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05_Figures.R
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05_Figures.R
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rm(list = ls())
source("00_system.R")
load("Datasets/app_dataset.RData")
# Kernels
if (T) {
createEllipse <- function(center, a, b, angle = 0, steps = 100) {
theta <- seq(0, 2 * pi, length.out = steps)
ellipse_points <- cbind(center[1] + a * cos(theta), center[2] + b * sin(theta))
ellipse_points <- ellipse_points %*% matrix(c(cos(angle), -sin(angle), sin(angle), cos(angle)), 2, 2)
return(ellipse_points)
}
if (T) {
pdf("Figures/univariate_r.pdf", width = master_width, height = master_height)
par(mfrow = c(1, 1), oma = master_oma, mar = master_mars)
layout(matrix(c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2), nrow = 1))
plot(
x = 0, y = 0, xlim = c(-2, 2), ylim = c(-2, 2), cex = 1,
xlab = "x", ylab = "y", pch = 20, cex.lab = 1.5, cex.axis = 1.5
)
abline(h = 0, lty = 2)
abline(v = 0, lty = 2)
r_vector_sq <- c(0.25, 0.5, 1, 2)
alpha_i <- pi / 2
for (ii in 1:length(r_vector_sq)) {
r_sq <- r_vector_sq[ii]
e_1 <- 1
e_2 <- r_sq
arrows(
x0 = 0, x1 = 1,
y0 = 0, y1 = 0, lwd = 2, lty = 1,
cex = 0.5, angle = 15, length = 0.1
)
arrows(
x0 = 0, x1 = 0,
y0 = 0, y1 = e_2, lwd = 2, lty = 1,
cex = 0.5, angle = 15, length = 0.1
)
ellipse_points <- createEllipse(c(0, 0),
a = 1,
b = r_sq, angle = 0, steps = 2000
)
lines(ellipse_points, col = viridis::viridis(n = length(r_vector_sq))[ii], lwd = 2.0)
}
legend(bty = "n","bottomright",
legend = c(expression(r^2 ~ "= 0.25", r^2 ~ "= 0.50", r^2 ~ "= 1.00", r^2 ~ "= 2.00")),
col = viridis::viridis(length(r_vector_sq)), lty = rep(1, length(r_vector_sq)), cex = 1.25
)
dev.off()
}
if (T) {
# univariate alpha
pdf("Figures/univariate_alpha.pdf", width = master_width, height = master_height)
par(mfrow = c(1, 1), oma = master_oma, mar = master_mars)
layout(matrix(c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2), nrow = 1))
plot(
x = 0, y = 0, xlim = c(-1.5, 1.5), ylim = c(-1, 1), asp = 1, cex = 1,
xlab = "x", ylab = "y", pch = 20, cex.lab = 1.5, cex.axis = 1.5
)
abline(h = 0, lty = 2)
abline(v = 0, lty = 2)
alpha_vector <- c(pi / 10, pi / 6, pi / 4, pi / 3)
for (ii in 1:length(alpha_vector)) {
r <- 1
alpha_i <- alpha_vector[ii]
A_part <- sqrt((r + 1)^2 - 4 * r * sin(alpha_i)^2)
e_1 <- 0.5 * ((r + 1) + sqrt((r + 1)^2 - 4 * r * sin(alpha_i)^2))
e_2 <- 0.5 * ((r + 1) - sqrt((r + 1)^2 - 4 * r * sin(alpha_i)^2))
a_a_1 <- 2 * r^(0.5) * cospi(alpha_i / pi)
a_b_1 <- r - 1 - A_part
e_b_1 <- 2 * r^(0.5) * cos(alpha_i)
d_a_1_new <- r - 1 + A_part
magnitude_vector_one <- sqrt((a_a_1)^2 + a_b_1^2)
y_length <- sqrt(e_2) / magnitude_vector_one
arrows(
x0 = 0, x1 = (-1) * y_length * a_a_1,
y0 = 0, y1 = (-1) * y_length * a_b_1, lwd = 2, lty = 1,
cex = 0.5, angle = 15, length = 0.1
)
magnitude_vector_two <- sqrt((e_b_1)^2 + (d_a_1_new)^2)
y_length <- sqrt(e_1) / magnitude_vector_two
arrows(
x0 = 0, x1 = y_length * e_b_1,
y0 = 0, y1 = y_length * d_a_1_new, lwd = 2, lty = 1,
cex = 0.5, angle = 15, length = 0.1
)
# Plot ellipse
ellipse_points <- createEllipse(c(0, 0),
a = sqrt((max(e_1, e_2))),
b = sqrt((min(e_1, e_2))),
atan2(x = e_b_1, y = d_a_1_new),
steps = 2000
)
lines(ellipse_points, col = viridis::viridis(n = length(alpha_vector))[ii], lwd = 2.0)
}
legend(bty = "n","bottomright",
legend = expression(omega ~ "=" ~ pi / 10, omega ~ "=" ~ pi / 6, omega ~ "=" ~ pi / 4, omega ~ "=" ~ pi / 3), col = viridis::viridis(length(alpha_vector)),
lwd = rep(2, length(alpha_vector)), lty = rep(1, length(alpha_vector)), cex = 1.25
)
dev.off()
