2 Plotting

(require plot)

The plot library provides the ability to make basic plots, fit curves to data, and some useful miscellaneous functions.

2.1 Plotting

The plot and plot3d functions generate plots that can be viewed in the DrScheme interactions window.

(plot   data            [ #:width width             #:height height             #:x-min x-min             #:x-max x-max             #:y-min y-min             #:y-max y-max             #:x-label x-label             #:y-label y-label             #:title title             #:fgcolor fgcolor             #:bgcolor bgcolor             #:lncolor lncolor])   →   (is-a?/c snip%)

data : ((is-a?/c 2d-view%) . -> . void?)

width : real? = 400

height : real? = 400

x-min : real? = -5

x-max : real? = 5

y-min : real? = -5

y-max : real? = 5

x-label : string? = "X axis"

y-label : string? = "Y axis"

title : string? = ""

fgcolor : (list/c byte? byte? byte) = '(0 0 0)

bgcolor : (list/c byte? byte? byte) = '(255 255 255)

lncolor : (list/c byte? byte? byte) = '(255 0 0)

Plots data in 2-D, where data is generated by functions like points or lines.

A data value is represented as a procedure that takes a 2d-view% instance and adds plot information to it.

(plot3d   data            [ #:width width             #:height height             #:x-min x-min             #:x-max x-max             #:y-min y-min             #:y-max y-max             #:z-min z-min             #:z-max z-max             #:alt alt             #:az az             #:x-label x-label             #:y-label y-label             #:z-label z-label             #:title title             #:fgcolor fgcolor             #:bgcolor bgcolor             #:lncolor lncolor])   →   (is-a?/c snip%)

data : ((is-a?/c 3d-view%) . -> . void?)

width : real? = 400

height : real? = 400

x-min : real? = -5

x-max : real? = 5

y-min : real? = -5

y-max : real? = 5

z-min : real? = -5

z-max : real? = 5

alt : real? = 30

az : real? = 45

x-label : string? = "X axis"

y-label : string? = "Y axis"

z-label : string? = "Z axis"

title : string? = ""

fgcolor : (list/c byte? byte? byte) = '(0 0 0)

bgcolor : (list/c byte? byte? byte) = '(255 255 255)

lncolor : (list/c byte? byte? byte) = '(255 0 0)

Plots data in 3-D, where data is generated by a function like surface. The arguments alt and az set the viewing altitude (in degrees) and the azimuth (also in degrees), respectively.

A 3-D data value is represented as a procedure that takes a 3d-view% instance and adds plot information to it.

(points vecs [#:sym sym #:color color])

→ ((is-a?/c 2d-view%) . -> . void?)

vecs : (listof (vector/c real? real?))

sym : (one-of/c 'square 'circle 'odot 'bullet) = 'square

color : plot-color? = 'black

Creates 2-D plot data (to be provided to plot) given a list of points specifying locations. The sym argument determines the appearance of the points.

(line   f            [ #:samples samples             #:width width             #:color color             #:mode mode             #:mapping mapping             #:t-min t-min             #:t-max t-min])   →   ((is-a?/c 2d-view%) . -> . void?)

f : (real? . -> . (or/c real? (vector real? real?)))

samples : exact-nonnegative-integer? = 150

width : exact-positive-integer? = 1

color : plot-color? = 'red

mode : (one-of/c 'standard 'parametric) = 'standard

mapping : (or-of/c 'cartesian 'polar) = 'cartesian

t-min : real? = -5

t-min : real? = 5

Creates 2-D plot data to draw a line.

The line is specified in either functional, i.e. y = f(x), or parametric, i.e. x,y = f(t), mode. If the function is parametric, the mode argument must be set to 'parametric. The t-min and t-max arguments set the parameter when in parametric mode.

(error-bars vecs [#:color color])

→ ((is-a?/c 2d-view%) . -> . void?)

vecs : (listof (vector/c real? real? real?))

color : plot-color? = 'black

Creates 2-D plot data for error bars given a list of vectors. Each vector specifies the center of the error bar (x,y) as the first two elements and its magnitude as the third.

