add visualization of the matrix Q wrt parameter a

scripts/plot_Qa_wrt_a.R

@@ -0,0 +1,45 @@
+# load local files
+source(here::here("R", "singular_values.R"))
+source(here::here("R", "graphon_distribution.R"))
+source(here::here("R","singular_value_plot.R"))
+
+# load libaries for data handling
+library(ggplot2)
+library(tidyr)
+library(dplyr)
+
+# Create a grid of a‑values
+a_grid <- seq(-20, 20, length.out = 200)
+
+# function which takes only a to compute Q_c
+make_matrix <- function(a) { compute_matrix(seed=4L,
+                              a= a,
+                              n = 2,
+                              K = 2,
+                              sample_X_fn = function(n) {matrix(rnorm(n), ncol = 1L)},
+                              fv = function(x) {dnorm(x, mean=0, sd=1)},
+                              Fv = function(x) {pnorm(x, mean=0, sd=1)},
+                              guard = 1e-12)}
+
+# Compute the matrices and reshape to long format
+df_entries <- tibble(a = a_grid) %>%
+  mutate(
+    M = purrr::map(a, make_matrix),                     # list‑column of matrices
+    m11 = purrr::map_dbl(M, ~ .x[1, 1]),
+    m12 = purrr::map_dbl(M, ~ .x[1, 2]),
+    m21 = purrr::map_dbl(M, ~ .x[2, 1]),
+    m22 = purrr::map_dbl(M, ~ .x[2, 2])
+  ) %>%
+  select(a, m11, m12, m21, m22) %>%
+  pivot_longer(-a, names_to = "entry", values_to = "value")
+
+# Plot
+ggplot(df_entries, aes(x = a, y = value, colour = entry, linetype = entry)) +
+  geom_line(linewidth = 1) +
+  labs(
+    title = "Matrix entries as a function of the parameter `a`",
+    x = "a",
+    y = "Matrix entry value",
+    colour = "Entry"
+  ) +
+  theme_minimal()