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testing_v3.R
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testing_v3.R
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## spde_v3.R Testing ##
#################
#### PRELIMS ####
#################
## Define directories ##
main_wd = "/Users/ls616/Google Drive/MPE CDT/PhD/Year 1/Code/Current"
fig_wd = "/Users/ls616/Desktop"
## Set directory ##
setwd(main_wd)
## Load functions from C ##
dyn.load("FFBS_spectral.so")
dyn.load("RML_spectral.so")
dyn.load("propagate_spectral.so")
dyn.load("tkf_spectral.so")
dyn.load("tkf2_spectral.so")
## Load additional libraries ##
library(mvtnorm)
library(coda)
library(microbenchmark)
library(lattice)
library(dlm)
library(RColorBrewer)
library(gtools)
## Load spde2019 functions ##
source("spde_v3.R")
#################
#############
#### BML ####
#############
## Setup ##
if(TRUE){
## Prelims ##
if(TRUE){
n = 6; t = 100; dt = 0.1; K = 7; nu = 1
}
## Observation Locations ##
if(TRUE){
## Observation locations
coords = list(c(1.4,1.6),c(4.3,4.7),c(1.3,4.2),c(4.7,1.9),c(3.3,3.2),
c(0.1,2.0),c(5.0,4.8),c(0.1,0.2),c(2.8,5.4),c(3.6,0.2))
coords = lapply(1:n^2,
function(i) as.numeric(expand.grid(0:(n-1),0:(n-1))[i,]))
## Observation locations 'indices'
coords_indices = sapply(coords,function(x) x[1]+n*x[2]+1)
## Number of observations
n_obs = length(coords)
## Observation location at all times
obs_loc = lapply(1:n_obs,function(j) matrix(coords[[j]],nrow=t,ncol=2,byrow=T))
## Plot observation locations
plot_obs = TRUE
if(plot_obs){
par(mfrow=c(1,1))
plot(sapply(coords,function(x) x)[1,],sapply(coords,function(x) x)[2,],
xlim = c(0,n-1),ylim=c(0,n-1),xlab=expression(x),ylab=expression(y),
main="Sensor Locations")
abline(v=0:(n-1),h=(0:n-1),col="gray92",lty=2)
}
}
## Parameters ##
if(TRUE){
## Signal parameters ##
param_sig = c(rho0 = 0.5, sigma2 = 0.2, zeta = 0.5,rho1 = 0.1, gamma = 2,
alpha = pi/4, mu_x = 0.3, mu_y = -0.3)
param_sig_i_t_dep = lapply(1:length(param_sig),
function(i) param_t_dep_func(1,param_sig[i]))
param_sig_t_dep =
param_sig_t_dep_func(param_sig_i_t_dep[[1]],param_sig_i_t_dep[[2]],
param_sig_i_t_dep[[3]],param_sig_i_t_dep[[4]],
param_sig_i_t_dep[[5]],param_sig_i_t_dep[[6]],
param_sig_i_t_dep[[7]],param_sig_i_t_dep[[8]])
## Observation parameters ##
m = 1; m_indices = list(coords_indices); tau2_vals = list(0.01)
param_obs = param_obs_func(m,m_indices,tau2_vals)
param_obs_t_dep = param_t_dep_func(list(1),list(param_obs))
## Observation bias ##
m1 = 0; m1_indices = list(coords_indices); bias_vals = list(0)
param_bias = param_bias_func(m1,m1_indices,bias_vals)
param_bias_t_dep = param_t_dep_func(list(1),list(param_bias))
## Parameter names ##
param_sig_names = list(parse(text="rho[0]"),parse(text="sigma^2"),
parse(text="zeta"),parse(text="rho[1]"),
parse(text="gamma"),parse(text="alpha"),
parse(text="mu[x]"),parse(text="mu[y]"))
param_obs_names = list(parse(text="tau^2"))
param_bias_names = list(parse(text="beta"))
## Number of parameters ##
n_param = length(param_sig)+param_obs$m+param_bias$m
}
## Signal Noise Weights ##
if(TRUE){
## Weighting Matrix (Physical Space) ##
grid = expand.grid(x = 0:(n-1),y = 0:(n-1))/n
centre_x = 6/12; centre_y = 7/12; sigma_x = 0.3; sigma_y = 0.3; rho = 0
