# Implementing A DelayedArray Backend

Hervé Pagès1

1Fred Hutchinson Cancer Research Center, Seattle, WA

#### 26 October 2021

#### Package

DelayedArray 0.20.0

# Contents

# 1 Introduction

The DelayedArray framework currently supports a small number of on-disk backends: HDF5 (via the HDF5Array package), GDS (via the GDSArray package), and VCF (via the VCFArray package). This can be extended to support other on-disk backends. In theory, it should be possible to implement a DelayedArray backend for any file format that has the capability to store array data with fast random access.

Let’s assume that the ADS format (Array Data Store) is such format (this is a made-up format for the purpose of this vignette only). Implementing a DelayedArray backend for ADS files should typically be done in a dedicated package (say ADSArray) that will depend on the DelayedArray package.

The ADSArray package will need to implement:

- A low-level class for representing a reference to an array located in an ADS file. We’ll refer to this class as “the seed class” and will name it ADSArraySeed.

- Two high-level classes that derive from DelayedArray: ADSArray and ADSMatrix. Only the latter is needed if the ADS format only supports 2-dimensional arrays.

- A “realization sink” class if you also want to support realization of DelayedArray objects as ADSArray objects. This is not documented yet.

The rest of this document covers the above topics in greater details. Some familiarity with writing R packages is assumed. Don’t hesitate to look at the source of the HDF5Array package for a real example of DelayedArray on-disk backend implementation.

# 2 Implementing the seed class

## 2.1 Class definition

A “seed object” should store at least the path or URL to the file. If the file format allows storing more than one array per file, then the seed object should also store any additional information needed to locate a particular array in the file.

The definition of the seed class will look something like this:

    setClass("ADSArraySeed",
        contains="Array",
        slots=c(
            filepath="character",
            ...
            ... additional slots needed
            ... to locate the array in the file
            ...
        )
    )

The `filepath` slot should be a single string that contains the absolute path to the ADS file so the object doesn’t break when the user changes the working directory (e.g. with `setwd()`).

Note that storing an open connection to the file should be avoided because connections don’t work properly in the context of a fork (e.g. when processing the seed object in parallel) and tend to break when serializing the object.

## 2.2 Constructor

It is highly recommended to provide a “seed constructor” e.g.:

    ADSArraySeed <- function(filepath, other args)
    {
        sanity checks
        ...
        filepath <- file_path_as_absolute(filepath)
        ...
        new("ADSArraySeed", filepath=filepath, other args)
    }

Note that `file_path_as_absolute()` is defined in the tools package so it needs to be imported by adding the following to the NAMESPACE file of the ADSArray package:

    importFrom(tools, file_path_as_absolute)

and adding tools to the `Imports` field of the DESCRIPTION file of the package.

## 2.3 The seed contract

Seed objects are expected to comply with the “seed contract” i.e. to support `dim()`, `dimnames()`, and `extract_array()`. This is normally done by implementing methods for these generics, but, as we will see below, explicitly defining `dim()` or `dimnames()` methods is rarely needed.

### 2.3.1 dim() and dimnames()

For example, the `dim()` method for ADSArraySeed objects could look like this:

    ### An implementation that extracts the dimensions from the file
    ### each time the method is called.
    setMethod("dim", "ADSArraySeed",
        function(x)
        {
            - open the connection to the file
            - on.exit(close the connection)
            - extract the dimensions and return them in an integer vector
        }
    )

Note that the above `dim()` method consults the ADS file each time it’s called. However this can be avoided by adding a `dim` (and `dimnames`) slot (of type `integer` for `dim`, of type `list` for `dimnames`) to the ADSArraySeed class, and to populate it at construction time, so this information is retrieved from the file only once. With this approach `dim()` and `dimnames()` work out-of-the-box on ADSArraySeed objects i.e. there is no need to define `dim()` and `dimnames()` methods for these objects. This is because the `dim()` and `dimnames()` primitive functions in base R return the content of these slots if present.

If the ADS format does not allow storage of the dimnames, then there is no need to implement a `dimnames()` method or to add a `dimnames()` slot to the ADSArraySeed class. Calling `dimnames(x)` then will simply return `NULL` for any ADSArraySeed object `x`.

