PLoT collection: Quick Start

[Note: This guide is excerpted from the official documentation available
 from Help Desk.]

2.1  Making basic plots

   After loading the correct module using (require (lib "plot.ss"
   "plot")) try (plot (line (lambda (x) x)))

   Any other function with the contract number -> number can be plotted
   using the same form. To plot multiple items, use the functions mix and
   mix* to combine the items to be plotted

(plot
 (mix
  (line (lambda (x) (sin x)))
  (line (lambda (x) (cos x)))))

   The display area and appearance of the plot can be changed by adding
   parenthesized argument/value pairs after the first argument

(plot
 (line (lambda (x) (sin x)))
 (x-min -1) (x-max 1) (title "Sin(x)"))

   The appearance of each individual plot item can be altered by adding
   parameter-value pairs after the data.

(plot
 (line
  (lambda (x) x)
  (color 'green) (width 3)))

   Besides plotting lines from functions in 2d, the plotter can also
   render a variety of other datums in several ways:
     * Discreet data, such as

(define data
 (list
  (vector 1 1 2)
  (vector 2 2 2)))
       can be interpreted in several ways
          + As points: (plot (points data))
          + As Error Data: (plot (error-bars data))
     * A function of two variables, such as
(define 3dfun (lambda (x y) (* (sin x) (sin y))))
       can be plotted on a 2d graph
          + Using contours to represent height (z)
(plot (contour 3dfun))
          + Using color shading
(plot (shade 3dfun))
          + Using a gradient field
(plot (field (gradient 3dfun)))
       or in a 3d box
          + Displaying only the top of the surface
(plot3d (surface 3dfun))

[8]2.2  Curve Fitting

   The scheme-plot library uses a Non-Linear Least Squares fit algorithm
   to fit parametrized functions to given data.

   To fit a particular function to a curve:
    1. Set up the independent and dependent variable data. The first item
       in each vector is the independent var, the second is the result.
       The last item must is the weight of the error - we can leave it as
       1 since all the items weigh the same.
(define data '(#(0 3 1)
               #(1 5 1)
               #(2 7 1)
               #(3 9 1)
               #(4 11 1)))

    2. Set up the function to be fitted using fit. This particular
       function looks like a line. The independent variables must come
       before the parameters.
(define fit-fun
 (lambda (x m b) (+ b (* m x))))
    3. If possible, come up with some guesses for the values of the
       parameters. The guesses can be left as one, but each parameter
       must be named.
    4. Do the fit - the details of the function are described in [9]Curve
       Fitting section
(define fit-result
  (fit
   fit-fun
   ((m 1) (b 1))
   data)
    5. View the resulting parameters
(fit-result-final-params fit-result) ; will produce ((m 2) (b 3))

    6. For some visual feedback of the fit result, plot the function with
       the new parameters. For convenience, the structure that is
       returned by the fit command has already created the function.
(plot (mix
        (points data)
        (line (fit-result-function fit-result)))
      (y-max 15))

   A more realistic example can be found in demos/fit-demo-2.ss

[10]2.3  Creating Custom Plots

   Defining custom plots is simple : a Plot-item (that is passed to plot
   or mix) is just a function that acts on a [11]view . Both the 2d and
   3d view snip have several drawing functions defined that the plot-item
   can call in any order. The full details of the view interface can be
   found in the [12]plot-extend.ss section.

   For example, if we wanted to create a constructor that creates
   Plot-items that draw dashed-lines given a number-number function we
   could do the following:

; Load the required modules
(require (lib "class.ss")
         (lib "etc.ss")
         (lib "plot-extend.ss" "plot"))


; Set up the constructor
(define-plot-type dashed-line
  fun 2dview (x-min x-max) ((samples 100) (segments 20) (color 'red) (width 1))
  (let* ((dash-size (/ (- x-max x-min) segments))
         (x-lists (build-list
                   (/ segments 2)
                   (lambda (index)
                     (x-values
                      (/ samples segments)
                      (+ x-min (* 2 index dash-size))
                      (+ x-min (* (add1 ( * 2 index)) dash-size)))))))
    (send* 2dview
           (set-line-color color)
           (set-line-width width))
    (for-each
     (lambda (dash)
       (send 2dview plot-line
              (map (lambda (x) (vector x (fun x))) dash)))
     x-lists)))

; Plot a test case
(plot (dashed-line (lambda (x) x) (color 'blue)))