# Applying Functions

## Apply Functions to `matrixset` Matrices

There are two ways to apply functions to the matrices of a `matrixset` object. The first one is through the `apply_*` family, which will be covered here.

The second is through `mutate_matrix()`, covered in the next section.

There are 3 functions in the `apply_*` family:

- `apply_matrix()`: The functions must take a matrix as input. In base R, this is similar to simply calling `fun(matrix_object)`.
- `apply_row()`: The functions must take a vector as input. The vector will be a matrix row. In base R, this is akin to `apply(matrix_object, 1, fun, simplify = FALSE)`.
- `apply_column()`: The functions must take a vector as input. The vector will be a matrix column. In base R, this is similar to `apply(matrix_object, 2, fun, simplify = FALSE)`.

Each of these function will loop on the `matrixset` object’s matrices to apply the functions. In the case of `apply_row()` and `apply_column()`, an additional loop on the margin (row or column, as applicable) is executed, so that the functions are applied to each matrix and margin.

To see the functions in action, we will use the following object:

    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

We will use the following custom printing functions for compactness purposes.

    show_matrix <- function(x) {
      if (nrow(x) > 4) {
        newx <- head(x, 4)
        storage.mode(newx) <- "character"
        newx <- rbind(newx, rep("...", ncol(x)))
      }  else newx <- x
      newx
    }
    show_vector <- function(x) {
      newx <- if (length(x) > 4) {
        c(as.character(x[1:4]), "...")
      } else x
      newx
    }
    show_lst <- function(x) {
      lapply(x, function(u) {
        if (is.matrix(u)) show_matrix(u) else if (is.vector(u)) show_vector(u) else u
      })
    }

So now, let’s see the `apply_matrix()` in action.

    library(magrittr)
    library(purrr)
    out <- animals_ms %>%
       apply_matrix(exp,
                    mean(.m, trim=.1),
                    foo=asinh,
                    pow = 2^.m,
                    reg = ~ {
                      is_alive <- !is_extinct
                      lm(.m ~ is_alive + class)
                      })
    # out[[1]] %>% map(~ if (is.matrix(.x)) {head(.x, 5)} else .x)
    show_lst(out[[1]])
    #> $exp
    #>                 body                    brain
    #> Mountain beaver "3.85742553069697"      "3294.46807528384"
    #> Cow             "8.84981281719581e+201" "5.08821958272978e+183"
    #> Grey wolf       "5996785676464821"      "7.91025688556692e+51"
    #> Goat            "1029402857448.45"      "8.78750163583702e+49"
    #>                 "..."                   "..."
    #>
    #> $`mean(.m, trim = 0.1)`
    #> [1] 335.1291
    #>
    #> $foo
    #>                 body               brain
    #> Mountain beaver "1.10857244179685" "2.78880004092018"
    #> Cow             "6.83518574234833" "6.74052075680554"
    #> Grey wolf       "4.28598038575143" "5.47648105816811"
    #> Goat            "4.01346111184316" "5.43809821197888"
    #>                 "..."              "..."
    #>
    #> $pow
    #>                 body                    brain
    #> Mountain beaver "2.54912125463852"      "274.374006409291"
    #> Cow             "9.52682052708738e+139" "2.16614819853189e+127"
    #> Grey wolf       "86381301347.2935"      "9.39906129562518e+35"
    #> Goat            "212075099.808884"      "4.15383748682786e+34"
    #>                 "..."                   "..."
    #>
    #> $reg
    #>
    #> Call:
    #> lm(formula = .m ~ is_alive + class)
    #>
    #> Coefficients:
    #>                    body       brain
    #> (Intercept)         36033.33      91.50
    #> is_aliveTRUE       -35997.00      28.00
    #> classDinosaurs            NA         NA
    #> classElephantidae    4564.17    5038.00
    #> classEquidae          317.72     417.50
    #> classFeline            15.32     -28.20
    #> classMacropodidae      -1.33     -63.50
    #> classPrimate           31.26     372.50
    #> classRodent           -35.44    -114.67
    #> classRuminant         232.96     228.75
    #> classSus              155.67      60.50
    #> classTalpidae         -36.21    -116.50