weights = with(grid,sech2d(x = x,y = y, centre_x = centre_x,
centre_y = centre_y, sigma_x = sigma_x,
sigma_y=sigma_y, rho = rho))
weights_mat = weights_mat_func(weights)
## Weighting Matrix (Spectral Space) ##
spec_weights_mat = spec_weights_mat_func(n = n, K = K,
weights_mat = weights_mat)
## Alternative: No Weighting Matrix ##
weights = NULL; spec_weights_mat = NULL
}
## SPDE_FT object ##
if(TRUE){
SPDE_FT = spde_initialise(n,t,K)
wave = SPDE_FT$wave
cosine_indices = SPDE_FT$cosine_indices
n_cos = SPDE_FT$n_cos
n_cos_sin = length(cosine_indices)
K = SPDE_FT$K
}
## Simulate Y_t ##
if(TRUE){
spde_sim = spde_simulation(n,t,param_sig_t_dep,param_obs_t_dep,
param_bias_t_dep,seed = 1,n_obs = n_obs,
obs_loc = obs_loc, weights = weights, dt = dt)
y_sim = spde_sim$y
}
## Weighting matrix ##
if(TRUE){
W_coords = NULL; W = diag(1,n^2)
coords2 = lapply(1:n^2,function(i) as.numeric(expand.grid(0:(n-1),0:(n-1))[i,]))
Phi = Phi_f(wave,cosine_indices,n_cos,n,n_obs=n^2,coords = coords2)
W_fourier = t(Phi)%*%W%*%Phi
}
## Initial parameters ##
if(TRUE){
param0 = c(rho0 = 0.25, sigma2 = 0.5, zeta = 0.2,rho1 = 0.2, gamma = 1.5,
alpha = pi/3, mu_x = 0.1, mu_y = -0.2, tau2 = 0.05)
param_sig0 = param0[1:8]
param_obs0 = param_obs_func(m,m_indices,list(param0[9]))
param_bias0 = param_bias_func(m1,m1_indices,list(0))
}
## Log indices ##
if(TRUE){
log_indices = c(1,2,3,4,5,8+(1:param_obs0$m))
}
## Parameter plot limits ##
if(TRUE){
plot_limits = cbind(0.5*sapply(1:8, function(i) min(abs(param_sig0[[i]]),abs(param_sig[[i]]))*abs(param_sig[[i]])/param_sig[[i]]),
1.5*sapply(1:8, function(i) max(abs(param_sig0[[i]]),abs(param_sig[[i]]))*abs(param_sig[[i]])/param_sig[[i]]))
plot_limits = rbind(plot_limits,
cbind(0,1.5*max(unlist(param_obs$tau2_vals),unlist(param_obs0$tau2_vals))))
plot_limits = rbind(plot_limits,
cbind(0,1.5*max(unlist(param_bias$bias_vals),unlist(param_bias0$bias_vals))))
plot_limits = t(apply(plot_limits,1,sort))
plot_limits = lapply(1:dim(plot_limits)[1],function(i) plot_limits[i,])
}
## Parameters to estimate ##
if(TRUE){
grad_params = 1:n_param
}
## Hessian indices ##
if(TRUE){
hessian_indices = NULL
}
## Number of iterations ##
if(TRUE){
n_iterations = 1000
}
## Step sizes ##
if(TRUE){
## Initial step-size vector ##
step_size_vec = 0.005*c(0.01,0.1,0.1,0.005,0.05,0.01,0.01,0.01,0.001)
## Step size matrix ##
step_size = matrix(0,nrow=n_iterations,ncol=n_param)
for (i in 1:dim(step_size)[1]){
step_size[i,] = step_size_vec
}
}
## Parameter estimation period ##
if(TRUE){
param_est_starts = list(3000,2000,3000,3000,4000,2000,2000,2000,1000)
param_est_ends = rep(list(n_iterations),n_param)
}
## Plot vertical (burn in) lines? ##
if(TRUE){
plot_vertical = FALSE
}
## Plot Point Frequency ##
if(TRUE){
plot_point_freq = 5
}
## Plot Frequency ##
if(TRUE){
plot_freq = 50
}
## Filename ##
if(TRUE){
filename = paste("n",n,"_t",t,"_nobs",n_obs,sep="")
plot_filename = paste(filename,".pdf",sep="")
}
## Save ##
if(TRUE){
save = FALSE
save_plot = FALSE
}
## Print Iteration Frequency ##
if(TRUE){
print_iter_freq = 10
}
## Back Track Line Search? ##
if(TRUE){
back_track = FALSE
}
## Back Track Line Search Tolerance ##
if(TRUE){
back_track_tol = 1e-10
}
## Back Track Line Search for Each Param? ##
if(TRUE){
