scripts/univariate_Gaussian/bayesian_fusion/similar_means_example.R
In rchan26/hierarchicalFusion: Divide-and-Conquer Monte Carlo Fusion
library(DCFusion)
seed <- 1994
set.seed(seed)
nsamples <- 10000
C <- 10
mean <- 0
beta <- 1/C
a_mesh_vanilla <- seq(0, 0.005, length.out = 6)
a_mesh_gen <- seq(0, 1, length.out = 6)
diffusion_estimator <- 'NB'
ESS_threshold <- 0.5
CESS_0_threshold <- 0.2
vanilla_b <- 1
k1 <- NULL
k2 <- NULL
k3 <- 1
k4 <- 1
data_sizes <- c(1000, 5000, 10000, 20000, 30000, 40000, 50000)
a_results <- list('vanilla' = list(), 'generalised' = list())
b_results <- list('vanilla' = list(), 'generalised' = list())
c_results <- list('vanilla' = list(), 'generalised' = list())
d_results <- list('vanilla' = list(), 'generalised' = list())
SSH_adaptive_results <- list('vanilla' = list(), 'generalised' = list())
for (i in 1:length(data_sizes)) {
set.seed(seed*i)
sd <- sqrt(1/data_sizes[i])
opt_bw <- ((4*sd^5)/(3*nsamples))^(1/5)
curve(dnorm(x, mean = mean, sd = sd), mean-4*sd, mean+4*sd,
main = paste('m:', data_sizes[i]))
input_samples <- lapply(1:C, function(i) rnorm_tempered(N = nsamples,
mean = mean,
sd = sd,
beta = beta))
print(paste('##### m:', data_sizes[i]))
print(paste('sd:', sd))
print(paste('var:', sd^2))
print(paste('sub_posterior var (true):', C*sd^2))
print(paste('sub_posterior var:', sapply(input_samples, var)))
##### Fixed user-specified parameters #####
print('### performing standard Bayesian Fusion (with standard mesh)')
input_particles <- initialise_particle_sets(samples_to_fuse = input_samples,
multivariate = FALSE,
number_of_steps = length(a_mesh_vanilla))
a_BF_standard <- parallel_GBF_uniGaussian(particles_to_fuse = input_particles,
N = nsamples,
m = C,
time_mesh = a_mesh_vanilla,
means = rep(mean, C),
sds = rep(sd, C),
betas = rep(beta, C),
precondition_values = rep(1, C),
ESS_threshold = ESS_threshold,
diffusion_estimator = diffusion_estimator,
seed = seed*i)
print('### performing Bayesian Fusion with a preconditioning matrix (with standard mesh)')
input_particles <- initialise_particle_sets(samples_to_fuse = input_samples,
multivariate = FALSE,
number_of_steps = length(a_mesh_gen))
a_BF_generalised <- parallel_GBF_uniGaussian(particles_to_fuse = input_particles,
N = nsamples,
m = C,
time_mesh = a_mesh_gen,
means = rep(mean, C),
sds = rep(sd, C),
betas = rep(beta, C),
precondition_values = sapply(input_samples, var),
ESS_threshold = ESS_threshold,
diffusion_estimator = diffusion_estimator,
seed = seed*i)
# save results
a_results$vanilla[[i]] <- list('CESS_0' = a_BF_standard$CESS[1],
'CESS_j' = a_BF_standard$CESS[2:length(a_BF_standard$CESS)],
'CESS_j_avg' = mean(a_BF_standard$CESS[2:length(a_BF_standard$CESS)]),
'n' = length(a_BF_standard$CESS),
'time_mesh' = a_BF_standard$particles$time_mesh,
'time' = a_BF_standard$time,
'IAD' = integrated_abs_distance_uniGaussian(
fusion_post = resample_particle_y_samples(particle_set = a_BF_standard$particles,
multivariate = FALSE,
resampling_method = 'resid',
seed = seed*i)$y_samples,
mean = 0,
sd = sd,
beta = 1,
bw = opt_bw))
a_results$generalised[[i]] <- list('CESS_0' = a_BF_generalised$CESS[1],
'CESS_j' = a_BF_generalised$CESS[2:length(a_BF_generalised$CESS)],
'CESS_j_avg' = mean(a_BF_generalised$CESS[2:length(a_BF_generalised$CESS)]),
'n' = length(a_BF_generalised$CESS),
'time_mesh' = a_BF_generalised$particles$time_mesh,
'time' = a_BF_generalised$time,
'IAD' = integrated_abs_distance_uniGaussian(
fusion_post = resample_particle_y_samples(particle_set = a_BF_generalised$particles,
multivariate = FALSE,
resampling_method = 'resid',
seed = seed*i)$y_samples,
mean = 0,
sd = sd,
beta = 1,
bw = opt_bw))
# plot
lines(density(resample_particle_y_samples(particle_set = a_BF_standard$particles,
multivariate = FALSE,
resampling_method = 'resid',
seed = seed*i)$y_samples),
col = 'red')
lines(density(resample_particle_y_samples(particle_set = a_BF_generalised$particles,
multivariate = FALSE,
resampling_method = 'resid',
seed = seed*i)$y_samples),
col = 'red', lty = 2)
##### Recommended scaling of T, fixed n #####
print('### performing standard Bayesian Fusion (with recommended T, fixed n)')
vanilla_guide <- BF_guidance(condition = 'SH',
CESS_0_threshold = CESS_0_threshold,
C = C,
d = 1,
data_size = data_sizes[i],
b = vanilla_b,
sub_posterior_means = sapply(input_samples, mean),
k1 = k1,
k3 = k3,
k4 = k4,
vanilla = TRUE)
b_mesh_vanilla <- seq(0, vanilla_guide$min_T, length.out = 6)
input_particles <- initialise_particle_sets(samples_to_fuse = input_samples,
multivariate = FALSE,
number_of_steps = length(b_mesh_vanilla))
b_BF_standard <- parallel_GBF_uniGaussian(particles_to_fuse = input_particles,
N = nsamples,
m = C,
time_mesh = b_mesh_vanilla,
means = rep(mean, C),
sds = rep(sd, C),
betas = rep(beta, C),
precondition_values = rep(1, C),
ESS_threshold = ESS_threshold,
diffusion_estimator = diffusion_estimator,
seed = seed*i)
print('### performing Bayesian Fusion with a preconditioning matrix (with recommended T, fixed n)')
gen_guide <- BF_guidance(condition = 'SH',
CESS_0_threshold = CESS_0_threshold,
C = C,
d = 1,
data_size = data_sizes[i],
sub_posterior_means = sapply(input_samples, mean),
precondition_matrices = sapply(input_samples, var),
inv_precondition_matrices = 1/sapply(input_samples, var),
k1 = k1,
k3 = k3,
k4 = k4,
vanilla = FALSE)
b_mesh_gen <- seq(0, gen_guide$min_T, length.out = 6)
input_particles <- initialise_particle_sets(samples_to_fuse = input_samples,
multivariate = FALSE,
number_of_steps = length(b_mesh_gen))
b_BF_generalised <- parallel_GBF_uniGaussian(particles_to_fuse = input_particles,
N = nsamples,
m = C,
time_mesh = b_mesh_gen,
means = rep(mean, C),
sds = rep(sd, C),
betas = rep(beta, C),
precondition_values = sapply(input_samples, var),
ESS_threshold = ESS_threshold,
diffusion_estimator = diffusion_estimator,
seed = seed*i)
# save results
b_results$vanilla[[i]] <- list('CESS_0' = b_BF_standard$CESS[1],
'CESS_j' = b_BF_standard$CESS[2:length(b_BF_standard$CESS)],
'CESS_j_avg' = mean(b_BF_standard$CESS[2:length(b_BF_standard$CESS)]),
'n' = length(b_BF_standard$CESS),
'time_mesh' = b_BF_standard$particles$time_mesh,
'time' = b_BF_standard$time,
'IAD' = integrated_abs_distance_uniGaussian(
fusion_post = resample_particle_y_samples(particle_set = b_BF_standard$particles,
multivariate = FALSE,
resampling_method = 'resid',
seed = seed*i)$y_samples,
mean = 0,
sd = sd,
beta = 1,
bw = opt_bw))
b_results$generalised[[i]] <- list('CESS_0' = b_BF_generalised$CESS[1],
'CESS_j' = b_BF_generalised$CESS[2:length(b_BF_generalised$CESS)],
'CESS_j_avg' = mean(b_BF_generalised$CESS[2:length(b_BF_generalised$CESS)]),
'n' = length(b_BF_generalised$CESS),
'time_mesh' = b_BF_generalised$particles$time_mesh,
'time' = b_BF_generalised$time,
'IAD' = integrated_abs_distance_uniGaussian(
fusion_post = resample_particle_y_samples(particle_set = b_BF_generalised$particles,
multivariate = FALSE,
resampling_method = 'resid',
seed = seed*i)$y_samples,
mean = 0,
sd = sd,
beta = 1,
bw = opt_bw))
# plot
lines(density(resample_particle_y_samples(particle_set = b_BF_standard$particles,
multivariate = FALSE,
resampling_method = 'resid',
seed = seed*i)$y_samples),
col = 'blue')
lines(density(resample_particle_y_samples(particle_set = b_BF_generalised$particles,
multivariate = FALSE,
resampling_method = 'resid',
seed = seed*i)$y_samples),
col = 'blue', lty = 2)
##### Recommended scaling of T, regular mesh #####
print('### performing standard Bayesian Fusion (with recommended T, regular mesh)')
input_particles <- initialise_particle_sets(samples_to_fuse = input_samples,
multivariate = FALSE,
number_of_steps = length(vanilla_guide$mesh))
c_BF_standard <- parallel_GBF_uniGaussian(particles_to_fuse = input_particles,
N = nsamples,
m = C,
time_mesh = vanilla_guide$mesh,
means = rep(mean, C),
sds = rep(sd, C),
betas = rep(beta, C),
precondition_values = rep(1, C),
ESS_threshold = ESS_threshold,
diffusion_estimator = diffusion_estimator,
seed = seed*i)
print('### performing Bayesian Fusion with a preconditioning matrix (with recommended T, regular mesh)')
input_particles <- initialise_particle_sets(samples_to_fuse = input_samples,
multivariate = FALSE,
number_of_steps = length(gen_guide$mesh))
c_BF_generalised <- parallel_GBF_uniGaussian(particles_to_fuse = input_particles,
N = nsamples,
m = C,
time_mesh = gen_guide$mesh,
means = rep(mean, C),
sds = rep(sd, C),
betas = rep(beta, C),
precondition_values = sapply(input_samples, var),
ESS_threshold = ESS_threshold,
diffusion_estimator = diffusion_estimator,
seed = seed*i)
# save results
c_results$vanilla[[i]] <- list('CESS_0' = c_BF_standard$CESS[1],
'CESS_j' = c_BF_standard$CESS[2:length(c_BF_standard$CESS)],
'CESS_j_avg' = mean(c_BF_standard$CESS[2:length(c_BF_standard$CESS)]),
'n' = length(c_BF_standard$CESS),
'time_mesh' = c_BF_standard$particles$time_mesh,
'time' = c_BF_standard$time,
'IAD' = integrated_abs_distance_uniGaussian(
fusion_post = resample_particle_y_samples(particle_set = c_BF_standard$particles,
multivariate = FALSE,
resampling_method = 'resid',
seed = seed*i)$y_samples,
mean = 0,
sd = sd,
beta = 1,
bw = opt_bw))
c_results$generalised[[i]] <- list('CESS_0' = c_BF_generalised$CESS[1],
'CESS_j' = c_BF_generalised$CESS[2:length(c_BF_generalised$CESS)],
'CESS_j_avg' = mean(c_BF_generalised$CESS[2:length(c_BF_generalised$CESS)]),