We have showcased several features of the `apply_*` functions:

- Many functions can be supplied at once.
- Functions can be supplied by bare function name. Note that this mean that only the current matrix will be used as input. You can also supply the function call or even, when submitting a one-sided formula, complex expressions.
- The name of the function result can be controlled.
- Object traits are accessible by bare name. The condition for this to work is that traits are unique across row and column annotation.

You probably have noticed the use of `.m`. This is a pronoun that is accessible inside `apply_matrix()` and refers to the current matrix in the internal loop. Similar pronouns exists for `apply_row()` and `apply_column()`, and they are respecticely `.i` and `.j`.

The returned object is a list of lists. The first layer is for each matrix and the second layer is for each function call.

Let’s now showcase the row/column version with a `apply_column()` example:

    out <- animals_ms %>%
       apply_column(exp,
                    mean(.j, trim=.1),
                    foo=asinh,
                    pow = 2^.j,
                    reg = ~ {
                      is_alive <- !is_extinct
                      lm(.j ~ is_alive + class)
                      })
    out[[1]] %>% map(show_lst)
    #> $body
    #> $body$exp
    #> [1] "3.85742553069697"      "8.84981281719581e+201" "5996785676464821"
    #> [4] "1029402857448.45"      "..."
    #>
    #> $body$`mean(.j, trim = 0.1)`
    #> [1] 879.0059
    #>
    #> $body$foo
    #> [1] "1.10857244179685" "6.83518574234833" "4.28598038575143" "4.01346111184316"
    #> [5] "..."
    #>
    #> $body$pow
    #> [1] "2.54912125463852"      "9.52682052708738e+139" "86381301347.2935"
    #> [4] "212075099.808884"      "..."
    #>
    #> $body$reg
    #>
    #> Call:
    #> lm(formula = .j ~ is_alive + class)
    #>
    #> Coefficients:
    #>       (Intercept)       is_aliveTRUE     classDinosaurs  classElephantidae
    #>          36033.33          -35997.00                 NA            4564.17
    #>      classEquidae        classFeline  classMacropodidae       classPrimate
    #>            317.72              15.32              -1.33              31.26
    #>       classRodent      classRuminant           classSus      classTalpidae
    #>            -35.44             232.96             155.67             -36.21
    #>
    #>
    #>
    #> $brain
    #> $brain$exp
    #> [1] "3294.46807528384"      "5.08821958272978e+183" "7.91025688556692e+51"
    #> [4] "8.78750163583702e+49"  "..."
    #>
    #> $brain$`mean(.j, trim = 0.1)`
    #> [1] 240.425
    #>
    #> $brain$foo
    #> [1] "2.78880004092018" "6.74052075680554" "5.47648105816811" "5.43809821197888"
    #> [5] "..."
    #>
    #> $brain$pow
    #> [1] "274.374006409291"      "2.16614819853189e+127" "9.39906129562518e+35"
    #> [4] "4.15383748682786e+34"  "..."
    #>
    #> $brain$reg
    #>
    #> Call:
    #> lm(formula = .j ~ is_alive + class)
    #>
    #> Coefficients:
    #>       (Intercept)       is_aliveTRUE     classDinosaurs  classElephantidae
    #>              91.5               28.0                 NA             5038.0
    #>      classEquidae        classFeline  classMacropodidae       classPrimate
    #>             417.5              -28.2              -63.5              372.5
    #>       classRodent      classRuminant           classSus      classTalpidae
    #>            -114.7              228.7               60.5             -116.5

The idea is similar, but in the returned object, there is a third list layer: the first layer for the matrices, the second layer for the columns (it would be rows for `apply_row()`) and the third layer for the functions.