If the ADS format allows storage of the dimnames, make sure that `dimnames()` always returns them in the standard form, that is:

- The dimnames must be returned as a `NULL` (if the dataset has no dimnames) or as an ordinary list with one list element per dimension in the dataset.

- Each element in the returned list is either `NULL` or a character vector of length the extend of the dataset along the corresponding dimension. It is particularly important to make sure that the vectors in the list returned by `dimnames()` are character vectors. Other types like factors or integer vectors are not allowed and will break downstream code.

### 2.3.2 extract_array()

`extract_array()` is a generic function defined in the DelayedArray package:

    library(DelayedArray)
    ?extract_array

It takes 2 arguments: `x` and `index`. `x` is the seed object to extract array values from. `index` must be an unnamed list of subscripts as positive integer vectors, one vector per seed dimension. Empty and missing subscripts (represented by `integer(0)` and `NULL` list elements, respectively) are allowed. The subscripts in `index` can contain duplicated indices. They cannot contain NAs or non-positive values.

The `extract_array()` method must return an ordinary array of the appropriate type (i.e. `integer`, `double`, etc…). For example, if `x` is an ADSArraySeed object representing an M x N on-disk matrix of complex numbers, `extract_array(x, list(NULL, 2L))` must return its 2nd column as an M x 1 ordinary matrix of type `complex`.

Note that the `extract_array()` method needs to support empty and missing subscripts e.g. `extract_array(x, list(NULL, integer(0)))` must return an M x 0 matrix of type `complex` and `extract_array(x, list(integer(0), integer(0)))` a 0 x 0 matrix of type `complex`. This last edge case is important because the `type()` and `show()` methods for DelayedArray objects rely on it to work. More precisely, once the `extract_array()` method supports an `index` with empty integer vectors, the following should work:

    seed <- ADSArraySeed(...)
    M <- DelayedArray(seed)
    type(M)
    show(M)

Finally note that subscripts are allowed to contain duplicated indices so things like `extract_array(seed, list(c(1:3, 3:1), 2L))` need to be supported.

## 2.4 What to import?

Make sure the NAMESPACE file of the ADSArray package contains at least the following imports:

    import(methods)
    importFrom(tools, file_path_as_absolute)

    import(BiocGenerics)
    import(S4Vectors)
    import(IRanges)
    import(DelayedArray)

Unless you have a good reason for it, don’t try to selectively import things from the methods, BiocGenerics, S4Vectors, IRanges, and DelayedArray packages. This will only complicate maintenance of the ADSArray package in the long run and has no real benefits (contrary to popular belief).

Add methods, BiocGenerics, and DelayedArray to the `Depends` field of the DESCRIPTION file of the package, and tools, S4Vectors, and IRanges to its `Imports` field.

## 2.5 Testing

Make sure to export the ADSArraySeed class, its constructor, and the `dim`, `dimnames`, and `extract_array` methods.

At this point, you should be able to wrap an ADSArraySeed object `seed` in a DelayedArray object with `DelayedArray(seed)`, and this should return a fully functional DelayedArray object.

# 3 Implementing high-level classes ADSArray and ADSMatrix

These classes are not strictly needed but add a nice level of convenience.

## 3.1 ADSArray class definition

An ADSArray or ADSMatrix object is a DelayedArray derivative that doesn’t carry delayed operations yet. As soon as the user will start operating on it, it will be degraded to a DelayedArray instance.

The ADSArray and ADSMatrix classes should extend the DelayedArray and DelayedMatrix classes, respectively, without adding any slot to them.

So just:

    setClass("ADSArray",
        contains="DelayedArray",
        representation(seed="ADSArraySeed")
    )

We’ll define the ADSMatrix class later.

## 3.2 The ADSArray() constructor

Add a `DelayedArray()` method for ADSArraySeed objects that does:

    setMethod("DelayedArray", "ADSArraySeed",
        function(seed) new_DelayedArray(seed, Class="ADSArray")
    )

Now you should be able to construct an ADSArray object with:

    DelayedArray(ADSArraySeed(...))

