```ruby
require 'rack/auth/basic'

class BasicAuth < ::Rack::Auth::Basic
  def call(env)
    return @app.call(env) unless env_matching_path

    super(env)
  end

  private

  def env_matching_path
    swagger_endpoints = Rswag::Ui.config.swagger_endpoints[:urls]
    swagger_endpoints.find do |endpoint|
      base_path = base_path(endpoint[:url])
      env_base_path = base_path(env['PATH_INFO'])

      base_path == env_base_path
    end
  end

  def base_path(url)
    url.downcase.split('/')[1]
  end
end
```

Define BasicAuth in Rswag::Ui module
user
```ruby
# frozen_string_literal: true

require 'rack/auth/basic'

module Rswag
  module Ui
    # Extend Rack HTTP Basic Authentication, as per RFC 2617.
    # @api private
    #
    class BasicAuth < ::Rack::Auth::Basic
      def call(env)
        return @app.call(env) unless env_matching_path

        super(env)
      end

      private

      def env_matching_path
        Rswag::Ui.config.swagger_endpoints[:urls].find do |endpoint|
          base_path(endpoint[:url]) == env_base_path
        end
      end

      def env_base_path
        base_path(env['PATH_INFO'])
      end

      def base_path(url)
        url.downcase.split('/')[1]
      end
    end
  end
end
```
assistant