}
# How does r and omega affects the tilt?
if (T) {
alpha_vector <- log(seq(exp(0 + 1e-2), exp(pi / 2 - 1e-2), length.out = 1000))
r_vector <- seq(0.05, 0.95, length.out = 10)
pdf("Figures/angle_analysis.pdf", width = master_width, height = master_height)
par(mfrow = c(1, 1), oma = master_oma, mar = master_mars)
layout(matrix(c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2), nrow = 1))
vector_change_alpha <- numeric(length = length(alpha_vector))
for (jj in 1:length(r_vector)) {
r <- r_vector[jj]
for (ii in 1:length(alpha_vector)) {
alpha_i <- alpha_vector[ii]
A_part <- sqrt((r + 1)^2 - 4 * r * sinpi(alpha_i / pi)^2)
e_b_1 <- 2 * r^(0.5) * cos(alpha_i)
d_a_1_new <- r - 1 + A_part
vector_change_alpha[ii] <- atan2(x = e_b_1, y = d_a_1_new) # * 180 / pi
}
if (jj == 1) {
plot(
x = alpha_vector, y = vector_change_alpha, type = "l", ylim = c(0, pi / 4 + 0.1),
col = viridis::viridis(length(r_vector))[jj], cex = 1, lwd = 2,
xlab = expression(omega), ylab = "rotation angle", pch = 20,
cex.lab = 1.5, cex.axis = 1.5,
xaxt = "n", yaxt = "n"
)
abline(h = pi / 4, col = "blue", lty = 2)
abline(v = pi / 2, col = "blue", lty = 2)
} else {
lines(
x = alpha_vector,
y = vector_change_alpha,
col = viridis::viridis(length(r_vector))[jj], lwd = 2
)
}
}
axis(1, at = c(0, pi / 8, pi / 4, pi / 3, pi / 2), labels = c(0, expression(pi / 8), expression(pi / 4), expression(pi / 3), expression(pi / 2)), cex.lab = 1.5, cex.axis = 1.5)
axis(2, at = c(0, pi / 12, pi / 6, pi / 4), labels = c(0, expression(pi / 12), expression(pi / 6), expression(pi / 4)), cex.lab = 1.5, cex.axis = 1.5)
par(mar = c(4.5, 0, 0.5, 2.5))
tmp_z <- matrix(1:10, nrow = 1)
tmp_x <- 1
tmp_y <- seq(min(r_vector), max(r_vector), len = 10)
tmp_y <- r_vector
image(tmp_x, tmp_y, tmp_z, col = viridis::viridis(11), axes = FALSE, xlab = "", ylab = "")
axis(4, lwd = 2, cex.axis = 1.5, at = seq(0.05, 0.95, length.out = 10))
dev.off()
}
if (T) {
alpha_vector <- c(pi / 8, pi / 3, pi / 2.1)
r_vector <- c(0.3, 0.5, 0.9)^2
vec_letters <- c("a", "b", "c")
for (jj in 1:length(r_vector)) {
pdf(paste0("Figures/bivariate_alpha_r_simp_", vec_letters[jj], ".pdf"), width = master_width, height = master_height)
par(mfrow = c(1, 1), oma = master_oma, mar = master_mars)
layout(matrix(c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2), nrow = 1))
plot(
x = 0, y = 0, xlim = c(-1.1, 1.1), ylim = c(-1.1, 1.1), asp = 1, cex = 1,
xlab = "x", ylab = "y", pch = 20, cex.lab = 1.5, cex.axis = 1.5
)
abline(h = 0, lty = 2)
abline(v = 0, lty = 2)
r <- r_vector[jj]
for (ii in 1:length(alpha_vector)) {
alpha_i <- alpha_vector[ii]
if (alpha_i == pi / 2) {
print("linear independent eigenvectors")
r <- r_vector[ii]
A_stuff <- sqrt((r + 1)^2 - 4 * r * sin(alpha_i)^2)
e_1 <- ((r + 1) + sqrt((r + 1)^2 - 4 * r * sin(alpha_i)^2))
e_2 <- ((r + 1) - sqrt((r + 1)^2 - 4 * r * sin(alpha_i)^2))
magnitude_vector_one <- sqrt((0)^2 + 1^2)
y_length <- sqrt(max(e_2, e_1)) / magnitude_vector_one
arrows(
x0 = 0, x1 = ifelse(r > 1, 0, y_length),
y0 = 0, y1 = ifelse(r > 1, y_length, 0), lwd = 2, lty = 1,
cex = 0.5, angle = 5, length = 0.1
)
magnitude_vector_two <- sqrt((1)^2 + (0)^2)
y_length <- sqrt(min(e_1, e_2)) / magnitude_vector_two
arrows(
x0 = 0, x1 = ifelse(r > 1, y_length, 0),
y0 = 0, y1 = ifelse(r > 1, 0, y_length), lwd = 2, lty = 1,
cex = 0.5, angle = 5, length = 0.1
)
ellipse_points <- createEllipse(c(0, 0),
a = sqrt(ifelse(r > 1, (min(e_1, e_2)), max(e_1, e_2))),
b = sqrt(ifelse(r > 1, (max(e_1, e_2)), min(e_1, e_2))), 0, steps = 2000
)