(vector-field   f      [ #:width width       #:color color       #:style style])

→ ((is-a?/c 2d-view%) . -> . void?)

f : ((vector real? real?) . -> . (vector real? real?))

width : exact-positive-integer? = 1

color : plot-color? = 'red

style : (one-of/c 'scaled 'normalized 'read) = 'scaled

Creates 2-D plot data to draw a vector-field from a vector-valued function.

(contour   f            [ #:samples samples             #:width width             #:color color             #:levels levels])   →   ((is-a?/c 2d-view%) . -> . void?)

f : (real? real? . -> . real?)

samples : exact-nonnegative-integer? = 50

width : exact-positive-integer? = 1

color : plot-color? = 'black

levels   :   (or/c exact-nonnegative-integer?       (listof real?))   =   10

Creates 2-D plot data to draw contour lines, rendering a 3-D function a 2-D graph cotours (respectively) to represent the value of the function at that position.

(shade f [#:samples samples #:levels levels])

→ ((is-a?/c 2d-view%) . -> . void?)

f : (real? real? . -> . real?)

samples : exact-nonnegative-integer? = 50

levels   :   (or/c exact-nonnegative-integer?       (listof real?))   =   10

Creates 2-D plot data to draw like contour, except using shading instead of contour lines.

(surface   f            [ #:samples samples             #:width width             #:color color])   →   ((is-a?/c 3d-view%) . -> . void?)

f : (real? real? . -> . real?)

samples : exact-nonnegative-integer? = 50

width : exact-positive-integer? = 1

color : plot-color? = 'black

Creates 3-D plot data to draw a 3-D surface in a 2-D box, showing only the top of the surface.

(mix data ...+) → (any/c . -> . void?)

data : (any/c . -> . void?)

Creates a procedure that calls each data on its argument in order. Thus, this function can composes multiple plot datas into a single data.

(plot-color? v) → boolean?

v : any/c

Returns #t if v is one of the following symbols, #f otherwise:

'white 'black 'yellow 'green 'aqua 'pink

'wheat 'grey 'blown 'blue 'violet 'cyan

'turquoise 'magenta 'salmon 'red

2.2 Curve Fitting

PLoT uses the standard Non-Linear Least Squares fit algorithm for curve fitting. The code that implements the algorithm is public domain, and is used by the gnuplot package.

(fit f guess-list data) → fit-result?

f : (real? ... . -> . real?)

guess-list : (list/c (cons symbol? real?))

data   :   (or/c (list-of (vector/c real? real? real?))       (list-of (vector/c real? real? real? real?)))

Attempts to fit a fittable function to the data that is given. The guess-list should be a set of arguments and values. The more accurate your initial guesses are, the more likely the fit is to succeed; if there are no good values for the guesses, leave them as 1.

(struct   fit-result  ( rms         variance         names         final-params         std-error         std-error-percent         function))

rms : real?

variance : real?

names : (listof symbol?)

final-params : (listof real?)

std-error : (listof real?)

std-error-percent : (listof real?)

function : (real? ... . -> . real?)

The params field contains an associative list of the parameters specified in fit and their values. Note that the values may not be correct if the fit failed to converge. For a visual test, use the function field to get the function with the parameters in place and plot it along with the original data.

2.3 Miscellaneous Functions

(derivative f [h]) → (real? . -> . real?)

f : (real? . -> . real?)

h : real? = 1e-06

Creates a function that evaluates the numeric derivative of f. The given h is the divisor used in the calculation.

(gradient f [h])

→ ((vector/c real? real?) . -> . (vector/c real? real?))

f : (real? real? . -> . real?)

h : real? = 1e-06

Creates a vector-valued function that the numeric gradient of f.

(make-vec fx fy)

→ ((vector/c real? real?) . -> . (vector/c real? real?))

fx : (real? real? . -> . real?)

fy : (real? real? . -> . real?)

Creates a vector-values function from two parts.