Services & ResourcesWolfram ForumsMathGroup Archive

[Date Index] [Thread Index] [Author Index]

Re: NMinimize Error In Evaluation

• To: mathgroup at smc.vnet.net
• Subject: [mg85079] Re: NMinimize Error In Evaluation
• From: Mark Fisher <particlefilter at gmail.com>
• Date: Sun, 27 Jan 2008 05:47:11 -0500 (EST)
• References: <200801150813.DAA11621@smc.vnet.net> <fnet62$iea$1@smc.vnet.net>

On Jan 26, 4:06 am, "Jason S. Kong" <kon... at gmail.com> wrote:
> Hi, I am asking again since I have not received a response on this
> issue and would really desire some counsel in regards to this issue.
>
> Thanks,
>
> -Jason S. Kong
>
> On Jan 15, 2008 3:13 AM, Jason S. Kong <kon... at gmail.com> wrote:
>
>
>
>
>
> > Hi,
>
> > I have been having an issue with NMinimize in an attempt to try to do
> > some optimization routines.
>
> > First, here is the background:
>
> > I want to simulate some data that was experimentally determined, and
> > there are a large variety of variables involved.  I do not believe
> > there is a simple, analytical solution to obtain my results, so I
> > decided to optimize it numerically, that is, NMinimize.  Below I have
> > some data and the method by which I attempted to solve this.  At the
> > end, you will see the error I get, preventing me from being able to
> > utilize NMinimize.  Any help on this issue would be greatly
> > appreciated, as this is not the first time I have had to abandon a
> > problem due to the same error!
>
> > At the end, I wanted to see if NMinimize had problems with functions
> > inside of NMinimize by writing a quick "roar" program, but it
> > functioned fine.
>
> > Thanks,
>
> > -Jason S. Kong
>
> > ---
>
> > xvals = {6.`, 12.`, 18.`, 24.`, 36.`, 48.`, 60.`, 75.`, 90.`, 120.`,
> >    150.`, 180.`, 210.`, 240.`, 270.`, 300.`, 390.`, 480.`, 570.`,
> >    660.`, 750.`, 840.`, 912.`, 930.`, 1020.`, 1110.`, 1200.`, 1350.`,
> >    1524.`, 1800.`, 2442.`};
>
> > yvals = {0.03049534752960375`, 0.030612029204239437`,
> >    0.03088344092567462`, 0.03106269103453524`, 0.03132902963968192`,
> >    0.031313810290816396`, 0.03167484706668189`, 0.031816894322760116`,
> >     0.03173995205905108`, 0.031799138415750335`, 0.03183126815224423`,
> >     0.03200882722234201`, 0.03196570573388969`, 0.032041802478217314`,
> >     0.03191751112914886`, 0.03214072824584322`, 0.03222950778089211`,
> >    0.03230898660274541`, 0.03230306796707548`, 0.03227516582748868`,
> >    0.032589699037376185`, 0.03284927348747152`, 0.03289831361159377`,
> >    0.03300231249550818`, 0.03331853674415852`, 0.033540908341471456`,
> >    0.03361869612456192`, 0.033647443783530136`, 0.033538371783327206`,
> >     0.033603476775696396`, 0.03364321618662304`};
>
> > ListPlot[{xvals, yvals} // Transpose]
>
> > equilibrium[C1_, C2_, C3_, C4_, C5_] := Solve[
> >     {C1 == var2/(var1 var5),
> >      C2 == var3/var2,
> >      C3 == var4/var2,
> >      var1 + var2 + var3 + var4 == C4,