'n' = length(c_BF_generalised$CESS),
'time_mesh' = c_BF_generalised$particles$time_mesh,
'time' = c_BF_generalised$time,
'IAD' = integrated_abs_distance_uniGaussian(
fusion_post = resample_particle_y_samples(particle_set = c_BF_generalised$particles,
multivariate = FALSE,
resampling_method = 'resid',
seed = seed*i)$y_samples,
mean = 0,
sd = sd,
beta = 1,
bw = opt_bw))
# plot
lines(density(resample_particle_y_samples(particle_set = c_BF_standard$particles,
multivariate = FALSE,
resampling_method = 'resid',
seed = seed*i)$y_samples),
col = 'green')
lines(density(resample_particle_y_samples(particle_set = c_BF_generalised$particles,
multivariate = FALSE,
resampling_method = 'resid',
seed = seed*i)$y_samples),
col = 'green', lty = 2)
##### Recommended scaling of T, adaptive mesh #####
print('### performing standard Bayesian Fusion (with recommended T, adaptive mesh)')
input_particles <- initialise_particle_sets(samples_to_fuse = input_samples,
multivariate = FALSE,
number_of_steps = length(vanilla_guide$mesh))
d_BF_standard <- parallel_GBF_uniGaussian(particles_to_fuse = input_particles,
N = nsamples,
m = C,
time_mesh = vanilla_guide$mesh,
means = rep(mean, C),
sds = rep(sd, C),
betas = rep(beta, C),
precondition_values = rep(1, C),
ESS_threshold = ESS_threshold,
sub_posterior_means = sapply(input_samples, mean),
adaptive_mesh = TRUE,
adaptive_mesh_parameters = list('data_size' = data_sizes[i],
'b' = vanilla_b,
'k3' = k3,
'k4' = k4,
'vanilla' = TRUE),
diffusion_estimator = diffusion_estimator,
seed = seed*i)
print('### performing Bayesian Fusion with a preconditioning matrix (with recommended T, adaptive mesh)')
input_particles <- initialise_particle_sets(samples_to_fuse = input_samples,
multivariate = FALSE,
number_of_steps = length(gen_guide$mesh))
d_BF_generalised <- parallel_GBF_uniGaussian(particles_to_fuse = input_particles,
N = nsamples,
m = C,
time_mesh = gen_guide$mesh,
means = rep(mean, C),
sds = rep(sd, C),
betas = rep(beta, C),
precondition_values = sapply(input_samples, var),
ESS_threshold = ESS_threshold,
sub_posterior_means = sapply(input_samples, mean),
adaptive_mesh = TRUE,
adaptive_mesh_parameters = list('data_size' = data_sizes[i],
'k3' = k3,
'k4' = k4,
'vanilla' = FALSE),
diffusion_estimator = diffusion_estimator,
seed = seed*i)
# save results
d_results$vanilla[[i]] <- list('CESS_0' = d_BF_standard$CESS[1],
'CESS_j' = d_BF_standard$CESS[2:length(d_BF_standard$CESS)],
'CESS_j_avg' = mean(d_BF_standard$CESS[2:length(d_BF_standard$CESS)]),
'n' = length(d_BF_standard$CESS),
'time_mesh' = d_BF_standard$particles$time_mesh,
'time' = d_BF_standard$time,
'IAD' = integrated_abs_distance_uniGaussian(
fusion_post = resample_particle_y_samples(particle_set = d_BF_standard$particles,
multivariate = FALSE,
resampling_method = 'resid',
seed = seed*i)$y_samples,
mean = 0,
sd = sd,
beta = 1,
bw = opt_bw))
d_results$generalised[[i]] <- list('CESS_0' = d_BF_generalised$CESS[1],
'CESS_j' = d_BF_generalised$CESS[2:length(d_BF_generalised$CESS)],
'CESS_j_avg' = mean(d_BF_generalised$CESS[2:length(d_BF_generalised$CESS)]),
'n' = length(d_BF_generalised$CESS),
'time_mesh' = d_BF_generalised$particles$time_mesh,
'time' = d_BF_generalised$time,
'IAD' = integrated_abs_distance_uniGaussian(
fusion_post = resample_particle_y_samples(particle_set = d_BF_generalised$particles,
multivariate = FALSE,
resampling_method = 'resid',
seed = seed*i)$y_samples,
mean = 0,
sd = sd,
beta = 1,
bw = opt_bw))
# plot
lines(density(resample_particle_y_samples(particle_set = d_BF_standard$particles,
multivariate = FALSE,
resampling_method = 'resid',
seed = seed*i)$y_samples),
col = 'purple')
lines(density(resample_particle_y_samples(particle_set = d_BF_generalised$particles,
multivariate = FALSE,
resampling_method = 'resid',
seed = seed*i)$y_samples),
col = 'purple', lty = 2)
##### SSH: Recommended scaling of T, adaptive mesh #####
print('### SSH: performing standard Bayesian Fusion (with recommended T, adaptive mesh)')
vanilla_guide_SSH <- BF_guidance(condition = 'SSH',
CESS_0_threshold = CESS_0_threshold,
C = C,
d = 1,
data_size = data_sizes[i],
b = vanilla_b,
sub_posterior_means = sapply(input_samples, mean),
k1 = k1,
k2 = k2,
k3 = k3,
k4 = k4,
vanilla = TRUE)
input_particles <- initialise_particle_sets(samples_to_fuse = input_samples,
multivariate = FALSE,
number_of_steps = length(vanilla_guide_SSH$mesh))
SSH_adaptive_standard <- parallel_GBF_uniGaussian(particles_to_fuse = input_particles,
N = nsamples,
m = C,
time_mesh = vanilla_guide_SSH$mesh,
means = rep(mean, C),
sds = rep(sd, C),
betas = rep(beta, C),
precondition_values = rep(1, C),
ESS_threshold = ESS_threshold,
sub_posterior_means = sapply(input_samples, mean),
adaptive_mesh = TRUE,
adaptive_mesh_parameters = list('data_size' = data_sizes[i],
'b' = vanilla_b,
'k3' = k3,
'k4' = k4,
'vanilla' = TRUE),
diffusion_estimator = diffusion_estimator,
seed = seed*i)
print('### SSH: performing Bayesian Fusion with a preconditioning matrix (with recommended T, adaptive mesh)')
gen_guide_SSH <- BF_guidance(condition = 'SSH',
CESS_0_threshold = CESS_0_threshold,
C = C,
d = 1,
data_size = data_sizes[i],
sub_posterior_means = sapply(input_samples, mean),
precondition_matrices = sapply(input_samples, var),
inv_precondition_matrices = 1/sapply(input_samples, var),
k1 = k1,
k2 = k2,
k3 = k3,
k4 = k4,
vanilla = FALSE)
input_particles <- initialise_particle_sets(samples_to_fuse = input_samples,
multivariate = FALSE,
number_of_steps = length(gen_guide_SSH$mesh))
SSH_adaptive_generalised <- parallel_GBF_uniGaussian(particles_to_fuse = input_particles,
N = nsamples,
m = C,
time_mesh = gen_guide_SSH$mesh,
means = rep(mean, C),
sds = rep(sd, C),
betas = rep(beta, C),
precondition_values = sapply(input_samples, var),
ESS_threshold = ESS_threshold,
sub_posterior_means = sapply(input_samples, mean),
adaptive_mesh = TRUE,
adaptive_mesh_parameters = list('data_size' = data_sizes[i],
'k3' = k3,
'k4' = k4,
'vanilla' = FALSE),
diffusion_estimator = diffusion_estimator,
seed = seed*i)
# save results
SSH_adaptive_results$vanilla[[i]] <- list('CESS_0' = SSH_adaptive_standard$CESS[1],
'CESS_j' = SSH_adaptive_standard$CESS[2:length(SSH_adaptive_standard$CESS)],
'CESS_j_avg' = mean(SSH_adaptive_standard$CESS[2:length(SSH_adaptive_standard$CESS)]),
'n' = length(SSH_adaptive_standard$CESS),
'time_mesh' = SSH_adaptive_standard$particles$time_mesh,
'time' = SSH_adaptive_standard$time,
'IAD' = integrated_abs_distance_uniGaussian(
fusion_post = resample_particle_y_samples(particle_set = SSH_adaptive_standard$particles,
multivariate = FALSE,
resampling_method = 'resid',
seed = seed*i)$y_samples,
mean = 0,
sd = sd,
beta = 1,
bw = opt_bw))
SSH_adaptive_results$generalised[[i]] <- list('CESS_0' = SSH_adaptive_generalised$CESS[1],
'CESS_j' = SSH_adaptive_generalised$CESS[2:length(SSH_adaptive_generalised$CESS)],
'CESS_j_avg' = mean(SSH_adaptive_generalised$CESS[2:length(SSH_adaptive_generalised$CESS)]),
'n' = length(SSH_adaptive_generalised$CESS),
'time_mesh' = SSH_adaptive_generalised$particles$time_mesh,
'time' = SSH_adaptive_generalised$time,
'IAD' = integrated_abs_distance_uniGaussian(
fusion_post = resample_particle_y_samples(particle_set = SSH_adaptive_generalised$particles,
multivariate = FALSE,
resampling_method = 'resid',
seed = seed*i)$y_samples,
mean = 0,
sd = sd,
beta = 1,
bw = opt_bw))
# plot
lines(density(resample_particle_y_samples(particle_set = SSH_adaptive_standard$particles,
multivariate = FALSE,
resampling_method = 'resid',
seed = seed*i)$y_samples),
col = 'orange')
lines(density(resample_particle_y_samples(particle_set = SSH_adaptive_generalised$particles,
multivariate = FALSE,
resampling_method = 'resid',
seed = seed*i)$y_samples),
col = 'orange', lty = 2)
}
##### vanilla plots #####
##### Fixed user-specified parameters #####
plot(x = data_sizes,
y = sapply(1:length(data_sizes), function(i) a_results$vanilla[[i]]$CESS_0)/nsamples,
type = 'b', pch = 20, lty = 1, lwd = 3, ylim = c(0,1), xaxt = 'n', yaxt ='n', xlab = '', ylab = '')
lines(x = data_sizes,
y = sapply(1:length(data_sizes), function(i) a_results$vanilla[[i]]$CESS_j_avg)/nsamples,
pch = 20, lty = 2, lwd = 3, type = 'b')
for (ii in 1:length(data_sizes)) {
cess_j <- lapply(1:length(data_sizes), function(i) a_results$vanilla[[i]]$CESS_j/nsamples)[[ii]]
points(x = rep(data_sizes[ii], length(cess_j)), y = cess_j, cex = 0.5)
}
axis(1, at = c(1000, seq(10000, 50000, 10000)),
labels = c(1000, seq(10000, 50000, 10000)), font = 2, cex = 1.5)
axis(1, at = seq(0, 50000, 5000), labels = rep("", 11), lwd.ticks = 0.5)
mtext('Data Sizes', 1, 2.75, font = 2, cex = 1.5)
axis(2, at = seq(0, 1, 0.2), labels = c("0.0", seq(0.2, 0.8, 0.2), "1.0"),
font = 2, cex = 1.5)
axis(2, at = seq(0, 1, 0.1), labels = rep("", 11), lwd.ticks = 0.5,
font = 2, cex = 1.5)
mtext('CESS / N', 2, 2.75, font = 2, cex = 1.5)
##### Recommended scaling of T, fixed n #####
plot(x = data_sizes,
y = sapply(1:length(data_sizes), function(i) b_results$vanilla[[i]]$CESS_0)/nsamples,
type = 'b', pch = 20, lty = 1, lwd = 3, ylim = c(0,1), xaxt = 'n', yaxt ='n', xlab = '', ylab = '')
lines(x = data_sizes,
y = sapply(1:length(data_sizes), function(i) b_results$vanilla[[i]]$CESS_j_avg)/nsamples,
pch = 20, lty = 2, lwd = 3, type = 'b')
for (ii in 1:length(data_sizes)) {
cess_j <- lapply(1:length(data_sizes), function(i) b_results$vanilla[[i]]$CESS_j/nsamples)[[ii]]
