# A Gentle Introduction to matrixset

## What is a matrixset?

It’s a container of matrices, each having the same number of rows and columns and the same dimnames. Moreover, each dimname must uniquely identify elements.

Both `matrix` and special matrices (from `Matrix` package) objects can be used.

While there is minimal support for `NULL` dimnames (and that is bound to change at some point in the future), it is strongly recommended to provide meaningful dimnames. One of the main reason for this is that annotation is impossible with `NULL` dimnames.

In addition, as alluded above, a `matrixset` can store independent row and column annotations. This meta information is stored, and available, in the form of data frames - one for row information and one for column. The annotation names are referred to as traits.

This latter feature makes `matrixset` especially attractive even if it stores only a single matrix, because several methods have been developed to manipulate `matrixset`s, accounting for annotations.

## Why a matrixset?

Many problems that `matrixset` can tackle could be solved via a `data.frame` and more specifically using the `tidyverse` suite.

Three reasons for which you may want to use a `matrixset` instead are:

- object size. The `data.frame` needed to store the same information as a `matrixset` can be significantly bigger.
- You can store sparse matrices and other special matrices of package `Matrix`. This is one of very few ways (maybe even the only way) to annotate special matrices. In addition, dealing with special matrices make the object size argument even more striking when comparing to the data frame strategy.
- You actually need a matrix format, for example for running a PCA.

## How to create a matrixset?

To illustrate how to build a `matrixset`, we will use the animal dataset from the MASS package.

    animals <- as.matrix(MASS::Animals)
    head(animals)
    #>                     body brain
    #> Mountain beaver     1.35   8.1
    #> Cow               465.00 423.0
    #> Grey wolf          36.33 119.5
    #> Goat               27.66 115.0
    #> Guinea pig          1.04   5.5
    #> Dipliodocus     11700.00  50.0

This is a matrix with 28 rows and 2 columns.

There is two ways to create a `matrixset` object: `matrixset()` or `as_matrixset()`.

Let’s first take a look at `matrixset()`.

    animals_ms <- matrixset(animals)
    #> Error in list_names(matrix_set): The list elements must be named

Oops! Looks like something didn’t work. That’s because matrices must be named when building a `matrixset`.

    animals_ms <- matrixset(msr = animals)
    animals_ms
    #> matrixset of 1 28 × 2 matrices
    #>
    #> matrix_set: msr
    #> A 28 × 2 <dbl> matrix
    #>                   body  brain
    #> Mountain beaver   1.35   8.10
    #>             ...    ...    ...
    #>             Pig 192.00 180.00
    #>
    #>
    #> row_info:
    #> # A tibble: 28 × 1
    #>    .rowname
    #>    <chr>
    #>  1 Mountain beaver
    #>  2 Cow
    #>  3 Grey wolf
    #>  4 Goat
    #>  5 Guinea pig
    #>  6 Dipliodocus
    #>  7 Asian elephant
    #>  8 Donkey
    #>  9 Horse
    #> 10 Potar monkey
    #> # ℹ 18 more rows
    #>
    #>
    #> column_info:
    #> # A tibble: 2 × 1
    #>   .colname
    #>   <chr>
    #> 1 body
    #> 2 brain

The `as_matrixset()` function will provide a generic name.

    as_matrixset(animals)
    #> matrixset of 1 28 × 2 matrices
    #>
    #> matrix_set: ..1
    #> A 28 × 2 <dbl> matrix
    #>                   body  brain
    #> Mountain beaver   1.35   8.10
    #>             ...    ...    ...
    #>             Pig 192.00 180.00
    #>
    #>
    #> row_info:
    #> # A tibble: 28 × 1
    #>    .rowname
    #>    <chr>
    #>  1 Mountain beaver
    #>  2 Cow
    #>  3 Grey wolf
    #>  4 Goat
    #>  5 Guinea pig
    #>  6 Dipliodocus
    #>  7 Asian elephant
    #>  8 Donkey
    #>  9 Horse
    #> 10 Potar monkey
    #> # ℹ 18 more rows
    #>
    #>
    #> column_info:
    #> # A tibble: 2 × 1
    #>   .colname
    #>   <chr>
    #> 1 body
    #> 2 brain

It is recommended to use the `matrixset()` function and provide a meaningful matrix name, as some functionalities will make use of matrix names. It will also be easier to refer to the matrices when there is more than one.