back_track_independent = TRUE
back_track_param = 1:n_param
}
## Back Track Line Search Time Independent? ##
if(TRUE){
back_track_time_independent = FALSE
}
## Back Track Scale ##
if(TRUE){
back_track_scale = 0.2
}
}
## BML ##
if(TRUE){
if(n_obs == n^2){
BML_test2 = BML_spectral(w = y_sim, n = n, t = t, K = K,
param_obs0 = param_obs0, param_sig0 = param_sig0,
n_param = n_param,grad_params = grad_params,
step_size = step_size,log_scale = FALSE,
log_indices = log_indices,
hessian_indices = hessian_indices,
n_iterations = n_iterations,
plot = TRUE, plot_limits = plot_limits,
param_obs_true = param_obs_t_dep,
param_sig_true = param_sig_t_dep,
param_obs_names = param_obs_names,
param_sig_names = param_sig_names,
param_est_starts = param_est_starts,
param_est_ends = param_est_ends,
plot_point_freq = plot_point_freq,
plot_freq = plot_freq,save_plot = save_plot,
plot_filename = plot_filename, save = save,
filename = filename, mean_param = TRUE,
print_iter_freq = print_iter_freq,
back_track = back_track,
back_track_tol = back_track_tol,
back_track_independent = back_track_independent,
back_track_time_independent = back_track_time_independent,
back_track_scale = back_track_scale,
back_track_param = back_track_param,
plot_vertical = plot_vertical,
W_fourier = W_fourier, dt = dt)
}
if(n_obs < n^2){
BML_test = BML(y = y_sim, n = n, t = t, K = K, param_obs0 = param_obs0,
param_sig0 = param_sig0, param_bias0 = param_bias0,
n_param = n_param, grad_params = grad_params,
step_size = step_size, log_scale = FALSE,
log_indices = log_indices, hessian_indices = hessian_indices,
n_obs = n_obs, coords = coords, n_iterations = n_iterations,
spec_weights_mat = spec_weights_mat, plot = TRUE,
plot_limits = plot_limits,
param_obs_true = param_obs_t_dep,
param_sig_true = param_sig_t_dep,
param_bias_true = param_bias_t_dep,
param_obs_names = param_obs_names,
param_sig_names = param_sig_names,
param_bias_names = param_bias_names,
param_est_starts = param_est_starts,
param_est_ends = param_est_ends,
plot_point_freq = plot_point_freq, plot_freq = plot_freq,
save_plot = save_plot, plot_filename = plot_filename,
save = save, filename = filename, mean_param = TRUE,
print_iter_freq = print_iter_freq,
back_track = back_track, back_track_tol = back_track_tol,
back_track_independent = back_track_independent,
back_track_time_independent = back_track_time_independent,
back_track_scale = back_track_scale,
back_track_param = back_track_param,
plot_vertical = plot_vertical,
W_fourier = W_fourier, dt = dt)
}
}
#############
#############
#### RML ####
#############
## Setup ##
if(TRUE){
## Prelims ##
if(TRUE){
n = 6; t = 10000; dt = 1; K = 10; nu = 1
}
## Observation Locations ##
if(TRUE){
all_obs = FALSE
## Observation locations
if(!all_obs){
coords = list(c(1.4,1.6),c(4.3,4.7),c(1.3,4.2),c(4.7,1.9),c(3.3,3.2),
c(0.1,2.0),c(5.0,4.8),c(0.1,0.2),c(2.8,5.4),c(3.6,0.2),
c(2.5,1.6),c(2.5,3.0),c(2.8,4.2),c(3.02,2.0))
}
if(all_obs){
coords = lapply(1:n^2,
function(i) as.numeric(expand.grid(0:(n-1),0:(n-1))[i,]))
}
## Observation locations 'indices'
coords_indices = sapply(coords,function(x) x[1]+n*x[2]+1)
## Number of observations
n_obs = length(coords)
## Observation location at all times
obs_loc = lapply(1:n_obs,function(j) matrix(coords[[j]],nrow=t,ncol=2,byrow=T))
