add heatmap for visualization

scripts/plot_Qa_wrt_a.R

@@ -8,6 +8,7 @@ library(ggplot2)
 library(tidyr)
 library(dplyr)
 
+# Line plots -------------------------------------------------------------------
 # Create a grid of a‑values
 a_grid <- seq(-20, 20, length.out = 200)
 
@@ -42,4 +43,40 @@ ggplot(df_entries, aes(x = a, y = value, colour = entry, linetype = entry)) +
     y = "Matrix entry value",
     colour = "Entry"
   ) +
-  theme_minimal()
+  theme_minimal()
+
+# Heat map for a single larger matrix ------------------------------------------
+
+# Choose a value of a
+a0 <- -10
+M0 <-  compute_matrix(seed=1L,
+                      a= a0,
+                      n = 50,
+                      K = 50,
+                      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)
+
+# Convert to a tidy data frame for ggplot
+df_heat <- as.data.frame(M0) %>%
+  mutate(row = row_number()) %>%
+  pivot_longer(-row, names_to = "col", values_to = "value") %>%
+  mutate(
+    col = as.integer(gsub("V", "", col)),   # turn "V1","V2" into 1,2
+    row = factor(row, levels = rev(unique(row)))   # reverse y‑axis for proper orientation
+  )
+
+ggplot(df_heat, aes(x = col, y = row, fill = value)) +
+  geom_tile(colour = "grey30", size = 0.5) +
+  scale_fill_gradient2(
+    low = "steelblue", mid = "white", high = "tomato",
+    midpoint = 0.5, limits = c(min(df_heat$value), max(df_heat$value))
+  ) +
+  labs(
+    title = sprintf("Heat‑map of the matrix at a = %.2f", a0),
+    x = "Column", y = "Row", fill = "Value"
+  ) +
+  theme_minimal() +
+  theme(axis.text = element_blank(),
+        axis.ticks = element_blank())