We saw in the `animals_ms` printout that default row annotation (`row_info`) and column annotation (`column_info`) were created at the time of object building.

Meta info always contains the row names and column names. We will see later how to add more annotation.

Let’s see an example on how to include more than one matrix.

    log_animals <- log(animals)
    ms <- matrixset(msr = animals, log_msr = log_animals)
    ms
    #> matrixset of 2 28 × 2 matrices
    #>
    #> matrix_set: msr
    #> A 28 × 2 <dbl> matrix
    #>                   body  brain
    #> Mountain beaver   1.35   8.10
    #>             ...    ...    ...
    #>             Pig 192.00 180.00
    #>
    #> matrix_set: log_msr
    #> A 28 × 2 <dbl> matrix
    #>                 body brain
    #> Mountain beaver 0.30  2.09
    #>             ...  ...   ...
    #>             Pig 5.26  5.19
    #>
    #>
    #> row_info:
    #> # A tibble: 28 × 1
    #>    .rowname
    #>    <chr>
    #>  1 Mountain beaver
    #>  2 Cow
    #>  3 Grey wolf
    #>  4 Goat
    #>  5 Guinea pig
    #>  6 Dipliodocus
    #>  7 Asian elephant
    #>  8 Donkey
    #>  9 Horse
    #> 10 Potar monkey
    #> # ℹ 18 more rows
    #>
    #>
    #> column_info:
    #> # A tibble: 2 × 1
    #>   .colname
    #>   <chr>
    #> 1 body
    #> 2 brain

It may happen that the matrices are stored in a list. No problem, the list can be used as input for `matrixset`.

    ms2 <- matrixset(list(msr = animals, log_msr = log_animals))
    identical(ms, ms2)
    #> [1] TRUE

It is also possible to add a matrix to an already existing object.

    animals_ms <- add_matrix(animals_ms, log_msr = log_animals)
    identical(ms, animals_ms)
    #> [1] TRUE

## How to annotate

One way is to do it at the object creation step. Suppose we have the following animal information (which are rows in our object).

    library(tidyverse)
    animal_info <- MASS::Animals %>%
      rownames_to_column("Animal") %>%
      mutate(is_extinct = case_when(Animal %in% c("Dipliodocus", "Triceratops", "Brachiosaurus") ~ TRUE,
                                    TRUE ~ FALSE),
             class = case_when(Animal %in% c("Mountain beaver", "Guinea pig", "Golden hamster", "Mouse", "Rabbit", "Rat") ~ "Rodent",
                               Animal %in% c("Potar monkey", "Gorilla", "Human", "Rhesus monkey", "Chimpanzee") ~ "Primate",
                               Animal %in% c("Cow", "Goat", "Giraffe", "Sheep") ~ "Ruminant",
                               Animal %in% c("Asian elephant", "African elephant") ~ "Elephantidae",
                               Animal %in% c("Grey wolf") ~ "Canine",
                               Animal %in% c("Cat", "Jaguar") ~ "Feline",
                               Animal %in% c("Donkey", "Horse") ~ "Equidae",
                               Animal == "Pig" ~ "Sus",
                               Animal == "Mole" ~ "Talpidae",
                               Animal == "Kangaroo" ~ "Macropodidae",
                               TRUE ~ "Dinosaurs")) %>%
      select(-body, -brain)
    animal_info
    #>              Animal is_extinct        class
    #> 1   Mountain beaver      FALSE       Rodent
    #> 2               Cow      FALSE     Ruminant
    #> 3         Grey wolf      FALSE       Canine
    #> 4              Goat      FALSE     Ruminant
    #> 5        Guinea pig      FALSE       Rodent
    #> 6       Dipliodocus       TRUE    Dinosaurs
    #> 7    Asian elephant      FALSE Elephantidae
    #> 8            Donkey      FALSE      Equidae
    #> 9             Horse      FALSE      Equidae
    #> 10     Potar monkey      FALSE      Primate
    #> 11              Cat      FALSE       Feline
    #> 12          Giraffe      FALSE     Ruminant
    #> 13          Gorilla      FALSE      Primate
    #> 14            Human      FALSE      Primate
    #> 15 African elephant      FALSE Elephantidae
    #> 16      Triceratops       TRUE    Dinosaurs
    #> 17    Rhesus monkey      FALSE      Primate
    #> 18         Kangaroo      FALSE Macropodidae
    #> 19   Golden hamster      FALSE       Rodent
    #> 20            Mouse      FALSE       Rodent
    #> 21           Rabbit      FALSE       Rodent
    #> 22            Sheep      FALSE     Ruminant
    #> 23           Jaguar      FALSE       Feline
    #> 24       Chimpanzee      FALSE      Primate
    #> 25              Rat      FALSE       Rodent
    #> 26    Brachiosaurus       TRUE    Dinosaurs
    #> 27             Mole      FALSE     Talpidae
    #> 28              Pig      FALSE          Sus