points(x = rep(data_sizes[ii], length(cess_j)), y = cess_j, cex = 0.5)
}
axis(1, at = c(1000, seq(10000, 50000, 10000)),
labels = c(1000, seq(10000, 50000, 10000)), font = 2, cex = 1.5)
axis(1, at = seq(0, 50000, 5000), labels = rep("", 11), lwd.ticks = 0.5)
mtext('Data Sizes', 1, 2.75, font = 2, cex = 1.5)
axis(2, at = seq(0, 1, 0.2), labels = c("0.0", seq(0.2, 0.8, 0.2), "1.0"),
font = 2, cex = 1.5)
axis(2, at = seq(0, 1, 0.1), labels = rep("", 11), lwd.ticks = 0.5,
font = 2, cex = 1.5)
mtext('CESS / N', 2, 2.75, font = 2, cex = 1.5)
##### Recommended scaling of T, regular mesh #####
plot(x = data_sizes,
y = sapply(1:length(data_sizes), function(i) c_results$vanilla[[i]]$CESS_0)/nsamples,
type = 'b', pch = 20, lty = 1, lwd = 3, ylim = c(0,1), xaxt = 'n', yaxt ='n', xlab = '', ylab = '')
lines(x = data_sizes,
y = sapply(1:length(data_sizes), function(i) c_results$vanilla[[i]]$CESS_j_avg)/nsamples,
pch = 20, lty = 2, lwd = 3, type = 'b')
for (ii in 1:length(data_sizes)) {
cess_j <- lapply(1:length(data_sizes), function(i) c_results$vanilla[[i]]$CESS_j/nsamples)[[ii]]
points(x = rep(data_sizes[ii], length(cess_j)), y = cess_j, cex = 0.5)
}
axis(1, at = c(1000, seq(10000, 50000, 10000)),
labels = c(1000, seq(10000, 50000, 10000)), font = 2, cex = 1.5)
axis(1, at = seq(0, 50000, 5000), labels = rep("", 11), lwd.ticks = 0.5)
mtext('Data Sizes', 1, 2.75, font = 2, cex = 1.5)
axis(2, at = seq(0, 1, 0.2), labels = c("0.0", seq(0.2, 0.8, 0.2), "1.0"),
font = 2, cex = 1.5)
axis(2, at = seq(0, 1, 0.1), labels = rep("", 11), lwd.ticks = 0.5,
font = 2, cex = 1.5)
mtext('CESS / N', 2, 2.75, font = 2, cex = 1.5)
##### Recommended scaling of T, adaptive mesh #####
plot(x = data_sizes,
y = sapply(1:length(data_sizes), function(i) d_results$vanilla[[i]]$CESS_0)/nsamples,
type = 'b', pch = 20, lty = 1, lwd = 3, ylim = c(0,1), xaxt = 'n', yaxt ='n', xlab = '', ylab = '')
lines(x = data_sizes,
y = sapply(1:length(data_sizes), function(i) d_results$vanilla[[i]]$CESS_j_avg)/nsamples,
pch = 20, lty = 2, lwd = 3, type = 'b')
for (ii in 1:length(data_sizes)) {
cess_j <- lapply(1:length(data_sizes), function(i) d_results$vanilla[[i]]$CESS_j/nsamples)[[ii]]
points(x = rep(data_sizes[ii], length(cess_j)), y = cess_j, cex = 0.5)
}
axis(1, at = c(1000, seq(10000, 50000, 10000)),
labels = c(1000, seq(10000, 50000, 10000)), font = 2, cex = 1.5)
axis(1, at = seq(0, 50000, 5000), labels = rep("", 11), lwd.ticks = 0.5)
mtext('Data Sizes', 1, 2.75, font = 2, cex = 1.5)
axis(2, at = seq(0, 1, 0.2), labels = c("0.0", seq(0.2, 0.8, 0.2), "1.0"),
font = 2, cex = 1.5)
axis(2, at = seq(0, 1, 0.1), labels = rep("", 11), lwd.ticks = 0.5,
font = 2, cex = 1.5)
mtext('CESS / N', 2, 2.75, font = 2, cex = 1.5)
##### Compare regular mesh and adaptive mesh times #####
plot(x = c_results$vanilla[[1]]$time_mesh,
y = rep(data_sizes[1]-500, length(c_results$vanilla[[1]]$time_mesh)),
type = 'b', pch = 20, lty = 1, lwd = 3, ylim = c(0,50000),
xaxt = 'n', yaxt ='n', xlab = '', ylab = '')
for (i in 2:length(data_sizes)) {
lines(x = c_results$vanilla[[i]]$time_mesh,
y = rep(data_sizes[i]-500, length(c_results$vanilla[[i]]$time_mesh)),
type = 'b', pch = 20, lty = 1, lwd = 3)
}
for (i in 1:length(data_sizes)) {
lines(x = d_results$vanilla[[i]]$time_mesh,
y = rep(data_sizes[i]+500, length(d_results$vanilla[[i]]$time_mesh)),
type = 'b', pch = 4, lty = 2, lwd = 3)
}
max(sapply(1:length(data_sizes), function(i) c_results$vanilla[[i]]$time_mesh))
axis(1, at = seq(0, 0.03, 0.01), labels = seq(0, 0.03, 0.01), font = 2, cex = 1.5)
axis(1, at = seq(0, 0.03, 0.005), labels = rep("", 7), lwd.ticks = 0.5)
mtext('Time', 1, 2.75, font = 2, cex = 1.5)
axis(2, at = c(1000, seq(10000, 50000, 10000)),
labels = c(1000, seq(10000, 50000, 10000)), font = 2, cex = 1.5)
axis(2, at = seq(0, 50000, 5000), labels = rep("", 11), lwd.ticks = 0.5)
mtext('Data Sizes', 2, 2.75, font = 2, cex = 1.5)
# plot(x = d_results$vanilla[[1]]$time_mesh,
# y = rep(data_sizes[1], length(d_results$vanilla[[1]]$time_mesh)),
# type = 'b', pch = 20, lty = 1, lwd = 3, ylim = c(0,50000),
# xaxt = 'n', yaxt ='n', xlab = '', ylab = '')
# for (i in 1:length(data_sizes)) {
# lines(x = d_results$vanilla[[i]]$time_mesh,
# y = rep(data_sizes[i], length(d_results$vanilla[[i]]$time_mesh)),
# type = 'b', pch = 20, lty = 1, lwd = 3)
# }
# # max(sapply(1:length(data_sizes), function(i) max(d_results$vanilla[[i]]$time_mesh)))
# axis(1, at = seq(0, 0.03, 0.01), labels = seq(0, 0.03, 0.01), font = 2, cex = 1.5)
# axis(1, at = seq(0, 0.03, 0.005), labels = rep("", 7), lwd.ticks = 0.5)
# mtext('Time', 1, 2.75, font = 2, cex = 1.5)
# axis(2, at = c(1000, seq(10000, 50000, 10000)), labels = c(1000, seq(10000, 50000, 10000)), font = 2, cex = 1.5)
# axis(2, at = seq(0, 50000, 5000), labels = rep("", 11), lwd.ticks = 0.5)
# mtext('Data Sizes', 2, 2.75, font = 2, cex = 1.5)
##### SSH: Recommended scaling of T, adaptive mesh #####
plot(x = data_sizes,
y = sapply(1:length(data_sizes), function(i) SSH_adaptive_results$vanilla[[i]]$CESS_0)/nsamples,
type = 'b', pch = 20, lty = 1, lwd = 3, ylim = c(0,1), xaxt = 'n', yaxt ='n', xlab = '', ylab = '')
lines(x = data_sizes,
y = sapply(1:length(data_sizes), function(i) SSH_adaptive_results$vanilla[[i]]$CESS_j_avg)/nsamples,
pch = 20, lty = 2, lwd = 3, type = 'b')
for (ii in 1:length(data_sizes)) {
cess_j <- lapply(1:length(data_sizes), function(i) SSH_adaptive_results$vanilla[[i]]$CESS_j/nsamples)[[ii]]
points(x = rep(data_sizes[ii], length(cess_j)), y = cess_j, cex = 0.5)
}
axis(1, at = c(1000, seq(10000, 50000, 10000)),
labels = c(1000, seq(10000, 50000, 10000)), font = 2, cex = 1.5)
axis(1, at = seq(0, 50000, 5000), labels = rep("", 11), lwd.ticks = 0.5)
mtext('Data Sizes', 1, 2.75, font = 2, cex = 1.5)
axis(2, at = seq(0, 1, 0.2), labels = c("0.0", seq(0.2, 0.8, 0.2), "1.0"),
font = 2, cex = 1.5)
axis(2, at = seq(0, 1, 0.1), labels = rep("", 11), lwd.ticks = 0.5,
font = 2, cex = 1.5)
mtext('CESS / N', 2, 2.75, font = 2, cex = 1.5)
##### IAD #####
plot(x = data_sizes,
y = sapply(1:length(data_sizes), function(i) a_results$vanilla[[i]]$IAD),
type = 'b', pch = 1, lty = 1, lwd = 3, ylim = c(0,0.6), xaxt = 'n', yaxt ='n', xlab = '', ylab = '')
lines(x = data_sizes,
y = sapply(1:length(data_sizes), function(i) b_results$vanilla[[i]]$IAD),
pch = 2, lty = 2, lwd = 3, type = 'b')
lines(x = data_sizes,
y = sapply(1:length(data_sizes), function(i) c_results$vanilla[[i]]$IAD),
pch = 3, lty = 3, lwd = 3, type = 'b')
lines(x = data_sizes,
y = sapply(1:length(data_sizes), function(i) d_results$vanilla[[i]]$IAD),
pch = 4, lty = 4, lwd = 3, type = 'b')
lines(x = data_sizes,
y = sapply(1:length(data_sizes), function(i) SSH_adaptive_results$vanilla[[i]]$IAD),
pch = 5, lty = 5, lwd = 3, type = 'b')
axis(1, at = c(1000, seq(10000, 50000, 10000)),
labels = c(1000, seq(10000, 50000, 10000)), font = 2, cex = 1.5)
axis(1, at = seq(0, 50000, 5000), labels = rep("", 11), lwd.ticks = 0.5)
mtext('Data Sizes', 1, 2.75, font = 2, cex = 1.5)
axis(2, at = seq(0, 1, 0.1), labels = c("0.0", seq(0.1, 0.9, 0.1), "1.0"),
font = 2, cex = 1.5)
axis(2, at = seq(0, 1, 0.1), labels=rep("", 11), lwd.ticks = 0.5,
font = 2, cex = 1.5)
mtext('Integrated Absolute Distance', 2, 2.75, font = 2, cex = 1.5)
legend(x = 250, y = 0.6,
legend = c('Fixed T, fixed n',
'SH rec. T, fixed n',
'SH rec. T, reg. mesh',
'SH rec. T, adapt. mesh',
'SSH rec. T, adapt. mesh'),
lty = 1:5,
pch = 1:5,
lwd = rep(3, 5),
cex = 1.25,
text.font = 2,
bty = 'n')
##### time #####
plot(x = data_sizes,
y = log(sapply(1:length(data_sizes), function(i) a_results$vanilla[[i]]$time)),
type = 'b', pch = 1, lty = 1, lwd = 3, ylim = c(1,5), xaxt = 'n', yaxt ='n', xlab = '', ylab = '')
lines(x = data_sizes,
y = log(sapply(1:length(data_sizes), function(i) b_results$vanilla[[i]]$time)),
pch = 2, lty = 2, lwd = 3, type = 'b')
lines(x = data_sizes,
y = log(sapply(1:length(data_sizes), function(i) c_results$vanilla[[i]]$time)),
pch = 3, lty = 3, lwd = 3, type = 'b')
lines(x = data_sizes,
y = log(sapply(1:length(data_sizes), function(i) d_results$vanilla[[i]]$time)),
pch = 4, lty = 4, lwd = 3, type = 'b')
lines(x = data_sizes,
y = log(sapply(1:length(data_sizes), function(i) SSH_adaptive_results$vanilla[[i]]$time)),
pch = 5, lty = 5, lwd = 3, type = 'b')
axis(1, at = c(1000, seq(10000, 50000, 10000)),
labels = c(1000, seq(10000, 50000, 10000)), font = 2, cex = 1.5)
axis(1, at = seq(0, 50000, 5000), labels = rep("", 11), lwd.ticks = 0.5)
mtext('Data Sizes', 1, 2.75, font = 2, cex = 1.5)
axis(2, at = seq(0, 5, 1), labels = seq(0, 5, 1), font = 2, cex = 1.5)
mtext('log(Elapsed time in seconds)', 2, 2.75, font = 2, cex = 1.5)
legend(x = 0, y = 5,
legend = c('Fixed T, fixed n',
'SH rec. T, fixed n',
'SH rec. T, reg. mesh',
'SH rec. T, adapt. mesh',
'SSH rec. T, adapt. mesh'),
lty = 1:5,
pch = 1:5,
lwd = rep(3, 5),
cex = 1.25,
text.font = 2,
bty = 'n')
##### generalised plots #####
##### Fixed user-specified parameters #####
plot(x = data_sizes,
y = sapply(1:length(data_sizes), function(i) a_results$generalised[[i]]$CESS_0)/nsamples,
type = 'b', pch = 20, lty = 1, lwd = 3, ylim = c(0,1), xaxt = 'n', yaxt ='n', xlab = '', ylab = '')
lines(x = data_sizes,
y = sapply(1:length(data_sizes), function(i) a_results$generalised[[i]]$CESS_j_avg)/nsamples,
pch = 20, lty = 2, lwd = 3, type = 'b')
