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Re: Map-like behaviour for functions of more than a single argument?
*To*: mathgroup at smc.vnet.net
*Subject*: [mg64539] Re: Map-like behaviour for functions of more than a single argument?
*From*: Bill Rowe <readnewsciv at earthlink.net>
*Date*: Mon, 20 Feb 2006 22:31:18 -0500 (EST)
*Sender*: owner-wri-mathgroup at wolfram.com
On 2/20/06 at 6:29 AM, anonmous69 at netscape.net (Matt) wrote:
>I was wondering if there's a way to achieve the functionality of Map,
>but with functions of more than one argument?
Yes, several different ways.
>An example of how I'm 'working around' my perceived limitation of
>Map functionality:
>Clear[f, g]; f[z_, func_] := Module[{result}, result =
>func[Complex[Sequence @@ z]];
>{Re[result], Im[result]}]; g[z_] := f[z, #1^2 & ];
>Which, using 'g', I can use Map on a list of ordered pairs:
>g /@ {{x,y}, {x,y}, {x,y}, {x,y}, etc.}
The same output can be obtained with MapThread as follows:
MapThread[Complex[Sequence@##]^2&, Transpose[data]]
where
data = {{x,y}, {x,y}, {x,y}, {x,y}, etc.}
Note, this could also be done as:
MapThread[Complex[#1,#2]^2&, Transpose[data]]
which I think is a bit more clear as to what is being done. But the most compact way I know to get the same result would be:
(Complex@@@data)^2
Written less compactly, this last is
Apply[Complex, data, {1}]^2
And using this method, I could use Sin as follows:
Sin[Complex@@@data]
--
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