# Run Time Recording

    # Load relevant libraries
    library(SurprisalAnalysis)
    library(ggplot2)
    library(peakRAM)

Please uncomment the below and run

    #setting seed to ensure reproducibility
    set.seed(123)

    #params
    n_genes       <- 1000
    sample_counts <- c(5, 10, 20, 50, 100)
    n_reps        <- 3

    #' Function records run time and RAM peak usage
    #'
    #' @param n_genes number of genes
    #' @param n_samples
    #'
    #' @return run time and RAM peak usage
    #' @export
    time_ram_single_run <- function(n_genes, n_samples) {
      elapsed <- NA_real_
      pr <- peakRAM({

        expr_matrix <- matrix(
          rlnorm(n = n_genes * n_samples, meanlog = 2, sdlog = 1),
          nrow = n_genes,
          ncol = n_samples
        )
        expr_df <- as.data.frame(expr_matrix)
        rownames(expr_df) <- paste0("Gene", seq_len(n_genes))
        colnames(expr_df) <- paste0("Sample", seq_len(n_samples))

        t0 <- Sys.time()
        res <- surprisal_analysis(expr_df)
        t1 <- Sys.time()
        elapsed <- as.numeric(difftime(t1, t0, units = "secs"))
      })
      list(
        time_sec = elapsed,
        peak_ram_mib = pr$Peak_RAM_Used_MiB[1]
      )
    }

    #store info

    results_df <- data.frame(
      n_samples               = integer(length(sample_counts)),
      mean_time               = numeric(length(sample_counts)),
      sd_time                 = numeric(length(sample_counts)),
      ci_lower                = numeric(length(sample_counts)),
      ci_upper                = numeric(length(sample_counts)),
      mean_peak_ram_mib       = numeric(length(sample_counts)),
      sd_peak_ram_mib         = numeric(length(sample_counts)),
      ci_lower_peak_ram_mib   = numeric(length(sample_counts)),
      ci_upper_peak_ram_mib   = numeric(length(sample_counts)),
      stringsAsFactors = FALSE
    )

    ci_halfwidth_fun <- function(x, n) {
      sdev <- sd(x)
      se   <- sdev / sqrt(n)
      qt(0.975, df = n - 1) * se
    }

    for (i in seq_along(sample_counts)) {
      s <- sample_counts[i]
      rep_times <- numeric(n_reps)
      rep_ram   <- numeric(n_reps)

      for (r in seq_len(n_reps)) {
        gc()
        tr <- time_ram_single_run(n_genes = n_genes, n_samples = s)
        rep_times[r] <- tr$time_sec
        rep_ram[r]   <- tr$peak_ram_mib
      }

      mu_time <- mean(rep_times)
      sd_time <- sd(rep_times)
      hw_time <- ci_halfwidth_fun(rep_times, n_reps)

      mu_ram  <- mean(rep_ram)
      sd_ram  <- sd(rep_ram)
      hw_ram  <- ci_halfwidth_fun(rep_ram, n_reps)

      results_df[i, ] <- list(
        s,
        mu_time, sd_time, mu_time - hw_time, mu_time + hw_time,
        mu_ram,  sd_ram,  mu_ram  - hw_ram,  mu_ram  + hw_ram
      )
      print(i)
      message(sprintf(
        "n_samples = %3d : time = %.4f s (sd=%.4f, 95%% CI=[%.4f, %.4f]);  peak RAM = %.2f MiB (sd=%.2f, 95%% CI=[%.2f, %.2f])",
        s, mu_time, sd_time, mu_time - hw_time, mu_time + hw_time,
        mu_ram, sd_ram, mu_ram - hw_ram, mu_ram + hw_ram
      ))
    }

    print(results_df)

    model_cubic <- lm(mean_time ~ poly(n_samples, 3), data = results_df)
    summary(model_cubic)

    results_df$pred_cubic <- predict(model_cubic, newdata = results_df)

    ggplot(results_df, aes(x = n_samples, y = mean_time)) +
      geom_ribbon(aes(ymin = mean_time - sd_time, ymax = mean_time + sd_time),
                  fill = "steelblue", alpha = 0.2) +
      geom_point(color = "steelblue4", size = 2, shape=8, stroke=1.5) +
      geom_line(color = "steelblue4") +
      stat_smooth(method = "lm",
                  formula = y ~ poly(x, 3),
                  se = FALSE,
                  color = "firebrick",
                  linetype = "dashed",
                  size = 1) +
      labs(
        x = "Number of samples",
        y = "Average elapsed time (seconds)",
        title = sprintf("SurprisalAnalysis Runtime vs. Number of Samples\n(gene count = %d; mean ± 95%% CI over %d runs)", n_genes, n_reps), tag="A"
      ) +
      theme_minimal(base_size = 12)

    is_bytes <- max(results_df$mean_peak_ram_mib, na.rm = TRUE) > 1e5
    scale_factor <- if (is_bytes) 1/(1024^2) else 1

    use_ci <- all(c("ci_lower_peak_ram_mib", "ci_upper_peak_ram_mib") %in% names(results_df))

    df_plot <- within(results_df, {
      mean_ram_plot  <- mean_peak_ram_mib * scale_factor
      lower_ram_plot <- (if (use_ci) ci_lower_peak_ram_mib else mean_peak_ram_mib - sd_peak_ram_mib) * scale_factor
      upper_ram_plot <- (if (use_ci) ci_upper_peak_ram_mib else mean_peak_ram_mib + sd_peak_ram_mib) * scale_factor
    })

    ggplot(df_plot, aes(x = n_samples, y = mean_ram_plot)) +
      geom_ribbon(aes(ymin = lower_ram_plot, ymax = upper_ram_plot),
                  fill = "steelblue", alpha = 0.2) +
      geom_point(color = "steelblue4", size = 2, shape=8, stroke = 1.5) +
      geom_line(color = "steelblue4") +
      scale_x_continuous(breaks = sample_counts) +
      labs(
        title = sprintf("SurprisalAnalysis Peak RAM vs. Number of Samples\n(gene count = %d; mean ± 95%% CI over %d runs)", n_genes, n_reps),
        x = "Number of Samples",
        y = "Peak RAM (MiB)", tag="B"
      ) +
      theme_minimal(base_size = 12)

