--- title: "Introduction to aion" author: "N. Frerebeau" date: "`r Sys.Date()`" output: markdown::html_format: options: toc: true number_sections: true bibliography: bibliography.bib vignette: > %\VignetteIndexEntry{Introduction to aion} %\VignetteEngine{knitr::knitr} %\VignetteEncoding{UTF-8} --- ```{r, include = FALSE} knitr::opts_chunk$set( collapse = TRUE, comment = "#>" ) ``` ```{r setup} library(aion) ``` Base R ships with a lot of functionality useful for time series, in particular in the **stats** package. However, these features are not adapted to most archaeological time series. These are indeed defined for a given calendar era, they can involve dates very far in the past and the sampling of the observation time is (in most cases) not constant. **aion** provides a system of classes and methods to represent and work with such time-series. # Calendars **aion** currently supports both Julian and Gregorian calendars (with the most common eras for the latter, e.g. Before Present, Common Era...). A calendar can be defined using the `calendar()` function: ```{r} ## Create a calendar object ## (Gregorian Common Era) calendar("CE") ``` Or by using the shortcuts: ```{r} ## Common Era (Gregorian) CE() ## Before Present (Gregorian) BP() ``` When creating date vectors or time series, you *must* specify the calendar corresponding to your data (see below). This allows to select the correct method for converting dates to *rata die*. **Outputs generated by aion are expressed in _rata die_ by default (this can be modified on a per-function basis).** The only two exceptions are the `plot()` and `format()` functions, which default to the calendar specified in the package options (see below). You can change the default calendar to be used throughout the package by modifying the `aion.calendar` option, or on a per-function basis. ```{r} ## Get default calendar getOption("aion.calendar") ## Change default calendar to BP options(aion.calendar = BP()) getOption("aion.calendar") ## Set it back to Gregorian Common Era options(aion.calendar = CE()) getOption("aion.calendar") ``` # Vectors of dates In base R, dates are represented by default as the number of days since 1970-01-01 (Gregorian), with negative values for earlier dates (see `help(Date)`). **aion** uses a different approach: it allows to create date vectors represented as *rata die* (Reingold and Dershowitz 2018), i.e. as number of days since 01-01-01 (Gregorian)[^1]. This makes it possible to get rid of a specific calendar and to make calculations easier. It is then possible to convert a vector of *rata die* into dates or (decimal) years of any calendar. The `fixed()` function allows to create a vector of *rata die* from dates belonging to a specific calendar: ```{r} ## Convert 2000-02-29 (Gregorian) to rata die fixed(2000, 02, 29, calendar = calendar("CE")) ## If days and months are missing, decimal years are expected fixed(2000.161, calendar = calendar("CE")) ``` A *rata die* vector can be converted into dates (or years) of a particular calendar: ```{r} ## Create a vector of 10 years BP (Gregorian) ## (every 20 years starting from 2000 BP) (years <- seq(from = 20000, by = -20, length.out = 10)) ## Convert years to rata die (rd <- fixed(years, calendar = calendar("BP"))) ## Convert back to Gregorian years as_year(rd, calendar = calendar("CE")) # Common Era as_year(rd, calendar = calendar("BP")) # Before Present as_year(rd, calendar = calendar("b2k")) # Before 2000 ``` *Rata die* can be represented as (nicely formated) character vectors: ```{r} format(rd) # Default calendar (Gregorian Common Era) format(rd, prefix = "ka", calendar = calendar("BP")) ``` The *rata die* vector provides the internal time representation of the **aion** time-series (if you want to work with numeric vectors that represent year-based time scales, you may be interested in the [**era**](https://github.com/joeroe/era) package). # Time series A time series is a sequence of observation time and value pairs with strictly increasing observation times. A time series object is an $n \times m \times p$ array, with $n$ being the number of observations, $m$ being the number of series and with the $p$ columns of the third dimension containing extra variables for each series. It can be created from a numeric `vector`, `matrix` or `array`. ```{r} ## Get ceramic counts (data from Husi 2022) data("loire", package = "folio") ## Keep only variables whose total is at least 600 keep <- c("01f", "01k", "01L", "08e", "08t", "09b", "15i", "15q") ## Get time midpoints mid <- rowMeans(loire[, c("lower", "upper")]) ## Create time-series (X <- series( object = loire[, keep], time = mid, calendar = calendar("AD") )) ``` Time series terminal and sampling times can be retrieved and expressed according to different calendars (**remember that outputs are expressed in _rata die_ by default**): ```{r} ## Time series duration span(X) # Default: rata die span(X, calendar = CE()) ## Time of first observation start(X) # Default: rata die start(X, calendar = CE()) ## Time of last observation end(X) # Default: rata die end(X, calendar = CE()) ## Sampling times time(X, calendar = BP()) ``` Plot one or more time series: ```{r plot-multiple, fig.width=7, fig.height=5} ## Multiple plot (default calendar) plot( x = X, type = "h" # histogram like vertical lines ) ``` ```{r plot-single, fig.width=7, fig.height=3.5} ## Extract the first series Y <- X[, 1, ] ## Plot a single series plot( Y, type = "h", # histogram like vertical lines calendar = b2k(), # b2k time scale panel.first = graphics::grid() # Add a grid ) year_axis(side = 3, calendar = CE()) # Add a secondary time axis mtext(format(CE()), side = 3, line = 3) # Add secondary axis title ``` Note that **aion** uses the astronomical notation for Gregorian years (there *is* a year 0). # References Reingold, Edward M., and Nachum Dershowitz. 2018. *Calendrical Calculations: The Ultimate Edition*. 4th ed. Cambridge University Press. . [^1]: It is intended that the *rata die* should be an integer value, but this is not enforced in the internal representation.