Tricks_L-O_18.html

Options, OptionQ

OptionQ details

OptionQ isn't documented in The Mathematica Book or the Help Browser, but it's helpful when defining a function with options. OptionQ does however have the usage message shown below.

In the cells below we see OptionQ is True when it's given a Rule, a
RuleDelayed or a list of these things. You get an error message if you give
OptionQ more than one argument.

ClearAll["Global`*"] ; OptionQ[opt1True] OptionQ[opt2var2] OptionQ[{opt115, opt2Automatic, opt3False, opt4All}]

OptionQ also returns True when it's given nested lists of options.

As indicated in the usage message OptionQ returns False when it's given a
single argument with any other form. This is seen in the next cell.

OptionQ[2]  OptionQ[h[2]]  OptionQ[{Opt1All, 2}]  OptionQ[{Opt1All, h[2]}]  OptionQ[h[Opt1All]]

Typical use of OptionQ

The next cell defines a function that takes options. This function takes one required argument and optional arguments are allowed as long as they all pass OptionQ. The form (opts___?OptionQ) is perhaps the most frequent use of BlankNullSequence ( ___ ie. "Tripple Blank"). Notice this allows for a single option, a sequence of options, or no options.

$foo[expr_, opts___ ? OptionQ] := {expr, h @@ Flatten[{opts}]}$

Each usage of foo in the next cell matches the definition of foo above.

foo[x + y]  foo[x + y, opt115, opt2Automatic, opt3False] ɯ ... False}]  foo[x + y, {opt115, {opt2Automatic}}, opt3False]

The definition of foo doesn't apply to the next example because 6 isn't an
option.

Getting the setting of Options

Section  2.3.10 of The Mathematica Book suggests using the form
    name/.{opts}/.Options[f]
to get the setting of an option.  This technique is used below to get  the PlotStyle and Axes settings for a function.

ClearAll[PlotFunction, x] ; Options[PlotFunction] = {PlotStyleGrayLevel[0], Ima ... ;PlotStyle="<>ToString[style], "ImageSize="<>ToString[size]] ]

In the next cell PlotFunction performs as expected when given no options, one
option, or two options.

$PlotFunction[x^2] <br /> PlotFunction[x^2, PlotStyleThickness[0.03]] <br /> PlotFunction[x^2, PlotStyleThickness[0.03], ImageSize {xx, yy}]$

$MakeGraphic[x^2, PlotStyle=Thickness[0.03], ImageSize={xx, yy}]$

In the next cell Plot alows us to provide a list of options rather than a
sequence of options. For consistency we would like our PlotFunction to allow
us to give a list of options as well.

Unfortunately our PlotFunction defined above has a problem when a list of
option is given in the next cell.

$PlotFunction[x^2, {PlotStyleThickness[0.03], ImageSize {400, 250}}]$

The way to avoid the problem in the last exaple is to use a different method for getting the option settings. Instead the following form should normally be used to get option settings.
{var1,var2,var3}={opt1,opt2,opt3}/.Flatten[{opts,Options[f]}]
This more robust method is used in the next cell.

ClearAll[PlotFunction] ; Options[PlotFunction] = {PlotStyleGrayLevel[0], ImageS ... ;PlotStyle="<>ToString[style], "ImageSize="<>ToString[size]] ]

The next cell demonstrates that the new version of PlotFunction can take any
way of expressing options that passes the OptionQ test.

$PlotFunction[x^2] <br /> PlotFunction[x^2, PlotStyleThickness[0.03]] <br /> PlotFuncti ... otStyleGrayLevel[0], {{ImageSizeAutomatic}, Ticks->Automatic}, Axes->True}]$

$MakeGraphic[x^2, PlotStyle=Thickness[0.03], ImageSize={xx, yy}]$

$MakeGraphic[x^2, PlotStyle=Thickness[0.03], ImageSize={400, 250}]$

Created by Mathematica (May 16, 2004)