of that point under the model. Parameters ---------- mean : matrix mean of a multivariate normal distribution written as a nx1 matrix covariance: matrix covariance matrix of a multivariate normal distribution x : matrix (None) point at which to evaluate the normal distribution Notes ---------- If you specify x then this function returns the likelihood p(x|mean,covariance). If you leave x unspecified then this will return a sample from the normal distribution specified by the mean and covariance. """ if x is not None: # TODO what's the normalising constant of a multivariate G? const = 1.0 return const * pb.exp(-0.5*(x-mean).T * covariance.I * (x-mean)) else: return pb.multivariate_normal(mean.A.flatten(),covariance,[1]).T
#Define sensor geometry sensor_center=pb.matrix([[0],[0]]) sensor_width=0.9**2 sensor_kernel=basis(sensor_center,sensor_width,dimension) #Define sigmoidal activation function and inverse synaptic time constant fmax=10 v0=2 varsigma=0.8 act_fun=ActivationFunction(v0,fmax,varsigma) #inverse synaptic time constant zeta=100 #define field initialasation and number of iterations for estimation mean=[0]*len(Phi) P0=10*pb.eye(len(mean)) x0=pb.matrix(pb.multivariate_normal(mean,P0,[1])).T number_of_iterations=10 #ignore first 100 observations allowing the model's initial transients to die out First_n_observations=100 #populate the model NF_model=NF(NF_Connectivity_kernel,sensor_kernel,obs_locns,observation_locs_mm,gamma,gamma_weight,Sigma_varepsilon,act_fun,zeta,Ts,field_space,spacestep) IDE_model=IDE(IDE_Connectivity_kernel,IDE_field,sensor_kernel,obs_locns,gamma,gamma_weight,Sigma_varepsilon,act_fun,x0,P0,zeta,Ts,field_space,spacestep) #generate the Neural Field model NF_model.gen_ssmodel() V,Y=NF_model.simulate(T) #generate the reduced model (state space model) IDE_model.gen_ssmodel() #estimate the states, the connectivity kernel parameters and the synaptic dynamics ps_estimate=para_state_estimation(IDE_model) ps_estimate.itrerative_state_parameter_estimation(Y[First_n_observations:],number_of_iterations)
sensor_kernel=basis(sensor_center,sensor_width,dimension) #Define sigmoidal activation function and inverse synaptic time constant #~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ fmax=1 v0=1.8 varsigma=0.56 act_fun=ActivationFunction.ActivationFunction(v0,fmax,varsigma) #inverse synaptic time constant zeta=100 #define field initialasation and number of iterations for estimation #~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ mean=[0]*len(Phi) P0=10*pb.eye(len(mean)) x0=pb.multivariate_normal(mean,P0,[1]).T number_of_iterations=10 #ignore first 100 observations allowing the model's initial transients to die out First_n_observations=100 #populate the model NF_model=NF(NF_Connectivity_kernel,sensor_kernel,obs_locns,gamma,gamma_weight,Sigma_varepsilon,act_fun,zeta,Ts,field_space_x_y,spacestep) IDE_model=IDE(IDE_Connectivity_kernel,field,sensor_kernel,obs_locns,gamma,gamma_weight,Sigma_varepsilon,act_fun,x0,P0,zeta,Ts,field_space_x_y,spacestep) #generate Neural Field model NF_model.gen_ssmodel() V,Y=NF_model.simulate(T) #generate the reduced model (state space model) IDE_model.gen_ssmodel() #estimate the states, the connectivity kernel parameters and the synaptic dynamics #~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ps_estimate=para_state_estimation(IDE_model) ps_estimate.itrerative_state_parameter_estimation(Y[First_n_observations:],number_of_iterations)
