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MathGroup Archive 2006

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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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