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From: Joe Hays on 27 Apr 2010 04:05
So, on this topic I'd like to ask the group for some pointers...

*First Observation:*
I generally have a vector function that I need to pass to NMinimize and/or
FindMinimum. I have not had success with either of the following
definitions,

f(myVec_?NumericQ):= Module[{}, <*body of function definition*>]

nor,

f(myVec_?VectorQ):= Module[{}, <*body of function definition*>]

the only thing I have found to work is,

f(myVec_):= Module[{}, <*body of function definition*
>]/;VectorQ[myVec,NumericQ]

This was very difficult to find, and as I recall, I didn't find it in the
documentation but in a forum posting. I hope the Wolfram folks consider
adding an example when dealing with a vector valued function in their
documentation.

*Now, a question:*
Not only do I have a vector valued function to be minimized but I also have
additional arguments that I need to pass to the function for proper
evaluation. So, if I make the following definition,

f(myVec_, myParam_, myModel_):= Module[{}, <*body of function definition*
>]/;VectorQ[myVec,NumericQ]

where myParam is just a constant and myModel is a sybolic set of equations.
If I then pass this function definition to NMinimize/FindMinimum by,

myParam = <*some Real constant>;*
myModel = <*some symbolic equation>;*
NMinimize[ f[myVec, myParam, myModel], myVec ]

will Mathematica try to symbolically evaluate myModel?

Sorry, this is likely a Rookie question but I've had really poor performance
with both NMinimize and FindMinimum with multiple problems I've tried with
it. I'm trying to find reasons as to why this performance is so poor. It's
likely due to my poor Mathematica code (in the body), or my formulation,
however, I have been curious about this specific question for some time now.
So, if anyone has more insight to this mechanism of bypassing symbolic
evaluations (or not) your comments.

Joe

On Mon, Apr 26, 2010 at 7:32 AM, Ingolf Dahl <ingolf.dahl(a)telia.com> wrote:

> Best LAI,
> Yes, if you followed the thread back, you see that we also have understood
> that we might introduce an extra function f(a_?NumericQ,b_?NumericQ, ...),
> but we (I guess I can include Alexey Popkov and Joe Hays in "we") sometimes
> find that way clumsy. If we ask Mathematica to evaluate NMinimize, this
> function is described to "minimizes f numerically with respect to x." But
> it
> does not only this: it also first tries to evaluate f symbolically. I find
> it reasonable that there should be a way to opt-out from this symbolic
> evaluation. It would be convenient to have an option to NMinimize for this
> purpose.
>
> Ingolf Dahl
> Sweden
>
> -----Original Message-----
> From: Anh Ngoc LAI [mailto:laianhngoc(a)yahoo.com]
> Sent: den 26 april 2010 10:50
> To: mathgroup(a)smc.vnet.net
> Subject: Re: problems with NMinimize
>
> Hi,
>
> One way to solve this problem (if i understand your problem) is to define
> your function so that only evaluates when its argument is numeric, as
> follow:
>
> f(a_?NumericQ,b_?NumericQ, ...) == ...
>
> LAI.
>
> --- On Sun, 4/25/10, Alexey Popkov <lehin.p(a)gmail.com> wrote:
>
> From: Alexey Popkov <lehin.p(a)gmail.com>
> Subject: Re: problems with NMinimize
> To: mathgroup(a)smc.vnet.net
> Date: Sunday, April 25, 2010, 6:25 AM
>
>
> "Ingolf Dahl" <ingolf.dahl(a)physics.gu.se>
> =D1=81=D0=BE=D0=BE=D0=B1=D1=89=D0=
> =B8=D0=BB/=D1=81=D0=BE=D0=BE=D0=B1=D1=89=D0=B8=D0=BB=D0=B0 =D0=B2
> =D0=BD=D0=
> =BE=D0=B2=D0=BE=D1=81=D1=82=D1=8F=D1=85
> =D1=81=D0=BB=D0=B5=D0=B4=D1=83=D1=8E=D1=89=D0=B5=D0=B5: news:hqu8ai$rol$1@s
> =
> mc.vnet.net...
> > Is there any serious Mathematica user in this forum, which has not
> > stumbled
> > on this problem one or several times, when NMinimize, or some other
> > function, tries to evaluate a numeric function symbolically first, before
> > inserting the numbers? Sometimes it would be nice to have an option,
> > SymbolicEvaluation->False, which could be set for NMinimize in these
> > cases.
> > It is not always so convenient to have to define an extra function just
> to
> > take care of this. I think there is a whole group of commands acting
> > similarly to NMinimize.
> >
> > Ingolf Dahl
> > Sweden
>
> I totally agree with you. I do not see anything reasonable in that
> obviously
> numerical function (for example, NMinimize, FindMinimum, etc.) is trying
> for
> some reason to perform symbolic computation.
>
>
>


From: Bob Hanlon on 27 Apr 2010 08:08

f1[v_?(VectorQ[#, NumericQ] &), x_] :=
"Numeric Vector and " <> ToString[x];

f2[v : {_?NumericQ ..}, x_] :=
"Numeric Vector and " <> ToString[x];

f3[v_, x_] :=
"Numeric Vector and " <> ToString[x] /;
VectorQ[v, NumericQ];

a = 1;

data = {
{{a, 2, c}, z},
{{a, 2, Pi}, z},
{{a, 2, {3, 4}}, z}
};

f1 @@@ data

{f1({1,2,c},z),Numeric Vector and z,f1({1,2,{3,4}},z)}

f2 @@@ data

{f2({1,2,c},z),Numeric Vector and z,f2({1,2,{3,4}},z)}

f3 @@@ data

{f3({1,2,c},z),Numeric Vector and z,f3({1,2,{3,4}},z)}

The form VectorQ[expr, test] is in the documentation for VectorQ. Further, there under More Information it states:

VectorQ[expr, NumberQ] tests whether expr is a vector of numbers.

and the examples include

VectorQ[{a, 1.2}, NumericQ]


Bob Hanlon

---- Joe Hays <hays.joe(a)gmail.com> wrote:

=============
So, on this topic I'd like to ask the group for some pointers...

