From 25fe0903be82ecf7fa1fd9d5ee1f23eb90b4ee1d Mon Sep 17 00:00:00 2001 From: Niclas Date: Wed, 20 May 2026 17:02:33 +0200 Subject: [PATCH] adjust plots --- scripts/plot_Qa_wrt_a.R | 13 ++--- scripts/plot_non_normal_X.qmd | 95 ++++++++++++++++++++++++++++++---- scripts/results.RData | Bin 0 -> 265247 bytes 3 files changed, 93 insertions(+), 15 deletions(-) create mode 100644 scripts/results.RData diff --git a/scripts/plot_Qa_wrt_a.R b/scripts/plot_Qa_wrt_a.R index 2f7a009..e957de8 100644 --- a/scripts/plot_Qa_wrt_a.R +++ b/scripts/plot_Qa_wrt_a.R @@ -13,7 +13,7 @@ library(dplyr) a_grid <- seq(-20, 20, length.out = 200) # function which takes only a to compute Q_c -make_matrix <- function(a) { compute_matrix(seed=4L, +make_matrix <- function(a) { compute_matrix(seed=11513215L, a= a, n = 2, K = 2, @@ -46,17 +46,18 @@ ggplot(df_entries, aes(x = a, y = value, colour = entry, linetype = entry)) + theme_minimal() # Heat map for a single larger matrix ------------------------------------------ - +# TODO Daten für 2x2 und 3x3 an Michael schicken # Choose a value of a -a0 <- -10 -M0 <- compute_matrix(seed=1L, +a0 <- 2 +M0 <- compute_matrix(seed=9L, a= a0, - n = 50, - K = 50, + n = 2, + K = 2, 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) +M0 # Convert to a tidy data frame for ggplot df_heat <- as.data.frame(M0) %>% diff --git a/scripts/plot_non_normal_X.qmd b/scripts/plot_non_normal_X.qmd index 2c7a9f7..c0e05d9 100644 --- a/scripts/plot_non_normal_X.qmd +++ b/scripts/plot_non_normal_X.qmd @@ -76,14 +76,16 @@ for (a in as) { ```{r k = n^alpha plotting, rate = 1} # plot the results results01 |> - filter(param_a %in% c(0, 10, 20)) |> + filter(param_a %in% c(2, 6, 12) & param_alpha <= 0.12) |> mutate(param_a = as.factor(param_a), param_alpha = as.factor(param_alpha)) |> group_by(param_a, param_alpha) |> ggplot(aes(dim_n, ssv, col=param_a, shape=param_alpha, interaction(param_a, param_alpha))) + geom_point(size=1.5) + geom_line() + - geom_function(fun = function(x) {sqrt(x)}, colour="black") + + geom_line(aes(dim_n, sqrt(dim_n) / dim_k, shape=param_alpha), linetype = 2) + + geom_point(size=1.5) + + #geom_function(fun = function(x) {sqrt(x)}, colour="black") + #scale_y_log10() + theme_bw() + labs(x=latex2exp::TeX("$n$"), @@ -135,14 +137,16 @@ for (a in as) { ```{r k = n^alpha plotting, rate = 3} results02 |> - filter(param_a %in% c(0, 10, 20)) |> + filter(param_a %in% c(0, 10, 20) & param_alpha < 0.12) |> mutate(param_a = as.factor(param_a), param_alpha = as.factor(param_alpha)) |> group_by(param_a, param_alpha) |> ggplot(aes(dim_n, ssv, col=param_a, shape=param_alpha, interaction(param_a, param_alpha))) + geom_point(size=1.5) + geom_line() + - geom_function(fun = function(x) {sqrt(x)}, colour="black") + + geom_line(aes(dim_n, sqrt(dim_n) / dim_k, shape=param_alpha), linetype = 2) + + geom_point(size=1.5) + + #geom_function(fun = function(x) {sqrt(x)}, colour="black") + #scale_y_log10() + theme_bw() + labs(x=latex2exp::TeX("$n$"), @@ -203,7 +207,9 @@ results03 |> ggplot(aes(dim_n, ssv, col=param_a, shape=param_alpha, interaction(param_a, param_alpha))) + geom_point(size=1.5) + geom_line() + - geom_function(fun = function(x) {sqrt(x)}, colour="black") + + geom_line(aes(dim_n, sqrt(dim_n) / dim_k, shape=param_alpha), linetype = 2) + + geom_point(size=1.5) + + #geom_function(fun = function(x) {sqrt(x)}, colour="black") + #scale_y_log10() + theme_bw() + labs(x=latex2exp::TeX("$n$"), @@ -259,14 +265,16 @@ for (a in as) { ```{r k = n^alpha plotting, U[0,1]} results04 |> - filter(param_a %in% c(0, 10, 20)) |> + filter(param_a %in% c(2, 10, 20) & param_alpha < 0.22 & param_alpha > 0.12) |> mutate(param_a = as.factor(param_a), param_alpha = as.factor(param_alpha)) |> group_by(param_a, param_alpha) |> ggplot(aes(dim_n, ssv, col=param_a, shape=param_alpha, interaction(param_a, param_alpha))) + geom_point(size=1.5) + geom_line() + - geom_function(fun = function(x) {sqrt(x)}, colour="black") + + geom_line(aes(dim_n, sqrt(dim_n) / dim_k, shape=param_alpha), linetype = 2) + + geom_point(size=1.5) + + #geom_function(fun = function(x) {sqrt(x)}, colour="black") + #scale_y_log10() + theme_bw() + labs(x=latex2exp::TeX("$n$"), @@ -327,7 +335,9 @@ results05 |> ggplot(aes(dim_n, ssv, col=param_a, shape=param_alpha, interaction(param_a, param_alpha))) + geom_point(size=1.5) + geom_line() + - geom_function(fun = function(x) {sqrt(x)}, colour="black") + + geom_line(aes(dim_n, sqrt(dim_n) / dim_k, shape=param_alpha), linetype = 2) + + geom_point(size=1.5) + + #geom_function(fun = function(x) {sqrt(x)}, colour="black") + #scale_y_log10() + theme_bw() + labs(x=latex2exp::TeX("$n$"), @@ -387,7 +397,9 @@ results06 |> ggplot(aes(dim_n, ssv * dim_k, col=param_a, shape=param_alpha, interaction(param_a, param_alpha))) + geom_point(size=1.5) + geom_line() + - geom_function(fun = function(x) {x^(0.5)}, colour="black") + + geom_line(aes(dim_n, sqrt(dim_n) / dim_k, shape=param_alpha), linetype = 2) + + geom_point(size=1.5) + + #geom_function(fun = function(x) {x^(0.5)}, colour="black") + #scale_y_log10() + theme_bw() + labs(x=latex2exp::TeX("$n$"), @@ -422,3 +434,68 @@ results06 |> results <- list(results01, results02, results03, results04, results05, results06) save(results, file="results.RData") ``` + +## Two dimensional example + +```{r k = n^alpha data generation with two dimensions, rate = 1} +#| cache: true +#| echo: false +#| collapse: true +ns <- seq(100, 1000, 100) +a <- c(1, 1) / sqrt(2) +a_norms <- seq(0, 20, 2) +alphas <- seq(0.1, 0.5, 0.1) + +set.seed(100) +results07 <- data.frame(dim_n = integer(), + dim_k = integer(), + param_a = double(), + param_alpha = double(), + ssv = double()) +for (a_norm in a_norms) { + for (i in 1:length(ns)) { + for (j in 1:length(alphas)) { + n <- ns[i] + K <- floor(n^alphas[j]) + if (!K > 0) next # skip if K is equal to zero + # use the default seed 1L + Q <- compute_matrix(seed=1L, + a= a_norm * a, + n = n, + K = K, + sample_X_fn = function(n) {matrix(rexp(2 * n), ncol = 2L)}, + fv = function(x) {dnorm(x, mean=0, sd=1)}, + Fv = function(x) {pnorm(x, mean=0, sd=1)}, + guard = 1e-12) + + ssv <- compute_minmax_sv(Q)[["smallest_singular_value"]] + + current_res <- data.frame(dim_n = n, dim_k = K, param_a = a_norm, param_alpha=alphas[j], ssv =ssv) + results07 <- rbind(results07, current_res) + } + } +} +``` + +```{r k = n^alpha plotting, rate = 1} +# plot the results +results07 |> + filter(param_a %in% c(10, 20) & param_alpha < 0.12) |> + mutate(param_a = as.factor(param_a), + param_alpha = as.factor(param_alpha)) |> + group_by(param_a, param_alpha) |> + ggplot(aes(dim_n, ssv, col=param_a, shape=param_alpha, interaction(param_a, param_alpha))) + + geom_point(size=1.5) + + geom_line() + + geom_line(aes(dim_n, sqrt(dim_n) / dim_k, shape=param_alpha), linetype = 2) + + geom_point(size=1.5) + + #geom_function(fun = function(x) {sqrt(x)}, colour="black") + + #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 $a$."), + subtitle = latex2exp::TeX(("Hyperparameter $k = n^{\\alpha}$. Black line is $\\sqrt{n}$, and $X \\sim Exp(1)$")), + colour=latex2exp::TeX("$a$"), + shape=latex2exp::TeX("$\\alpha$")) +``` \ No newline at end of file diff --git a/scripts/results.RData b/scripts/results.RData new file mode 100644 index 0000000000000000000000000000000000000000..13773393a5f2bb9ef92ddbb26ff0c91b2dade79f GIT binary patch literal 265247 zcmeFYg;yN^*5;c83m)7hKyV8h+=2%P?he7-8yXGn5L^=+8h3Yhm&V;48faw5IluGH zy!Xx@aPOMwRcn>)=h>gyyXsqAwYtf|-@p0S2j=+6MMdqXtpOcN2}vsW=g*(cdtSRw zzxl+!ii&&{5&io8yNd8HmCuTz(m0B&Z;(Hrpr{DvH51WUTKhDG>C#70C2;Mc`H`3#dCREj<%fFeXp7`8rZ z5Om9^^w+=thEWYfa-k=CJe@+%R|Xj6>QXN zx&-B&L&=+MZ23c_G3*S+T7yH$q>XGpG|D1UbQny)L+($zL+;&frY%KvY(HX4W9-!W zv>h0X>sE%`wG9G~wF%CabqSo_srTt<5S*21eOyr=fG}(cG~!%#A@NkRt-9%alvV3P zAW|C`z;QG;9jVs&c%|0oRffan9{37`?5sYJ#;_&!fHUP5_*lgzsHFWdUaha+gkgIO z=W=xD?yF^Bg!V@o^}YgE29u2;4cZFPpz;_XgK_Kul82iq;}7kRFzN&O2^R#Q7y<_4 z!D1XG(?Dnak63E29NU{i8uay|ry3twKryBa+ap7FI!1xcIv*9vV?Hr#-woXvbt73c 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