Re: How to operate on strictly numerical functions ?
- To: mathgroup at smc.vnet.net
- Subject: [mg24115] Re: How to operate on strictly numerical functions ?
- From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
- Date: Wed, 28 Jun 2000 02:11:39 -0400 (EDT)
- Organization: Universitaet Leipzig
- References: <firstname.lastname@example.org>
- Sender: owner-wri-mathgroup at wolfram.com
Hi, atleast your example works with ClearAll[x, tstFn1] tstFn1[x_?NumericQ] := x^2 << NumericalMath`NLimit` ClearAll[u, v] ND[N[tstFn1[u]], u, 1.] Out=2. Regards Jens Mark Harder wrote: > > 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:= > ClearAll[x, tstFn1] > tstFn1[x_] := If[NumericQ[x ], Return[x^2];, Print["NonNumeric x > and/or y."];] > > In:=tstFn1 > Out=4 > In:=tstFn1[u] > > & try to use ND on this function: > > <<NumericalMath`NLimit` > > In:=ClearAll[u, v] > ND[tstFn1[u ], u, 1.] > Out= 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