We can then use the `matrixset()` function (it works with `as_matrixset()` too).

    ms <- matrixset(msr = animals, log_msr = log_animals, row_info = animal_info,
                    row_key = "Animal")
    ms
    #> matrixset of 2 28 × 2 matrices
    #>
    #> matrix_set: msr
    #> A 28 × 2 <dbl> matrix
    #>                   body  brain
    #> Mountain beaver   1.35   8.10
    #>             ...    ...    ...
    #>             Pig 192.00 180.00
    #>
    #> matrix_set: log_msr
    #> A 28 × 2 <dbl> matrix
    #>                 body brain
    #> Mountain beaver 0.30  2.09
    #>             ...  ...   ...
    #>             Pig 5.26  5.19
    #>
    #>
    #> row_info:
    #> # A tibble: 28 × 3
    #>    .rowname        is_extinct class
    #>    <chr>           <lgl>      <chr>
    #>  1 Mountain beaver FALSE      Rodent
    #>  2 Cow             FALSE      Ruminant
    #>  3 Grey wolf       FALSE      Canine
    #>  4 Goat            FALSE      Ruminant
    #>  5 Guinea pig      FALSE      Rodent
    #>  6 Dipliodocus     TRUE       Dinosaurs
    #>  7 Asian elephant  FALSE      Elephantidae
    #>  8 Donkey          FALSE      Equidae
    #>  9 Horse           FALSE      Equidae
    #> 10 Potar monkey    FALSE      Primate
    #> # ℹ 18 more rows
    #>
    #>
    #> column_info:
    #> # A tibble: 2 × 1
    #>   .colname
    #>   <chr>
    #> 1 body
    #> 2 brain

Notice how we used the `row_key` argument to specify how to link the two objects together.

Another option is the `row_info<-()` function. Note that here you need a column with the same tag as in the `matrixset` object.

    row_info(ms2) <- animal_info %>% rename(.rowname = Animal)
    identical(ms, ms2)
    #> [1] TRUE

We’ll finish the annotation section by introducing the `join` and the `annotate` methods.

    animals_ms <- animals_ms %>%
      join_row_info(animal_info, by = c(".rowname" = "Animal"))
    identical(ms, animals_ms)
    #> [1] TRUE
    animals_ms <- animals_ms %>%
      annotate_column(unit = case_when(.colname == "body" ~ "kg",
                                       TRUE ~ "g"))
    animals_ms
    #> matrixset of 2 28 × 2 matrices
    #>
    #> matrix_set: msr
    #> A 28 × 2 <dbl> matrix
    #>                   body  brain
    #> Mountain beaver   1.35   8.10
    #>             ...    ...    ...
    #>             Pig 192.00 180.00
    #>
    #> matrix_set: log_msr
    #> A 28 × 2 <dbl> matrix
    #>                 body brain
    #> Mountain beaver 0.30  2.09
    #>             ...  ...   ...
    #>             Pig 5.26  5.19
    #>
    #>
    #> row_info:
    #> # A tibble: 28 × 3
    #>    .rowname        is_extinct class
    #>    <chr>           <lgl>      <chr>
    #>  1 Mountain beaver FALSE      Rodent
    #>  2 Cow             FALSE      Ruminant
    #>  3 Grey wolf       FALSE      Canine
    #>  4 Goat            FALSE      Ruminant
    #>  5 Guinea pig      FALSE      Rodent
    #>  6 Dipliodocus     TRUE       Dinosaurs
    #>  7 Asian elephant  FALSE      Elephantidae
    #>  8 Donkey          FALSE      Equidae
    #>  9 Horse           FALSE      Equidae
    #> 10 Potar monkey    FALSE      Primate
    #> # ℹ 18 more rows
    #>
    #>
    #> column_info:
    #> # A tibble: 2 × 2
    #>   .colname unit
    #>   <chr>    <chr>
    #> 1 body     kg
    #> 2 brain    g

