---
title: "About Vector Arguments"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{About Vector Arguments}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

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

```{r setup, include = FALSE}
library(dplyr)
library(matsbyname)
library(tibble)
```

## Introduction

The `*apply_byname()` family of functions are used internally by many functions in `matsbyname`.
These functions
(`unaryapply_byname()`, `binaryapply_byname()`, `naryapply_byname()`)
allow additional arguments, besides the matrices that are being transformed, 
which are passed via `.FUNdots`.
Getting `.FUNdots` right can be challenging, and 
this vignette provides some background and explanation
to those challenges.
After reading this vignette, 
both callers of these functions and programmers who use these functions
will be in a better position 
to take advantage 
of the various `*apply_byname()` functions.


## An example

To see how the `.FUNdots` argument works, 
let's make an example function that takes advantage of `unaryapply_byname()`.
`mysum()` adds entries in matrix `a`, 
the result depending upon the value of `margin`. 

```{r}
mysum <- function(a, margin = c(1, 2)) {
  sum_func <- function(a_mat, margin) {
    # When we get here, we will have a single matrix a
    if (1 %in% margin & 2 %in% margin) {
      return(sum(a_mat))
    }
    if (margin == 1) {
      return(rowSums(a_mat) %>% matrix(nrow = nrow(a_mat)))
    }
    if (margin == 2) {
      return(colSums(a_mat) %>% matrix(ncol = ncol(a_mat)))
    }
  }
  unaryapply_byname(sum_func, a, .FUNdots = list(margin = margin))
}
```

Structuring `mysum()` as shown above provides several interesting capabilities.
First, `mysum()` works with single matrices.

```{r}
m <- matrix(1:4, nrow = 2, byrow = TRUE)
m
# Works for single matrices
mysum(m, margin = 1)
mysum(m, margin = 2)
mysum(m, margin = c(1, 2))
```

Second, `mysum()` works with lists.

```{r}
# Works for lists of matrices
mysum(list(one = m, two = m), margin = 1)
mysum(list(one = m, two = m), margin = 2)
```

Finally, `mysum()` works within data frames.

```{r}
# Works in data frames and tibbles
DF <- tibble::tibble(mcol = list(m, m, m))
res <- DF %>% 
  dplyr::mutate(
    rsums = mysum(mcol, margin = 1), 
    csums = mysum(mcol, margin = 2)
  )
res$rsums
res$csums
```


## The problem

In the above examples, `margin` was only `1` or `2`, not `c(1, 2)` for the list and data frame examples.
Let's see what happens when `margin = c(1, 2)` and `a` is a list.

```{r}
tryCatch(mysum(list(m, m, m), margin = c(1, 2)), 
         error = function(e) {strwrap(e, width = 60)})
```

To understand better what is happening, let's try when the list argument to `mysum()` has length `2`.

```{r}
mysum(list(m, m), margin = c(1, 2))
```

`margin = c(1, 2)` is interpreted by `unaryapply_byname()` as 
"use `margin = 1` for the first `m` in the list, and
use `margin = 2` for the second `m` in the list.

Now we see why passing `margin = c(1, 2)` failed for a list of length `3` (`list(m, m, m)`):
`unaryapply_byname()` applied `margin = 1` for the first `m`, `margin = 2` for the second `m`.
But the third `m` had no margin available for it.

We also see why passing `margin = c(1, 2)` was successful for a list of length `2` (`list(m, m)`):
`unaryapply_byname()` applied `margin = 1` for the first `m`, `margin = 2` for the second `m`.
In that case, we had exactly as many items in margin (2) as items in the list passed to `a` (2).

Now that we understand the problem, how do we fix it?
In other words, how can we apply `margin = c(1, 2)` to all entries in `list(m, m, m)`?
Or, better yet, how could we apply 
`margin = 1` to the first `m`, 
`margin = 2` to the second `m`, and
`margin = c(1, 2)` to the third `m`?


## The fix

Fixes to the problem identified above can be provided by either the caller or (partially) by the programmer
in three ways:

* wrap vector arguments in a list (a caller fix), 
* use the `prep_vector_arg()` function (a programmer fix), and 
* use a data frame (a caller fix).