for (ii in 1:length(data_sizes)) {
cess_j <- lapply(1:length(data_sizes), function(i) a_results$generalised[[i]]$CESS_j/nsamples)[[ii]]
points(x = rep(data_sizes[ii], length(cess_j)), y = cess_j, cex = 0.5)
}
axis(1, at = c(1000, seq(10000, 50000, 10000)),
labels = c(1000, seq(10000, 50000, 10000)), font = 2, cex = 1.5)
axis(1, at = seq(0, 50000, 5000), labels = rep("", 11), lwd.ticks = 0.5)
mtext('Data Sizes', 1, 2.75, font = 2, cex = 1.5)
axis(2, at = seq(0, 1, 0.2), labels = c("0.0", seq(0.2, 0.8, 0.2), "1.0"),
font = 2, cex = 1.5)
axis(2, at = seq(0, 1, 0.1), labels = rep("", 11), lwd.ticks = 0.5,
font = 2, cex = 1.5)
mtext('CESS / N', 2, 2.75, font = 2, cex = 1.5)
##### Recommended scaling of T, fixed n #####
plot(x = data_sizes,
y = sapply(1:length(data_sizes), function(i) b_results$generalised[[i]]$CESS_0)/nsamples,
type = 'b', pch = 20, lty = 1, lwd = 3, ylim = c(0,1), xaxt = 'n', yaxt ='n', xlab = '', ylab = '')
lines(x = data_sizes,
y = sapply(1:length(data_sizes), function(i) b_results$generalised[[i]]$CESS_j_avg)/nsamples,
pch = 20, lty = 2, lwd = 3, type = 'b')
for (ii in 1:length(data_sizes)) {
cess_j <- lapply(1:length(data_sizes), function(i) b_results$generalised[[i]]$CESS_j/nsamples)[[ii]]
points(x = rep(data_sizes[ii], length(cess_j)), y = cess_j, cex = 0.5)
}
axis(1, at = c(1000, seq(10000, 50000, 10000)),
labels = c(1000, seq(10000, 50000, 10000)), font = 2, cex = 1.5)
axis(1, at = seq(0, 50000, 5000), labels = rep("", 11), lwd.ticks = 0.5)
mtext('Data Sizes', 1, 2.75, font = 2, cex = 1.5)
axis(2, at = seq(0, 1, 0.2), labels = c("0.0", seq(0.2, 0.8, 0.2), "1.0"),
font = 2, cex = 1.5)
axis(2, at = seq(0, 1, 0.1), labels = rep("", 11), lwd.ticks = 0.5,
font = 2, cex = 1.5)
mtext('CESS / N', 2, 2.75, font = 2, cex = 1.5)
##### Recommended scaling of T, regular mesh #####
plot(x = data_sizes,
y = sapply(1:length(data_sizes), function(i) c_results$generalised[[i]]$CESS_0)/nsamples,
type = 'b', pch = 20, lty = 1, lwd = 3, ylim = c(0,1), xaxt = 'n', yaxt ='n', xlab = '', ylab = '')
lines(x = data_sizes,
y = sapply(1:length(data_sizes), function(i) c_results$generalised[[i]]$CESS_j_avg)/nsamples,
pch = 20, lty = 2, lwd = 3, type = 'b')
for (ii in 1:length(data_sizes)) {
cess_j <- lapply(1:length(data_sizes), function(i) c_results$generalised[[i]]$CESS_j/nsamples)[[ii]]
points(x = rep(data_sizes[ii], length(cess_j)), y = cess_j, cex = 0.5)
}
axis(1, at = c(1000, seq(10000, 50000, 10000)),
labels = c(1000, seq(10000, 50000, 10000)), font = 2, cex = 1.5)
axis(1, at = seq(0, 50000, 5000), labels = rep("", 11), lwd.ticks = 0.5)
mtext('Data Sizes', 1, 2.75, font = 2, cex = 1.5)
axis(2, at = seq(0, 1, 0.2), labels = c("0.0", seq(0.2, 0.8, 0.2), "1.0"),
font = 2, cex = 1.5)
axis(2, at = seq(0, 1, 0.1), labels = rep("", 11), lwd.ticks = 0.5,
font = 2, cex = 1.5)
mtext('CESS / N', 2, 2.75, font = 2, cex = 1.5)
##### Recommended scaling of T, adaptive mesh #####
plot(x = data_sizes,
y = sapply(1:length(data_sizes), function(i) d_results$generalised[[i]]$CESS_0)/nsamples,
type = 'b', pch = 20, lty = 1, lwd = 3, ylim = c(0,1), xaxt = 'n', yaxt ='n', xlab = '', ylab = '')
lines(x = data_sizes,
y = sapply(1:length(data_sizes), function(i) d_results$generalised[[i]]$CESS_j_avg)/nsamples,
pch = 20, lty = 2, lwd = 3, type = 'b')
for (ii in 1:length(data_sizes)) {
cess_j <- lapply(1:length(data_sizes), function(i) d_results$generalised[[i]]$CESS_j/nsamples)[[ii]]
points(x = rep(data_sizes[ii], length(cess_j)), y = cess_j, cex = 0.5)
}
axis(1, at = c(1000, seq(10000, 50000, 10000)),
labels = c(1000, seq(10000, 50000, 10000)), font = 2, cex = 1.5)
axis(1, at = seq(0, 50000, 5000), labels = rep("", 11), lwd.ticks = 0.5)
mtext('Data Sizes', 1, 2.75, font = 2, cex = 1.5)
axis(2, at = seq(0, 1, 0.2), labels = c("0.0", seq(0.2, 0.8, 0.2), "1.0"),
font = 2, cex = 1.5)
axis(2, at = seq(0, 1, 0.1), labels = rep("", 11), lwd.ticks = 0.5,
font = 2, cex = 1.5)
mtext('CESS / N', 2, 2.75, font = 2, cex = 1.5)
##### Compare regular mesh and adaptive mesh times #####
plot(x = c_results$generalised[[1]]$time_mesh,
y = rep(data_sizes[1]-500, length(c_results$generalised[[1]]$time_mesh)),
type = 'b', pch = 20, lty = 1, lwd = 3, ylim = c(0,50000),
xaxt = 'n', yaxt ='n', xlab = '', ylab = '')
for (i in 2:length(data_sizes)) {
lines(x = c_results$generalised[[i]]$time_mesh,
y = rep(data_sizes[i]-500, length(c_results$generalised[[i]]$time_mesh)),
type = 'b', pch = 20, lty = 1, lwd = 3)
}
for (i in 1:length(data_sizes)) {
lines(x = d_results$generalised[[i]]$time_mesh,
y = rep(data_sizes[i]+500, length(d_results$generalised[[i]]$time_mesh)),
type = 'b', pch = 4, lty = 2, lwd = 3)
}
max(sapply(1:length(data_sizes), function(i) max(c_results$generalised[[i]]$time_mesh)))
axis(1, at = seq(0, 3, 1), labels = seq(0, 3, 1), font = 2, cex = 1.5)
axis(1, at = seq(0, 3, 0.5), labels = rep("", 7), lwd.ticks = 0.5)
mtext('Time', 1, 2.75, font = 2, cex = 1.5)
axis(2, at = c(1000, seq(10000, 50000, 10000)),
labels = c(1000, seq(10000, 50000, 10000)), font = 2, cex = 1.5)
axis(2, at = seq(0, 50000, 5000), labels = rep("", 11), lwd.ticks = 0.5)
mtext('Data Sizes', 2, 2.75, font = 2, cex = 1.5)
##### SSH: Recommended scaling of T, adaptive mesh #####
plot(x = data_sizes,
y = sapply(1:length(data_sizes), function(i) SSH_adaptive_results$vanilla[[i]]$CESS_0)/nsamples,
type = 'b', pch = 20, lty = 1, lwd = 3, ylim = c(0,1), xaxt = 'n', yaxt ='n', xlab = '', ylab = '')
lines(x = data_sizes,
y = sapply(1:length(data_sizes), function(i) SSH_adaptive_results$vanilla[[i]]$CESS_j_avg)/nsamples,
pch = 20, lty = 2, lwd = 3, type = 'b')
for (ii in 1:length(data_sizes)) {
cess_j <- lapply(1:length(data_sizes), function(i) SSH_adaptive_results$generalised[[i]]$CESS_j/nsamples)[[ii]]
points(x = rep(data_sizes[ii], length(cess_j)), y = cess_j, cex = 0.5)
}
axis(1, at = c(1000, seq(10000, 50000, 10000)),
labels = c(1000, seq(10000, 50000, 10000)), font = 2, cex = 1.5)
axis(1, at = seq(0, 50000, 5000), labels = rep("", 11), lwd.ticks = 0.5)
mtext('Data Sizes', 1, 2.75, font = 2, cex = 1.5)
axis(2, at = seq(0, 1, 0.2), labels = c("0.0", seq(0.2, 0.8, 0.2), "1.0"),
font = 2, cex = 1.5)
axis(2, at = seq(0, 1, 0.1), labels = rep("", 11), lwd.ticks = 0.5,
font = 2, cex = 1.5)
mtext('CESS / N', 2, 2.75, font = 2, cex = 1.5)
##### IAD #####
plot(x = data_sizes,
y = sapply(1:length(data_sizes), function(i) a_results$generalised[[i]]$IAD),
type = 'b', pch = 1, lty = 1, lwd = 3, ylim = c(0,0.6), xaxt = 'n', yaxt ='n', xlab = '', ylab = '')
lines(x = data_sizes,
y = sapply(1:length(data_sizes), function(i) b_results$generalised[[i]]$IAD),
pch = 2, lty = 2, lwd = 3, type = 'b')
lines(x = data_sizes,
y = sapply(1:length(data_sizes), function(i) c_results$generalised[[i]]$IAD),
pch = 3, lty = 3, lwd = 3, type = 'b')
lines(x = data_sizes,
y = sapply(1:length(data_sizes), function(i) d_results$generalised[[i]]$IAD),
pch = 4, lty = 4, lwd = 3, type = 'b')
lines(x = data_sizes,
y = sapply(1:length(data_sizes), function(i) SSH_adaptive_results$generalised[[i]]$IAD),
pch = 5, lty = 5, lwd = 3, type = 'b')
axis(1, at = c(1000, seq(10000, 50000, 10000)),
labels = c(1000, seq(10000, 50000, 10000)), font = 2, cex = 1.5)
axis(1, at = seq(0, 50000, 5000), labels = rep("", 11), lwd.ticks = 0.5)
mtext('Data Sizes', 1, 2.75, font = 2, cex = 1.5)
axis(2, at = seq(0, 1, 0.1), labels = c("0.0", seq(0.1, 0.9, 0.1), "1.0"),
font = 2, cex = 1.5)
axis(2, at = seq(0, 1, 0.1), labels=rep("", 11), lwd.ticks = 0.5,
font = 2, cex = 1.5)
mtext('Integrated Absolute Distance', 2, 2.75, font = 2, cex = 1.5)
legend(x = 0, y = 0.6,
legend = c('Fixed T, fixed n',
'SH rec. T, fixed n',
'SH rec. T, reg. mesh',
'SH rec. T, adapt. mesh',
'SSH rec. T, adapt. mesh'),
lty = 1:5,
pch = 1:5,
lwd = rep(3, 5),
cex = 1.25,
text.font = 2,
bty = 'n')
##### time #####
plot(x = data_sizes,
y = log(sapply(1:length(data_sizes), function(i) a_results$generalised[[i]]$time)),
type = 'b', pch = 1, lty = 1, lwd = 3, ylim = c(1,5), xaxt = 'n', yaxt ='n', xlab = '', ylab = '')
lines(x = data_sizes,
y = log(sapply(1:length(data_sizes), function(i) b_results$generalised[[i]]$time)),
pch = 2, lty = 2, lwd = 3, type = 'b')
lines(x = data_sizes,
y = log(sapply(1:length(data_sizes), function(i) c_results$generalised[[i]]$time)),
pch = 3, lty = 3, lwd = 3, type = 'b')
lines(x = data_sizes,
y = log(sapply(1:length(data_sizes), function(i) d_results$generalised[[i]]$time)),
pch = 4, lty = 4, lwd = 3, type = 'b')
lines(x = data_sizes,
y = log(sapply(1:length(data_sizes), function(i) SSH_adaptive_results$generalised[[i]]$time)),
pch = 5, lty = 5, lwd = 3, type = 'b')
axis(1, at = c(1000, seq(10000, 50000, 10000)),
labels = c(1000, seq(10000, 50000, 10000)), font = 2, cex = 1.5)
axis(1, at = seq(0, 50000, 5000), labels = rep("", 11), lwd.ticks = 0.5)
mtext('Data Sizes', 1, 2.75, font = 2, cex = 1.5)
axis(2, at = seq(0, 5, 1), labels = seq(0, 5, 1), font = 2, cex = 1.5)
mtext('log(Elapsed time in seconds)', 2, 2.75, font = 2, cex = 1.5)
legend(x = 0, y = 5,
legend = c('Fixed T, fixed n',
'SH rec. T, fixed n',
'SH rec. T, reg. mesh',
'SH rec. T, adapt. mesh',
'SSH rec. T, adapt. mesh'),
lty = 1:5,
pch = 1:5,
lwd = rep(3, 5),
cex = 1.25,
text.font = 2,
bty = 'n')
save.image('bf_similar_means_example.RData')
rchan26/hierarchicalFusion documentation built on Sept. 11, 2022, 10:30 p.m.
