2.1 Graphing Tutorial ¶
In (plotutils graph), there is one monolithic graphing function
called graph with dozens of options. We’ll demonstrate a couple
of them in this tutorial.
2.1.1 Graphing Functions ¶
First let’s explore how to graph mathematical functions. Let’s say you have a mathematical function to plot such as “sin(x)”. This example script calls graph with three arguments.
- A procedure of one numerical argument that returns a numerical value
- The start of the X range
- The end of the X range
;;; graph-sine-wave.scm — Sine function over one full period
;;; y = sin(x), sampled densely on [0, 2π].
;;; This is the canonical periodic waveform used in trigonometry,
;;; signal processing, and Fourier analysis.
(use-modules (srfi srfi-1)
(plotutils graph))
(define pi (* 4.0 (atan 1.0)))
(define (output-format-from-filename path)
(let loop ((i (- (string-length path) 1)))
(cond
((< i 0) "svg")
((char=? (string-ref path i) #\.)
(let ((ext (string-downcase (substring path (+ i 1) (string-length path)))))
(if (string=? ext "eps") "ps" ext)))
(else (loop (- i 1))))))
(define (main args)
(let* ((output-file (if (> (length args) 1) (cadr args) "graph-sine-wave.svg"))
(output-format (output-format-from-filename output-file))
(n 600)
(xmin 0.0)
(xmax (* 2.0 pi))
(step (/ (- xmax xmin) n))
(xs (iota n xmin step))
(ys (map sin xs)))
(with-output-to-file output-file
(lambda ()
(graph xs ys
#:output-format output-format
#:bitmap-size "1000x1000"
#:top-label "Sine Wave y = sin(x)"
#:x-label "x"
#:y-label "sin(x)"
#:x-limits (list 0.0 (* 2.0 pi))
#:y-limits '(-1.2 1.2)
#:grid-style 3
#:line-width 0.004
#:font-name "HersheySerif"))
#:binary #t)))
(main (command-line))
The script samples a few hundred points of the procedure and plots the result.
You can also call graph with four arguments. In that case, the
fourth argument is the step size on the x-axis.
Here’s the same plot with just a dozen sample points
;;; graph-sine-wave2.scm — Sine function with only a dozen points
;;; y = sin(x), sampled sparsely with 12 points across [0, 2π].
;;; This illustrates how low sampling density affects the visual
;;; approximation of a smooth periodic function.
(use-modules (srfi srfi-1)
(plotutils graph))
(define pi (* 4.0 (atan 1.0)))
(define (output-format-from-filename path)
(let loop ((i (- (string-length path) 1)))
(cond
((< i 0) "svg")
((char=? (string-ref path i) #\.)
(let ((ext (string-downcase (substring path (+ i 1) (string-length path)))))
(if (string=? ext "eps") "ps" ext)))
(else (loop (- i 1))))))
(define (main args)
(let* ((output-file (if (> (length args) 1) (cadr args) "graph-sine-wave2.svg"))
(output-format (output-format-from-filename output-file))
(n 12)
(xmin 0.0)
(xmax (* 2.0 pi))
(step (/ (- xmax xmin) (- n 1)))
(xs (iota n xmin step))
(ys (map sin xs)))
(with-output-to-file output-file
(lambda ()
(graph xs ys
#:output-format output-format
#:bitmap-size "1000x1000"
#:top-label "Sine Wave y = sin(x) (12 points)"
#:x-label "x"
#:y-label "sin(x)"
#:x-limits (list 0.0 (* 2.0 pi))
#:y-limits '(-1.2 1.2)
#:grid-style 3
#:line-width 0.004
#:symbol '(4 0.03)
#:font-name "HersheySerif"))
#:binary #t)))
(main (command-line))
2.1.2 Graphing Data ¶
In the previous section, we explored how to call graph when
the first argument was a function.
In this section we’ll be calling graph using lists of data. When
using data, you either call graph with a single list of data, or
create an xy plot using two lists of data.
(define x (list -1 0 1 2 3 4 5)) (define y (list 1 2 1 2 1 2 1)) ;; Plot the y data with an automatic abscissa (graph y) ;; Plot the x,y pairs (graph x y)
You can also plot multiple graphs on the same axes using the merge
helper procedure.
(define x1 (list -1 0 1 2 3 4 5)) (define y2 (list 1 2 1 2 1 2 1)) (define x2 (list -1 0 1 2 3 4 5)) (define y2 (list 8 7 6 5 4 3 3)) (graph (merge x1 x2) (merge y1 y2))