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Notebook[{

Cell[CellGroupData[{
Cell["The package FilterOptions", "Title"],

Cell["\<\
Bernd Thaller
Institute for Mathematics
University of Graz\
\>", "Subsubsection"],

Cell[CellGroupData[{

Cell["\<\
Source: Roman Maeder, Programming in Mathematica
Second Edition, Addison-Wesley 1991 (Third Edition, Addison-Wesley, 1996)

Mathematica Standard Packages\
\>", "Subsubtitle"],

Cell[CellGroupData[{

Cell["Listing", "Section"],

Cell[TextData[{
  StyleBox["It is the main purpose of FilterOptions to choose from a given \
sequence of options a sub sequence fitting to a given ", "Text"],
  StyleBox["Mathematica", "Text",
    FontSlant->"Italic"],
  StyleBox[" command. The package FilterOptions.m is one of ", "Text"],
  StyleBox["Mathematica", "Text",
    FontSlant->"Italic"],
  StyleBox["'a standard packages. The code by Roman Maeder is as follows.", 
    "Text"]
}], "Text"],

Cell["\<\
BeginPackage[\"Utilities`FilterOptions`\"]

FilterOptions::usage = \"FilterOptions[symbol, options..] returns a sequence
\tof those options that are valid options for symbol.
\tFilterOptions[{opts..}, options..] filters out options with names opts.\"

Begin[\"`Private`\"]

FilterOptions[ command_Symbol, options___ ] :=
\tFilterOptions[ First /@ Options[command], options ]

FilterOptions[ opts_List, options___ ] :=
\tSequence @@ Select[ Flatten[{options}], MemberQ[opts, First[#]]& ]

End[ ]

Protect[ FilterOptions ]

EndPackage[ ]
\
\>", "Program"]
}, Closed]],

Cell[CellGroupData[{

Cell[TextData[{
  "The ",
  StyleBox["Mathematica",
    FontSlant->"Italic"],
  " command \"Sequence\""
}], "Section"],

Cell[TextData[{
  "Let us analyze what this package does. In ",
  StyleBox["Mathematica",
    FontSlant->"Italic"],
  ", options are usually given as a list of rules. Consider, for example, "
}], "Text"],

Cell[CellGroupData[{

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\>", "Input"],

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  "As an experienced ",
  StyleBox["Mathematica",
    FontSlant->"Italic"],
  " user you will notice that the options Axes->{True,False}, Frame->True, \
PlotLabel->\"Sine-Function\" are not really given as a list. The braces {} \
are missing. A list with missing braces is called a \"Sequence\" in ",
  StyleBox["Mathematica",
    FontSlant->"Italic"],
  ". Sequence is ",
  StyleBox["Mathematica",
    FontSlant->"Italic"],
  "'s representation for the set of arguments of a function taking several \
arguments. The difference to List can be seen from the following example"
}], "Text"],

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Cell["Analysis of the command FilterOptions", "Section"],

Cell["The command", "Text"],

Cell["\<\
FilterOptions[ opts_List, options___ ] :=
\tSequence @@ Select[ Flatten[{options}], MemberQ[opts, First[#]]& ]\
\>", \
"Input"],

Cell["\<\
takes a list of option names as the first argument. For \
example,\
\>", "Text"],

Cell["\<\
optionnames = {AspectRatio, Frame, PlotLabel, PrecisionGoal};\
\>", \
"Input"],

Cell["\<\
The pattern options___ matches zero or more arguments. Options are \
usually a sequence of rules. In our example, \
\>", "Text"],

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Cell["\<\
optionsequence = Sequence[Axes->{True,False}, Frame->True, \
PlotLabel->\"Sine-Function\", AccuracyGoal->10]\
\>", "Input"],

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Cell["\<\
It returns just those options of the sequence, whose names are \
contained in the given list opts. How is this achieved? Consider first the \
command\
\>", "Text"],

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Cell["\<\
{options} creates a list from the given sequence \"options\" by \
adding the braces. The command Select[list,test] picks out those elements \
from the list, for which test gives \"True\". Here the test is MemberQ[opts, \
First[#]]&. It is applied to each element of the list {options}. If it gives \
\"True\", that element is kept, otherwise it is deleted. Thus the second \
argument of Select must be a function that can be applied to each element of \
the list and evaluates either to True or to False. Let us consider an example\
\
\>", "Text"],

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Cell["options = Sequence @@ Options[Plot]", "Input"],

Cell[BoxData[
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(Here the operator @@ (\"Apply\") replaces the head List by the \
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\>", "Text"],

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Now we map (/@) the test-function to the list \"{options}\". (The \
command Map or /@ applies the function to each element in the list).\
\>", \
"Text"],

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Select keeps only those elements of the list {options} for which \
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\>", "Text"],

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}], "Text"],

Cell[CellGroupData[{

Cell["\<\
Sequence @@ Select[{options}, MemberQ[optionnames, \
First[#]]&]\
\>", "Input"],

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Cell["\<\
Flattening the list {options} is done in case that the second \
argument \"options\" of FilterOptions is already given as a list. In that \
case {options} would be an expression of the form {{optionsequence}}. Flatten \
deletes the inner braces of the list.\
\>", "Text"],

Cell["Next, consider the command", "Text"],

Cell["\<\
FilterOptions[ command_Symbol, options___ ] :=
\tFilterOptions[ First /@ Options[command], options ]\
\>", "Input"],

Cell["\<\
It just calles FilterOptions with the fist command being a list of \
option names. For example,\
\>", "Text"],

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Cell["command = NIntegrate", "Input"],

Cell[BoxData[
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Cell["Options[command]", "Input"],

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Cell["First /@ Options[command]", "Input"],

Cell[BoxData[
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Cell["Now, let us try this:", "Text"],

Cell[CellGroupData[{

Cell["optionsequence", "Input"],

Cell[BoxData[
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Cell["FilterOptions[NIntegrate, optionsequence]", "Input"],

Cell[BoxData[
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}, Open  ]]
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Cell["Examples", "Section"],

Cell["Prevent shadowing:", "Text"],

Cell["Remove [FilterOptions]", "Input"],

Cell["Load the package:", "Text"],

Cell["<<Utilities`FilterOptions`", "Input"],

Cell[CellGroupData[{

Cell["FilterOptions[Graphics,Options[Plot3D]]", "Input"],

Cell[BoxData[
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      DefaultFont \[RuleDelayed] $DefaultFont, 
      DisplayFunction \[RuleDelayed] $DisplayFunction, 
      FormatType \[RuleDelayed] $FormatType, 
      TextStyle \[RuleDelayed] $TextStyle]\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell["\<\
options = Join[Options[Simplify], Options[Integrate], \
Options[Plot]]\
\>", "Input"],

Cell[BoxData[
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      DisplayFunction \[RuleDelayed] $DisplayFunction, 
      FormatType \[RuleDelayed] $FormatType, 
      TextStyle \[RuleDelayed] $TextStyle}\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell["FilterOptions[Integrate,options]", "Input"],

Cell[BoxData[
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