add function for plotting singular values automatically
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Niclas
222
R/singular_value_plot.R
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222
R/singular_value_plot.R
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# Load function ----------------------------------------------------------------
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source(here::here("R", "singular_values.R"))
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source(here::here("R", "graphon_distribution.R"))
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# Convert a call or character to a nicely formatted character string.
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# * If the user supplied a character, we keep it unchanged.
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# * If the user supplied a call (e.g. quote(20 / sqrt(x))) we deparse it
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# and collapse the result to a single line.
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expr_to_label <- function(expr) {
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if (is.character(expr)) {
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expr
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} else {
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# deparse returns a character vector; collapse to one line
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paste(deparse(expr), collapse = "")
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}
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}
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#' Compute the smallest singular value of a sequence of matrices Q(K)
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#'
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#' @title Smallest singular values for a family of matrices Q(K)
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#' @description
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#' For a given vector of coefficients `a`, sample size `n` and a maximum
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#' rank `maxK`, this function repeatedly calls `compute_matrix()` to build a
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#' matrix `Q` for each rank `K = 1, …, maxK`. The smallest singular value of
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#' each `Q` is extracted with `compute_minmax_sv()`. The result can be
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#' returned as a numeric vector and, if desired, plotted together with a
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#' user‑supplied reference curve.
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#'
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#' @param a Numeric vector of coefficients that are passed to `compute_matrix()`.
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#' @param n Positive integer, the sample size used inside the sampling function.
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#' @param maxK Positive integer, the largest rank `K` for which a matrix `Q`
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#' will be built. The function will evaluate `K = 1:maxK`.
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#' @param seed Integer (default = 1) used as the random‑seed argument for
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#' `compute_matrix()`. Supplying a seed makes the whole procedure
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#' reproducible.
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#' @param sampler_fn Function that draws a sample of size `n`. It must accept a
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#' single argument `n` and return a **numeric matrix** with `n` rows and
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#' one column (the shape used in the original script). The default is a
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#' thin wrapper around `rnorm()`.
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#' @param fv Function giving the density of the underlying distribution
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#' (default = `dnorm`). It is passed unchanged to `compute_matrix()`.
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#' @param Fv Function giving the cumulative distribution function
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#' (default = `pnorm`). It is passed unchanged to `compute_matrix()`.
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#' @param guard Positive numeric guard used inside `compute_matrix()` to avoid
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#' division‑by‑zero or log‑of‑zero problems (default = `1e-12`).
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#' @param plot Logical, whether to produce a quick base‑R plot of the
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#' smallest singular values (`TRUE` by default). If `FALSE` the function
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#' only returns the numeric vector.
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#' @param add_curve Logical, whether to overlay a reference curve on the plot.
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#' Ignored when `plot = FALSE`. Default = `TRUE`.
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#' @param curve_expr Expression (as a *character* or *call*) that defines the
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#' reference curve. The default reproduces the line you used
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#' `20 / sqrt(x)`. The expression must be a valid R expression in which the
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#' variable `x` stands for the horizontal axis.
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#' @param curve_from,curve_to Numeric limits for the reference curve. By
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#' default they are set to the range of `K` (`1:maxK`).
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#' @param curve_col Colour of the reference curve (default = `"red"`).
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#' @param curve_lwd Line width of the reference curve (default = 2).
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#' @param log_plot If True, then the y-axis is on a log scale.
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#' @return A list with the following components
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#' \item{K}{Integer vector `1:maxK`.}
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#' \item{sv}{Numeric vector of the smallest singular values for each `K`.}
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#' \item{plot}{If `plot = TRUE`, the value returned by `graphics::plot()`
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#' (normally `NULL`). If `plot = FALSE` this element is omitted.}
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#' @examples
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#' ## Run the whole routine with the defaults
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#' res <- smallest_sv_sequence(
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#' a = c(0.4), n = 400, maxK = 20,
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#' seed = 3, guard = 1e-12
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#' )
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#' head(res$sv)
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#'
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#' ## Supply a custom sampler (e.g., uniform)
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#' my_sampler <- function(m) matrix(runif(m, -1, 1), ncol = 1)
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#' res2 <- smallest_sv_sequence(
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#' a = c(0.4), n = 400, maxK = 10,
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#' sampler_fn = my_sampler,
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#' plot = FALSE
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#' )
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#' plot(res2$K, res2$sv, type = "b")
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#' @importFrom graphics plot lines curve
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#' @export
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smallest_sv_sequence <- function(
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a,
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n,
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maxK,
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seed = 1L,
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sampler_fn = function(m) matrix(rnorm(m), ncol = 1L),
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fv = dnorm,
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Fv = pnorm,
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guard = 1e-12,
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plot = TRUE,
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add_curve = TRUE,
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curve_expr = quote(20 / sqrt(x)),
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curve_from = NULL,
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curve_to = NULL,
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curve_col = "red",
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curve_lwd = 2,
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log_plot = FALSE
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) {
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## 1. Input validation =======================================================
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if (!is.numeric(a) || length(a) == 0) {
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stop("`a` must be a non‑empty numeric vector.")
