adjusted plot
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@@ -256,7 +256,7 @@ title(main="Vectors for a rescaled to norm one.")
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#| cache: true
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#| cache: true
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#| echo: false
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#| echo: false
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#| collapse: true
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#| collapse: true
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ns <- seq(100, 1000, 100)
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ns <- seq(250, 10000, 250)
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as <- c(1.0, 2, 5, 10, 20)
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as <- c(1.0, 2, 5, 10, 20)
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alphas <- seq(0.1, 0.5, 0.1)
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alphas <- seq(0.1, 0.5, 0.1)
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@@ -271,7 +271,7 @@ for (a in as) {
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for (j in 1:length(alphas)) {
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for (j in 1:length(alphas)) {
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n <- ns[i]
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n <- ns[i]
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K <- floor(n^alphas[j])
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K <- floor(n^alphas[j])
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if (!K > 0) next # skip if K is equal to zero
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if (!K > 1) next # skip if K is equal to zero lr one
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# use the default seed 1L
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# use the default seed 1L
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Q <- compute_matrix(seed=1L,
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Q <- compute_matrix(seed=1L,
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a= a,
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a= a,
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@@ -293,14 +293,16 @@ for (a in as) {
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```{r hyperparameter n / k^alpha = const plotting}
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```{r hyperparameter n / k^alpha = const plotting}
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results |>
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results |>
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filter(param_alpha > 0.21 & param_alpha <= 0.32) |>
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mutate(param_alpha = as.factor(param_alpha),
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mutate(param_alpha = as.factor(param_alpha),
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param_a = as.factor(param_a)) |>
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param_a = as.factor(param_a)) |>
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group_by(param_a, param_alpha) |>
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group_by(param_a, param_alpha) |>
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filter(dim_k == max(dim_k)) |>
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# filter(dim_k == max(dim_k)) |>
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ggplot(aes(dim_n, ssv, col=param_a, shape=param_alpha)) +
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ggplot(aes(dim_n, ssv, col=param_a, shape=param_alpha)) +
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geom_point(size=1.5) +
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geom_point(size=3.5) +
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geom_line() +
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geom_line(size=1.5) +
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#scale_y_log10() +
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geom_function(fun = function(x) {( sqrt(x)) / (floor(x^0.3))}, col="black" )+
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# scale_y_log10() +
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theme_bw() +
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theme_bw() +
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labs(x=latex2exp::TeX("$n$"),
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labs(x=latex2exp::TeX("$n$"),
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y=latex2exp::TeX("Smallest singular value of $Q$"),
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y=latex2exp::TeX("Smallest singular value of $Q$"),
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