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MathGroup Archive 2000

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How to operate on strictly numerical functions ?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg24102] How to operate on strictly numerical functions ?
  • From: "Mark Harder" <harderm at ucs.orst.edu>
  • Date: Tue, 27 Jun 2000 00:51:56 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

    Some of the Mathematica functions made for numerical procedures 
appear to actually evaluate by substitution of symbolic variables with 
replacement rules. An example of this, which has blocked me for more 
than a week now, is NonlinearRegress, which seems to evaluate the 
user-supplied model function symbolically, then evaluate the resulting 
expression through replacement of the independent variables and the 
current set of adjustable parameters through replacement rules that it 
constructs.  My model function requires evaluation of the SVD (with 
SingularValues[] ) of a matrix computed from the independent variables 
and the parameters of the model, and so NonlinearRegress fails, since 
SingularValues[] can't accept a non-numeric matrix.  A simpler example I 
have encountered is the numeric derivative function, which I'll use to 
illustrate my problem.
    First, construct a simple test function which, through an If[] test, 
won't evaluate for non-numeric arguments:
In[804]:=
ClearAll[x, tstFn1]
tstFn1[x_] := If[NumericQ[x  ], Return[x^2];, Print["NonNumeric x 
and/or y."];]

In[808]:=tstFn1[2]
Out[808]=4
In[809]:=tstFn1[u]

& try to use ND[] on this function:

<<NumericalMath`NLimit`

In[806]:=ClearAll[u, v]
            ND[tstFn1[u ], u, 1.]
Out[807]= 0

    So, I'm looking for some means of modifying testFn1 to cause ND to 
evaluate it only after numeric substitution for u.  Is there some way of 
Hold-ing evaluation until numeric values are assigned to arguments of a 
function?  Is this sort of thing impossible in Mathematica?  Do I have 
to write my own numeric routines for finding derivatives, gradients, 
Jacobians, least-squares fits, etc. by procedural routines ala FORTRAN?  
Thanks for any help you can offer.

mark e. harder

harderm at ucs.orst.edu



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