Note as well the use of the `.j` pronoun instead of `.m`.

### Grouped Data

The `apply_*` functions understand data grouping and will execute on the proper matrix/vector subsets.

    animals_ms %>%
      row_group_by(class) %>%
      apply_matrix(exp,
                   mean(.m, trim=.1),
                   foo=asinh,
                   pow = 2^.m,
                   reg = ~ {
                     is_alive <- !is_extinct
                     lm(.m ~ is_alive)
                     })
    #> $msr
    #> # A tibble: 11 × 2
    #>    class        .vals
    #>    <chr>        <list>
    #>  1 Canine       <named list [5]>
    #>  2 Dinosaurs    <named list [5]>
    #>  3 Elephantidae <named list [5]>
    #>  4 Equidae      <named list [5]>
    #>  5 Feline       <named list [5]>
    #>  6 Macropodidae <named list [5]>
    #>  7 Primate      <named list [5]>
    #>  8 Rodent       <named list [5]>
    #>  9 Ruminant     <named list [5]>
    #> 10 Sus          <named list [5]>
    #> 11 Talpidae     <named list [5]>
    #>
    #> $log_msr
    #> # A tibble: 11 × 2
    #>    class        .vals
    #>    <chr>        <list>
    #>  1 Canine       <named list [5]>
    #>  2 Dinosaurs    <named list [5]>
    #>  3 Elephantidae <named list [5]>
    #>  4 Equidae      <named list [5]>
    #>  5 Feline       <named list [5]>
    #>  6 Macropodidae <named list [5]>
    #>  7 Primate      <named list [5]>
    #>  8 Rodent       <named list [5]>
    #>  9 Ruminant     <named list [5]>
    #> 10 Sus          <named list [5]>
    #> 11 Talpidae     <named list [5]>

As one can see, the output format differs in situation of grouping. We still end up with a list with an element for each matrix, but each of these element is now a `tibble`.

Each tibble has a column called `.vals`, where the function results are stored. This column is a list, one element per group. The group labels are given by the other columns of the tibble. For a given group, things are like the ungrouped version: further sub-lists for rows/columns - if applicable - and function values.

### Simplified Results

Similar to the `apply()` function that has a `simplify` argument, the output structured can be simplified, baring two conditions:

- Each function returns a vector, where a vector is every object for which `is.vector` returns `TRUE`.
- Each vector must be of the same length \(\geq\) 1.

If the conditions are met, each `apply_*` function has two simplified version available: `_dfl` and `dfw`.

Below is the `_dfl` flavor in action. We point out two things to notice:

- For `apply_column_dfl` (and `_dfw`), a `.column` column stores the column ID (`.row` for `apply_row_*`).
- We wrapped the `lm` result in a `list` so that the outcome is vector.

    animals_ms %>%
        apply_matrix_dfl(mean(.m, trim=.1),
                         MAD=mad,
                         reg = ~ {
                             is_alive <- !is_extinct
                             list(lm(.m ~ is_alive + class))
                         })
    #> $msr
    #> # A tibble: 1 × 3
    #>   `mean(.m, trim = 0.1)`   MAD reg
    #>                    <dbl> <dbl> <list>
    #> 1                   335.  155. <mlm>
    #>
    #> $log_msr
    #> # A tibble: 1 × 3
    #>   `mean(.m, trim = 0.1)`   MAD reg
    #>                    <dbl> <dbl> <list>
    #> 1                   4.18  2.35 <mlm>

    animals_ms %>%
        apply_column_dfl(mean(.j, trim=.1),
                         MAD=mad,
                         reg = ~ {
                             is_alive <- !is_extinct
                             list(lm(.j ~ is_alive + class))
                         })
    #> $msr
    #> # A tibble: 2 × 4
    #>   .colname `mean(.j, trim = 0.1)`   MAD reg
    #>   <chr>                     <dbl> <dbl> <list>
    #> 1 body                       879.  79.5 <lm>
    #> 2 brain                      240. 193.  <lm>
    #>
    #> $log_msr
    #> # A tibble: 2 × 4
    #>   .colname `mean(.j, trim = 0.1)`   MAD reg
    #>   <chr>                     <dbl> <dbl> <list>
    #> 1 body                       3.78  3.38 <lm>
    #> 2 brain                      4.49  1.71 <lm>

If using `apply_column_dfw` in this context, you wouldn’t notice a difference in output format.