> >      var5 + var2 + var3 + 2 var4 == C5}, {var1, var2, var3, var4,
> >      var5}, WorkingPrecision -> 100] // N // Chop
>
> > imagine[tests_] :=
> >  Select[tests,
> >   And @@ {(Re[var1 /. #] == var1 /. #), (Re[var2 /. #] ==
> >         var2 /. #), (Re[var3 /. #] == var3 /. #), (Re[var4 /. #] ==
> >         var4 /. #), (Re[var5 /. #] == var5 /. #)} &]
>
> > dynamics[C1_, C2_, C3_, C4_, C5_] :=
> >  Select[imagine[
> >    equilibrium[C1, C2, C3, C4,
> >     C5]], #[[1, 2]] > 0 && #[[2, 2]] > 0 && #[[3, 2]] > 0 &]
>
> > data1[C1_, C2_, C3_, C4_,
> >   C5_] := {C5, var1} /. dynamics[C1, C2, C3, C4, C5] // Flatten
> > data2[C1_, C2_, C3_, C4_,
> >   C5_] := {C5, var2 + var3} /. dynamics[C1, C2, C3, C4, C5] //
> >   Flatten
> > data3[C1_, C2_, C3_, C4_,
> >   C5_] := {C5, var5} /. dynamics[C1, C2, C3, C4, C5] // Flatten
>
> > go[C1_, C2_, C3_, C4_, R1_, R2_, R3_] := (
> >   listdata1 = data1[C1, C2, C3, C4, #] & /@ xvals;
> >   listdata2 = data2[C1, C2, C3, C4, #] & /@ xvals;
> >   listdata3 = data3[C1, C2, C3, C4, #] & /@ xvals;
> >   r1 = (R1 #)/C4 & /@ (listdata1 // Transpose)[[2]];
> >   r2 = (R2 #)/C4 & /@ (listdata2 // Transpose)[[2]];
> >   r3 = (R3 #)/C4 & /@ (listdata3 // Transpose)[[2]];
> >   calcyvals = r1 + r2 + r3;
> >   error = Total[(calcyvals - yvals)^2])
>
> > NMinimize[{go[c1, c2, c3, 25, ra1, ra2, ra3],
> >   c1 > 0 && c2 > 0 && c3 > 0 && ra1 > 0 && ra2 > ra1 &&
> >    ra3 > ra2}, {c1, c2, c3, ra1, ra2, ra3}]
>
> > NMinimize::nnum: The function value (-0.0336474+0.04 var1+0.04 \
> > (var2+var3)+0.04 var5)^2+(-0.0336432+0.04 var1+0.04 (var2+var3)+0.04 \
> > var5)^2+(-<<20>>+<<2>>+0.04 \
> > var5)^2+(<<1>>)^2+<<1>>^2+<<1>><<1>><<1>>+(<<1>>)^2+(<<1>>)^2+(-0.\
> > 0328493+0.04 var1+<<1>>+0.04 var5)^2+<<21>> is not a number at \
> > {c1,c2,c3,ra1,ra2,ra3} = {2.,2.,2.,1.,1.,1.}. >>
>
> > NMinimize[{(-0.0336474 + (ra1 var1)/25 + 1/25 ra2 (var2 + var3) + (
> >      ra3 var5)/25)^2 + (-0.0336432 + (ra1 var1)/25 +
> >      1/25 ra2 (var2 + var3) + (ra3 var5)/25)^2 + (-0.0336187 + (
> >      ra1 var1)/25 + 1/25 ra2 (var2 + var3) + (ra3 var5)/
> >      25)^2 + (-0.0336035 + (ra1 var1)/25 + 1/25 ra2 (var2 + var3) + (
> >      ra3 var5)/25)^2 + (-0.0335409 + (ra1 var1)/25 +
> >      1/25 ra2 (var2 + var3) + (ra3 var5)/25)^2 + (-0.0335384 + (
> >      ra1 var1)/25 + 1/25 ra2 (var2 + var3) + (ra3 var5)/
> >      25)^2 + (-0.0333185 + (ra1 var1)/25 + 1/25 ra2 (var2 + var3) + (
> >      ra3 var5)/25)^2 + (-0.0330023 + (ra1 var1)/25 +
> >      1/25 ra2 (var2 + var3) + (ra3 var5)/25)^2 + (-0.0328983 + (
> >      ra1 var1)/25 + 1/25 ra2 (var2 + var3) + (ra3 var5)/
> >      25)^2 + (-0.0328493 + (ra1 var1)/25 + 1/25 ra2 (var2 + var3) + (
> >      ra3 var5)/25)^2 + (-0.0325897 + (ra1 var1)/25 +
> >      1/25 ra2 (var2 + var3) + (ra3 var5)/25)^2 + (-0.032309 + (
> >      ra1 var1)/25 + 1/25 ra2 (var2 + var3) + (ra3 var5)/
> >      25)^2 + (-0.0323031 + (ra1 var1)/25 + 1/25 ra2 (var2 + var3) + (
