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MathGroup Archive 2007

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Re: Evaluation Question

  • To: mathgroup at smc.vnet.net
  • Subject: [mg76464] Re: Evaluation Question
  • From: Albert <awnl at arcor.net>
  • Date: Wed, 23 May 2007 05:02:55 -0400 (EDT)
  • References: <f2u57d$k2n$1@smc.vnet.net>

hoffmannick wrote:
> Can anyone help me solve the following problem?
> 
> I have a function of 3 variables, let's say
> f[a_, b_, c_] = a + b + c
> 
> Now I need to evaluate the function at some given points.  To evaluate
> at a single point I would do
> f[0,0,1]
> 
> For the point (0,0,1)
> 
> Now here is the main question.
> I need to evaluate this function at the points (0,0,0) through (1,1,1)
> That would be the points:
> 0,0,0
> 0,0,1
> 0,1,0
> 0,1,1
> 1,0,0
> 1,0,1
> 1,1,0
> 1,1,1
> 
> I'm testing these for approx 32 different functions.  Is there an easy
> way that I can define the function and then have it test all the
> points for me?  It will always be those finite points listed above.
> 
> I looked into the mathematica documentation and it said how to do this
> with a function of a single variable, but it didn't say how to do it a
> function of more than one variable.
> 
> I really appreciate your help
> 
> 
I think the easiest for this case is to use a special Form of Apply:

In[32]:=
f[a_, b_, c_] = a + b + c
Out[32]=
a + b + c
In[33]:=
points = {{0, 0, 0}, {1, 0, 0}, {0, 1, 0}}
Out[33]=
{{0, 0, 0}, {1, 0, 0}, {0, 1, 0}}
In[35]:=
Apply[f, points, {1}]
Out[35]=
{0, 1, 1}

that's a shortcut for it:

In[34]:=
f @@@ points
Out[34]=
{0, 1, 1}


this also works, but is more elaborate for multiple arguments:

In[40]:=
Map[Apply[f, #] &, points]
Out[40]=
{0, 1, 1}
In[41]:=
f @@@ points
Out[41]=
{0, 1, 1}



hth,

albert


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