### Wrap vector arguments in a list

If the caller is more specific, flexibility is gained.
By wrapping `c(1, 2)` in a `list()`, the caller indicates 
"Take this margin (`c(1, 2)`), 
replicate it as many times as we have items in our `a` list, 
using one `c(1, 2)` for each item in the list."

```{r}
mysum(list(m, m, m), margin = list(c(1, 2)))
```

The caller can also supply different `margin`s for each item in the list of matrices.

```{r}
mysum(list(m, m, m), margin = list(1, 2, c(1, 2)))
```

But the caller must provide either `1` or `length(a)` items in the `margin` argument, 
else an error is emitted.

```{r}
tryCatch(mysum(list(m, m, m), margin = list(1, 2)), 
         error = function(e) {strwrap(e, width = 60)})
```

### Use the `prep_vector_arg()` function

To the extent possible, programmers should remove burdens on users of their functions.
So, it would be helpful if there were a way to automatically wrap vector arguments in lists.
To that end, `matsbyname` includes the `prep_vector_arg()` function.
`prep_vector_arg()` uses heuristics to wrap vector arguments in lists, 
if needed and when possible.

`mysum2()` demonstrates the use of `prep_vector_arg()`.

```{r}
mysum2 <- function(a, margin = c(1, 2)) {
  margin <- prep_vector_arg(a, margin)
  sum_func <- function(a_mat, margin) {
    # When we get here, we will have a single matrix a
    if (1 %in% margin & 2 %in% margin) {
      return(sum(a_mat))
    }
    if (margin == 1) {
      return(rowSums(a_mat) %>% matrix(nrow = nrow(a_mat)))
    }
    if (margin == 2) {
      return(colSums(a_mat) %>% matrix(ncol = ncol(a_mat)))
    }
  }
  unaryapply_byname(sum_func, a, .FUNdots = list(margin = margin))
}
```

If 

* argument `a` is a list, 
* the vector argument (in this case `margin`) is not a list, and
* the vector argument's length is greater than 1 but not equal to the length of a,

then `prep_vector_arg()` wraps the vector argument (in this case `margin`)
in a `list()`, thereby relieving the caller of having to remember to 
make it into a `list`.

```{r}
mysum2(list(m, m, m), margin = c(1, 2))
```

Note that if the length of the vector argument is equal to the length of the list in `a`,
the caller's intention is ambiguous, and 
the vector argument is passed without modification.

```{r}
mysum2(list(m, m), margin = c(1, 2))
```

If the caller wants `c(1, 2)` to be applied to each item in the `a` list,
the caller must wrap `c(1, 2)` in a list.

```{r}
mysum2(list(m, m), margin = list(c(1, 2)))
```


### Use a data frame

The reason `prep_vector_arg()` cannot *always* wrap vector arguments in a list
is that data frame columns are extracted as vectors when they are atomic.

```{r}
DF2 <- tibble::tibble(mcol = list(m, m), margin = c(1, 2))
DF2
DF2$margin %>% class()
```

It would be a mistake to wrap `DF2$margin` in a `list()` 
for the following call to `mysum2`, because
the caller's intent is clearly 
"apply `margin = 1` for the first row and 
`margin = 2` for the second row.

```{r}
res2 <- DF2 %>% 
  dplyr::mutate(
    sums = mysum2(mcol, margin = margin)
  )
res2$sums
```

The good news is that within the context of a data frame, the caller's intent is unambiguous.

```{r}
DF3 <- tibble::tibble(mcol = list(m, m, m), margin = list(1, c(1, 2), c(1, 2))) %>% 
  dplyr::mutate(
    sumcol = mysum2(mcol, margin = margin)
  )
DF3$sumcol
```

## Summary

Dealing with vector arguments to the various `*apply_byname()` functions can be tricky.
But there are three ways to solve any problems that arise:

* wrap vector arguments in a list (a caller fix), 
* use the `prep_vector_arg()` function (a programmer fix), and 
* use a data frame (a caller fix).

This vignette illustrated all three fixes.