## Plot observation locations
plot_obs = FALSE
if(plot_obs){
par(mfrow=c(1,1))
plot(sapply(coords,function(x) x)[1,],sapply(coords,function(x) x)[2,],
xlim = c(0,n-1),ylim=c(0,n-1),xlab=expression(x),ylab=expression(y),
main="Sensor Locations")
abline(v=0:(n-1),h=(0:n-1),col="gray92",lty=2)
}
}
## Parameters ##
if(TRUE){
## Signal parameters ##
param_sig = c(rho0 = 0.5, sigma2 = 0.2, zeta = 0.5,rho1 = 0.1, gamma = 2,
alpha = pi/4, mu_x = 0.3, mu_y = -0.3)
time_dep_sig_param = FALSE
if(!time_dep_sig_param){
param_sig_i_t_dep = lapply(1:length(param_sig),
function(i) param_t_dep_func(1,param_sig[i]))
param_sig_t_dep =
param_sig_t_dep_func(param_sig_i_t_dep[[1]],param_sig_i_t_dep[[2]],
param_sig_i_t_dep[[3]],param_sig_i_t_dep[[4]],
param_sig_i_t_dep[[5]],param_sig_i_t_dep[[6]],
param_sig_i_t_dep[[7]],param_sig_i_t_dep[[8]])
}
if(time_dep_sig_param){
rho0_t_dep = param_t_dep_func(list(1,16000),list(param_sig[1],0.5*param_sig[1]))
sigma2_t_dep = param_t_dep_func(list(1,10000),list(param_sig[2],2*param_sig[2]))
zeta_t_dep = param_t_dep_func(list(1,27000),list(param_sig[3],0.2))
rho1_t_dep = param_t_dep_func(list(1,22000),list(param_sig[4],2*param_sig[4]))
gamma_t_dep = param_t_dep_func(list(1,31000),list(param_sig[5],1.2))
alpha_t_dep = param_t_dep_func(list(1,25000),list(param_sig[6],1.1))
mu_x_t_dep = param_t_dep_func(list(1,13000),list(param_sig[7],.3*param_sig[7]))
mu_y_t_dep = param_t_dep_func(list(1,19000),list(param_sig[8],param_sig[8]+0.2))
param_sig_t_dep = param_sig_t_dep_func(rho0_t_dep,sigma2_t_dep,zeta_t_dep,
rho1_t_dep,gamma_t_dep,alpha_t_dep,
mu_x_t_dep,mu_y_t_dep)
}
## Observation parameters ##
mult_noise = FALSE
time_dep_obs_noise = FALSE
if(mult_noise){
m = 3;
m_indices = list(coords_indices[1:3],coords_indices[4:6],coords_indices[7:10])
tau2_vals = list(0.01,0.1,0.3)
}
if(!mult_noise){
m = 1; m_indices = list(coords_indices[1:n_obs]); tau2_vals = list(0.01)
}
param_obs = param_obs_func(m,m_indices,tau2_vals)
param_obs_t_dep = param_t_dep_func(list(1),list(param_obs))
if(time_dep_obs_noise){
param_obs_t_dep = param_t_dep_func(list(1,4000,7000,15000,19000),
list(param_obs,
param_obs_func(1,m_indices,list(0.05)),
param_obs_func(1,m_indices,list(0.03)),
param_obs_func(1,m_indices,list(0.1)),
param_obs_func(1,m_indices,list(0.02))))
}
## Observation bias ##
mult_bias = FALSE
if(mult_bias){
m1 = 2
m1_indices = list(coords_indices[1:5],coords_indices[6:10])
bias_vals = list(0,2)
}
if(!mult_bias){
m1 = 0; m1_indices = list(coords_indices[1:n_obs]); bias_vals = list(0)
}
param_bias = param_bias_func(m1,m1_indices,bias_vals)
param_bias_t_dep = param_t_dep_func(list(1),list(param_bias))
## Parameter names ##
param_sig_names = list(parse(text="rho[0]"),parse(text="sigma^2"),
parse(text="zeta"),parse(text="rho[1]"),
parse(text="gamma"),parse(text="alpha"),
parse(text="mu[x]"),parse(text="mu[y]"))
param_obs_names = list(parse(text="tau^2"))
param_bias_names = list(parse(text="beta"))
## Number of parameters ##
n_param = length(param_sig)+param_obs$m+param_bias$m
}
## Signal Noise Weights ##
if(TRUE){
## Weighting Matrix (Physical Space) ##
grid = expand.grid(x = 0:(n-1),y = 0:(n-1))/n
centre_x = 6/12; centre_y = 7/12; sigma_x = 0.3; sigma_y = 0.3; rho=0