> >      ra3 var5)/25)^2 + (-0.0322752 + (ra1 var1)/25 +
> >      1/25 ra2 (var2 + var3) + (ra3 var5)/25)^2 + (-0.0322295 + (
> >      ra1 var1)/25 + 1/25 ra2 (var2 + var3) + (ra3 var5)/
> >      25)^2 + (-0.0321407 + (ra1 var1)/25 + 1/25 ra2 (var2 + var3) + (
> >      ra3 var5)/25)^2 + (-0.0320418 + (ra1 var1)/25 +
> >      1/25 ra2 (var2 + var3) + (ra3 var5)/25)^2 + (-0.0320088 + (
> >      ra1 var1)/25 + 1/25 ra2 (var2 + var3) + (ra3 var5)/
> >      25)^2 + (-0.0319657 + (ra1 var1)/25 + 1/25 ra2 (var2 + var3) + (
> >      ra3 var5)/25)^2 + (-0.0319175 + (ra1 var1)/25 +
> >      1/25 ra2 (var2 + var3) + (ra3 var5)/25)^2 + (-0.0318313 + (
> >      ra1 var1)/25 + 1/25 ra2 (var2 + var3) + (ra3 var5)/
> >      25)^2 + (-0.0318169 + (ra1 var1)/25 + 1/25 ra2 (var2 + var3) + (
> >      ra3 var5)/25)^2 + (-0.0317991 + (ra1 var1)/25 +
> >      1/25 ra2 (var2 + var3) + (ra3 var5)/25)^2 + (-0.03174 + (
> >      ra1 var1)/25 + 1/25 ra2 (var2 + var3) + (ra3 var5)/
> >      25)^2 + (-0.0316748 + (ra1 var1)/25 + 1/25 ra2 (var2 + var3) + (
> >      ra3 var5)/25)^2 + (-0.031329 + (ra1 var1)/25 +
> >      1/25 ra2 (var2 + var3) + (ra3 var5)/25)^2 + (-0.0313138 + (
> >      ra1 var1)/25 + 1/25 ra2 (var2 + var3) + (ra3 var5)/
> >      25)^2 + (-0.0310627 + (ra1 var1)/25 + 1/25 ra2 (var2 + var3) + (
> >      ra3 var5)/25)^2 + (-0.0308834 + (ra1 var1)/25 +
> >      1/25 ra2 (var2 + var3) + (ra3 var5)/25)^2 + (-0.030612 + (
> >      ra1 var1)/25 + 1/25 ra2 (var2 + var3) + (ra3 var5)/
> >      25)^2 + (-0.0304953 + (ra1 var1)/25 + 1/25 ra2 (var2 + var3) + (
> >      ra3 var5)/25)^2,
> >   c1 > 0 && c2 > 0 && c3 > 0 && ra1 > 0 && ra2 > ra1 &&
> >    ra3 > ra2}, {c1, c2, c3, ra1, ra2, ra3}]
>
> > go[2., 2., 2., 25, 1., 1., 1.]
>
> > 33275.9
>
> > roar[x_, y_] := x^2 + y^2
> > NMinimize[roar[x, y], {x, y}]
>
> > {0., {x -> 0., y -> 0.}}
>
> > --
> > Jason S. Kong
> > Graduate Student, Chen Lab
> > Department of Chemistry and Chemical Biology
> > Baker Laboratory, Cornell University
> > Ithaca, NY, 14853
>
> --
> Jason S. Kong
> Graduate Student, Chen Lab
> Department of Chemistry and Chemical Biology
> Baker Laboratory, Cornell University
> Ithaca, NY, 14853

Hi Jason,

NMinimize evaluates your function "go" symbolically before it
evaluates it numerically. (Evaluating go[c1, c2, c3, 25, ra1, ra2,
ra3] returns something that is not useful for further evaluation.) To
prevent this from happening, you can "trap" for symbolic arguments as
follows:

go[C1_?NumericQ, C2_, C3_, C4_, R1_, R2_, R3_] := ...

(Make sure you Clear[go] first.) This pattern only matches if the
first argument is numeric (i.e., a number or a symbol that represents
a number, such as Pi). After I did this, I didn't get the error
message. On the other hand, I didn't get a result after waiting 90
minutes.

--Mark

• References:
  • NMinimize Error In Evaluation
    • From: "Jason S. Kong" <kongjs@gmail.com>