*First Observation:*
I generally have a vector function that I need to pass to NMinimize and/or
FindMinimum. I have not had success with either of the following
definitions,

f(myVec_?NumericQ):= Module[{}, <*body of function definition*>]

nor,

f(myVec_?VectorQ):= Module[{}, <*body of function definition*>]

the only thing I have found to work is,

f(myVec_):= Module[{}, <*body of function definition*
>]/;VectorQ[myVec,NumericQ]

This was very difficult to find, and as I recall, I didn't find it in the
documentation but in a forum posting. I hope the Wolfram folks consider
adding an example when dealing with a vector valued function in their
documentation.

*Now, a question:*
Not only do I have a vector valued function to be minimized but I also have
additional arguments that I need to pass to the function for proper
evaluation. So, if I make the following definition,

f(myVec_, myParam_, myModel_):= Module[{}, <*body of function definition*
>]/;VectorQ[myVec,NumericQ]

where myParam is just a constant and myModel is a sybolic set of equations.
If I then pass this function definition to NMinimize/FindMinimum by,

myParam = <*some Real constant>;*
myModel = <*some symbolic equation>;*
NMinimize[ f[myVec, myParam, myModel], myVec ]

will Mathematica try to symbolically evaluate myModel?

Sorry, this is likely a Rookie question but I've had really poor performance
with both NMinimize and FindMinimum with multiple problems I've tried with
it. I'm trying to find reasons as to why this performance is so poor. It's
likely due to my poor Mathematica code (in the body), or my formulation,
however, I have been curious about this specific question for some time now.
So, if anyone has more insight to this mechanism of bypassing symbolic
evaluations (or not) your comments.

Joe

On Mon, Apr 26, 2010 at 7:32 AM, Ingolf Dahl <ingolf.dahl(a)telia.com> wrote:

> Best LAI,
> Yes, if you followed the thread back, you see that we also have understood
> that we might introduce an extra function f(a_?NumericQ,b_?NumericQ, ...),
> but we (I guess I can include Alexey Popkov and Joe Hays in "we") sometimes
> find that way clumsy. If we ask Mathematica to evaluate NMinimize, this
> function is described to "minimizes f numerically with respect to x." But
> it
> does not only this: it also first tries to evaluate f symbolically. I find
> it reasonable that there should be a way to opt-out from this symbolic
> evaluation. It would be convenient to have an option to NMinimize for this
> purpose.
>
> Ingolf Dahl
> Sweden
>
> -----Original Message-----
> From: Anh Ngoc LAI [mailto:laianhngoc(a)yahoo.com]
> Sent: den 26 april 2010 10:50
> To: mathgroup(a)smc.vnet.net
> Subject: Re: problems with NMinimize
>
> Hi,
>
> One way to solve this problem (if i understand your problem) is to define
> your function so that only evaluates when its argument is numeric, as
> follow:
>
> f(a_?NumericQ,b_?NumericQ, ...) == ...
>
> LAI.
>
> --- On Sun, 4/25/10, Alexey Popkov <lehin.p(a)gmail.com> wrote:
>
> From: Alexey Popkov <lehin.p(a)gmail.com>
> Subject: Re: problems with NMinimize
> To: mathgroup(a)smc.vnet.net
> Date: Sunday, April 25, 2010, 6:25 AM
>
>
> "Ingolf Dahl" <ingolf.dahl(a)physics.gu.se>
> =D1=81=D0=BE=D0=BE=D0=B1=D1=89=D0=
> =B8=D0=BB/=D1=81=D0=BE=D0=BE=D0=B1=D1=89=D0=B8=D0=BB=D0=B0 =D0=B2
> =D0=BD=D0=
> =BE=D0=B2=D0=BE=D1=81=D1=82=D1=8F=D1=85
> =D1=81=D0=BB=D0=B5=D0=B4=D1=83=D1=8E=D1=89=D0=B5=D0=B5: news:hqu8ai$rol$1@s
> =
> mc.vnet.net...
> > Is there any serious Mathematica user in this forum, which has not
> > stumbled
> > on this problem one or several times, when NMinimize, or some other
> > function, tries to evaluate a numeric function symbolically first, before
> > inserting the numbers? Sometimes it would be nice to have an option,
> > SymbolicEvaluation->False, which could be set for NMinimize in these
> > cases.
> > It is not always so convenient to have to define an extra function just
> to
> > take care of this. I think there is a whole group of commands acting
> > similarly to NMinimize.
> >
> > Ingolf Dahl
> > Sweden
>
> I totally agree with you. I do not see anything reasonable in that
> obviously
> numerical function (for example, NMinimize, FindMinimum, etc.) is trying
> for
> some reason to perform symbolic computation.
>
>
>



--

Bob Hanlon


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