estimators_logic <- function(input, output, react_values) {
  # Initialize a data frame to hold estimates.
  react_values$estimates_table <- data.frame(Dataset = character(0))
  # Initialize a list to hold added estimators.
  react_values$estimators <- list()

  add_id(input, output, react_values)
  add_idea(input, output, react_values)
  add_seq_bayes(input, output, react_values)
  add_wp(input, output, react_values)

  render_estimates(output, react_values)
  delete_estimators(input, react_values)
  export_estimates(output, react_values)
}

# If an estimator is added, ensure it is not a duplicate and add it to the list
# of estimators. This function should be called at the end of each
# estimator-specific 'add' function, after validating their parameters.
add_estimator <- function(method, new_estimator, output, react_values) {
  num_estimators <- length(react_values$estimators)

  # Check whether the new estimator is a duplicate, and warn if so.
  for (i in seq_len(num_estimators)) {
    if (identical(new_estimator, react_values$estimators[[i]])) {
      showNotification("Error: This estimator has already been added.",
        duration = 3, id = "notify-error"
      )
      return()
    }
  }

  # Add the new estimator to the list of estimators.
  react_values$estimators[[num_estimators + 1]] <- new_estimator

  showNotification("Estimator added successfully.",
    duration = 3, id = "notify-success"
  )

  # Evaluate all the new estimator on all existing datasets and create a new
  # column in the estimates table.
  update_estimates_col(new_estimator, react_values)
}

# Ensure serial intervals are specified as positive numbers.
validate_mu <- function(method, input, output) {
  mu <- suppressWarnings(as.numeric(trimws(input[[paste0("mu_", method)]])))
  if (is.na(mu) || mu <= 0) {
    output[[paste0("mu_", method, "_warn")]] <- renderText(
      "The serial interval must be a positive number."
    )
    return(NULL)
  }
  output[[paste0("mu_", method, "_warn")]] <- renderText("")
  mu
}

# Incidence Decay (ID).
add_id <- function(input, output, react_values) {
  observeEvent(input$add_id, {
    mu <- validate_mu("id", input, output)
    if (!is.null(mu)) {
      new_estimator <- list(
        method = "id", mu = mu, mu_units = input$mu_id_units
      )
      add_estimator("id", new_estimator, output, react_values)
    }
  })
}

# Incidence Decay and Exponential Adjustment (IDEA).
add_idea <- function(input, output, react_values) {
  observeEvent(input$add_idea, {
    mu <- validate_mu("idea", input, output)
    if (!is.null(mu)) {
      new_estimator <- list(
        method = "idea", mu = mu, mu_units = input$mu_idea_units
      )
      add_estimator("idea", new_estimator, output, react_values)
    }
  })
}

# Sequential Bayes (seqB).
add_seq_bayes <- function(input, output, react_values) {
  observeEvent(input$add_seq_bayes, {
    mu <- validate_mu("seq_bayes", input, output)

    kappa <- trimws(input$kappa)
    kappa <- if (kappa == "") 20 else suppressWarnings(as.numeric(kappa))

    if (is.na(kappa) || kappa <= 0) {
      output$kappa_warn <- renderText(
        "The maximum prior must be a positive number."
      )
    } else if (!is.null(mu)) {
      output$kappa_warn <- renderText("")
      new_estimator <- list(
        method = "seq_bayes", mu = mu,
        mu_units = input$mu_seq_bayes_units, kappa = kappa
      )
      add_estimator("seq_bayes", new_estimator, output, react_values)
    }
  })
}

# White and Pagano (WP).
add_wp <- function(input, output, react_values) {
  observeEvent(input$add_wp, {
    if (input$wp_mu_known == "Yes") {
      mu <- validate_mu("wp", input, output)
      if (!is.null(mu)) {
        new_estimator <- list(method = "wp",
          mu = mu, mu_units = input$mu_wp_units
        )
        add_estimator("wp", new_estimator, output, react_values)
      }
    } else {
      grid_length <- trimws(input$grid_length)
      max_shape <- trimws(input$max_shape)
      max_scale <- trimws(input$max_scale)

      suppressWarnings({
        grid_length <- if (grid_length == "") 100 else as.numeric(grid_length)
        max_shape <- if (max_shape == "") 10 else as.numeric(max_shape)
        max_scale <- if (max_scale == "") 10 else as.numeric(max_scale)
      })

      valid <- TRUE

      if (is.na(grid_length) || grid_length <= 0) {
        output$grid_length_warn <- renderText(
          "The grid length must be a positive integer."
        )
        valid <- FALSE
      } else {
        output$grid_length_warn <- renderText("")
      }

      if (is.na(max_shape) || max_shape <= 0) {
        output$max_shape_warn <- renderText(
          "The maximum shape must be a positive number."
        )
        valid <- FALSE
      } else {
        output$max_shape_warn <- renderText("")
      }

      if (is.na(max_scale) || max_scale <= 0) {
        output$max_scale_warn <- renderText(
          "The maximum scale must be a positive number."
        )
        valid <- FALSE
      } else {
        output$max_scale_warn <- renderText("")
      }

      if (valid) {
        new_estimator <- list(method = "wp", mu = NA, grid_length = grid_length,
          max_shape = max_shape, max_scale = max_scale
        )
        add_estimator("wp", new_estimator, output, react_values)
      }
    }
  })
}