lines(ellipse_points, col = viridis::viridis(n = length(alpha_vector))[ii], lwd = 2)
next
}
if (F) {
A_stuff <- sqrt((r + 1)^2 - 4 * r * sin(alpha_i)^2)
e_1 <- c(
2 * sqrt(r) * cos(alpha_i),
(r - 1 + A_stuff)
)
e_2 <- c(
2 * sqrt(r) * cos(alpha_i),
(r - 1 - A_stuff)
)
magnitude_1 <- sqrt(e_1[1]^2 + e_1[2]^2)
magnitude_2 <- sqrt(e_2[1]^2 + e_2[2]^2)
arrows(
x0 = 0, x1 = e_1[1],
y0 = 0, y1 = e_1[2], lwd = 2, lty = 1,
cex = 0.5, angle = 15, length = 0.1
)
arrows(
x0 = 0, x1 = e_2[1],
y0 = 0, y1 = e_2[2], lwd = 2, lty = 1,
cex = 0.5, angle = 15, length = 0.1
)
ellipse_points <- createEllipse(c(0, 0),
a = magnitude_1,
b = magnitude_2, atan2(x = e_1[2], y = e_1[1]), steps = 2000
)
lines(ellipse_points, col = viridis::viridis(n = length(alpha_vector))[ii], lwd = 2)
e_1 <- 0.5 * ((r + 1) + sqrt((r + 1)^2 - 4 * r * sin(alpha_i)^2))
e_2 <- 0.5 * ((r + 1) - sqrt((r + 1)^2 - 4 * r * sin(alpha_i)^2))
a_a_1 <- 2 * r^(0.5) * cospi(alpha_i / pi)
a_b_1 <- r - 1 - A_stuff
e_b_1 <- 2 * r^(0.5) * cos(alpha_i)
d_a_1_new <- r - 1 + A_stuff
magnitude_vector_one <- sqrt((a_a_1)^2 + a_b_1^2)
y_length <- sqrt(e_2) / magnitude_vector_one
magnitude_vector_two <- sqrt((e_b_1)^2 + (d_a_1_new)^2)
y_length <- sqrt(e_1) / magnitude_vector_two
arrows(
x0 = 0, x1 = y_length * e_b_1,
y0 = 0, y1 = y_length * d_a_1_new, lwd = 2, lty = 1,
cex = 0.5, angle = 15, length = 0.1
)
# Plot ellipse
ellipse_points <- createEllipse(c(0, 0),
a = sqrt((max(e_1, e_2))),
b = sqrt((min(e_1, e_2))), atan2(x = e_b_1, y = d_a_1_new), steps = 2000
)
lines(ellipse_points, col = viridis::viridis(n = length(alpha_vector))[ii], lwd = 2)
}
A_one <- sqrt((r + 1)^2 - 4 * r * sin(alpha_i)^2)
e_1 <- 0.5 * ((r + 1) + sqrt((r + 1)^2 - 4 * r * sin(alpha_i)^2))
e_2 <- 0.5 * ((r + 1) - sqrt((r + 1)^2 - 4 * r * sin(alpha_i)^2))
a_a_1 <- 2 * r^(0.5) * cospi(alpha_i / pi)
a_b_1 <- r - 1 - A_one
e_b_1 <- 2 * r^(0.5) * cos(alpha_i)
d_a_1_new <- r - 1 + A_one
magnitude_vector_one <- sqrt((a_a_1)^2 + a_b_1^2)
y_length <- sqrt(e_2) / magnitude_vector_one
arrows(
x0 = 0, x1 = (-1) * y_length * a_a_1,
y0 = 0, y1 = (-1) * y_length * a_b_1, lwd = 2, lty = 1,
cex = 0.5, angle = 15, length = 0.1
)
magnitude_vector_two <- sqrt((e_b_1)^2 + (d_a_1_new)^2)
y_length <- sqrt(e_1) / magnitude_vector_two
arrows(
x0 = 0, x1 = y_length * e_b_1,
y0 = 0, y1 = y_length * d_a_1_new, lwd = 2, lty = 1,
cex = 0.5, angle = 15, length = 0.1
)
# Plot ellipse
ellipse_points <- createEllipse(c(0, 0),
a = sqrt((max(e_1, e_2))),
b = sqrt((min(e_1, e_2))), atan2(x = e_b_1, y = d_a_1_new), steps = 2000
)
lines(ellipse_points, col = viridis::viridis(n = length(alpha_vector))[ii], lwd = 2)
}
legend(bty = "n","bottomright",
legend = c(expression(omega ~ "=" ~ pi / 8), expression(omega ~ "=" ~ pi / 3), expression(omega ~ "=" ~ 2 ~ pi / 10)), col = viridis::viridis(length(alpha_vector)),
lwd = rep(2, length(alpha_vector)), lty = rep(1, length(alpha_vector)), cex = 1.25
)
dev.off()
}
}
}
# Noisy / Categorical covariates plots
if (T) {
### Noisy how affect
locs_x <- seq(-10, 10, by = 0.05)
locs <- cbind(locs_x, rep(0, length(locs_x)))
create_covariate <- function(x) {
if (x < 0) {
tmp_x <- 1 / (1 + exp(-x - 5)) * 2
tmp_x <- tmp_x + abs(rnorm(1, 0, sd = tmp_x * 0.25))
} else {
tmp_x <- exp(-x + 5) / (1 + exp(-x + 5)) * 2
tmp_x <- tmp_x + abs(rnorm(1, 0, sd = tmp_x * 0.25))
}
}
v_cv <- Vectorize(create_covariate)
create_covariate_no_noise <- function(x) {
if (x < 0) {
tmp_x <- 1 / (1 + exp(-x - 5)) * 2
} else {
tmp_x <- exp(-x + 5) / (1 + exp(-x + 5)) * 2
}
}
