---
title: "Overview of DelayedMatrixStats"
author: "Peter Hickey"
date: "Modified: 05 Oct 2017. Compiled: `r format(Sys.Date(), '%d %b %Y')`"
output: BiocStyle::html_document
vignette: >
  %\VignetteIndexEntry{Overview of DelayedMatrixStats}
  %\VignetteEncoding{UTF-8}
  %\VignetteEngine{knitr::rmarkdown}
editor_options: 
  chunk_output_type: console
---

```{r, include = FALSE, setup}
knitr::opts_chunk$set(echo = TRUE, comment = "#>", collapse = TRUE,
                      message = FALSE)
```

# Overview

`r Biocpkg("DelayedMatrixStats")` ports the `r CRANpkg("matrixStats")` API 
to work with *DelayedMatrix* objects from the `r Biocpkg("DelayedArray")` 
package. It provides high-performing functions operating on rows and columns of 
*DelayedMatrix* objects, including all subclasses such as *RleArray* (from the 
`r Biocpkg("DelayedArray")` package) and *HDF5Array* (from the 
`r Biocpkg("HDF5Array")`) as well as supporting all types of *seeds*, such as 
*matrix* (from the *base* package) and *Matrix* (from the `r CRANpkg("Matrix")` 
package).

# How can DelayedMatrixStats help me?

The `r Biocpkg("DelayedArray")` package allows developers to store array-like 
data using in-memory or on-disk representations (e.g., in HDF5 files) and 
provides a common and familiar array-like interface for interacting with these 
data.

The `r Biocpkg("DelayedMatrixStats")` package is designed to make life easier 
for Bioconductor developers wanting to use `r Biocpkg("DelayedArray")` by 
providing a rich set of column-wise and row-wise summary functions. 

We briefly demonstrate and explain these two features using a simple example.
We'll simulate some (unrealistic) RNA-seq read counts data from 10,000 genes 
and 20 samples and store it on disk as a *HDF5Array*:

```{r data_sim, message = FALSE}
library(DelayedArray)

x <- do.call(cbind, lapply(1:20, function(j) {
  rpois(n = 10000, lambda = sample(20:40, 10000, replace = TRUE))
}))
colnames(x) <- paste0("S", 1:20)
x <- realize(x, "HDF5Array")
x
```

Suppose you wish to compute the standard deviation of the read counts for each 
gene. 

You might think to use `apply()` like in the following:

```{r apply}
system.time(row_sds <- apply(x, 1, sd))
head(row_sds)
```

This works, but takes quite a while.

Or perhaps you already know that the `r CRANpkg("matrixStats")` package 
provides a `rowSds()` function:

```{r matrixStats, error = TRUE}
matrixStats::rowSds(x)
```

Unfortunately (and perhaps unsurprisingly) this doesn't work. 
`r CRANpkg("matrixStats")` is designed for use on in-memory *matrix* objects. 
Well, why don't we just first realize our data in-memory and then use 
`r CRANpkg("matrixStats")`

```{r realization}
system.time(row_sds <- matrixStats::rowSds(as.matrix(x)))
head(row_sds)
```

This works and is many times faster than the `apply()`-based approach! However, 
it rather defeats the purpose of using a *HDF5Array* for storing the 
data since we have to bring all the data into memory at once to compute the 
result. 

Instead, we can use `DelayedMatrixStats::rowSds()`, which has the speed 
benefits of `matrixStats::rowSds()`[^speed] but without having to load the 
entire data into memory at once[^block_size]:

[^speed]: In fact, it currently uses `matrixStats::rowSds()` under the hood.
[^block_size]: In this case, it loads blocks of data row-by-row. The amount of 
data loaded into memory at any one time is controlled by the 
`DelayedArray.block.size` option; see `?DelayedArray::DelayedArray` for 
details. Notably, if the data are small enough (and the value of this option is 
large enough) then all the data is loaded as a single block, but this approach 
generalizes and still works when the data are too large to be loaded into 
memory in one block.

```{r DelayedMatrixStats}
library(DelayedMatrixStats)

system.time(row_sds <- rowSds(x))
head(row_sds)
```

Finally, by using `r Biocpkg("DelayedMatrixStats")` we can use the same code, 
(`colMedians(x)`) regardless of whether the input is an ordinary *matrix* or a 
*DelayedMatrix*. This is useful for packages wishing to support both types of 
objects, e.g., packages wanting to retain backward compatibility or during a 
transition period from *matrix*-based to *DelayeMatrix*-based objects.

# Supported methods

The initial release of `r Biocpkg("DelayedMatrixStats")` supports the complete 
set of column-wise and row-wise `r CRANpkg("matrixStats")` API[^api]. Please 
see the `r CRANpkg("matrixStats")` vignette 
([available online](https://cran.r-project.org/package=matrixStats/vignettes/matrixStats-methods.html)) 
for a summary these methods. The following table documents the API coverage and 
availability of ['seed-aware' methods](#seed_aware_methods) in the current 
version of `r Biocpkg("DelayedMatrixStats")`.