weights = with(grid,sech2d(x = x,y = y, centre_x = centre_x,
centre_y = centre_y, sigma_x = sigma_x,
sigma_y=sigma_y, rho=rho))
weights_mat = weights_mat_func(weights)
## Weighting Matrix (Spectral Space) ##
spec_weights_mat = spec_weights_mat_func(n = n, K = K,
weights_mat = weights_mat)
## Alternative: No Weighting Matrix ##
weights = NULL; spec_weights_mat = NULL
}
## SPDE_FT object ##
if(TRUE){
SPDE_FT = spde_initialise(n,t,K)
wave = SPDE_FT$wave
cosine_indices = SPDE_FT$cosine_indices
n_cos = SPDE_FT$n_cos
n_cos_sin = length(cosine_indices)
K = SPDE_FT$K
}
## Simulate Y_t ##
if(TRUE){
spde_sim = spde_simulation(n,t,param_sig_t_dep,param_obs_t_dep,
param_bias_t_dep,seed = 2,n_obs = n_obs,
obs_loc = obs_loc, weights = weights,dt=dt)
y_sim = spde_sim$y
}
## Weighting matrix ##
if(TRUE){
W_coords = NULL; W = diag(1,n^2)
coords2 = lapply(1:n^2,function(i) as.numeric(expand.grid(0:(n-1),0:(n-1))[i,]))
Phi = Phi_f(wave,cosine_indices,n_cos,n,n_obs=n^2,coords = coords2)
W_fourier = t(Phi)%*%W%*%Phi
}
## Initial parameters ##
if(TRUE){
param0 = c(rho0 = 0.25, sigma2 = 0.5, zeta = 0.3,rho1 = 0.2, gamma = 1.5,
alpha = pi/3, mu_x = 0.1, mu_y = -0.15, tau2 = 0.1)
param_sig0 = param0[1:8]
#param_sig0[6:8] = param_sig[6:8]
if(mult_noise){
param_obs0 = param_obs_func(m,m_indices,list(param0[9],0.3,0.1))
}
if(!mult_noise){
param_obs0 = param_obs_func(m,m_indices,list(param0[9]))
#param_obs0 = param_obs
}
if(mult_bias){
param_bias0 = param_bias_func(m1,m1_indices,list(0.9,1.1))
}
if(!mult_bias){
param_bias0 = param_bias_func(m1,m1_indices,list(0))
}
}
## Log indices ##
if(TRUE){
log_indices = c(1,2,3,4,5,8+(1:param_obs0$m))
}
## Parameter plot limits ##
if(TRUE){
plot_limits_auto = FALSE
if(plot_limits_auto){
plot_limits = cbind(0.5*sapply(1:8, function(i) min(abs(param_sig0[[i]]),abs(param_sig[[i]]))*abs(param_sig[[i]])/param_sig[[i]]),
1.5*sapply(1:8, function(i) max(abs(param_sig0[[i]]),abs(param_sig[[i]]))*abs(param_sig[[i]])/param_sig[[i]]))
plot_limits = rbind(plot_limits,
cbind(0,1.5*max(unlist(param_obs$tau2_vals),unlist(param_obs0$tau2_vals))))
plot_limits = rbind(plot_limits,
cbind(0,1.5*max(unlist(param_bias$bias_vals),unlist(param_bias0$bias_vals))))
plot_limits = t(apply(plot_limits,1,sort))
plot_limits = lapply(1:dim(plot_limits)[1],function(i) plot_limits[i,])
}
if(!plot_limits_auto){
plot_limits = rep(list(rep(0,2)),9)
plot_limits[[1]] = c(0.2,0.6)
plot_limits[[2]] = c(0.1,0.7)
plot_limits[[3]] = c(0.1,0.6)
plot_limits[[4]] = c(0.05,0.4)
plot_limits[[5]] = c(0.9,2.3)
plot_limits[[6]] = c(0.6,1.2)
plot_limits[[7]] = c(0.05,0.35)
plot_limits[[8]] = c(-0.35,0)
plot_limits[[9]] = c(0,0.5)
plot_limits[[10]] = c(0,2.5)
}
}
## Parameters to estimate ##
if(TRUE){
grad_params = 1:9
#grad_params = 9:13
}
## Hessian indices ##
if(TRUE){
hessian_indices = NULL
}
## Number of iterations ##
if(TRUE){
n_iterations = 1
}
## Step sizes ##
if(TRUE){
## Initial step-size vector ##
if(mult_noise && mult_bias){
step_size_vec = c(0.002,0.005,0.005,0.001,0.015,0.005,0.001,0.001,0.0004,0.0006,0.0003,0.0004,0.0004)
}
if(!mult_noise || !mult_bias){
step_size_vec = c(0.001,0.005,0.003,0.002,0.02,0.005,0.0003,0.0003,0.0005) # use for time_indep sim