v_cv_nn <- Vectorize(create_covariate_no_noise)
df_training <- data.frame(
"x" = locs[, 1],
"y" = locs[, 2],
"cov_x" = v_cv(locs[, 1])
)
list_formulas <- list(
"mean" = 0,
"std.dev" = as.formula(" ~ 1"),
"scale" = as.formula(" ~ 1 + cov_x"),
"aniso" = 0,
"tilt" = 0,
"smooth" = 2.5,
"nugget" = -Inf
)
CoCo_object <- coco(
type = "dense",
model.list = list_formulas,
locs = as.matrix(locs),
z = matrix(numeric(length = dim(df_training)[1]), ncol = 1),
data = df_training
)
####
df_training_nn <- data.frame(
"x" = locs[, 1],
"y" = locs[, 2],
"cov_x" = v_cv_nn(locs[, 1])
)
list_formulas <- list(
"mean" = 0,
"std.dev" = as.formula(" ~ 1"),
"scale" = as.formula(" ~ 1 + cov_x"),
"aniso" = 0,
"tilt" = 0,
"smooth" = 2.5,
"nugget" = -Inf
)
CoCo_object_nn <- coco(
type = "dense",
model.list = list_formulas,
locs = as.matrix(locs),
z = numeric(length = dim(df_training)[1]),
data = df_training_nn
)
no_noise_sim <- cocoSim(CoCo_object_nn,
pars = c(0, log(0.25), 1), seed = 181222 * 8,
standardize = FALSE
)
noise_sim <- cocoSim(CoCo_object,
pars = c(0, log(0.25), 1),
seed = 181222 * 8,
standardize = FALSE
)
pdf("Figures/noisy_covs_a.pdf", width = master_width, height = master_height)
par(mfrow = c(1, 1), oma = master_oma, mar = master_mars)
layout(matrix(c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2), nrow = 1))
plot(df_training_nn$x, df_training_nn$cov_x,
type = "l", col = "blue", ylim = c(-3.3, 3.3),
cex = 0.3, xlab = expression(s), ylab = expression(y), pch = 20, cex.lab = 1.5, cex.axis = 1.45, lwd = 2
)
lines(df_training_nn$x, no_noise_sim, col = "red", lwd = 2)
axis(4, col = "blue", cex.axis = 1.45)
dev.off()
pdf("Figures/noisy_covs_b.pdf", width = master_width, height = master_height)
par(mfrow = c(1, 1), oma = master_oma, mar = master_mars)
layout(matrix(c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2), nrow = 1))
plot(df_training$x, df_training$cov_x,
type = "l", col = "blue", ylim = c(-3.3, 3.3),
cex = 0.3, xlab = expression(s), ylab = expression(y), pch = 20, cex.lab = 1.5, cex.axis = 1.45, lwd = 2
)
lines(df_training$x, df_training_nn$cov_x, col = "blue", lty = 2, lwd = 2)
lines(df_training$x, noise_sim, col = "red", lwd = 2)
axis(4, col = "blue", cex.axis = 1.45)
dev.off()
## another one
locs_x <- seq(-10, 10, by = 0.05)
locs <- cbind(locs_x, rep(0, length(locs_x)))
create_covariate <- function(x) {
if (x < 0) {
0
} else {
1
}
}
v_cv <- Vectorize(create_covariate)
df_training <- data.frame(
"x" = locs[, 1],
"y" = locs[, 2],
"cov_x" = v_cv(locs[, 1])
)
list_formulas <- list(
"mean" = 0,
"std.dev" = as.formula(" ~ 1"),
"scale" = as.formula(" ~ 1 + cov_x"),
"aniso" = 0,
"tilt" = 0,
"smooth" = 2.5,
"nugget" = -Inf
)
CoCo_object <- coco(
type = "dense",
model.list = list_formulas,
locs = as.matrix(locs),
z = matrix(numeric(length = dim(df_training)[1]), ncol = 1),
data = df_training
)
one_jump <- cocoSim(CoCo_object,
pars = c(0, log(0.25), 3),
seed = 181222 * 2,
standardize = FALSE
)
create_covariate_many_jumps <- function(x) {
if (round(x, 0) %% 2 > 0) {
1
} else {
0
}
}
####
df_training_mc <- data.frame(
"x" = locs[, 1],
"y" = locs[, 2],
"cov_x" = Vectorize(create_covariate_many_jumps)(locs[, 1])
)
list_formulas <- list(
"mean" = 0,
"std.dev" = as.formula(" ~ 1"),
"scale" = as.formula(" ~ 1 + cov_x"),
"aniso" = 0,
"tilt" = 0,
"smooth" = 2.5,
"nugget" = -Inf
)
CoCo_object_nn <- coco(
type = "dense",
model.list = list_formulas,
locs = as.matrix(locs),
z = numeric(length = dim(df_training)[1]),
data = df_training_mc
)
many_jumps_nn <- cocoSim(CoCo_object_nn,