# Convert an estimator's specified serial interval to match the time units of
# the given dataset.
convert_mu_units <- function(data_units, estimator_units, mu) {
  if (data_units == "Days" && estimator_units == "Weeks") {
    return(mu * 7)
  } else if (data_units == "Weeks" && estimator_units == "Days") {
    return(mu / 7)
  }
  mu
}

# Add a column to the estimates table when a new estimator is added.
update_estimates_col <- function(estimator, react_values) {
  dataset_rows <- seq_len(nrow(react_values$data_table))
  estimates <- dataset_rows

  for (row in dataset_rows) {
    estimate <- eval_estimator(estimator, react_values$data_table[row, ])
    estimates[row] <- estimate
  }

  estimates <- data.frame(estimates)
  colnames(estimates) <- estimates_col_name(estimates, estimator)

  react_values$estimates_table <- cbind(
    react_values$estimates_table, estimates
  )
}

# Evaluate the specified estimator on the given dataset.
eval_estimator <- function(estimator, dataset) {
  cases <- as.integer(unlist(strsplit(dataset[, 3], ",")))

  if (estimator$method == "id") {
    mu <- convert_mu_units(dataset[, 2], estimator$mu_units, estimator$mu)
    estimate <- round(Rnaught::id(cases, mu), 2)
  } else if (estimator$method == "idea") {
    mu <- convert_mu_units(dataset[, 2], estimator$mu_units, estimator$mu)
    estimate <- round(Rnaught::idea(cases, mu), 2)
  } else if (estimator$method == "seq_bayes") {
    mu <- convert_mu_units(dataset[, 2], estimator$mu_units, estimator$mu)
    estimate <- round(Rnaught::seq_bayes(cases, mu, estimator$kappa), 2)
  } else if (estimator$method == "wp") {
    if (is.na(estimator$mu)) {
      estimate <- Rnaught::wp(cases, serial = TRUE,
        grid_length = estimator$grid_length,
        max_shape = estimator$max_shape, max_scale = estimator$max_scale
      )
      estimated_mu <- round(sum(estimate$supp * estimate$pmf), 2)
      estimate <- paste0(round(estimate$r0, 2), " (&#956; = ", estimated_mu,
        " ", tolower(dataset[, 2]), ")"
      )
    } else {
      mu <- convert_mu_units(dataset[, 2], estimator$mu_units, estimator$mu)
      estimate <- round(Rnaught::wp(cases, mu), 2)
    }
  }

  return(estimate)
}

# Create the column name of an estimator when it is
# added to the estimates table.
estimates_col_name <- function(estimates, estimator) {
  if (estimator$method == "id") {
    return(paste0("ID", " (&#956; = ", estimator$mu, " ",
      tolower(estimator$mu_units), ")"
    ))
  } else if (estimator$method == "idea") {
    return(paste0("IDEA", " (&#956; = ", estimator$mu, " ",
      tolower(estimator$mu_units), ")"
    ))
  } else if (estimator$method == "seq_bayes") {
    return(paste0("seqB", " (&#956; = ", estimator$mu, " ",
      tolower(estimator$mu_units), ", &#954; = ", estimator$kappa, ")"
    ))
  } else if (estimator$method == "wp") {
    if (is.na(estimator$mu)) {
      return(paste0("WP (", estimator$grid_length, ", ",
        round(estimator$max_shape, 3), ", ", round(estimator$max_scale, 3), ")"
      ))
    } else {
      return(paste0("WP", " (&#956; = ", estimator$mu, " ",
        tolower(estimator$mu_units), ")"
      ))
    }
  }
}

# Render the estimates table whenever it is updated.
render_estimates <- function(output, react_values) {
  observe({
    output$estimates_table <- DT::renderDataTable(react_values$estimates_table,
      selection = list(target = "column", selectable = c(0)),
      escape = FALSE, rownames = FALSE,
      options = list(
        columnDefs = list(list(className = "dt-left", targets = "_all"))
      ),
    )
  })
}

# Delete columns from the estimates table,
# as well as the corresponding estimators.
delete_estimators <- function(input, react_values) {
  observeEvent(input$estimators_delete, {
    cols_selected <- input$estimates_table_columns_selected
    react_values$estimators <- react_values$estimators[-cols_selected]
    react_values$estimates_table[, cols_selected + 1] <- NULL
  })
}

# Export estimates table as a CSV file.
export_estimates <- function(output, react_values) {
  output$estimates_export <- downloadHandler(
    filename = function() {
      paste0(
        "Rnaught_estimates_", format(Sys.time(), "%y-%m-%d_%H-%M-%S"), ".csv"
      )
    },
    content = function(file) {
      output_table <- data.frame(
        lapply(react_values$estimates_table, sub_entity)
      )
      colnames(output_table) <- sub_entity(
        colnames(react_values$estimates_table)
      )
      write.csv(output_table, file, row.names = FALSE)
    }
  )
}

# Substitute HTML entity codes with natural names.
sub_entity <- function(obj) {
  obj <- gsub("&#956;", "mu", obj)
  obj <- gsub("&#954;", "kappa", obj)
  obj
}