create plots with a dependence

scripts/plots_dimensions.qmd

@@ -44,7 +44,7 @@ library(latex2exp)
 #| cache: true
 #| echo: false
 #| collapse: true
-ns <- c(100, 200, 300, 400, 500)
+ns <- c(100, 200, 300, 400, 500, 600, 700, 800)
 Ks <- floor(sqrt(ns))
 as <- c(0.5, 1.0, 1.5, 2.0)
 
@@ -83,6 +83,7 @@ for (a in as) {
 #| collapse: true
 #| fig-cap: "Simulation of the smallest singular values w.r.t. a, n and k"
 results |>
+  filter(dim_n <= 400) |>
   mutate(param_a =  as.factor(param_a),
          dim_n = as.factor(dim_n)) |>
   group_by(param_a, dim_n) |>
@@ -119,4 +120,26 @@ summary(model1)
 plot(model1)
   
 ```
+## Plot of n vs. ssv
+
+```{r plot n vs ssv}
+results |>
+  filter(dim_k %in% c(2, 6, 10)) |>
+  mutate(param_a =  as.factor(param_a),
+         dim_k = as.factor(dim_k)) |>
+  group_by(param_a, dim_k) |>
+  ggplot(aes(dim_n, ssv, col=dim_k, shape=param_a, interaction(dim_k, param_a))) +
+  geom_point(size=1.5) +
+  geom_line() +
+  scale_y_log10() +
+  theme_bw() +
+  labs(x=latex2exp::TeX("$n$"),
+       y=latex2exp::TeX("Smallest singular value of $Q$"),
+       title=latex2exp::TeX("Smallest singular value of $Q$ with respect to $n$, $k$, and $a$."),
+       colour=latex2exp::TeX("$k$"),
+       shape=latex2exp::TeX("$a$"))
+```
+```{r}
+Q <- compute_matrix(1, a=0.5, n=10, K = 3, function(n) matrix(rnorm(n), ncol = 1L), fv=dnorm, Fv=pnorm)
+```