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library(DCFusion)
seed <- 1994
set.seed(seed)
nsamples <- 10000
C <- 10
mean <- 0
beta <- 1/C
a_mesh_vanilla <- seq(0, 0.005, length.out = 6)
a_mesh_gen <- seq(0, 1, length.out = 6)
diffusion_estimator <- 'NB'
ESS_threshold <- 0.5
CESS_0_threshold <- 0.2
vanilla_b <- 1
k1 <- NULL
k2 <- NULL
k3 <- 1
k4 <- 1
data_sizes <- c(1000, 5000, 10000, 20000, 30000, 40000, 50000)
a_results <- list('vanilla' = list(), 'generalised' = list())
b_results <- list('vanilla' = list(), 'generalised' = list())
c_results <- list('vanilla' = list(), 'generalised' = list())
d_results <- list('vanilla' = list(), 'generalised' = list())
SSH_adaptive_results <- list('vanilla' = list(), 'generalised' = list())
for (i in 1:length(data_sizes)) {
set.seed(seed*i)
sd <- sqrt(1/data_sizes[i])
opt_bw <- ((4*sd^5)/(3*nsamples))^(1/5)
curve(dnorm(x, mean = mean, sd = sd), mean-4*sd, mean+4*sd,
main = paste('m:', data_sizes[i]))
input_samples <- lapply(1:C, function(i) rnorm_tempered(N = nsamples,
mean = mean,
sd = sd,
beta = beta))
print(paste('##### m:', data_sizes[i]))
print(paste('sd:', sd))
print(paste('var:', sd^2))
print(paste('sub_posterior var (true):', C*sd^2))
print(paste('sub_posterior var:', sapply(input_samples, var)))
##### Fixed user-specified parameters #####
print('### performing standard Bayesian Fusion (with standard mesh)')
input_particles <- initialise_particle_sets(samples_to_fuse = input_samples,
multivariate = FALSE,
number_of_steps = length(a_mesh_vanilla))
a_BF_standard <- parallel_GBF_uniGaussian(particles_to_fuse = input_particles,
N = nsamples,
m = C,
time_mesh = a_mesh_vanilla,
means = rep(mean, C),
sds = rep(sd, C),
betas = rep(beta, C),
precondition_values = rep(1, C),
ESS_threshold = ESS_threshold,
diffusion_estimator = diffusion_estimator,
seed = seed*i)
print('### performing Bayesian Fusion with a preconditioning matrix (with standard mesh)')
input_particles <- initialise_particle_sets(samples_to_fuse = input_samples,
multivariate = FALSE,
number_of_steps = length(a_mesh_gen))
a_BF_generalised <- parallel_GBF_uniGaussian(particles_to_fuse = input_particles,
N = nsamples,
m = C,
time_mesh = a_mesh_gen,
means = rep(mean, C),
sds = rep(sd, C),
betas = rep(beta, C),
precondition_values = sapply(input_samples, var),
ESS_threshold = ESS_threshold,
diffusion_estimator = diffusion_estimator,
seed = seed*i)
# save results
a_results$vanilla[[i]] <- list('CESS_0' = a_BF_standard$CESS[1],
'CESS_j' = a_BF_standard$CESS[2:length(a_BF_standard$CESS)],
'CESS_j_avg' = mean(a_BF_standard$CESS[2:length(a_BF_standard$CESS)]),
'n' = length(a_BF_standard$CESS),
'time_mesh' = a_BF_standard$particles$time_mesh,
'time' = a_BF_standard$time,
'IAD' = integrated_abs_distance_uniGaussian(
fusion_post = resample_particle_y_samples(particle_set = a_BF_standard$particles,
multivariate = FALSE,
resampling_method = 'resid',
seed = seed*i)$y_samples,
mean = 0,
sd = sd,
beta = 1,
bw = opt_bw))
a_results$generalised[[i]] <- list('CESS_0' = a_BF_generalised$CESS[1],
'CESS_j' = a_BF_generalised$CESS[2:length(a_BF_generalised$CESS)],
'CESS_j_avg' = mean(a_BF_generalised$CESS[2:length(a_BF_generalised$CESS)]),
'n' = length(a_BF_generalised$CESS),
'time_mesh' = a_BF_generalised$particles$time_mesh,
'time' = a_BF_generalised$time,
'IAD' = integrated_abs_distance_uniGaussian(
fusion_post = resample_particle_y_samples(particle_set = a_BF_generalised$particles,
multivariate = FALSE,
resampling_method = 'resid',
seed = seed*i)$y_samples,
mean = 0,
sd = sd,
beta = 1,
bw = opt_bw))
# plot
lines(density(resample_particle_y_samples(particle_set = a_BF_standard$particles,
multivariate = FALSE,
resampling_method = 'resid',
seed = seed*i)$y_samples),
col = 'red')
lines(density(resample_particle_y_samples(particle_set = a_BF_generalised$particles,
multivariate = FALSE,
resampling_method = 'resid',
seed = seed*i)$y_samples),
col = 'red', lty = 2)
##### Recommended scaling of T, fixed n #####
print('### performing standard Bayesian Fusion (with recommended T, fixed n)')
vanilla_guide <- BF_guidance(condition = 'SH',
CESS_0_threshold = CESS_0_threshold,
C = C,
d = 1,
data_size = data_sizes[i],
b = vanilla_b,
sub_posterior_means = sapply(input_samples, mean),
k1 = k1,
k3 = k3,
k4 = k4,
vanilla = TRUE)
b_mesh_vanilla <- seq(0, vanilla_guide$min_T, length.out = 6)
input_particles <- initialise_particle_sets(samples_to_fuse = input_samples,
multivariate = FALSE,
number_of_steps = length(b_mesh_vanilla))
b_BF_standard <- parallel_GBF_uniGaussian(particles_to_fuse = input_particles,
N = nsamples,
m = C,
time_mesh = b_mesh_vanilla,
means = rep(mean, C),
sds = rep(sd, C),
betas = rep(beta, C),
precondition_values = rep(1, C),
ESS_threshold = ESS_threshold,
diffusion_estimator = diffusion_estimator,
seed = seed*i)
print('### performing Bayesian Fusion with a preconditioning matrix (with recommended T, fixed n)')
gen_guide <- BF_guidance(condition = 'SH',
CESS_0_threshold = CESS_0_threshold,
C = C,
d = 1,
data_size = data_sizes[i],
sub_posterior_means = sapply(input_samples, mean),
precondition_matrices = sapply(input_samples, var),
inv_precondition_matrices = 1/sapply(input_samples, var),
k1 = k1,
k3 = k3,
k4 = k4,
vanilla = FALSE)
b_mesh_gen <- seq(0, gen_guide$min_T, length.out = 6)
input_particles <- initialise_particle_sets(samples_to_fuse = input_samples,
multivariate = FALSE,
number_of_steps = length(b_mesh_gen))
b_BF_generalised <- parallel_GBF_uniGaussian(particles_to_fuse = input_particles,
N = nsamples,
m = C,
time_mesh = b_mesh_gen,
means = rep(mean, C),
sds = rep(sd, C),
betas = rep(beta, C),
precondition_values = sapply(input_samples, var),
ESS_threshold = ESS_threshold,
diffusion_estimator = diffusion_estimator,
seed = seed*i)
# save results
b_results$vanilla[[i]] <- list('CESS_0' = b_BF_standard$CESS[1],
'CESS_j' = b_BF_standard$CESS[2:length(b_BF_standard$CESS)],
'CESS_j_avg' = mean(b_BF_standard$CESS[2:length(b_BF_standard$CESS)]),
'n' = length(b_BF_standard$CESS),
'time_mesh' = b_BF_standard$particles$time_mesh,
'time' = b_BF_standard$time,
'IAD' = integrated_abs_distance_uniGaussian(
fusion_post = resample_particle_y_samples(particle_set = b_BF_standard$particles,
multivariate = FALSE,
resampling_method = 'resid',
seed = seed*i)$y_samples,
mean = 0,
sd = sd,
beta = 1,
bw = opt_bw))
b_results$generalised[[i]] <- list('CESS_0' = b_BF_generalised$CESS[1],
'CESS_j' = b_BF_generalised$CESS[2:length(b_BF_generalised$CESS)],
'CESS_j_avg' = mean(b_BF_generalised$CESS[2:length(b_BF_generalised$CESS)]),
'n' = length(b_BF_generalised$CESS),
'time_mesh' = b_BF_generalised$particles$time_mesh,
'time' = b_BF_generalised$time,
'IAD' = integrated_abs_distance_uniGaussian(
fusion_post = resample_particle_y_samples(particle_set = b_BF_generalised$particles,
multivariate = FALSE,
resampling_method = 'resid',
seed = seed*i)$y_samples,
mean = 0,
sd = sd,
beta = 1,
bw = opt_bw))
# plot
lines(density(resample_particle_y_samples(particle_set = b_BF_standard$particles,
multivariate = FALSE,
resampling_method = 'resid',
seed = seed*i)$y_samples),
col = 'blue')
lines(density(resample_particle_y_samples(particle_set = b_BF_generalised$particles,
multivariate = FALSE,
resampling_method = 'resid',
seed = seed*i)$y_samples),
col = 'blue', lty = 2)
##### Recommended scaling of T, regular mesh #####
print('### performing standard Bayesian Fusion (with recommended T, regular mesh)')
input_particles <- initialise_particle_sets(samples_to_fuse = input_samples,
multivariate = FALSE,
number_of_steps = length(vanilla_guide$mesh))
c_BF_standard <- parallel_GBF_uniGaussian(particles_to_fuse = input_particles,
N = nsamples,
m = C,
time_mesh = vanilla_guide$mesh,
means = rep(mean, C),
sds = rep(sd, C),
betas = rep(beta, C),
precondition_values = rep(1, C),
ESS_threshold = ESS_threshold,
diffusion_estimator = diffusion_estimator,
seed = seed*i)
print('### performing Bayesian Fusion with a preconditioning matrix (with recommended T, regular mesh)')
input_particles <- initialise_particle_sets(samples_to_fuse = input_samples,
multivariate = FALSE,
number_of_steps = length(gen_guide$mesh))
c_BF_generalised <- parallel_GBF_uniGaussian(particles_to_fuse = input_particles,
N = nsamples,
m = C,
time_mesh = gen_guide$mesh,
means = rep(mean, C),
sds = rep(sd, C),
betas = rep(beta, C),
precondition_values = sapply(input_samples, var),
ESS_threshold = ESS_threshold,
diffusion_estimator = diffusion_estimator,
seed = seed*i)
# save results
c_results$vanilla[[i]] <- list('CESS_0' = c_BF_standard$CESS[1],
'CESS_j' = c_BF_standard$CESS[2:length(c_BF_standard$CESS)],
'CESS_j_avg' = mean(c_BF_standard$CESS[2:length(c_BF_standard$CESS)]),
'n' = length(c_BF_standard$CESS),
'time_mesh' = c_BF_standard$particles$time_mesh,
'time' = c_BF_standard$time,
'IAD' = integrated_abs_distance_uniGaussian(
fusion_post = resample_particle_y_samples(particle_set = c_BF_standard$particles,
multivariate = FALSE,
resampling_method = 'resid',
seed = seed*i)$y_samples,
mean = 0,
sd = sd,
beta = 1,
bw = opt_bw))
c_results$generalised[[i]] <- list('CESS_0' = c_BF_generalised$CESS[1],
'CESS_j' = c_BF_generalised$CESS[2:length(c_BF_generalised$CESS)],
'CESS_j_avg' = mean(c_BF_generalised$CESS[2:length(c_BF_generalised$CESS)]),
'n' = length(c_BF_generalised$CESS),