The join operation joins the second meta info (`animal_info` in our example) to the relevant `matrixset` meta info.

The `annotate` operation works like dplyr’s `mutate()` does: you can modify existing annotation, create new ones or even remove them. It can use already existing annotation as well.

    animals_ms %>%
      annotate_column(us_unit = case_when(unit == "kg" ~ "lb",
                                       TRUE ~ "oz")) %>%
      column_info()
    #> # A tibble: 2 × 3
    #>   .colname unit  us_unit
    #>   <chr>    <chr> <chr>
    #> 1 body     kg    lb
    #> 2 brain    g     oz

The only annotation that can’t be modify or deleted via `annotate` is the the tag (typically, `.rowname` and `.colname`).

    animals_ms %>% annotate_column(.colname = NULL)
    #> Error in annotate_column.matrixset(., .colname = NULL): column tag (i.e., column info containing column names) can't be removed

There is one last method to provide annotation: `annotate_row_from_apply()`/ `annotate_column_from_apply()`. With this method, a matrix operation (for instance, the row average) can be stored as an annotation.

We strongly encourage you to have a look at the functions, and also `apply_row_dfw()/apply_column_dfw()`, upon which they are based.

## What to do with a matrixset

Many of the `array` operations are available for `matrixset`:

- Subseting operations `[` and `[[`. The subset `[` works like that of an array. The first argument is for rows, the second for columns and the third for matrices. It will return a `matrixset`, even if there is a single matrix returned as part of the subset. The `keep_annotation` argument (that always should be used after the 3 row/col/matrix arguments) will return only the matrix list.

  The operation `x[[m]]` is a wrapper to `x[,,m]`.

- Replacement method `[<-` Replaces matrix or matrices, in full or in part, by new values.

- `dimnames()` and the related `rownames()` and `colnames()`.

- The replacement versions: `dimnames<-()` and the related `rownames<-()` and `colnames<-()`. Note that `rownames<-()` and `colnames<-()` are what should be used for names replacement. The special annotation tag is modified this way.

- `dim()` and the related `nrow()` and `ncol()`

Other property methods specific to the `matrixset` object are available:

- `matrixnames()` (and the replacement version, `matrixnames<-()`) and `nmatrix()`
- Component extraction functions:
  - `matrix_elm()`: extracts a single matrix of the object, and returns it as a matrix
  - `row_info()` and `column_info()`: extracts the data frames that stores the annotation
  - `row_traits()` and `column_traits()`: returns the annotation names. The tag (column that stores the row/column names) is not returned.
- Component replacement functions
  - `matrix_elm<-()`: replaces a single matrix of the object
  - `row_info()<-` and `column_info()<-`: relaces whole annotation data frame
  - row_traits and `column_traits()`: replace annotation names. Tags cannot be replaced
- expansion/reduction functions `add_matrix()` and `remove_matrix()`.

Finally, many functions to manipulate or use the `matrixset` object, often taking inspiration from the `tidyverse`, have been made available

- `mutate_matrix()`: create, modify or delete matrices. Supports tidy evaluation and tidy selection (for matrix names and annotations)
- `apply_matrix()`, `apply_row()` and `apply_column()` (and all of their declinations): apply functions/expressions to matrices, their rows or their columns. They have intuitive and direct access to annotations.
- `arrange_row()` and `arrange_column()`: reorder rows and columns. Supports tidy selection for annotation
- `filter_row()` and `filter_column()`: subset rows or columns of matrices based on conditions that may use annotations.

All of these functions (except for `mutate_matrix()`) can be performed within groups - groups that could be defined using annotation. This is done by a prior call to `row_group_by()` and/or `column_group_by()`.