[^api]: **NOTE:** `colWeightedSds()`, `colWeightedVars()`, `rowWeightedSds()`, and 
`rowWeightedVars()` will be implemented/reinstated after resolving 
[a bug in `matrixStats::weightedVar()`](https://github.com/HenrikBengtsson/matrixStats/issues/105). `colAvgsPerRowSet()` will be implemented/reinstated upon the next CRAN release of **matrixStats** ([https://github.com/PeteHaitch/DelayedMatrixStats/issues/34](https://github.com/PeteHaitch/DelayedMatrixStats/issues/34))

```{r API, echo = FALSE}
matrixStats <- sort(grep("^(col|row)", 
                         getNamespaceExports("matrixStats"), 
                         value = TRUE))
# TODO: A better way of parsing DelayedMatrixStats NAMESPACE to get exported 
#       functions (will also need internal functions for api_df)
DelayedMatrixStats <- sort(grep("^(col|row)", 
                         getNamespaceExports("DelayedMatrixStats"), 
                         value = TRUE))

api_df <- data.frame(
  Method = paste0("`", matrixStats, "()`"),
  `Block processing` = ifelse(matrixStats %in% DelayedMatrixStats,
                              "✔",
                              "❌"),
  `_base::matrix_ optimized` = 
    ifelse(sapply(matrixStats, existsMethod, signature = "matrix"), 
           "✔", 
           "❌"),
  `_Matrix::Matrix_ optimized` = 
    ifelse(sapply(matrixStats, existsMethod, signature = "Matrix"), 
           "✔", 
           "❌"),
  `_DelayedArray::RleArray_ (_SolidRleArraySeed_) optimized` = 
    ifelse(sapply(matrixStats, existsMethod, signature = "SolidRleArraySeed"),
           "✔", 
           "❌"),
  `_DelayedArray::RleArray_  (_ChunkedRleArraySeed_) optimized` = 
    ifelse(sapply(matrixStats, existsMethod, signature = "ChunkedRleArraySeed"),
           "✔", 
           "❌"),
  `_HDF5Array::HDF5Matrix_ optimized` = 
    ifelse(sapply(matrixStats, existsMethod, signature = "HDF5ArraySeed"),
           "✔", 
           "❌"),
  `_base::data.frame_ optimized` = 
    ifelse(sapply(matrixStats, existsMethod, signature = "data.frame"),
           "✔", 
           "❌"),
  `_S4Vectors::DataFrame_ optimized` =
    ifelse(sapply(matrixStats, existsMethod, signature = "DataFrame"),
           "✔", 
           "❌"), 
  check.names = FALSE)
knitr::kable(api_df, row.names = FALSE)
```

# 'Seed-aware' methods {#seed_aware_methods}

As well as offering a familiar API, `r Biocpkg("DelayedMatrixStats")` provides 
'seed-aware' methods that are optimized for specific types of *DelayedMatrix* 
objects. 

To illustrate this idea, we will compare two ways of computing the column sums 
of a *DelayedMatrix* object:

1. The 'block-processing' strategy. This was developed in the `r Biocpkg("DelayedArray")` package and is available for all methods in the `r Biocpkg("DelayedMatrixStats")` through the `force_block_processing` argument
2. The 'seed-aware' strategy. This is implemented in the `r Biocpkg("DelayedMatrixStats")` and is optimized for both speed and memory but only for *DelayedMatrix* objects with certain types of *seed*.

We will demonstrate this by computing the column sums matrices with 20,000 rows 
and 600 columns where the data have different structure and are stored in 
*DelayedMatrix* objects with different types of seed:

- Dense data with values in $(0, 1)$ using an ordinary _matrix_ as the seed
- Sparse data with values in $[0, 1)$, where $60\%$ are zeros, using a _dgCMatrix_, a sparse matrix representation from the `r CRANpkg("Matrix")` package, as the seed
- Dense data in ${0, 1, \ldots, 100}$, where there are multiple runs of identical values, using a _RleArraySeed_ from the `r Biocpkg("DelayedArray")` package as the seed

We use the `r CRANpkg("microbenchmark")` package to measure running time and 
the `r CRANpkg("profmem")` package to measure the total memory allocations of 
each method. 