'time_mesh' = c_BF_generalised$particles$time_mesh,
'time' = c_BF_generalised$time,
'IAD' = integrated_abs_distance_uniGaussian(
fusion_post = resample_particle_y_samples(particle_set = c_BF_generalised$particles,
multivariate = FALSE,
resampling_method = 'resid',
seed = seed*i)$y_samples,
mean = 0,
sd = sd,
beta = 1,
bw = opt_bw))
# plot
lines(density(resample_particle_y_samples(particle_set = c_BF_standard$particles,
multivariate = FALSE,
resampling_method = 'resid',
seed = seed*i)$y_samples),
col = 'green')
lines(density(resample_particle_y_samples(particle_set = c_BF_generalised$particles,
multivariate = FALSE,
resampling_method = 'resid',
seed = seed*i)$y_samples),
col = 'green', lty = 2)
##### Recommended scaling of T, adaptive mesh #####
print('### performing standard Bayesian Fusion (with recommended T, adaptive mesh)')
input_particles <- initialise_particle_sets(samples_to_fuse = input_samples,
multivariate = FALSE,
number_of_steps = length(vanilla_guide$mesh))
d_BF_standard <- parallel_GBF_uniGaussian(particles_to_fuse = input_particles,
N = nsamples,
m = C,
time_mesh = vanilla_guide$mesh,
means = rep(mean, C),
sds = rep(sd, C),
betas = rep(beta, C),
precondition_values = rep(1, C),
ESS_threshold = ESS_threshold,
sub_posterior_means = sapply(input_samples, mean),
adaptive_mesh = TRUE,
adaptive_mesh_parameters = list('data_size' = data_sizes[i],
'b' = vanilla_b,
'k3' = k3,
'k4' = k4,
'vanilla' = TRUE),
diffusion_estimator = diffusion_estimator,
seed = seed*i)
print('### performing Bayesian Fusion with a preconditioning matrix (with recommended T, adaptive mesh)')
input_particles <- initialise_particle_sets(samples_to_fuse = input_samples,
multivariate = FALSE,
number_of_steps = length(gen_guide$mesh))
d_BF_generalised <- parallel_GBF_uniGaussian(particles_to_fuse = input_particles,
N = nsamples,
m = C,
time_mesh = gen_guide$mesh,
means = rep(mean, C),
sds = rep(sd, C),
betas = rep(beta, C),
precondition_values = sapply(input_samples, var),
ESS_threshold = ESS_threshold,
sub_posterior_means = sapply(input_samples, mean),
adaptive_mesh = TRUE,
adaptive_mesh_parameters = list('data_size' = data_sizes[i],
'k3' = k3,
'k4' = k4,
'vanilla' = FALSE),
diffusion_estimator = diffusion_estimator,
seed = seed*i)
# save results
d_results$vanilla[[i]] <- list('CESS_0' = d_BF_standard$CESS[1],
'CESS_j' = d_BF_standard$CESS[2:length(d_BF_standard$CESS)],
'CESS_j_avg' = mean(d_BF_standard$CESS[2:length(d_BF_standard$CESS)]),
'n' = length(d_BF_standard$CESS),
'time_mesh' = d_BF_standard$particles$time_mesh,
'time' = d_BF_standard$time,
'IAD' = integrated_abs_distance_uniGaussian(
fusion_post = resample_particle_y_samples(particle_set = d_BF_standard$particles,
multivariate = FALSE,
resampling_method = 'resid',
seed = seed*i)$y_samples,
mean = 0,
sd = sd,
beta = 1,
bw = opt_bw))
d_results$generalised[[i]] <- list('CESS_0' = d_BF_generalised$CESS[1],
'CESS_j' = d_BF_generalised$CESS[2:length(d_BF_generalised$CESS)],
'CESS_j_avg' = mean(d_BF_generalised$CESS[2:length(d_BF_generalised$CESS)]),
'n' = length(d_BF_generalised$CESS),
'time_mesh' = d_BF_generalised$particles$time_mesh,
'time' = d_BF_generalised$time,
'IAD' = integrated_abs_distance_uniGaussian(
fusion_post = resample_particle_y_samples(particle_set = d_BF_generalised$particles,
multivariate = FALSE,
resampling_method = 'resid',
seed = seed*i)$y_samples,
mean = 0,
sd = sd,
beta = 1,
bw = opt_bw))
# plot
lines(density(resample_particle_y_samples(particle_set = d_BF_standard$particles,
multivariate = FALSE,
resampling_method = 'resid',
seed = seed*i)$y_samples),
col = 'purple')
lines(density(resample_particle_y_samples(particle_set = d_BF_generalised$particles,
multivariate = FALSE,
resampling_method = 'resid',
seed = seed*i)$y_samples),
col = 'purple', lty = 2)
##### SSH: Recommended scaling of T, adaptive mesh #####
print('### SSH: performing standard Bayesian Fusion (with recommended T, adaptive mesh)')
vanilla_guide_SSH <- BF_guidance(condition = 'SSH',
CESS_0_threshold = CESS_0_threshold,
C = C,
d = 1,
data_size = data_sizes[i],
b = vanilla_b,
sub_posterior_means = sapply(input_samples, mean),
k1 = k1,
k2 = k2,
k3 = k3,
k4 = k4,
vanilla = TRUE)
input_particles <- initialise_particle_sets(samples_to_fuse = input_samples,
multivariate = FALSE,
number_of_steps = length(vanilla_guide_SSH$mesh))
SSH_adaptive_standard <- parallel_GBF_uniGaussian(particles_to_fuse = input_particles,
N = nsamples,
m = C,
time_mesh = vanilla_guide_SSH$mesh,
means = rep(mean, C),
sds = rep(sd, C),
betas = rep(beta, C),
precondition_values = rep(1, C),
ESS_threshold = ESS_threshold,
sub_posterior_means = sapply(input_samples, mean),
adaptive_mesh = TRUE,
adaptive_mesh_parameters = list('data_size' = data_sizes[i],
'b' = vanilla_b,
'k3' = k3,
'k4' = k4,
'vanilla' = TRUE),
diffusion_estimator = diffusion_estimator,
seed = seed*i)
print('### SSH: performing Bayesian Fusion with a preconditioning matrix (with recommended T, adaptive mesh)')
gen_guide_SSH <- BF_guidance(condition = 'SSH',
CESS_0_threshold = CESS_0_threshold,
C = C,
d = 1,
data_size = data_sizes[i],
sub_posterior_means = sapply(input_samples, mean),
precondition_matrices = sapply(input_samples, var),
inv_precondition_matrices = 1/sapply(input_samples, var),
k1 = k1,
k2 = k2,
k3 = k3,
k4 = k4,
vanilla = FALSE)
input_particles <- initialise_particle_sets(samples_to_fuse = input_samples,
multivariate = FALSE,
number_of_steps = length(gen_guide_SSH$mesh))
SSH_adaptive_generalised <- parallel_GBF_uniGaussian(particles_to_fuse = input_particles,
N = nsamples,
m = C,
time_mesh = gen_guide_SSH$mesh,
means = rep(mean, C),
sds = rep(sd, C),
betas = rep(beta, C),
precondition_values = sapply(input_samples, var),
ESS_threshold = ESS_threshold,
sub_posterior_means = sapply(input_samples, mean),
adaptive_mesh = TRUE,
adaptive_mesh_parameters = list('data_size' = data_sizes[i],
'k3' = k3,
'k4' = k4,
'vanilla' = FALSE),
diffusion_estimator = diffusion_estimator,
seed = seed*i)
# save results
SSH_adaptive_results$vanilla[[i]] <- list('CESS_0' = SSH_adaptive_standard$CESS[1],
'CESS_j' = SSH_adaptive_standard$CESS[2:length(SSH_adaptive_standard$CESS)],
'CESS_j_avg' = mean(SSH_adaptive_standard$CESS[2:length(SSH_adaptive_standard$CESS)]),
'n' = length(SSH_adaptive_standard$CESS),
'time_mesh' = SSH_adaptive_standard$particles$time_mesh,
'time' = SSH_adaptive_standard$time,
'IAD' = integrated_abs_distance_uniGaussian(
fusion_post = resample_particle_y_samples(particle_set = SSH_adaptive_standard$particles,
multivariate = FALSE,
resampling_method = 'resid',
seed = seed*i)$y_samples,
mean = 0,
sd = sd,
beta = 1,
bw = opt_bw))
SSH_adaptive_results$generalised[[i]] <- list('CESS_0' = SSH_adaptive_generalised$CESS[1],
'CESS_j' = SSH_adaptive_generalised$CESS[2:length(SSH_adaptive_generalised$CESS)],
'CESS_j_avg' = mean(SSH_adaptive_generalised$CESS[2:length(SSH_adaptive_generalised$CESS)]),
'n' = length(SSH_adaptive_generalised$CESS),
'time_mesh' = SSH_adaptive_generalised$particles$time_mesh,
'time' = SSH_adaptive_generalised$time,
'IAD' = integrated_abs_distance_uniGaussian(
fusion_post = resample_particle_y_samples(particle_set = SSH_adaptive_generalised$particles,
multivariate = FALSE,
resampling_method = 'resid',
seed = seed*i)$y_samples,
mean = 0,
sd = sd,
beta = 1,
bw = opt_bw))
# plot
lines(density(resample_particle_y_samples(particle_set = SSH_adaptive_standard$particles,
multivariate = FALSE,
resampling_method = 'resid',
seed = seed*i)$y_samples),
col = 'orange')
lines(density(resample_particle_y_samples(particle_set = SSH_adaptive_generalised$particles,
multivariate = FALSE,
resampling_method = 'resid',
seed = seed*i)$y_samples),
col = 'orange', lty = 2)
}
##### vanilla plots #####
##### Fixed user-specified parameters #####
plot(x = data_sizes,
y = sapply(1:length(data_sizes), function(i) a_results$vanilla[[i]]$CESS_0)/nsamples,
type = 'b', pch = 20, lty = 1, lwd = 3, ylim = c(0,1), xaxt = 'n', yaxt ='n', xlab = '', ylab = '')
lines(x = data_sizes,
y = sapply(1:length(data_sizes), function(i) a_results$vanilla[[i]]$CESS_j_avg)/nsamples,
pch = 20, lty = 2, lwd = 3, type = 'b')
for (ii in 1:length(data_sizes)) {
cess_j <- lapply(1:length(data_sizes), function(i) a_results$vanilla[[i]]$CESS_j/nsamples)[[ii]]
points(x = rep(data_sizes[ii], length(cess_j)), y = cess_j, cex = 0.5)
}
axis(1, at = c(1000, seq(10000, 50000, 10000)),
labels = c(1000, seq(10000, 50000, 10000)), font = 2, cex = 1.5)
axis(1, at = seq(0, 50000, 5000), labels = rep("", 11), lwd.ticks = 0.5)
mtext('Data Sizes', 1, 2.75, font = 2, cex = 1.5)
axis(2, at = seq(0, 1, 0.2), labels = c("0.0", seq(0.2, 0.8, 0.2), "1.0"),
font = 2, cex = 1.5)
axis(2, at = seq(0, 1, 0.1), labels = rep("", 11), lwd.ticks = 0.5,
font = 2, cex = 1.5)
mtext('CESS / N', 2, 2.75, font = 2, cex = 1.5)
##### Recommended scaling of T, fixed n #####
plot(x = data_sizes,
y = sapply(1:length(data_sizes), function(i) b_results$vanilla[[i]]$CESS_0)/nsamples,
type = 'b', pch = 20, lty = 1, lwd = 3, ylim = c(0,1), xaxt = 'n', yaxt ='n', xlab = '', ylab = '')
lines(x = data_sizes,
y = sapply(1:length(data_sizes), function(i) b_results$vanilla[[i]]$CESS_j_avg)/nsamples,
pch = 20, lty = 2, lwd = 3, type = 'b')
for (ii in 1:length(data_sizes)) {
cess_j <- lapply(1:length(data_sizes), function(i) b_results$vanilla[[i]]$CESS_j/nsamples)[[ii]]
