# Frequently Asked Questions

## What is the algebraic structure of AlgebraOfGraphics?

AlgebraOfGraphics is based on two operators, `+`

and `*`

. These two operators induce a semiring structure, with a small caveat. Addition is commutative only up to the drawing order. For example, `visual(Lines) + visual(Scatter)`

is slightly different from `visual(Scatter) + visual(Lines)`

, in that the former draws the scatter on top of the lines, and the latter draws the lines on top of the scatter. As a consequence, only right distributivity holds with full generality, whereas left distributivity only holds up to the drawing order.

## Why is the mapping pair syntax different from DataFrames?

The transformations passed within a mapping, e.g. `mapping(:x => log => "log(x)")`

, are applied element-wise. Operations that require the whole column are not supported on purpose. An important reason to prefer element-wise operations (other than performance) is that whole-column operations can be error prone in this setting, especially when

- the data is grouped or
- different datasets are used.

If you do need column-wise transformations, consider implementing a custom analysis, such as `density`

, which takes the whole data as input, or apply the transformation directly in your data before passing it to AlgebraOfGraphics.

See also Pair syntax for a detailed description of the pair syntax within a `mapping`

.

## What is the difference between axis scales and data transformations?

There are two overlapping but distinct ways to rescale data.

- Keep the data as is and use a nonlinear scale, e.g.
`axis=(xscale=log,)`

. - Transform the data directly, e.g.
`mapping(:x => log => "log(x)")`

.

Note that the resulting plots may "look different" in some cases. Consider for instance the following example.

```
using AlgebraOfGraphics
using AlgebraOfGraphics: density
df = (x = exp.(randn(1000)),)
kde1 = data(df) * mapping(:x) * density()
draw(kde1, axis=(width=225, height=225, xscale=log,))
```

```
df = (x = exp.(randn(1000)),)
kde2 = data(df) * mapping(:x => log => "log(x)") * density()
draw(kde2, axis=(width=225, height=225))
```

The two plots look different. The first represents the pdf of `x`

in a log scale, while the second represents the pdf of `log(x)`

in a linear scale. The two curves differ by a factor `1 / x`

, the derivative of `log(x)`

. See e.g. this post for some mathematical background on the topic.

In general, the second approach (plotting the density of `log(x)`

) could be considered more principled, as it preserves the proportionality between area and probability mass. On the contrary, the first approach (plotting the density of `x`

in a log scale) breaks this proportionality relationship.

A similar reasoning applies to histograms:

```
using AlgebraOfGraphics
df = (x = exp.(rand(1000)),)
hist1 = data(df) * mapping(:x) * histogram()
draw(hist1, axis=(width=225, height=225, xscale=log))
```

```
df = (x = exp.(rand(1000)),)
hist2 = data(df) * mapping(:x => log => "log(x)") * histogram()
draw(hist2, axis=(width=225, height=225))
```

The data transformation approach is preferable as it produces uniform bins, which are easier to interpret.

## How to combine `AlgebraOfGraphics`

with plain `Makie`

plots?

Since `AlgebraOfGraphics`

is built upon the `Makie`

ecosystem we can easily combine plots from both packages. Two approaches can be taken. Firstly, by using `draw!`

you can pass a `Figure`

or `FigurePosition`

created by `Makie`

to be used by `AlgebraOfGraphics`

, e.g.

```
f, a, p = lines(0..2pi, sin; figure = (resolution = (600, 400),))
df = (x = exp.(rand(1000)),)
hist1 = data(df) * mapping(:x => log => "log(x)") * histogram()
draw!(f[1, 2], hist1)
```

Alternatively, we can create the `AlgebraOfGraphics`

figure first and then add in additional plain `Makie`

axes alongside the result by accessing the `.figure`

field of `fg`

, e.g.

```
df = (x = exp.(rand(1000)),)
hist2 = data(df) * mapping(:x => log => "log(x)") * histogram()
fg = draw(hist2; figure = (resolution = (600, 400),))
lines(fg.figure[1, 2], 0..2pi, cos)
```

When setting the `width`

and `height`

dimensions of each axis manually you will need to call `AlgebraOfGraphics.resizetocontent!(fg)`

before displaying the figure such that each axis is sized correctly.