pars = c(0, log(0.25), 3, log(2.5)), seed = 181222 * 2,
standardize = FALSE
)
pdf("Figures/categorical_covs_a.pdf", width = master_width, height = master_height)
par(mfrow = c(1, 2), oma = master_oma, mar = master_mars)
layout(matrix(c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2), nrow = 1))
plot(df_training$x, df_training$cov_x,
type = "l", col = "blue", ylim = c(-3.3, 3.3),
cex = 0.3, xlab = expression(s), ylab = expression(y), pch = 20, cex.lab = 1.5, cex.axis = 1.45, lwd = 2
)
axis(4, cex.lab = 1.5, cex.axis = 1.45, col = "blue")
lines(df_training$x, one_jump, col = "red", lwd = 2)
dev.off()
pdf("Figures/categorical_covs_b.pdf", width = master_width, height = master_height)
par(mfrow = c(1, 2), oma = master_oma, mar = master_mars)
layout(matrix(c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2), nrow = 1))
plot(df_training_mc$x, df_training_mc$cov_x,
type = "l", col = "blue", ylim = c(-3.3, 3.3),
cex = 0.3, xlab = expression(s), ylab = expression(y), pch = 20, cex.lab = 1.5, cex.axis = 1.45, lwd = 2
)
lines(df_training_mc$x, many_jumps_nn, col = "red", lwd = 2)
axis(4, cex.lab = 1.5, cex.axis = 1.45, col = "blue")
dev.off()
}
# Plot regularization example plots
if (T) {
sample_sizes <- 250 + 400
create_covariate_one <- Vectorize(function(x) {
return(sin(x * 10))
if (x < 0) {
0
} else {
1
}
})
seq_x <- seq(0, 1, length.out = floor(sqrt(750)))
locs <- expand.grid(seq_x, seq_x)
df_training_mc <- data.frame(
"x" = locs[, 1],
"y" = locs[, 2],
"cov_x" = create_covariate_one(locs[, 1]),
"cov_y" = create_covariate_one(locs[, 2]),
"cov_xy" = create_covariate_one(locs[, 1] * locs[, 2])
)
list_formulas <- list(
"mean" = as.formula(" ~ 1 + cov_x + cov_y"),
"std.dev" = as.formula(" ~ 1 + cov_x + cov_y"),
"scale" = as.formula(" ~ 1 + cov_x + cov_y"),
"aniso" = 0,
"tilt" = 0,
"smooth" = 1.5,
"nugget" = -Inf
)
CoCo_object_nn <- coco(
type = "dense",
model.list = list_formulas,
locs = as.matrix(locs),
z = numeric(length = dim(df_training_mc)[1]),
data = df_training_mc
)
intensity_effect <- seq(0, 5, length.out = 30)
list_results <- list()
true_pars <- c(
c(0, 0.25, -0.25) * 2,
0, 0.5, 0.25,
log(0.25), -0.25, 0.2
)
regula_sim <- cocoSim(
coco.object = CoCo_object_nn,
n = 1,
type = "classic",
pars = true_pars, seed = 181222,
standardize = TRUE
)
lambda_seq <- seq(0,1,length.out = 50)
# Correctly specified
if(T){
vector_lambda_cs <- numeric(length = length(lambda_seq))
cond_numbers_cs <- numeric(length = length(lambda_seq))
log_liks_cs <- numeric(length = length(lambda_seq))
RMSPE_vector_cs <- numeric(length = length(lambda_seq))
CRPS_vector_cs <- numeric(length = length(lambda_seq))
matrix_parameters_cs <- matrix(ncol = 10, nrow = length(lambda_seq))
for (ii in 1:length(lambda_seq)) {
list_formulas <- list(
"mean" = as.formula(" ~ 1 + cov_x + cov_y"),
"std.dev" = as.formula(" ~ 1 + cov_x + cov_y"),
"scale" = as.formula(" ~ 1 + cov_x + cov_y"),
"aniso" = 0,
"tilt" = 0,
"smooth" = as.formula(" ~ 1"),
"nugget" = -Inf
)
set.seed(12222)
index_training <- sort(sample(650, 250))
to_use <- (c(regula_sim[1, index_training]) - mean(c(regula_sim[1, index_training]))) / sd(c(regula_sim[1, index_training]))
CoCo_object_ms <- coco(
type = "dense",
model.list = list_formulas,
locs = as.matrix(locs[index_training, ]),
z = to_use,
data = df_training_mc[index_training, ],
info = list(
"lambda" = lambda_seq[ii],
"smooth_limits" = c(0.5, 3)
)
)
tmp_boundaries <- getBoundaries(CoCo_object_ms, -20, 20)
Optim_new <- cocoOptim(
coco.object = CoCo_object_ms,
ncores = ncores,
