# Load function ----------------------------------------------------------------
source(here::here("R", "singular_values.R"))
source(here::here("R", "graphon_distribution.R"))
source(here::here("R", "singular_value_plot.R"))

# Nearly match with sample function --------------------------------------------
# v ~ N(0,1) and X ~ discrete Uniform on [1:n]
smallest_sv_sequence(
  a = c(0.5),
  n = 400,
  maxK= 20,
  sampler_fn = sample,
  guard=1e-12,
  plot=TRUE,
  curve_expr = quote(20 / sqrt(x))
)

# Normally distributed X ~ N(0,1) and v ~ N(0,1) -------------------------------
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,
  curve_expr = quote(20 / exp(x^1.32))
)

# Uniform distributed X ~ U[0,1] and v ~ N(0,1) --------------------------------
smallest_sv_sequence(
  a = c(0.5),
  n = 400,
  maxK = 20,
  sampler_fn =function(n) matrix(runif(n), ncol = 1L),
  guard=1e-12,
  plot=TRUE,
  curve_expr = quote(20 / x^2)
)