points(x = rep(data_sizes[ii], length(cess_j)), y = cess_j, cex = 0.5)
}
axis(1, at = c(1000, seq(10000, 50000, 10000)),
labels = c(1000, seq(10000, 50000, 10000)), font = 2, cex = 1.5)
axis(1, at = seq(0, 50000, 5000), labels = rep("", 11), lwd.ticks = 0.5)
mtext('Data Sizes', 1, 2.75, font = 2, cex = 1.5)
axis(2, at = seq(0, 1, 0.2), labels = c("0.0", seq(0.2, 0.8, 0.2), "1.0"),
font = 2, cex = 1.5)
axis(2, at = seq(0, 1, 0.1), labels = rep("", 11), lwd.ticks = 0.5,
font = 2, cex = 1.5)
mtext('CESS / N', 2, 2.75, font = 2, cex = 1.5)
##### Recommended scaling of T, regular mesh #####
plot(x = data_sizes,
y = sapply(1:length(data_sizes), function(i) c_results$vanilla[[i]]$CESS_0)/nsamples,
type = 'b', pch = 20, lty = 1, lwd = 3, ylim = c(0,1), xaxt = 'n', yaxt ='n', xlab = '', ylab = '')
lines(x = data_sizes,
y = sapply(1:length(data_sizes), function(i) c_results$vanilla[[i]]$CESS_j_avg)/nsamples,
pch = 20, lty = 2, lwd = 3, type = 'b')
for (ii in 1:length(data_sizes)) {
cess_j <- lapply(1:length(data_sizes), function(i) c_results$vanilla[[i]]$CESS_j/nsamples)[[ii]]
points(x = rep(data_sizes[ii], length(cess_j)), y = cess_j, cex = 0.5)
}
axis(1, at = c(1000, seq(10000, 50000, 10000)),
labels = c(1000, seq(10000, 50000, 10000)), font = 2, cex = 1.5)
axis(1, at = seq(0, 50000, 5000), labels = rep("", 11), lwd.ticks = 0.5)
mtext('Data Sizes', 1, 2.75, font = 2, cex = 1.5)
axis(2, at = seq(0, 1, 0.2), labels = c("0.0", seq(0.2, 0.8, 0.2), "1.0"),
font = 2, cex = 1.5)
axis(2, at = seq(0, 1, 0.1), labels = rep("", 11), lwd.ticks = 0.5,
font = 2, cex = 1.5)
mtext('CESS / N', 2, 2.75, font = 2, cex = 1.5)
##### Recommended scaling of T, adaptive mesh #####
plot(x = data_sizes,
y = sapply(1:length(data_sizes), function(i) d_results$vanilla[[i]]$CESS_0)/nsamples,
type = 'b', pch = 20, lty = 1, lwd = 3, ylim = c(0,1), xaxt = 'n', yaxt ='n', xlab = '', ylab = '')
lines(x = data_sizes,
y = sapply(1:length(data_sizes), function(i) d_results$vanilla[[i]]$CESS_j_avg)/nsamples,
pch = 20, lty = 2, lwd = 3, type = 'b')
for (ii in 1:length(data_sizes)) {
cess_j <- lapply(1:length(data_sizes), function(i) d_results$vanilla[[i]]$CESS_j/nsamples)[[ii]]
points(x = rep(data_sizes[ii], length(cess_j)), y = cess_j, cex = 0.5)
}
axis(1, at = c(1000, seq(10000, 50000, 10000)),
labels = c(1000, seq(10000, 50000, 10000)), font = 2, cex = 1.5)
axis(1, at = seq(0, 50000, 5000), labels = rep("", 11), lwd.ticks = 0.5)
mtext('Data Sizes', 1, 2.75, font = 2, cex = 1.5)
axis(2, at = seq(0, 1, 0.2), labels = c("0.0", seq(0.2, 0.8, 0.2), "1.0"),
font = 2, cex = 1.5)
axis(2, at = seq(0, 1, 0.1), labels = rep("", 11), lwd.ticks = 0.5,
font = 2, cex = 1.5)
mtext('CESS / N', 2, 2.75, font = 2, cex = 1.5)
##### Compare regular mesh and adaptive mesh times #####
plot(x = c_results$vanilla[[1]]$time_mesh,
y = rep(data_sizes[1]-500, length(c_results$vanilla[[1]]$time_mesh)),
type = 'b', pch = 20, lty = 1, lwd = 3, ylim = c(0,50000),
xaxt = 'n', yaxt ='n', xlab = '', ylab = '')
for (i in 2:length(data_sizes)) {
lines(x = c_results$vanilla[[i]]$time_mesh,
y = rep(data_sizes[i]-500, length(c_results$vanilla[[i]]$time_mesh)),
type = 'b', pch = 20, lty = 1, lwd = 3)
}
for (i in 1:length(data_sizes)) {
lines(x = d_results$vanilla[[i]]$time_mesh,
y = rep(data_sizes[i]+500, length(d_results$vanilla[[i]]$time_mesh)),
type = 'b', pch = 4, lty = 2, lwd = 3)
}
max(sapply(1:length(data_sizes), function(i) c_results$vanilla[[i]]$time_mesh))
axis(1, at = seq(0, 0.03, 0.01), labels = seq(0, 0.03, 0.01), font = 2, cex = 1.5)
axis(1, at = seq(0, 0.03, 0.005), labels = rep("", 7), lwd.ticks = 0.5)
mtext('Time', 1, 2.75, font = 2, cex = 1.5)
axis(2, at = c(1000, seq(10000, 50000, 10000)),
labels = c(1000, seq(10000, 50000, 10000)), font = 2, cex = 1.5)
axis(2, at = seq(0, 50000, 5000), labels = rep("", 11), lwd.ticks = 0.5)
mtext('Data Sizes', 2, 2.75, font = 2, cex = 1.5)
# plot(x = d_results$vanilla[[1]]$time_mesh,
# y = rep(data_sizes[1], length(d_results$vanilla[[1]]$time_mesh)),
# type = 'b', pch = 20, lty = 1, lwd = 3, ylim = c(0,50000),
# xaxt = 'n', yaxt ='n', xlab = '', ylab = '')
# for (i in 1:length(data_sizes)) {
# lines(x = d_results$vanilla[[i]]$time_mesh,
# y = rep(data_sizes[i], length(d_results$vanilla[[i]]$time_mesh)),
# type = 'b', pch = 20, lty = 1, lwd = 3)
# }
# # max(sapply(1:length(data_sizes), function(i) max(d_results$vanilla[[i]]$time_mesh)))
# axis(1, at = seq(0, 0.03, 0.01), labels = seq(0, 0.03, 0.01), font = 2, cex = 1.5)
# axis(1, at = seq(0, 0.03, 0.005), labels = rep("", 7), lwd.ticks = 0.5)
# mtext('Time', 1, 2.75, font = 2, cex = 1.5)
# axis(2, at = c(1000, seq(10000, 50000, 10000)), labels = c(1000, seq(10000, 50000, 10000)), font = 2, cex = 1.5)
# axis(2, at = seq(0, 50000, 5000), labels = rep("", 11), lwd.ticks = 0.5)
# mtext('Data Sizes', 2, 2.75, font = 2, cex = 1.5)
##### SSH: Recommended scaling of T, adaptive mesh #####
plot(x = data_sizes,
y = sapply(1:length(data_sizes), function(i) SSH_adaptive_results$vanilla[[i]]$CESS_0)/nsamples,
type = 'b', pch = 20, lty = 1, lwd = 3, ylim = c(0,1), xaxt = 'n', yaxt ='n', xlab = '', ylab = '')
lines(x = data_sizes,
y = sapply(1:length(data_sizes), function(i) SSH_adaptive_results$vanilla[[i]]$CESS_j_avg)/nsamples,
pch = 20, lty = 2, lwd = 3, type = 'b')
for (ii in 1:length(data_sizes)) {
cess_j <- lapply(1:length(data_sizes), function(i) SSH_adaptive_results$vanilla[[i]]$CESS_j/nsamples)[[ii]]
points(x = rep(data_sizes[ii], length(cess_j)), y = cess_j, cex = 0.5)
}
axis(1, at = c(1000, seq(10000, 50000, 10000)),
labels = c(1000, seq(10000, 50000, 10000)), font = 2, cex = 1.5)
axis(1, at = seq(0, 50000, 5000), labels = rep("", 11), lwd.ticks = 0.5)
mtext('Data Sizes', 1, 2.75, font = 2, cex = 1.5)
axis(2, at = seq(0, 1, 0.2), labels = c("0.0", seq(0.2, 0.8, 0.2), "1.0"),
font = 2, cex = 1.5)
axis(2, at = seq(0, 1, 0.1), labels = rep("", 11), lwd.ticks = 0.5,
font = 2, cex = 1.5)
mtext('CESS / N', 2, 2.75, font = 2, cex = 1.5)
##### IAD #####
plot(x = data_sizes,
y = sapply(1:length(data_sizes), function(i) a_results$vanilla[[i]]$IAD),
type = 'b', pch = 1, lty = 1, lwd = 3, ylim = c(0,0.6), xaxt = 'n', yaxt ='n', xlab = '', ylab = '')
lines(x = data_sizes,
y = sapply(1:length(data_sizes), function(i) b_results$vanilla[[i]]$IAD),
pch = 2, lty = 2, lwd = 3, type = 'b')
lines(x = data_sizes,
y = sapply(1:length(data_sizes), function(i) c_results$vanilla[[i]]$IAD),
pch = 3, lty = 3, lwd = 3, type = 'b')
lines(x = data_sizes,
y = sapply(1:length(data_sizes), function(i) d_results$vanilla[[i]]$IAD),
pch = 4, lty = 4, lwd = 3, type = 'b')
lines(x = data_sizes,
y = sapply(1:length(data_sizes), function(i) SSH_adaptive_results$vanilla[[i]]$IAD),
pch = 5, lty = 5, lwd = 3, type = 'b')
axis(1, at = c(1000, seq(10000, 50000, 10000)),
labels = c(1000, seq(10000, 50000, 10000)), font = 2, cex = 1.5)
axis(1, at = seq(0, 50000, 5000), labels = rep("", 11), lwd.ticks = 0.5)
mtext('Data Sizes', 1, 2.75, font = 2, cex = 1.5)
axis(2, at = seq(0, 1, 0.1), labels = c("0.0", seq(0.1, 0.9, 0.1), "1.0"),
font = 2, cex = 1.5)
axis(2, at = seq(0, 1, 0.1), labels=rep("", 11), lwd.ticks = 0.5,
font = 2, cex = 1.5)
mtext('Integrated Absolute Distance', 2, 2.75, font = 2, cex = 1.5)
legend(x = 250, y = 0.6,
legend = c('Fixed T, fixed n',
'SH rec. T, fixed n',
'SH rec. T, reg. mesh',
'SH rec. T, adapt. mesh',
'SSH rec. T, adapt. mesh'),
lty = 1:5,
pch = 1:5,
lwd = rep(3, 5),
cex = 1.25,
text.font = 2,
bty = 'n')
##### time #####
plot(x = data_sizes,
y = log(sapply(1:length(data_sizes), function(i) a_results$vanilla[[i]]$time)),
type = 'b', pch = 1, lty = 1, lwd = 3, ylim = c(1,5), xaxt = 'n', yaxt ='n', xlab = '', ylab = '')
lines(x = data_sizes,
y = log(sapply(1:length(data_sizes), function(i) b_results$vanilla[[i]]$time)),
pch = 2, lty = 2, lwd = 3, type = 'b')
lines(x = data_sizes,
y = log(sapply(1:length(data_sizes), function(i) c_results$vanilla[[i]]$time)),
pch = 3, lty = 3, lwd = 3, type = 'b')
lines(x = data_sizes,
y = log(sapply(1:length(data_sizes), function(i) d_results$vanilla[[i]]$time)),
pch = 4, lty = 4, lwd = 3, type = 'b')
lines(x = data_sizes,
y = log(sapply(1:length(data_sizes), function(i) SSH_adaptive_results$vanilla[[i]]$time)),
pch = 5, lty = 5, lwd = 3, type = 'b')
axis(1, at = c(1000, seq(10000, 50000, 10000)),
labels = c(1000, seq(10000, 50000, 10000)), font = 2, cex = 1.5)
axis(1, at = seq(0, 50000, 5000), labels = rep("", 11), lwd.ticks = 0.5)
mtext('Data Sizes', 1, 2.75, font = 2, cex = 1.5)
axis(2, at = seq(0, 5, 1), labels = seq(0, 5, 1), font = 2, cex = 1.5)
mtext('log(Elapsed time in seconds)', 2, 2.75, font = 2, cex = 1.5)
legend(x = 0, y = 5,
legend = c('Fixed T, fixed n',
'SH rec. T, fixed n',
'SH rec. T, reg. mesh',
'SH rec. T, adapt. mesh',
'SSH rec. T, adapt. mesh'),
lty = 1:5,
pch = 1:5,
lwd = rep(3, 5),
cex = 1.25,
text.font = 2,
bty = 'n')
##### generalised plots #####
##### Fixed user-specified parameters #####
plot(x = data_sizes,
y = sapply(1:length(data_sizes), function(i) a_results$generalised[[i]]$CESS_0)/nsamples,
type = 'b', pch = 20, lty = 1, lwd = 3, ylim = c(0,1), xaxt = 'n', yaxt ='n', xlab = '', ylab = '')
lines(x = data_sizes,
y = sapply(1:length(data_sizes), function(i) a_results$generalised[[i]]$CESS_j_avg)/nsamples,
pch = 20, lty = 2, lwd = 3, type = 'b')
