Function curves: geom_function

Mix.install([
  {:giggly, path: Path.join(__DIR__, "..")},
  {:kino, "~> 0.19"}
  ])

About this notebook

This notebook follows the examples on ggplot2's reference page for geom_function(), which covers stat_function() too, in the order the page gives them. Each example shows ggplot2's code first and then Giggly's. An example Giggly cannot draw yet keeps its ggplot2 code and names what it is waiting for, so the page is also a list of what remains.

geom_function() draws a function of x as a curve. Its stat, stat_function(), calls the function at evenly spaced values across the x axis, and the results are joined with a line, or drawn with another geom. That makes it easy to lay a curve over a plot of data, such as a distribution's density over the data's own. Giggly has neither yet, nor the line a curve is drawn with.

A curve over data

# geom_function() is useful for overlaying functions
set.seed(1492)
ggplot(data.frame(x = rnorm(100)), aes(x)) +
  geom_density() +
  geom_function(fun = dnorm, colour = "red")

R draws the data at random from the standard normal distribution, and the curve is that distribution's density, dnorm.

Not in Giggly yet: geom_function().

A function without data

# To plot functions without data, specify range of x-axis
base <-
  ggplot() +
  xlim(-5, 5)

base + geom_function(fun = dnorm)

With no data to train the x scale, xlim() gives it the range to draw the function over.

Not in Giggly yet: a plot with no data and geom_function().

Passing arguments to the function

base + geom_function(fun = dnorm, args = list(mean = 2, sd = .5))

Not in Giggly yet: a plot with no data, and geom_function() and its args option.

The points behind the curve

# The underlying mechanics evaluate the function at discrete points
# and connect the points with lines
base + stat_function(fun = dnorm, geom = "point")

base + stat_function(fun = dnorm, geom = "point", n = 20)

n is the number of points the function is evaluated at; ggplot2 takes 101 unless told otherwise.

Not in Giggly yet: a plot with no data, and stat_function() and its geom and n options.

A filled curve

base + stat_function(fun = dnorm, geom = "polygon", color = "blue", fill = "blue", alpha = 0.5)

Not in Giggly yet: a plot with no data, stat_function() and its geom option, and geom_polygon().

Fewer points on the line

base + geom_function(fun = dnorm, n = 20)

Not in Giggly yet: a plot with no data, and geom_function() and its n option.

Two functions on one plot

# Two functions on the same plot
base +
  geom_function(aes(colour = "normal"), fun = dnorm) +
  geom_function(aes(colour = "t, df = 1"), fun = dt, args = list(df = 1))

Each layer maps colour to a constant, so the legend names each curve.

Not in Giggly yet: a plot with no data, and geom_function() and its args option.

A function of your own

# Using a custom anonymous function
base + geom_function(fun = \(x) 0.5 * exp(-abs(x)))
# or using lambda syntax:
# base + geom_function(fun = ~ 0.5 * exp(-abs(.x)))
# or using a custom named function:
# f <- function(x) 0.5 * exp(-abs(x))
# base + geom_function(fun = f)

The commented lines are two other ways R writes the same function.

Not in Giggly yet: a plot with no data and geom_function().

The function's own range

# Using xlim to restrict the range of function
ggplot(data.frame(x = rnorm(100)), aes(x)) +
geom_density() +
geom_function(fun = dnorm, colour = "red", xlim=c(-1, 1))

# Using xlim to widen the range of function
ggplot(data.frame(x = rnorm(100)), aes(x)) +
geom_density() +
geom_function(fun = dnorm, colour = "red", xlim=c(-7, 7))

A layer's xlim sets the range the function is evaluated over, narrower or wider than the data's.

Not in Giggly yet: geom_function() and its xlim option.