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}
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if (!is.numeric(n) || length(n) != 1L || n <= 0 || n != as.integer(n)) {
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stop("`n` must be a positive integer.")
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}
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if (!is.numeric(maxK) || length(maxK) != 1L || maxK <= 0 ||
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maxK != as.integer(maxK)) {
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stop("`maxK` must be a positive integer.")
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}
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if (!is.function(sampler_fn)) {
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stop("`sampler_fn` must be a function that takes a single integer argument `n`.")
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}
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if (!is.function(fv) || !is.function(Fv)) {
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stop("`fv` and `Fv` must be corresponding density functions and cdf (e.g., dnorm/ pnorm).")
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}
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if (!is.numeric(guard) || length(guard) != 1L || guard <= 0) {
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stop("`guard` must be a single positive numeric value.")
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}
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if (!is.logical(plot) || length(plot) != 1L) {
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stop("`plot` must be a single logical value.")
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}
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if (!is.logical(add_curve) || length(add_curve) != 1L) {
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stop("`add_curve` must be a single logical value.")
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}
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if (!inherits(curve_expr, "call") && !is.character(curve_expr)) {
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stop("`curve_expr` must be a call (e.g., quote(20/sqrt(x))) or a character string.")
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}
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## 2. Prepare storage ========================================================
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K_vec <- seq_len(maxK)
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smallest_sv <- numeric(maxK)
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## 3. Main loop – build Q(K) and extract the smallest singular value =========
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for (K in K_vec) {
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Q <- compute_matrix(
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seed = seed,
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a = a,
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n = n,
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K = K,
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sample_X_fn = sampler_fn,
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fv = fv,
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Fv = Fv,
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guard = guard
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)
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sv_res <- compute_minmax_sv(Q)
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if (!is.list(sv_res) || is.null(sv_res$smallest_singular_value)) {
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stop("`compute_minmax_sv()` must return a list containing `$smallest_singular_value`.")
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}
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smallest_sv[K] <- sv_res$smallest_singular_value
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}
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## 4. Plotting (optional) ====================================================
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if (plot) {
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## Basic scatter/line plot of the singular values
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plot_args <- list(
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x = K_vec,
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y = smallest_sv,
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type = "b",
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pch = 19,
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col = "steelblue",
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xlab = "K subdivisions",
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ylab = "Smallest singular value of Q",
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main = "Smallest singular value vs. K"
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)
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if (log_plot) plot_args$log <- "y"
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do.call(graphics::plot, plot_args)
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# graphics::plot(
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# K_vec, smallest_sv,
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# type = "b", pch = 19, col = "steelblue",
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# xlab = "K subdivisions", ylab = "Smallest singular value of Q",
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# main = "Smallest singular value vs. K"
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# )
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## Add the reference curve if requested
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if (add_curve) {
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## Determine sensible defaults for the curve limits
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if (is.null(curve_from)) curve_from <- min(K_vec)
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if (is.null(curve_to)) curve_to <- max(K_vec)
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## `curve()` expects an *expression* where `x` is the variable.
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## If the user supplied a character string we turn it into a call.
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if (is.character(curve_expr)) curve_expr <- parse(text = curve_expr)[[1L]]
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curve_fun <- function(x) eval(curve_expr)
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graphics::curve(
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expr = curve_fun,
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from = curve_from,
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to = curve_to,
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add = TRUE,
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col = curve_col,
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lwd = curve_lwd
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)
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# add label with the curve expression
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label_txt <- expr_to_label(curve_expr)
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x_pos <- curve_from + 0.9 * (curve_to - curve_from)
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y_pos <- 0.9 * max(smallest_sv)
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graphics::text(
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x = x_pos, y = y_pos,
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labels = label_txt,
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col = curve_col,
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pos = 4, # 4 = right‑justified (so the text sits left of the point)
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offset = 0.5, # a small gap between the point and the text
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cex = 0.9 # slightly smaller than default text size
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)
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}
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}
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## 5. Return a tidy list =====================================================
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out <- list(
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K = K_vec,
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sv = smallest_sv
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)
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# if (plot) out$plot <- NULL ## the plot is already drawn; we return NULL for consistency
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out
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}
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