for (ii in 1:length(data_sizes)) {
cess_j <- lapply(1:length(data_sizes), function(i) a_results$generalised[[i]]$CESS_j/nsamples)[[ii]]
points(x = rep(data_sizes[ii], length(cess_j)), y = cess_j, cex = 0.5)
}
axis(1, at = c(1000, seq(10000, 50000, 10000)),
labels = c(1000, seq(10000, 50000, 10000)), font = 2, cex = 1.5)
axis(1, at = seq(0, 50000, 5000), labels = rep("", 11), lwd.ticks = 0.5)
mtext('Data Sizes', 1, 2.75, font = 2, cex = 1.5)
axis(2, at = seq(0, 1, 0.2), labels = c("0.0", seq(0.2, 0.8, 0.2), "1.0"),
font = 2, cex = 1.5)
axis(2, at = seq(0, 1, 0.1), labels = rep("", 11), lwd.ticks = 0.5,
font = 2, cex = 1.5)
mtext('CESS / N', 2, 2.75, font = 2, cex = 1.5)
##### Recommended scaling of T, fixed n #####
plot(x = data_sizes,
y = sapply(1:length(data_sizes), function(i) b_results$generalised[[i]]$CESS_0)/nsamples,
type = 'b', pch = 20, lty = 1, lwd = 3, ylim = c(0,1), xaxt = 'n', yaxt ='n', xlab = '', ylab = '')
lines(x = data_sizes,
y = sapply(1:length(data_sizes), function(i) b_results$generalised[[i]]$CESS_j_avg)/nsamples,
pch = 20, lty = 2, lwd = 3, type = 'b')
for (ii in 1:length(data_sizes)) {
cess_j <- lapply(1:length(data_sizes), function(i) b_results$generalised[[i]]$CESS_j/nsamples)[[ii]]
points(x = rep(data_sizes[ii], length(cess_j)), y = cess_j, cex = 0.5)
}
axis(1, at = c(1000, seq(10000, 50000, 10000)),
labels = c(1000, seq(10000, 50000, 10000)), font = 2, cex = 1.5)
axis(1, at = seq(0, 50000, 5000), labels = rep("", 11), lwd.ticks = 0.5)
mtext('Data Sizes', 1, 2.75, font = 2, cex = 1.5)
axis(2, at = seq(0, 1, 0.2), labels = c("0.0", seq(0.2, 0.8, 0.2), "1.0"),
font = 2, cex = 1.5)
axis(2, at = seq(0, 1, 0.1), labels = rep("", 11), lwd.ticks = 0.5,
font = 2, cex = 1.5)
mtext('CESS / N', 2, 2.75, font = 2, cex = 1.5)
##### Recommended scaling of T, regular mesh #####
plot(x = data_sizes,
y = sapply(1:length(data_sizes), function(i) c_results$generalised[[i]]$CESS_0)/nsamples,
type = 'b', pch = 20, lty = 1, lwd = 3, ylim = c(0,1), xaxt = 'n', yaxt ='n', xlab = '', ylab = '')
lines(x = data_sizes,
y = sapply(1:length(data_sizes), function(i) c_results$generalised[[i]]$CESS_j_avg)/nsamples,
pch = 20, lty = 2, lwd = 3, type = 'b')
for (ii in 1:length(data_sizes)) {
cess_j <- lapply(1:length(data_sizes), function(i) c_results$generalised[[i]]$CESS_j/nsamples)[[ii]]
points(x = rep(data_sizes[ii], length(cess_j)), y = cess_j, cex = 0.5)
}
axis(1, at = c(1000, seq(10000, 50000, 10000)),
labels = c(1000, seq(10000, 50000, 10000)), font = 2, cex = 1.5)
axis(1, at = seq(0, 50000, 5000), labels = rep("", 11), lwd.ticks = 0.5)
mtext('Data Sizes', 1, 2.75, font = 2, cex = 1.5)
axis(2, at = seq(0, 1, 0.2), labels = c("0.0", seq(0.2, 0.8, 0.2), "1.0"),
font = 2, cex = 1.5)
axis(2, at = seq(0, 1, 0.1), labels = rep("", 11), lwd.ticks = 0.5,
font = 2, cex = 1.5)
mtext('CESS / N', 2, 2.75, font = 2, cex = 1.5)
##### Recommended scaling of T, adaptive mesh #####
plot(x = data_sizes,
y = sapply(1:length(data_sizes), function(i) d_results$generalised[[i]]$CESS_0)/nsamples,
type = 'b', pch = 20, lty = 1, lwd = 3, ylim = c(0,1), xaxt = 'n', yaxt ='n', xlab = '', ylab = '')
lines(x = data_sizes,
y = sapply(1:length(data_sizes), function(i) d_results$generalised[[i]]$CESS_j_avg)/nsamples,
pch = 20, lty = 2, lwd = 3, type = 'b')
for (ii in 1:length(data_sizes)) {
cess_j <- lapply(1:length(data_sizes), function(i) d_results$generalised[[i]]$CESS_j/nsamples)[[ii]]
points(x = rep(data_sizes[ii], length(cess_j)), y = cess_j, cex = 0.5)
}
axis(1, at = c(1000, seq(10000, 50000, 10000)),
labels = c(1000, seq(10000, 50000, 10000)), font = 2, cex = 1.5)
axis(1, at = seq(0, 50000, 5000), labels = rep("", 11), lwd.ticks = 0.5)
mtext('Data Sizes', 1, 2.75, font = 2, cex = 1.5)
axis(2, at = seq(0, 1, 0.2), labels = c("0.0", seq(0.2, 0.8, 0.2), "1.0"),
font = 2, cex = 1.5)
axis(2, at = seq(0, 1, 0.1), labels = rep("", 11), lwd.ticks = 0.5,
font = 2, cex = 1.5)
mtext('CESS / N', 2, 2.75, font = 2, cex = 1.5)
##### Compare regular mesh and adaptive mesh times #####
plot(x = c_results$generalised[[1]]$time_mesh,
y = rep(data_sizes[1]-500, length(c_results$generalised[[1]]$time_mesh)),
type = 'b', pch = 20, lty = 1, lwd = 3, ylim = c(0,50000),
xaxt = 'n', yaxt ='n', xlab = '', ylab = '')
for (i in 2:length(data_sizes)) {
lines(x = c_results$generalised[[i]]$time_mesh,
y = rep(data_sizes[i]-500, length(c_results$generalised[[i]]$time_mesh)),
type = 'b', pch = 20, lty = 1, lwd = 3)
}
for (i in 1:length(data_sizes)) {
lines(x = d_results$generalised[[i]]$time_mesh,
y = rep(data_sizes[i]+500, length(d_results$generalised[[i]]$time_mesh)),
type = 'b', pch = 4, lty = 2, lwd = 3)
}
max(sapply(1:length(data_sizes), function(i) max(c_results$generalised[[i]]$time_mesh)))
axis(1, at = seq(0, 3, 1), labels = seq(0, 3, 1), font = 2, cex = 1.5)
axis(1, at = seq(0, 3, 0.5), labels = rep("", 7), lwd.ticks = 0.5)
mtext('Time', 1, 2.75, font = 2, cex = 1.5)
axis(2, at = c(1000, seq(10000, 50000, 10000)),
labels = c(1000, seq(10000, 50000, 10000)), font = 2, cex = 1.5)
axis(2, at = seq(0, 50000, 5000), labels = rep("", 11), lwd.ticks = 0.5)
mtext('Data Sizes', 2, 2.75, font = 2, cex = 1.5)
##### SSH: Recommended scaling of T, adaptive mesh #####
plot(x = data_sizes,
y = sapply(1:length(data_sizes), function(i) SSH_adaptive_results$vanilla[[i]]$CESS_0)/nsamples,
type = 'b', pch = 20, lty = 1, lwd = 3, ylim = c(0,1), xaxt = 'n', yaxt ='n', xlab = '', ylab = '')
lines(x = data_sizes,
y = sapply(1:length(data_sizes), function(i) SSH_adaptive_results$vanilla[[i]]$CESS_j_avg)/nsamples,
pch = 20, lty = 2, lwd = 3, type = 'b')
for (ii in 1:length(data_sizes)) {
cess_j <- lapply(1:length(data_sizes), function(i) SSH_adaptive_results$generalised[[i]]$CESS_j/nsamples)[[ii]]
points(x = rep(data_sizes[ii], length(cess_j)), y = cess_j, cex = 0.5)
}
axis(1, at = c(1000, seq(10000, 50000, 10000)),
labels = c(1000, seq(10000, 50000, 10000)), font = 2, cex = 1.5)
axis(1, at = seq(0, 50000, 5000), labels = rep("", 11), lwd.ticks = 0.5)
mtext('Data Sizes', 1, 2.75, font = 2, cex = 1.5)
axis(2, at = seq(0, 1, 0.2), labels = c("0.0", seq(0.2, 0.8, 0.2), "1.0"),
font = 2, cex = 1.5)
axis(2, at = seq(0, 1, 0.1), labels = rep("", 11), lwd.ticks = 0.5,
font = 2, cex = 1.5)
mtext('CESS / N', 2, 2.75, font = 2, cex = 1.5)
##### IAD #####
plot(x = data_sizes,
y = sapply(1:length(data_sizes), function(i) a_results$generalised[[i]]$IAD),
type = 'b', pch = 1, lty = 1, lwd = 3, ylim = c(0,0.6), xaxt = 'n', yaxt ='n', xlab = '', ylab = '')
lines(x = data_sizes,
y = sapply(1:length(data_sizes), function(i) b_results$generalised[[i]]$IAD),
pch = 2, lty = 2, lwd = 3, type = 'b')
lines(x = data_sizes,
y = sapply(1:length(data_sizes), function(i) c_results$generalised[[i]]$IAD),
pch = 3, lty = 3, lwd = 3, type = 'b')
lines(x = data_sizes,
y = sapply(1:length(data_sizes), function(i) d_results$generalised[[i]]$IAD),
pch = 4, lty = 4, lwd = 3, type = 'b')
lines(x = data_sizes,
y = sapply(1:length(data_sizes), function(i) SSH_adaptive_results$generalised[[i]]$IAD),
pch = 5, lty = 5, lwd = 3, type = 'b')
axis(1, at = c(1000, seq(10000, 50000, 10000)),
labels = c(1000, seq(10000, 50000, 10000)), font = 2, cex = 1.5)
axis(1, at = seq(0, 50000, 5000), labels = rep("", 11), lwd.ticks = 0.5)
mtext('Data Sizes', 1, 2.75, font = 2, cex = 1.5)
axis(2, at = seq(0, 1, 0.1), labels = c("0.0", seq(0.1, 0.9, 0.1), "1.0"),
font = 2, cex = 1.5)
axis(2, at = seq(0, 1, 0.1), labels=rep("", 11), lwd.ticks = 0.5,
font = 2, cex = 1.5)
mtext('Integrated Absolute Distance', 2, 2.75, font = 2, cex = 1.5)
legend(x = 0, y = 0.6,
legend = c('Fixed T, fixed n',
'SH rec. T, fixed n',
'SH rec. T, reg. mesh',
'SH rec. T, adapt. mesh',
'SSH rec. T, adapt. mesh'),
lty = 1:5,
pch = 1:5,
lwd = rep(3, 5),
cex = 1.25,
text.font = 2,
bty = 'n')
##### time #####
plot(x = data_sizes,
y = log(sapply(1:length(data_sizes), function(i) a_results$generalised[[i]]$time)),
type = 'b', pch = 1, lty = 1, lwd = 3, ylim = c(1,5), xaxt = 'n', yaxt ='n', xlab = '', ylab = '')
lines(x = data_sizes,
y = log(sapply(1:length(data_sizes), function(i) b_results$generalised[[i]]$time)),
pch = 2, lty = 2, lwd = 3, type = 'b')
lines(x = data_sizes,
y = log(sapply(1:length(data_sizes), function(i) c_results$generalised[[i]]$time)),
pch = 3, lty = 3, lwd = 3, type = 'b')
lines(x = data_sizes,
y = log(sapply(1:length(data_sizes), function(i) d_results$generalised[[i]]$time)),
pch = 4, lty = 4, lwd = 3, type = 'b')
lines(x = data_sizes,
y = log(sapply(1:length(data_sizes), function(i) SSH_adaptive_results$generalised[[i]]$time)),
pch = 5, lty = 5, lwd = 3, type = 'b')
axis(1, at = c(1000, seq(10000, 50000, 10000)),
labels = c(1000, seq(10000, 50000, 10000)), font = 2, cex = 1.5)
axis(1, at = seq(0, 50000, 5000), labels = rep("", 11), lwd.ticks = 0.5)
mtext('Data Sizes', 1, 2.75, font = 2, cex = 1.5)
axis(2, at = seq(0, 5, 1), labels = seq(0, 5, 1), font = 2, cex = 1.5)
mtext('log(Elapsed time in seconds)', 2, 2.75, font = 2, cex = 1.5)
legend(x = 0, y = 5,
legend = c('Fixed T, fixed n',
'SH rec. T, fixed n',
'SH rec. T, reg. mesh',
'SH rec. T, adapt. mesh',
'SSH rec. T, adapt. mesh'),
lty = 1:5,
pch = 1:5,
lwd = rep(3, 5),
cex = 1.25,
text.font = 2,
bty = 'n')
save.image('bf_similar_means_example.RData')
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