In each case, the 'seed-aware' method is many times faster and allocates 
substantially lower total memory.

```{r benchmarking, message = FALSE, echo = TRUE, error = TRUE}
library(DelayedMatrixStats)
library(Matrix)
library(microbenchmark)
library(profmem)

set.seed(666)

# -----------------------------------------------------------------------------
# Dense with values in (0, 1)
# Fast, memory-efficient column sums of DelayedMatrix with ordinary matrix seed
#

# Generate some data
dense_matrix <- matrix(runif(20000 * 600), 
                       nrow = 20000,
                       ncol = 600)

# Benchmark
dm_matrix <- DelayedArray(dense_matrix)
class(seed(dm_matrix))
dm_matrix
microbenchmark(
  block_processing = colSums2(dm_matrix, force_block_processing = TRUE),
  seed_aware = colSums2(dm_matrix),
  times = 10)
total(profmem(colSums2(dm_matrix, force_block_processing = TRUE)))
total(profmem(colSums2(dm_matrix)))

# -----------------------------------------------------------------------------
# Sparse (60% zero) with values in (0, 1)
# Fast, memory-efficient column sums of DelayedMatrix with ordinary matrix seed
#

# Generate some data
sparse_matrix <- dense_matrix
zero_idx <- sample(length(sparse_matrix), 0.6 * length(sparse_matrix))
sparse_matrix[zero_idx] <- 0

# Benchmark
dm_dgCMatrix <- DelayedArray(Matrix(sparse_matrix, sparse = TRUE))
class(seed(dm_dgCMatrix))
dm_dgCMatrix
microbenchmark(
  block_processing = colSums2(dm_dgCMatrix, force_block_processing = TRUE),
  seed_aware = colSums2(dm_dgCMatrix),
  times = 10)
total(profmem(colSums2(dm_dgCMatrix, force_block_processing = TRUE)))
total(profmem(colSums2(dm_dgCMatrix)))

# -----------------------------------------------------------------------------
# Dense with values in {0, 100} featuring runs of identical values
# Fast, memory-efficient column sums of DelayedMatrix with Rle-based seed
#

# Generate some data
runs <- rep(sample(100, 500000, replace = TRUE), rpois(500000, 100))
runs <- runs[seq_len(20000 * 600)]
runs_matrix <- matrix(runs, 
                      nrow = 20000,
                      ncol = 600)

# Benchmark
dm_rle <- RleArray(Rle(runs),
                   dim = c(20000, 600))
class(seed(dm_rle))
dm_rle
microbenchmark(
  block_processing = colSums2(dm_rle, force_block_processing = TRUE),
  seed_aware = colSums2(dm_rle),
  times = 10)
total(profmem(colSums2(dm_rle, force_block_processing = TRUE)))
total(profmem(colSums2(dm_rle)))
```

The development of 'seed-aware' methods is ongoing work (see the [Roadmap](#roadmap)), and for now only a few methods and seed-types have a 
'seed-aware' method.

An extensive set of benchmarks is under development at [http://peterhickey.org/BenchmarkingDelayedMatrixStats/](http://peterhickey.org/BenchmarkingDelayedMatrixStats/). 

# Delayed operations

A key feature of a _DelayedArray_ is the ability to register 'delayed 
operations'. For example, let's compute `sin(dm_matrix)`:

```{r sin}
system.time(sin_dm_matrix <- sin(dm_matrix))
```

This instantaneous because the operation is not actually performed, rather 
it is registered and only performed when the object is _realized_. All methods 
in `r Biocpkg("DelayedMatrixStats")` will correctly realise these delayed 
operations before computing the final result. For example, let's compute  
`colSums2(sin_dm_matrix)` and compare check we get the correct answer:

```{r colSums2_sin}
all.equal(colSums2(sin_dm_matrix), colSums(sin(as.matrix(dm_matrix))))
```

# Roadmap {#roadmap}

The initial version of `r Biocpkg("DelayedMatrixStats")` provides complete 
coverage of the `r CRANpkg("matrixStats")` column-wise and row-wise API[^api], 
allowing package developers to use these functions with _DelayedMatrix_ objects 
as well as with ordinary _matrix_ objects. This should simplify package 
development and assist authors to support to their software for large datasets 
stored in disk-backed data structures such as _HDF5Array_. Such large datasets 
are increasingly common with the rise of single-cell genomics.

Future releases of `r Biocpkg("DelayedMatrixStats")` will improve the 
performance of these methods, specifically by developing additional 'seed-aware' 
methods. The plan is to prioritise commonly used methods (e.g.,  
`colMeans2()`/`rowMeans2()`, `colSums2()`/`rowSums2()`, etc.) and the 
development of 'seed-aware' methods for the _HDF5Matrix_ class. To do so, we 
will leverage the `r Biocpkg("beachmat")` package. Proof-of-concept code 
has shown that this can greatly increase the performance when analysing such 
disk-backed data.

Importantly, all package developers using methods from 
`r Biocpkg("DelayedMatrixStats")` will immediately gain from performance 
improvements to these low-level routines. By using 
`r Biocpkg("DelayedMatrixStats")`, package developers will be able to focus on 
higher level programming tasks and address important scientific questions and 
technological challenges in high-throughput biology.
