143 lines
4.6 KiB
Plaintext
143 lines
4.6 KiB
Plaintext
PLoT collection: Quick Start
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[Note: This guide is excerpted from the official documentation available
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from Help Desk.]
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2.1 Making basic plots
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After loading the correct module using (require (lib "plot.ss"
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"plot")) try (plot (line (lambda (x) x)))
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Any other function with the contract number -> number can be plotted
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using the same form. To plot multiple items, use the functions mix and
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mix* to combine the items to be plotted
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(plot
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(mix
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(line (lambda (x) (sin x)))
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(line (lambda (x) (cos x)))))
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The display area and appearance of the plot can be changed by adding
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parenthesized argument/value pairs after the first argument
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(plot
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(line (lambda (x) (sin x)))
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(x-min -1) (x-max 1) (title "Sin(x)"))
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The appearance of each individual plot item can be altered by adding
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parameter-value pairs after the data.
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(plot
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(line
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(lambda (x) x)
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(color 'green) (width 3)))
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Besides plotting lines from functions in 2d, the plotter can also
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render a variety of other datums in several ways:
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* Discreet data, such as
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(define data
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(list
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(vector 1 1 2)
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(vector 2 2 2)))
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can be interpreted in several ways
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+ As points: (plot (points data))
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+ As Error Data: (plot (error-bars data))
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* A function of two variables, such as
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(define 3dfun (lambda (x y) (* (sin x) (sin y))))
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can be plotted on a 2d graph
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+ Using contours to represent height (z)
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(plot (contour 3dfun))
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+ Using color shading
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(plot (shade 3dfun))
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+ Using a gradient field
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(plot (field (gradient 3dfun)))
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or in a 3d box
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+ Displaying only the top of the surface
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(plot3d (surface 3dfun))
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[8]2.2 Curve Fitting
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The scheme-plot library uses a Non-Linear Least Squares fit algorithm
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to fit parametrized functions to given data.
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To fit a particular function to a curve:
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1. Set up the independent and dependent variable data. The first item
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in each vector is the independent var, the second is the result.
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The last item must is the weight of the error - we can leave it as
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1 since all the items weigh the same.
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(define data '(#(0 3 1)
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#(1 5 1)
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#(2 7 1)
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#(3 9 1)
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#(4 11 1)))
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2. Set up the function to be fitted using fit. This particular
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function looks like a line. The independent variables must come
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before the parameters.
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(define fit-fun
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(lambda (x m b) (+ b (* m x))))
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3. If possible, come up with some guesses for the values of the
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parameters. The guesses can be left as one, but each parameter
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must be named.
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4. Do the fit - the details of the function are described in [9]Curve
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Fitting section
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(define fit-result
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(fit
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fit-fun
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((m 1) (b 1))
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data)
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5. View the resulting parameters
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(fit-result-final-params fit-result) ; will produce ((m 2) (b 3))
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6. For some visual feedback of the fit result, plot the function with
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the new parameters. For convenience, the structure that is
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returned by the fit command has already created the function.
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(plot (mix
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(points data)
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(line (fit-result-function fit-result)))
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(y-max 15))
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A more realistic example can be found in demos/fit-demo-2.ss
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[10]2.3 Creating Custom Plots
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Defining custom plots is simple : a Plot-item (that is passed to plot
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or mix) is just a function that acts on a [11]view . Both the 2d and
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3d view snip have several drawing functions defined that the plot-item
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can call in any order. The full details of the view interface can be
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found in the [12]plot-extend.ss section.
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For example, if we wanted to create a constructor that creates
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Plot-items that draw dashed-lines given a number-number function we
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could do the following:
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; Load the required modules
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(require (lib "class.ss")
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(lib "etc.ss")
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(lib "plot-extend.ss" "plot"))
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; Set up the constructor
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(define-plot-type dashed-line
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fun 2dview (x-min x-max) ((samples 100) (segments 20) (color 'red) (width 1))
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(let* ((dash-size (/ (- x-max x-min) segments))
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(x-lists (build-list
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(/ segments 2)
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(lambda (index)
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(x-values
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(/ samples segments)
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(+ x-min (* 2 index dash-size))
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(+ x-min (* (add1 ( * 2 index)) dash-size)))))))
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(send* 2dview
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(set-line-color color)
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(set-line-width width))
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(for-each
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(lambda (dash)
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(send 2dview plot-line
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(map (lambda (x) (vector x (fun x))) dash)))
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x-lists)))
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; Plot a test case
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(plot (dashed-line (lambda (x) x) (color 'blue)))
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