boundaries = tmp_boundaries,
optim.type = "mle"
)
cond_numbers_cs[ii] <- getCondNumber(Optim_new)
log_liks_cs[ii] <- getLoglik(Optim_new)
preds_aa <- cocoPredict(Optim_new,
newdataset = df_training_mc[-index_training, ],
newlocs = as.matrix(locs[-index_training, ]),
type = "pred"
)
to_use_pred <- (c(regula_sim[1, -index_training]) - mean(c(regula_sim[1, index_training]))) / sd(c(regula_sim[1, index_training]))
RMSPE_vector_cs[ii] <- sqrt(mean((to_use_pred - (preds_aa$trend + preds_aa$mean))^2))
CRPS_vector_cs[ii] <- mean(getCRPS(to_use_pred,mean.pred = preds_aa$trend + preds_aa$mean,sd.pred = preds_aa$sd.pred))
matrix_parameters_cs[ii, ] <- unlist(getEstims(Optim_new))[c(1:3,4:9,16)]
}
# Prediction metrics under well specified model
if(T){
pdf("Figures/regu_pred.pdf", width = master_width_large, height = master_height)
master_mars_2 <- master_mars
master_mars_2[2] <- master_mars_2[2] + 1.9
par(mfrow = c(1, 1), oma = master_oma, mar = master_mars_2)
layout(matrix(c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2), nrow = 1))
plot(lambda_seq, CRPS_vector_cs / CRPS_vector_cs[1], type = 'l',
xlab = expression(lambda), ylab = expression("Ratio wrt. " * hat(bold(vartheta))[ML]), lwd = 2, cex.lab = 1.5, cex.axis = 1.5,
xaxt = "n", yaxt = "n",xaxs = "i", yaxs = "i", ylim = c(0.94, 1.06))
abline(h = 1, lty = 3, lwd = 2, col = 'gray90')
lines(lambda_seq, RMSPE_vector_cs / RMSPE_vector_cs[1], col = 'red',lwd = 2)
legend(bty = "n",'topleft',legend = c("RMSPE", "CRPS"),
lty = c(1, 1),
col = c('black', 'red'), ncol = 1, cex = 1.25
)
axis(side = 1, cex.axis = 1.5)
axis(side = 2, cex.axis = 1.5)
dev.off()
}
# Condition Number under well specified model
if(T){
pdf("Figures/regu_cn.pdf", width = master_width_large, height = master_height)
master_mars_2 <- master_mars
master_mars_2[2] <- master_mars_2[2] + 1.9
par(mfrow = c(1, 1), oma = master_oma, mar = master_mars_2)
layout(matrix(c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2), nrow = 1))
plot(lambda_seq, cond_numbers_cs / cond_numbers_cs[1], type = 'l',
xlab = expression(lambda), ylab = expression("Ratio wrt. " * hat(bold(vartheta))[ML]), lwd = 2, cex.lab = 1.5, cex.axis = 1.5,
xaxt = "n", yaxt = "n",xaxs = "i",yaxs = "i",ylim = c(0,1.05))
axis(side = 1, cex.axis = 1.5)
axis(side = 2, cex.axis = 1.5)
abline(h = 1, lty = 3, lwd = 2, col = 'gray90')
dev.off()
}
# Relative bias under well specified model
if(T){
pdf("Figures/regu_bias.pdf", width = master_width_large, height = master_height)
master_mars_2 <- master_mars
master_mars_2[2] <- master_mars_2[2] + 1.9
par(mfrow = c(1, 1), oma = master_oma, mar = master_mars_2)
layout(matrix(c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2), nrow = 1))
matplot_plot <- apply(matrix_parameters_cs, MARGIN = 1, function(x) x - matrix_parameters_cs[1, ])
matplot(x = lambda_seq, y = t(matplot_plot), type = 'l', lty = c(1,1,1,1,1,1,1,1,1,1),
col = c(1,'gray90', 'gray90', 2, 'gray90', 'gray90', 3, 'gray90', 'gray90', 4), xaxs = "i", yaxs = "i",
ylab =expression("Change wrt. " * hat(bold(vartheta))[ML]),
xlab = expression(lambda), lwd = 2, ylim = c(-1.5,1.2), cex.lab = 1.5, cex.axis = 1.5)
legend(bty = "n",'topleft', legend = c(expression(beta[0]),
expression(alpha[1]),
expression(theta[ms * "," * 1]),
expression(xi[1]),
's.v. coefs.'), lty = c(1, 1, 1, 1, 1),
col = c(1, 2, 3, 4, 'gray90'), cex = 1.25, lwd = 2, ncol = 3)
dev.off()
master_mars[2] <- master_mars[2] - 0.6
}
}
}
# Plot Covariates
if (T) {
df_app <- all_dfs[[4]]
if (T) {
if (T) {