The difference between the two lies when the vectors are of length > 1.

    animals_ms %>%
        apply_row_dfl(rg = range(.i),
                      qt = quantile(.i, probs = c(.25, .75)))
    #> $msr
    #> # A tibble: 56 × 5
    #>    .rowname        rg.name     rg qt.name     qt
    #>    <chr>           <chr>    <dbl> <chr>    <dbl>
    #>  1 Mountain beaver ..1       1.35 25%       3.04
    #>  2 Mountain beaver ..2       8.1  75%       6.41
    #>  3 Cow             ..1     423    25%     434.
    #>  4 Cow             ..2     465    75%     454.
    #>  5 Grey wolf       ..1      36.3  25%      57.1
    #>  6 Grey wolf       ..2     120.   75%      98.7
    #>  7 Goat            ..1      27.7  25%      49.5
    #>  8 Goat            ..2     115    75%      93.2
    #>  9 Guinea pig      ..1       1.04 25%       2.16
    #> 10 Guinea pig      ..2       5.5  75%       4.38
    #> # ℹ 46 more rows
    #>
    #> $log_msr
    #> # A tibble: 56 × 5
    #>    .rowname        rg.name     rg qt.name    qt
    #>    <chr>           <chr>    <dbl> <chr>   <dbl>
    #>  1 Mountain beaver ..1     0.300  25%     0.748
    #>  2 Mountain beaver ..2     2.09   75%     1.64
    #>  3 Cow             ..1     6.05   25%     6.07
    #>  4 Cow             ..2     6.14   75%     6.12
    #>  5 Grey wolf       ..1     3.59   25%     3.89
    #>  6 Grey wolf       ..2     4.78   75%     4.49
    #>  7 Goat            ..1     3.32   25%     3.68
    #>  8 Goat            ..2     4.74   75%     4.39
    #>  9 Guinea pig      ..1     0.0392 25%     0.456
    #> 10 Guinea pig      ..2     1.70   75%     1.29
    #> # ℹ 46 more rows

    animals_ms %>%
        apply_row_dfw(rg = range(.i),
                      qt = quantile(.i, probs = c(.25, .75)))
    #> $msr
    #> # A tibble: 28 × 5
    #>    .rowname        `rg ..1` `rg ..2` `qt 25%` `qt 75%`
    #>    <chr>              <dbl>    <dbl>    <dbl>    <dbl>
    #>  1 Mountain beaver     1.35      8.1     3.04     6.41
    #>  2 Cow               423       465     434.     454.
    #>  3 Grey wolf          36.3     120.     57.1     98.7
    #>  4 Goat               27.7     115      49.5     93.2
    #>  5 Guinea pig          1.04      5.5     2.16     4.38
    #>  6 Dipliodocus        50     11700    2962.    8788.
    #>  7 Asian elephant   2547      4603    3061     4089
    #>  8 Donkey            187.      419     245.     361.
    #>  9 Horse             521       655     554.     622.
    #> 10 Potar monkey       10       115      36.2     88.8
    #> # ℹ 18 more rows
    #>
    #> $log_msr
    #> # A tibble: 28 × 5
    #>    .rowname        `rg ..1` `rg ..2` `qt 25%` `qt 75%`
    #>    <chr>              <dbl>    <dbl>    <dbl>    <dbl>
    #>  1 Mountain beaver   0.300      2.09    0.748     1.64
    #>  2 Cow               6.05       6.14    6.07      6.12
    #>  3 Grey wolf         3.59       4.78    3.89      4.49
    #>  4 Goat              3.32       4.74    3.68      4.39
    #>  5 Guinea pig        0.0392     1.70    0.456     1.29
    #>  6 Dipliodocus       3.91       9.37    5.28      8.00
    #>  7 Asian elephant    7.84       8.43    7.99      8.29
    #>  8 Donkey            5.23       6.04    5.43      5.84
    #>  9 Horse             6.26       6.48    6.31      6.43
    #> 10 Potar monkey      2.30       4.74    2.91      4.13
    #> # ℹ 18 more rows