The `ADSArray` constructor should just do that:

    ADSArray <- function(filepath, other args)
        DelayedArray(ADSArraySeed(filepath, other args))

However, it’s also nice to be able to pass an ADSArraySeed object to this constructor (with `ADSArray(seed)`). This can easily be supported with something like:

    ### Works directly on an ADSArraySeed object, in which case it must be
    ### called with a single argument.
    ADSArray <- function(filepath, other args)
    {
        if (is(filepath, "ADSArraySeed")) {
            if (!(missing(other arg1) && missing(other arg2) && ...))
                stop(wmsg("ADSArray() must be called with a single argument ",
                          "when passed an ADSArraySeed object"))
            seed <- filepath
        } else {
            seed <- ADSArraySeed(filepath, other args)
        }
        DelayedArray(seed)
    }

## 3.3 ADSMatrix class definition

    setClass("ADSMatrix", contains=c("ADSArray", "DelayedMatrix"))

## 3.4 Going from ADSArray to ADSMatrix

Define a `matrixClass()` method for ADSArray objects as follow:

    setMethod("matrixClass", "ADSArray", function(x) "ADSMatrix")

`matrixClass()` is a generic function defined in the DelayedArray package. When passed an ADSArraySeed object, low-level constructor `new_DelayedArray` (see below) will generally return an ADSArray instance, except when the ADSArraySeed object is 2-dimensional, in which case it needs to return an ADSMatrix instance. It will obtain the name of the class of the object to return (`"ADSMatrix"` in this case) by calling `matrixClass`.

Also coercion from ADSArray to ADSMatrix needs to be supported with:

    setAs("ADSArray", "ADSMatrix", function(from) new("ADSMatrix", from))

This coercion will make sure that the end user gets the following error when trying to coerce an ADSArray object that is not 2-dimensional to ADSMatrix:

    as(x, "ADSMatrix")
    # Error in validObject(.Object) : invalid class "ADSMatrix" object:
    #     'x' must have exactly 2 dimensions

Without the above coercion method, `as(x, "ADSMatrix")` would silently return an invalid ADSMatrix object.

## 3.5 Going from ADSMatrix to ADSArray

The user should not be able to degrade an ADSMatrix object to an ADSArray object so `as(x, "ADSArray", strict=TRUE)` should fail or be a no-op when `x` is an ADSMatrix object. The easiest (and recommended) way to achieve this is to define the following coercion method:

    setAs("ADSMatrix", "ADSArray", function(from) from)  # no-op

## 3.6 Implementing optimized backend-specific methods

It is possible, and enouraged, to overwrite current DelayedArray block-processed operations (e.g. `max`, `colSums`, `%*%`, etc…) with optimized backend-specific methods. For example, let’s imagine that ADS files have the capability to store some precomputed stats about the dataset. Then one could define a fast `max()` method for ADSArray objects with something like:

    setMethod("max", "ADSArraySeed",
        function(x, na.rm=FALSE)
        {
            get the precomputed max from the file
        }
    )

    setMethod("max", "ADSArray",
        function(x, na.rm=FALSE) max(x@seed, na.rm=na.rm)
    )

Note that delayed operations like setting dimnames on an ADSArray object (with `dimnames(A) <- new_dimnames`) or transposing an ADSMatrix object (with `M2 <- t(M)`) will degrade the object to a DelayedArray or DelayedMatrix instance, causing `max(A)` and `max(M2)` to use the far less efficient block-processed `max()` method defined for DelayedArray objects. There is clearly room for improvement here and work will be done in the near future to make the `max()` method (and other block-processed methods) for DelayedArray objects try to take advantage of the backend-specific methods whenever it can.

However in the meantime, backend authors should resist the temptation to overwrite the `dimnames<-()` and `t()` methods for DelayedArray objects with backend-specific methods that modify the seed. This would be a violation of the “never touch the seed” principle which is central to the DelayedArray framework. More precisely, no matter what delayed operations are performed on a DelayedArray object, the seeds of the result should always be identical to the original seeds (e.g. `seed(t(M))` should always be identical to `seed(M)`).

## 3.7 What to export?

Make sure to export the ADSArray and ADSMatrix classes, the `ADSArray` constructor, the `coerce` methods, and any backend-specific method.

# 4 Testing

Install the ADSArray package and load it in a fresh R session:

    library(ADSArray)
    ... coming soon ...