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Re: Giving several functions the same argument

  • To: mathgroup at smc.vnet.net
  • Subject: [mg109624] Re: Giving several functions the same argument
  • From: Ingolf Dahl <ingolf.dahl at telia.com>
  • Date: Sat, 8 May 2010 07:08:43 -0400 (EDT)

Hi Simon.

Define 

backmap[funclist_, x__] := Apply[#1, {x}] & /@ funclist

Then 

backmap[{f, g}, x]

gives

{f[x], g[x]}

and 

backmap[{Sin[#1] &, Cos[#1] &}, x]

gives

{Sin[x], Cos[x]}

and

backmap[{Sin[#1] &, Cos[#1] &}, Pi/6]

gives

{1/2,Sqrt[3]/2}

You might also do

backmap[{f, g}, x, y]

which gives

{f[x, y], g[x, y]}


Best regards

Ingolf Dahl
Sweden

-----Original Message-----
From: Simon Pearce [mailto:Simon.Pearce at nottingham.ac.uk] 
Sent: den 7 maj 2010 12:28
To: mathgroup at smc.vnet.net
Subject: [mg109624] [mg109587] Giving several functions the same argument

Hi Mathgroup,



I have a list of pure functions, which I wish to apply to the same
argument. I can't seem to be able to thread the list of functions over
the argument in a simple way, all the commands like Apply and Map etc
take a single function. I can do it using Table and Part, but it seemed
like there should be a simple command that I'm missing.



For example:



In[1]:= functs = {Sin[#1] &, Cos[#1] &};



In[2]:= functs[x]



Out[2]= {Sin[#1] &, Cos[#1] &}[x]



I want to get the result {Sin[x],Cos[x]} out, without having to use
something of the form:



In[3]:= Table[functs[[i]][x], {i, 1, 2}]



Out[3]= {Sin[x], Cos[x]}



Which seems like it'd be less efficient when I try and use it on long
lists of functions.



Thanks,

Simon



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