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Combining pure functions to produce a new pure function

• To: mathgroup at smc.vnet.net
• Subject: [mg89705] Combining pure functions to produce a new pure function
• From: Mac <mwjdavidson at googlemail.com>
• Date: Wed, 18 Jun 2008 06:40:29 -0400 (EDT)

I have a function where one of the arguments is supposed to be a list
of pure functions. Tyhis is useful for an algorithm that can run using
multiple input functions. Based on a previous post some time ago

http://groups.google.com/group/comp.soft-sys.math.mathematica/browse_thread=
/thread/b1faadec497c657d/5cc40d169d8992b4?lnk=gst&q=pure+function+#5cc4=
0d169d8992b4

a method was proposed to address this. If I apply this method to list
arguments I get the following code and results:

In[60]:= h[f1_, f2_] :=
 Function[x,
  Evaluate[{f1[x], f2[x]} /.
    HoldPattern[Function[a_, b_]] -> Function[a, b][x]]]

Combine two simple pure functions - works as expected

In[58]:= h[# + 1 &, # + 2 &]
%[1]

Out[58]= Function[x$, {1 + x$, 2 + x$}]

Out[59]= {2, 3}

Combine two custom functions and I get the internal details of one
function and with the second one evaluated properly

In[66]:= h[forwardmodel["letoan", #] &, forwardmodel["saatchiphv", #]
&]
%[100]

Out[66]= Function[x$, {If[-10. - 32./biomass$491^0.434294 <= -15,
   10 Log[10, 10^(\[Gamma]1$491/10) Sin[27 =B0]],
   10 Log[10, 10^(\[Gamma]2$491/10) Sin[27 =B0]]],
  If[x$ > 2, -35.01 + 4.296 Log[x$], -35.01 + 4.296 Log[2]]}]

Out[67]= {If[-10. - 32./biomass$491^0.434294 <= -15,
  10 Log[10, 10^(\[Gamma]1$491/10) Sin[27 =B0]],
  10 Log[10, 10^(\[Gamma]2$491/10) Sin[27 =B0]]], -15.2262}

I can see that this effect is due to the evaluations of the function

 forwardmodel["letoan", #] &

so that the output no longer depends on the pure function variable $x.
Note that separately these functions work as expected. Here some
predicted radar backscatter coefficients.

In[69]:= forwardmodel["letoan", #] &[100]
forwardmodel["saatchiphv", #] &[100]

Out[69]= -17.6312

Out[70]= -15.2262

Can annybody suggest a general solution ?

Many thanks

Mac