Update FigA #55

src/docs_paper/2d.cpp

@@ -11,8 +11,8 @@ Type objective_function<Type>::operator()()
   Type nll;
   nll = Type(0.0);
 
-  Type phi1 = 0.3 * theta2;
-  Type phi2 = 0.5 * theta1 - 0.3 * theta2;
+  Type phi1 = 0.5 * theta1;
+  Type phi2 = 0.8 * theta1 - 0.5 * theta2;
 
   nll -= dsn(phi1, Type(2.0), true);
   nll -= dsn(phi2, Type(-2.0), true);

src/docs_paper/figures.R

@@ -1,15 +1,18 @@
-cols <- c("#56B4E9","#009E73", "#E69F00", "#F0E442", "#0072B2", "#D55E00", "#CC79A7", "#999999")
+library(tidyverse)
+library(patchwork)
 
-#' Fig A
+cols <- c("#56B4E9","#009E73", "#E69F00", "#F0E442", "#0072B2", "#D55E00", "#CC79A7", "#999999")
 
 TMB::compile("2d.cpp")
 dyn.load(TMB::dynlib("2d"))
 
 obj <- TMB::MakeADFun(data = list(), parameters = list(theta1 = 0, theta2 = 0), DLL = "2d")
 
+box_size <- 10
+
 grid <- expand.grid(
-  theta1 = seq(-8, 8, length.out = 400),
-  theta2 = seq(-8, 8, length.out = 400)
+  theta1 = seq(-box_size, box_size, length.out = box_size * 50),
+  theta2 = seq(-box_size, box_size, length.out = box_size * 50)
 )
 
 ground_truth <- cbind(grid, pdf = apply(grid, 1, function(x) exp(-1 * obj$fn(x))))
@@ -32,7 +35,7 @@ cov <- sd_out$cov.fixed
 
 figA0 <- ggplot(ground_truth, aes(x = theta1, y = theta2, z = pdf)) +
   geom_contour(col = "lightgrey") +
-  coord_fixed(xlim = c(-8, 8), ylim = c(-8, 8), ratio = 1) +
+  coord_fixed(xlim = c(-box_size, box_size), ylim = c(-box_size, box_size), ratio = 1) +
   labs(x = "", y = "") +
   theme_minimal() +
   guides(size = "none") +
@@ -93,7 +96,22 @@ mvQuad::rescale(gg5, m = mu, C = cov, dec.type = 1)
 figA5 <- add_points(figA0, gg5) +
   labs(size = "")
 
-figA <- (figA1 + figA2) / (figA3 + figA4 + figA5) +
+#' Scree
+lambda <- eigen(cov)$values
+
+figA6 <- data.frame(
+  n = 1:length(lambda),
+  tv = cumsum(lambda / sum(lambda))
+) %>%
+  ggplot(aes(x = as.factor(n), y = tv)) +
+  geom_point() +
+  geom_hline(yintercept = 0.9, col = "grey", linetype = "dashed") +
+  annotate("text", x = 1, y = 0.85, label = "90% of total variation explained", col = "grey") +
+  scale_y_continuous(labels = scales::percent, limits = c(0, 1)) +
+  labs(x = "PCA dimensions included", y = "Total variation explained") +
+  theme_minimal()
+
+figA <- (figA1 + figA2 + figA3) / (figA4 + figA5 + figA6) +
   plot_annotation(tag_levels = "A") &
   theme(plot.tag.position  = c(0.15, 0.95))
 

src/docs_paper/paper.Rmd

@@ -360,7 +360,7 @@ Samples from this mixture of Gaussians may be obtained by drawing a node $\z$ wi
 
 ## Principal components analysis \label{sec:pca}
 
-```{r aghq, fig.cap="The Gauss-Hermite quadrature nodes $\\z \\in \\mathcal{Q}(2, 3)$ for a two dimensional integral with three nodes per dimension (A). Adaption occurs based on the mode (B) and covariance matrix of the target via the Cholesky decomposition (C) or spectral decompostion (D) of the inverse curvature at the mode. In PCA-AGHQ (E) only nodes along the first $s$ principal components are kept. The integrand is $f(\\btheta) = \\text{sn}(0.3 \\theta_1, \\alpha = 2) \\cdot \\text{sn}(0.5 \\theta_1 - 0.3 \\theta_2, \\alpha = -2)$, where $\\text{sn}(\\cdot)$ is the standard skewnormal probability density function with shape parameter $\\alpha \\in \\mathbb{R}$."}
+```{r aghq, fig.cap="The Gauss-Hermite quadrature nodes $\\z \\in \\mathcal{Q}(2, 3)$ for a two dimensional integral with three nodes per dimension (A). Adaption occurs based on the mode (B) and covariance matrix of the target via the Cholesky decomposition (C) or spectral decompostion (D) of the inverse curvature at the mode. In PCA-AGHQ (E) only nodes along the first $s = 1$ principal components are kept. The Scree plot (F) shows that over 90% of variation is explained by keeping just the first principal component. The integrand is $f(\\btheta) = \\text{sn}(0.5 \\theta_1, \\alpha = 2) \\cdot \\text{sn}(0.8 \\theta_1 - 0.5 \\theta_2, \\alpha = -2)$, where $\\text{sn}(\\cdot)$ is the standard skewnormal probability density function with shape parameter $\\alpha \\in \\mathbb{R}$."}
 figA
 ```
 

src/docs_paper/script.R

@@ -1,17 +1,9 @@
 # orderly::orderly_develop_start("docs_paper")
 # setwd("src/docs_paper")
 
-#' Conversion of figures from .pdf to .jpeg at specified resolution
+#' Conversion of figures from .pdf at specified resolution
 Sys.setenv(PATH = paste(Sys.getenv("PATH"), "/opt/homebrew/bin", sep = ":"))
 
-convert_pdf_jpeg <- function(name) {
-  command <- paste0(
-    "convert -density 300 depends/", name, ".pdf -scene 1 -background white",
-    " -alpha remove -alpha off -quality 80 depends/", name, ".jpeg"
-  )
-  system(command)
-}
-
 convert_pdf_png <- function(name) {
   command <- paste0(
     "convert -density 300 depends/", name, ".pdf -scene 1 -background white",