#step_size_vec = c(0.001,0.002,0.0015,0.0015,0.006,0.0015,0.0002,0.0002,0.0001) # use for time_dep sim
step_size_vec[1] = 1/(dt^0.2)*step_size_vec[1]
step_size_vec[2] = 1/(dt^0.1)*step_size_vec[2]
step_size_vec[3] = 1/(dt^0.4)*step_size_vec[3]
step_size_vec[4] = 1/(dt^0.1)*step_size_vec[4]
step_size_vec[5] = 1/(dt^0.2)*step_size_vec[5]
step_size_vec[6] = 1/(dt^0.2)*step_size_vec[6]
step_size_vec[7:8] = 1/(dt^0.1)*step_size_vec[7:8]
}
## Contant step size? ##
constant_step_size = TRUE
## Step size matrix ##
step_size = matrix(0,nrow=n_iterations*t,ncol=n_param)
for (i in 1:dim(step_size)[1]){
if(constant_step_size){
step_size[i,] = step_size_vec
}
if(!constant_step_size){
step_size[i,] = 10*step_size_vec*rep(i^(-0.5),n_param)
}
}
step_size[500:10000,9] = 0.1*step_size[500:10000,9]
}
## Parameter estimation period ##
if(TRUE){
if(constant_step_size){
if(mult_noise && mult_bias){
param_est_starts = list(3000,2000,3000,3000,4000,2000,2000,2000,3000,3000,3000,3000,3000)
}
if(!mult_noise || !mult_bias){
param_est_starts = list(8000,8000,8000,8000,8000,8000,8000,8000,8000,1000)
}
}
if(!constant_step_size){
if(mult_noise && mult_bias){
param_est_starts = list(5000,5000,10000,5000,10000,4000,4000,4000,3000,3000,3000,3000,3000)
}
if(!mult_noise || !mult_bias){
param_est_starts = list(10000,10000,20000,5000,15000,15000,10000,10000,1000)
}
}
param_est_ends = rep(list(n_iterations*t),n_param)
if(time_dep_sig_param && time_dep_obs_noise){
param_est_starts = list(c(4000,19000),c(4000,12000),c(5000,31000),c(4000,24000),
c(5000,33000),c(5000,27000),c(4000,15000),c(4000,21000),
c(500,4500,7500,15500,19500))
param_est_ends = list(c(16000,t*n_iterations),c(10000,t*n_iterations),
c(27000,t*n_iterations),c(22000,t*n_iterations),
c(31000,t*n_iterations),c(25000,t*n_iterations),
c(13000,t*n_iterations),c(19000,t*n_iterations),
c(4000,7000,15000,19000,t*n_iterations))
}
}
## Plot vertical (burn in) lines? ##
if(TRUE){
plot_vertical = FALSE
}
## Plot Point Frequency ##
if(TRUE){
plot_point_freq = 20
}
## Plot Frequency ##
if(TRUE){
plot_freq = 500
}
## Filename ##
if(TRUE){
filename = paste("n",n,"_t",t,"_nobs",n_obs,sep="")
plot_filename = paste(filename,".pdf",sep="")
}
## Save ##
if(TRUE){
save = TRUE
save_plot = TRUE
}
## Print Iteration Frequency ##
if(TRUE){
print_iter_freq = 100
}
## Back Track Line Search? ##
if(TRUE){
back_track = FALSE
}
## Back Track Line Search Tolerance ##
if(TRUE){
back_track_tol = 1e-3
}
## Back Track Line Search for Each Param? ##
if(TRUE){
back_track_independent = FALSE
back_track_param = 1:n_param
}
## Back Track Line Search Time Independent? ##
if(TRUE){
back_track_time_independent = FALSE
}
## Back Track Scale ##
if(TRUE){
back_track_scale = 0.5
}
}
## RML ##
if(TRUE){
if(K==n^2 && n_obs == n^2){
RML_test = RML_spectral(w = y_sim, n = n, t = t, K = K,
param_obs0 = param_obs0, param_sig0 = param_sig0, n_param = n_param,
grad_params = grad_params, step_size = step_size,
log_scale = FALSE, log_indices = log_indices,
hessian_indices = hessian_indices,
n_iterations = n_iterations,
plot = TRUE, plot_limits = plot_limits,
param_obs_true = param_obs_t_dep,
param_sig_true = param_sig_t_dep,
param_obs_names = param_obs_names,
param_sig_names = param_sig_names,
param_est_starts = param_est_starts,
param_est_ends = param_est_ends,
