add plots for singular values vs variance

scripts/plot_sv_dependence_n.R

@@ -0,0 +1,93 @@
+# Load function ----------------------------------------------------------------
+source(here::here("R", "singular_values.R"))
+source(here::here("R", "graphon_distribution.R"))
+source(here::here("R", "singular_value_plot.R"))
+
+# https://stackoverflow.com/a/5790430
+resetPar <- function() {
+  dev.new()
+  op <- par(no.readonly = TRUE)
+  dev.off()
+  op
+}
+
+
+
+# Compare of parameters of Normal distribution ----------------------------------
+#
+out_n400_sd05 <- smallest_sv_sequence(
+  a = c(0.5),
+  n = 400,
+  maxK = 20,
+  sampler_fn =function(n) matrix(rnorm(n), ncol = 1L),
+  guard=1e-12,
+  plot=TRUE,
+  log_plot = TRUE,
+  fv = function(x) {dnorm(x, mean=0, sd=0.5)},
+  Fv = function(x) {pnorm(x, mean=0, sd=0.5)},
+  main_title="Smallest SV of v~ N(0,0.5^2) distribution, n = 400"
+)
+
+out_n800_sd05 <- smallest_sv_sequence(
+  a = c(0.5),
+  n = 800,
+  maxK = 20,
+  sampler_fn =function(n) matrix(rnorm(n), ncol = 1L),
+  guard=1e-12,
+  plot=TRUE,
+  log_plot = TRUE,
+  fv = function(x) {dnorm(x, mean=0, sd=0.5)},
+  Fv = function(x) {pnorm(x, mean=0, sd=0.5)},
+  main_title="Smallest SV of v~ N(0,0.5^2) distribution, n=800"
+)
+
+out_n400_sd2 <- smallest_sv_sequence(
+  a = c(0.5),
+  n = 400,
+  maxK = 20,
+  sampler_fn =function(n) matrix(rnorm(n), ncol = 1L),
+  guard=1e-12,
+  plot=TRUE,
+  log_plot = TRUE,
+  fv = function(x) {dnorm(x, mean=0, sd=2)},
+  Fv = function(x) {pnorm(x, mean=0, sd=2)},
+  main_title="Smallest SV of v~ N(0,2^2) distribution, n=400"
+)
+
+out_n800_sd2 <- smallest_sv_sequence(
+  a = c(0.5),
+  n = 800,
+  maxK = 20,
+  sampler_fn =function(n) matrix(rnorm(n), ncol = 1L),
+  guard=1e-12,
+  plot=TRUE,
+  log_plot = TRUE,
+  fv = function(x) {dnorm(x, mean=0, sd=2)},
+  Fv = function(x) {pnorm(x, mean=0, sd=2)},
+  main_title="Smallest SV of v~ N(0,4^2) distribution,n = 800"
+)
+
+par(mar = c(5, 4, 4, 8)) 
+plot(out_n400_sd05$K, out_n400_sd05$sv,
+     type = "b",
+     pch = 19,
+     col = "#D3BA68FF",
+     xlab = "K subdivisions",
+     ylab = "Smallest singular value of Q",
+     main="smallest SV for different variances of a normal distribution",
+     sub = "n = 400, a = 0.5",
+     log="y")
+lines(out_n400_sd2$K, out_n400_sd2$sv,
+      type="b", pch=19, col="#D5695DFF", add=TRUE)
+lines(out_n800_sd05$K, out_n800_sd05$sv,
+      type = "b", pch=19, col="#5D8CA8FF", add=TRUE)
+lines(out_n800_sd2$K, out_n800_sd2$sv,
+      type = "b", pch=19, col="#65A479FF", add=TRUE)
+par(xpd = TRUE)
+legend("topright",
+       inset=c(-0.2,0), 
+       legend=c("sd=0.5, n=400", "sd=0.5, n=800", "sd=2, n=400", "sd=2, n=800"), 
+       col=c("#D3BA68FF", "#D5695DFF","#5D8CA8FF", "#65A479FF" ), 
+       title="Legend",
+       pch = 16,
+       bty = "n")