png("Figures/illu_prec.png",
width = master_width * 3, height = master_height * 2, res = master_res,
units = "in"
)
par(mfrow = c(1, 1), oma = master_oma, mar = master_mars)
layout(matrix(c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2), nrow = 1))
tp_prec <- df_app$prec
plot(df_app[, 1], df_app[, 2],
col = tim.colors(128)[cut(tp_prec,
breaks = seq(min(tp_prec), max(tp_prec), length.out = 128), labels = F
)],
cex = 0.35, xlab = "Longitude (°)", ylab = "Latitude (°)", pch = 20, cex.axis = 2, cex.lab = 2, asp = 1
)
map(add = TRUE, resolution = 0,lwd=2)
rect(xleft = 7.029167 - 0.35, ybottom = 46.179167 - 0.35, xright = 7.029167 + 0.35, ytop = 46.179167 + 0.35, border = "blue", lwd = 2, lty = 1)
text(x = 7.029167 - 0.3, y = 46.179167 - 0.275, labels = "A", cex = 2)
rect(xleft = 9.029167 - 0.35, ybottom = 46.920833 - 0.35, xright = 9.029167 + 0.35, ytop = 46.920833 + 0.35, border = "blue", lwd = 2, lty = 1)
text(x = 9.029167 - 0.3, y = 46.920833 - 0.275, labels = "B", cex = 2)
rect(xleft = 7.354167 - 0.35, ybottom = 47.10417 - 0.35, xright = 7.354167 + 0.35, ytop = 47.10417 + 0.35, border = "blue", lwd = 2, lty = 1)
text(x = 7.354167 - 0.3, y = 47.10417 - 0.275, labels = "C", cex = 2)
# ref locations
points(x = 7.029167, y = 46.179167, pch=23,col='black',cex=2,bg='white')
points(x = 9.029167, y = 46.920833, pch=23,col='black',cex=2,bg='white')
points(x = 7.354167, y = 47.10417, pch=23,col='black',cex=2,bg='white')
master_mars_second_2 <- master_mars_second
master_mars_second_2[4] <- 7
par(mar = master_mars_second_2)
tmp_z <- matrix(1:100, nrow = 1)
tmp_x <- 1
tmp_y <- seq(min(tp_prec), max(tp_prec), len = 100)
image(tmp_x, tmp_y, tmp_z, col = tim.colors(128), axes = FALSE, xlab = "", ylab = "")
axis(4, lwd = 2, cex.axis = 2)
dev.off()
}
if (T) {
png("Figures/illu_wind.png",
width = master_width_large,
height = master_height_large, res = master_res,
units = "in"
)
par(mfrow = c(1, 1), oma = master_oma, mar = master_mars)
layout(matrix(c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2), nrow = 1))
tp_wind <- df_app$wind
plot(df_app[, 1], df_app[, 2],
col = tim.colors(128)[cut(tp_wind,
breaks = seq(min(tp_wind), max(tp_wind), length.out = 128), labels = F
)],
cex = 0.3, xlab = "Longitude (°)", ylab = "Latitude (°)", pch = 20, cex.lab = 1.5, cex.axis = 1.5
)
map(add = TRUE, resolution = 0)
par(mar = master_mars_second)
tmp_z <- matrix(1:100, nrow = 1)
tmp_x <- 1
tmp_y <- seq(min(tp_wind), max(tp_wind), len = 100) # supposing 3 and 2345 are the range of your data
image(tmp_x, tmp_y, tmp_z, col = tim.colors(128), axes = FALSE, xlab = "", ylab = "")
axis(4, lwd = 2, cex.axis = 1.5)
dev.off()
}
if (T) {
png("Figures/illu_cloud.png",
width = master_width_large,
height = master_height_large, res = master_res,
units = "in"
)
par(mfrow = c(1, 1), oma = master_oma, mar = master_mars)
layout(matrix(c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2), nrow = 1))
tp_wind <- df_app$cloud_c
plot(df_app[, 1], df_app[, 2],
col = tim.colors(128)[cut(tp_wind,
breaks = seq(min(tp_wind), max(tp_wind), length.out = 128), labels = F
)],
cex = 0.3, xlab = "Longitude (°)", ylab = "Latitude (°)", pch = 20, cex.lab = 1.5, cex.axis = 1.5
)
map(add = TRUE, resolution = 0)
par(mar = master_mars_second)
tmp_z <- matrix(1:100, nrow = 1)
tmp_x <- 1
tmp_y <- seq(min(tp_wind), max(tp_wind), len = 100) # supposing 3 and 2345 are the range of your data
image(tmp_x, tmp_y, tmp_z, col = tim.colors(128), axes = FALSE, xlab = "", ylab = "")
axis(4, lwd = 2, cex.axis = 1.5)
dev.off()
}