We can observe three things:

1. dfl stands for long and stacks the elements of the function output into different rows, adding a column to identify the different elements.
2. dfw stands for wide and put the elements of the function output into different columns.
3. Element names are made unique if necessary.

### Knowing the current context

It may happen that you need to get information about the current group. For this reason, the following context functions are made available:

- `current_n_row()` and `current_n_column()`. They each give the number of rows and columns, respectively, of the current matrix.

  They are the context equivalent of `nrow()` and `ncol()`.

- `current_row_info()` and `current_column_info()`. They give access to the current row/column annotation data frame. The are the context equivlent of `row_info()` and `column_info()`.

- `row_pos()` and `column_pos()`. They give the current row/column indices. The indices are the the ones before matrix subsetting.

- `row_rel_pos()` and `column_rel_pos()`. They give the row/column indices relative to the current matrix. They are equivalent to `seq_len(current_n_row())`/`seq_len(current_n_column())`.

For instance, a simple way of knowing the number of animals per group could be

    animals_ms %>%
        row_group_by(class) %>%
        apply_matrix_dfl(n=current_n_row()) %>%
        .$msr
    #> # A tibble: 11 × 2
    #>    class            n
    #>    <chr>        <int>
    #>  1 Canine           1
    #>  2 Dinosaurs        3
    #>  3 Elephantidae     2
    #>  4 Equidae          2
    #>  5 Feline           2
    #>  6 Macropodidae     1
    #>  7 Primate          5
    #>  8 Rodent           6
    #>  9 Ruminant         4
    #> 10 Sus              1
    #> 11 Talpidae         1

### With common row and column annotation trait

The context functions can also be of use when one or more traits are shared (in name) between rows and columns.

Here’s a pseudo-code example:

    # ms_object %>%
    #     apply_matrix( ~ {
    #       ctrt <- current_column_info()$common_trait
    #       rtrt <- current_row_info()$common_trait
    #
    #       do something with ctrt and rtrt
    #     })

### Pronouns, or dealing with ambiguous variables

It may happen that a variable in the calling environment shares its name with a trait of a `matrixset` object.

You can make it explicit which version of the variable you are using the pronouns `.data` (the trait annotation version) and `.env`.

## Quasi quotation

    reg_expr <- expr({
        is_alive <- !is_extinct
        list(lm(.j ~ is_alive + class))
    })

    animals_ms %>%
        apply_column_dfl(mean(.j, trim=.1),
                         MAD=mad,
                         reg = ~ !!reg_expr)
    #> $msr
    #> # A tibble: 2 × 4
    #>   .colname `mean(.j, trim = 0.1)`   MAD reg
    #>   <chr>                     <dbl> <dbl> <list>
    #> 1 body                       879.  79.5 <lm>
    #> 2 brain                      240. 193.  <lm>
    #>
    #> $log_msr
    #> # A tibble: 2 × 4
    #>   .colname `mean(.j, trim = 0.1)`   MAD reg
    #>   <chr>                     <dbl> <dbl> <list>
    #> 1 body                       3.78  3.38 <lm>
    #> 2 brain                      4.49  1.71 <lm>

## Multivariate

# mutate_matrix