plot_point_freq = plot_point_freq, plot_freq = plot_freq,
save_plot = save_plot, plot_filename = plot_filename,
save = save, filename = filename, mean_param = TRUE,
print_iter_freq = print_iter_freq,
back_track = back_track,
back_track_tol = back_track_tol,
back_track_independent = back_track_independent,
back_track_time_independent = back_track_time_independent,
back_track_scale = back_track_scale,
back_track_param = back_track_param,
plot_vertical = plot_vertical,
W_fourier = W_fourier, dt = dt)
}
if(K<n^2 || n_obs < n^2){
RML_test = RML(y = y_sim, n = n, t = t, K = K,
param_obs0 = param_obs0, param_sig0 = param_sig0,
param_bias0 = param_bias0, n_param = n_param,
grad_params = grad_params, step_size = step_size,
log_scale = FALSE, log_indices = log_indices,
hessian_indices = hessian_indices,
n_iterations = n_iterations,n_obs = n_obs, coords = coords,
spec_weights_mat = spec_weights_mat, plot = TRUE,
plot_limits = plot_limits,
param_obs_true = param_obs_t_dep,
param_sig_true = param_sig_t_dep,
param_bias_true = param_bias_t_dep,
param_obs_names = param_obs_names,
param_sig_names = param_sig_names,
param_bias_names = param_bias_names,
param_est_starts = param_est_starts,
param_est_ends = param_est_ends,
plot_point_freq = plot_point_freq, plot_freq = plot_freq,
save_plot = save_plot, plot_filename = plot_filename,
save = save, filename = filename, mean_param = TRUE,
print_iter_freq = print_iter_freq,
back_track = back_track, back_track_tol = back_track_tol,
back_track_independent = back_track_independent,
back_track_time_independent = back_track_time_independent,
back_track_scale = back_track_scale,
back_track_param = back_track_param,
plot_vertical = plot_vertical,
W_fourier = W_fourier, dt = dt)
}
}
#############
######################
#### BatchOptSens ####
######################
## Setup ##
if(TRUE){
## Prelims ##
if(TRUE){
n = 12; t = 15; dt = 1; K = 10; nu = 1
}
## Initial Observation Locations ##
if(TRUE){
## Coordinates ##
obs0 = list(c(8,5),c(4,6),c(5,4),c(7,4))
obs0 = list(c(12,12),c(1,1),c(1,11),c(11,1),c(11,11))
## Indices ##
obs0_indices = sapply(obs0,function(x) x[1]+n*x[2]+1)
## Number of observations ##
n_obs = length(obs0)
## Observation location at all times ##
obs_loc = lapply(1:n_obs,
function(j) matrix(obs0[[j]],nrow=t,ncol=2,byrow=T))
## Plot initial observation locations ##
plot_obs = TRUE
if(plot_obs){
par(mfrow=c(1,1))
plot(sapply(obs0,function(x) x)[1,],sapply(obs0,function(x) x)[2,],
xlim = c(0,n),ylim=c(0,n),xlab=expression(x),ylab=expression(y),
main="Sensor Locations")
abline(v=0:(n),h=(0:n),col="gray92",lty=2)
}
}
## Parameters ##
if(TRUE){
## Signal parameters ##
param_sig = c(rho0 = 0.5, sigma2 = 0.2, zeta = 0.5,rho1 = 0.1, gamma = 2,
alpha = pi/4, mu_x = 0.3, mu_y = -0.3)
param_sig_i_t_dep = lapply(1:length(param_sig),
function(i) param_t_dep_func(1,param_sig[i]))
param_sig_t_dep =
param_sig_t_dep_func(param_sig_i_t_dep[[1]],param_sig_i_t_dep[[2]],
param_sig_i_t_dep[[3]],param_sig_i_t_dep[[4]],
param_sig_i_t_dep[[5]],param_sig_i_t_dep[[6]],
param_sig_i_t_dep[[7]],param_sig_i_t_dep[[8]])
## Observation parameters ##
m = 1; m_indices = list(obs0_indices); tau2_vals = list(0.01)
param_obs = param_obs_func(m,m_indices,tau2_vals)