if (T) {
png("Figures/illu_elev.png",
width = master_width_large,
height = master_height_large, res = master_res,
units = "in"
)
par(mfrow = c(1, 1), oma = master_oma, mar = master_mars)
layout(matrix(c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2), nrow = 1))
tp_wind <- df_app$elevation
plot(df_app[, 1], df_app[, 2],
col = tim.colors(128)[cut(tp_wind,
breaks = seq(min(tp_wind), max(tp_wind), length.out = 128), labels = F
)],
cex = 0.3, xlab = "Longitude (°)", ylab = "Latitude (°)", pch = 20, cex.lab = 1.5, cex.axis = 1.5
)
map(add = TRUE, resolution = 0)
par(mar = master_mars_second)
tmp_z <- matrix(1:100, nrow = 1)
tmp_x <- 1
tmp_y <- seq(min(tp_wind), max(tp_wind), len = 100) # supposing 3 and 2345 are the range of your data
image(tmp_x, tmp_y, tmp_z, col = tim.colors(128), axes = FALSE, xlab = "", ylab = "")
axis(4, lwd = 2, cex.axis = 1.5)
dev.off()
}
if (T) {
png("Figures/illu_new_wind.png",
width = master_width_large,
height = master_height_large, res = master_res,
units = "in"
)
par(mfrow = c(1, 1), oma = master_oma, mar = master_mars)
layout(matrix(c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2), nrow = 1))
tp_wind <- df_app$new_wind
plot(df_app[, 1], df_app[, 2],
col = tim.colors(128)[cut(tp_wind,
breaks = seq(min(tp_wind), max(tp_wind), length.out = 128), labels = F
)],
cex = 0.3, xlab = "Longitude (°)", ylab = "Latitude (°)", pch = 20, cex.lab = 1.5, cex.axis = 1.5
)
map(add = TRUE, resolution = 0)
par(mar = master_mars_second)
tmp_z <- matrix(1:100, nrow = 1)
tmp_x <- 1
tmp_y <- seq(min(tp_wind), max(tp_wind), len = 100) # supposing 3 and 2345 are the range of your data
image(tmp_x, tmp_y, tmp_z, col = tim.colors(128), axes = FALSE, xlab = "", ylab = "")
axis(4, lwd = 2, cex.axis = 1.5)
dev.off()
}
if (T) {
png("Figures/illu_BIO04.png",
width = master_width_large,
height = master_height_large, res = master_res,
units = "in"
)
par(mfrow = c(1, 1), oma = master_oma, mar = master_mars)
layout(matrix(c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2), nrow = 1))
tp_wind <- df_app$BIO04
plot(df_app[, 1], df_app[, 2],
col = tim.colors(128)[cut(tp_wind,
breaks = seq(min(tp_wind), max(tp_wind), length.out = 128), labels = F
)],
cex = 0.3, xlab = "Longitude (°)", ylab = "Latitude (°)", pch = 20, cex.lab = 1.5, cex.axis = 1.5
)
map(add = TRUE, resolution = 0)
par(mar = master_mars_second)
tmp_z <- matrix(1:100, nrow = 1)
tmp_x <- 1
tmp_y <- seq(min(tp_wind), max(tp_wind), len = 100) # supposing 3 and 2345 are the range of your data
image(tmp_x, tmp_y, tmp_z, col = tim.colors(128), axes = FALSE, xlab = "", ylab = "")
axis(4, lwd = 2, cex.axis = 1.5)
dev.off()
}
if (T) {
png("Figures/illu_BIO15.png",
width = master_width_large,
height = master_height_large, res = master_res,
units = "in"
)
par(mfrow = c(1, 1), oma = master_oma, mar = master_mars)
layout(matrix(c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2), nrow = 1))
tp_wind <- df_app$BIO15
plot(df_app[, 1], df_app[, 2],
col = tim.colors(128)[cut(tp_wind,
breaks = seq(min(tp_wind), max(tp_wind), length.out = 128), labels = F
)],
cex = 0.3, xlab = "Longitude (°)", ylab = "Latitude (°)", pch = 20, cex.lab = 1.5, cex.axis = 1.5
)
map(add = TRUE, resolution = 0)
par(mar = master_mars_second)
tmp_z <- matrix(1:100, nrow = 1)
tmp_x <- 1
tmp_y <- seq(min(tp_wind), max(tp_wind), len = 100) # supposing 3 and 2345 are the range of your data
image(tmp_x, tmp_y, tmp_z, col = tim.colors(128), axes = FALSE, xlab = "", ylab = "")
axis(4, lwd = 2, cex.axis = 1.5)
dev.off()
}
}
}