    #write.csv(results_df, "~/Downloads/runtime_altering_samples_try_2.csv")

    ####Altering the number of genes

    #params
    n_samples_fixed <- 50
    gene_counts     <- c(100, 500, 1000, 2000, 5000)
    n_reps          <- 3

    results_genes_df <- data.frame(
      n_genes                 = integer(length(gene_counts)),
      mean_time               = numeric(length(gene_counts)),
      sd_time                 = numeric(length(gene_counts)),
      ci_lower                = numeric(length(gene_counts)),
      ci_upper                = numeric(length(gene_counts)),
      mean_peak_ram_mib       = numeric(length(gene_counts)),
      sd_peak_ram_mib         = numeric(length(gene_counts)),
      ci_lower_peak_ram_mib   = numeric(length(gene_counts)),
      ci_upper_peak_ram_mib   = numeric(length(gene_counts)),
      stringsAsFactors = FALSE
    )

    ci_halfwidth_fun <- function(x, n) {
      sdev <- sd(x); se <- sdev / sqrt(n); qt(0.975, df = n - 1) * se
    }

    for (i in seq_along(gene_counts)) {
      g <- gene_counts[i]
      rep_times <- numeric(n_reps)
      rep_ram   <- numeric(n_reps)

      for (r in seq_len(n_reps)) {
        gc()
        tr <- time_ram_single_run(n_genes = g, n_samples = n_samples_fixed)
        rep_times[r] <- tr$time_sec
        rep_ram[r]   <- tr$peak_ram_mib
      }

      mu_time <- mean(rep_times); sd_time <- sd(rep_times); hw_time <- ci_halfwidth_fun(rep_times, n_reps)
      mu_ram  <- mean(rep_ram);   sd_ram  <- sd(rep_ram);  hw_ram  <- ci_halfwidth_fun(rep_ram,   n_reps)

      results_genes_df[i, ] <- list(
        g,
        mu_time, sd_time, mu_time - hw_time, mu_time + hw_time,
        mu_ram,  sd_ram,  mu_ram  - hw_ram,  mu_ram  + hw_ram
      )

      message(sprintf(
        "n_genes = %5d : time = %.4f s (sd=%.4f, 95%% CI=[%.4f, %.4f]);  peak RAM = %.2f MiB (sd=%.2f, 95%% CI=[%.2f, %.2f])",
        g, mu_time, sd_time, mu_time - hw_time, mu_time + hw_time,
        mu_ram, sd_ram, mu_ram - hw_ram, mu_ram + hw_ram
      ))
    }

    print(results_genes_df)

    ggplot(results_genes_df, aes(x = n_genes, y = mean_time)) +
      geom_ribbon(aes(ymin = ci_lower, ymax = ci_upper),
                  fill = "steelblue", alpha = 0.2) +
      geom_point(color = "steelblue4", size = 2, shape = 8, stroke = 1.5) +
      geom_line(color = "steelblue4") +
      geom_smooth(method = "lm", se = FALSE, color = "firebrick", size = 1) +
      scale_x_continuous(breaks = gene_counts) +
      labs(
        x = "Number of genes",
        y = "Average elapsed time (seconds)",
        title = sprintf(
          "SurprisalAnalysis Runtime vs. Number of Genes\n(sample count = %d; mean ± 95%% CI over %d runs)",
          n_samples_fixed, n_reps
        ),
        tag = "C"
      ) +
      theme_minimal(base_size = 12)

    is_bytes_g <- max(results_genes_df$mean_peak_ram_mib, na.rm = TRUE) > 1e5
    scale_factor_g <- if (is_bytes_g) 1/(1024^2) else 1
    use_ci_g <- all(c("ci_lower_peak_ram_mib", "ci_upper_peak_ram_mib") %in% names(results_genes_df))

    df_plot_genes <- within(results_genes_df, {
      mean_ram_plot_g  <- mean_peak_ram_mib * scale_factor_g
      lower_ram_plot_g <- (if (use_ci_g) ci_lower_peak_ram_mib else mean_peak_ram_mib - sd_peak_ram_mib) * scale_factor_g
      upper_ram_plot_g <- (if (use_ci_g) ci_upper_peak_ram_mib else mean_peak_ram_mib + sd_peak_ram_mib) * scale_factor_g
    })

    ggplot(df_plot_genes, aes(x = n_genes, y = mean_ram_plot_g)) +
      geom_ribbon(aes(ymin = lower_ram_plot_g, ymax = upper_ram_plot_g),
                  fill = "steelblue", alpha = 0.2) +
      geom_point(color = "steelblue4", size = 2, shape = 8, stroke = 1.5) +
      geom_line(color = "steelblue4") +
      scale_x_continuous(breaks = gene_counts) +
      labs(
        title = sprintf("SurprisalAnalysis Peak RAM vs. Number of Genes\n(sample count = %d; mean ± 95%% CI over %d runs)", n_samples_fixed, n_reps),
        x = "Number of genes",
        y = "Peak RAM (MiB)",
        tag = "D"
      ) +
      theme_minimal(base_size = 12)

    #write.csv(results_genes_df, "~/Downloads/runtime_altering_genes_try_2.csv")