param_obs_t_dep = param_t_dep_func(list(1),list(param_obs))
## Observation bias ##
m1 = 0; m1_indices = list(obs0_indices); bias_vals = list(0)
param_bias = param_bias_func(m1,m1_indices,bias_vals)
param_bias_t_dep = param_t_dep_func(list(1),list(param_bias))
## Parameter names ##
param_sig_names = list(parse(text="rho[0]"),parse(text="sigma^2"),
parse(text="zeta"),parse(text="rho[1]"),
parse(text="gamma"),parse(text="alpha"),
parse(text="mu[x]"),parse(text="mu[y]"))
param_obs_names = list(parse(text="tau^2"))
param_bias_names = list(parse(text="beta"))
## Number of parameters ##
n_param = length(param_sig)+param_obs$m+param_bias$m
}
## Signal Noise Weights ##
if(TRUE){
grid = expand.grid(x = 0:(n-1),y = 0:(n-1))/n
centre_x = 4/12; centre_y = 5/12; sigma_x = 0.2; sigma_y = 0.2; rho = 0
weights = with(grid,sech2d(x = x,y = y, centre_x = centre_x,
centre_y = centre_y, sigma_x = sigma_x,
sigma_y=sigma_y, rho = rho))
weights_mat = weights_mat_func(weights)
spec_weights_mat = spec_weights_mat_func(n = n, K = K,
weights_mat = weights_mat)
weights = NULL; spec_weights_mat = NULL
}
## SPDE_FT object ##
if(TRUE){
SPDE_FT = spde_initialise(n,t,K)
wave = SPDE_FT$wave
cosine_indices = SPDE_FT$cosine_indices
n_cos = SPDE_FT$n_cos
n_cos_sin = length(cosine_indices)
K = SPDE_FT$K
}
## Simulate Y_t ##
if(TRUE){
spde_sim = spde_simulation(n,t,param_sig_t_dep,param_obs_t_dep,
param_bias_t_dep,seed = 1,n_obs = n_obs,
obs_loc = obs_loc, weights = weights, dt = dt)
y_sim = spde_sim$y
}
## Weighting matrix ##
if(TRUE){
## Weighting coordinates ##
W_coords = list(c(10,11),c(7,10),c(6,8),c(9,6))
## Weighting indices ##
W_indices = lapply(W_coords, function(A) A[2]*n+A[1]+1)
## Weighting matrix (physical space) ##
W = matrix(0,nrow=n^2,ncol=n^2)
diag(W)[unlist(W_indices)] = rep(10,length(W_coords))
## Alternative: no weighting ##
W_coords = NULL; diag(W) = rep(1,n^2);
## Weighting matrix (spectral space) ##
coords = lapply(1:n^2,function(i) as.numeric(expand.grid(0:(n-1),0:(n-1))[i,]))
Phi = Phi_f(wave,cosine_indices,n_cos,n,n_obs=n^2,coords = coords)
W_fourier = t(Phi)%*%W%*%Phi
}
## Number of iterations ##
if(TRUE){
n_iterations = 100
}
## Step sizes ##
if(TRUE){
## Initial step size vector ##
step_size_vec = c(0.05,0.05)
## Step size matrix ##
step_size_mat = matrix(0,nrow=n_iterations,ncol=2)
for (i in 1:n_iterations){
step_size_mat[i,]=step_size_vec
}
## Step size matrices for all sensors ##
step_size = rep(list(step_size_mat),n_obs)
}
## Observations to be optimised ##
if(TRUE){
grad_obs = 1
}
## Plot Point Frequency ##
if(TRUE){
plot_point_freq = 2
}
## Plot Frequency ##
if(TRUE){
plot_freq = 50
}
## Filenames ##
if(TRUE){
filename_plot = "offline_opt_sens.pdf"
filename_plot2d = "offline_opt_sens2d.pdf"
}
## Save plots? ##
if(TRUE){
save_plot = FALSE
save_plot2d = FALSE
}
## Plot grid? ##
if(TRUE){
grid = TRUE
}
## Print Iteration Frequency ##
if(TRUE){
print_iter_freq = 10
}
## Back Track Line Search? ##
if(TRUE){
back_track = FALSE
}
## Back Track Line Search Tolerance ##
if(TRUE){
back_track_tol = 1e-4
}
## Back Track Line Search for Each Param? ##
if(TRUE){
back_track_independent = TRUE
back_track_obs = 1:n_obs
}
## Back Track Line Search Time Independent? ##
if(TRUE){
back_track_time_independent = TRUE
}