Re: Re: NMinimize Error In Evaluation
- To: mathgroup at smc.vnet.net
- Subject: [mg85159] Re: [mg85059] Re: [mg84801] NMinimize Error In Evaluation
- From: "Jason S. Kong" <kongjs at gmail.com>
- Date: Wed, 30 Jan 2008 06:13:31 -0500 (EST)
- References: <200801150813.DAA11621@smc.vnet.net>
Thank you Mark and Andrzej!
These suggestions are delightfully helpful.
I noticed the following changes:
1. imagine function was greatly simplified. (Of course I'd do it the
longhand way! *smacks head*)
2. dynamics has an N function now incorporated within it. I presume
this is to force it to return a purely numeric answer? I didn't
notice this before.
3. of course, changing the go function in itself.
As you noted that there are many things I can still optimize, I'll
keep looking into it to find these issues. Thanks again for a start
at optimizing this code to perfect functionality.
-Jason S. Kong
On Jan 29, 2008 5:41 AM, Andrzej Kozlowski <akoz at mimuw.edu.pl> wrote:
> There are lots of problems and I can only describe some of them. First
> of all, change the definition of go to something like:
>
> go[C1_?NumberQ, C2_?NumberQ, C3_?NumberQ, C4_?NumberQ, R1_?NumberQ,
> R2_?NumberQ,
> R3_?NumberQ] := (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])
>
> I would also add a defintion of g0 on the boundary (where one of the
> C's is 0) otherwise you will get an error message (althogh the code
> will work).
>
> With these changes NMinimize should now work, but terribly slowly. To
> make the code more efficient one would need to totally re-write it but
> for this I cannot spare the itme, so I have made just one basic change
> (the compiled PreEquilibrium function) which at least gives a result
> in a reasonable time:
>
> PreEquilibrium =
> Compile[{C1, C2, C3, C4, C5},
> Evaluate[
> Block[{var1, var2, var3, var4, var5}, {var1, var2, var3, var4,
> var5} /.
> 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}]]]];
>
> equilibrium[C1_, C2_, C3_, C4_, C5_] :=
> Thread /@ (Thread[{V1, V2} ->
> PreEquilibrium[C1, C2, C3, C4, C5]] /. {V1 -> {var1, var2, var3,
> var4,
> var5}, V2 -> {var1, var2, var3, var4, var5}})
>
> imagine[tests_] :=
> Select[tests,
> And @@ {(Im[var1 /. #] == 0.), (Im[var2 /. #] == 0.), (Im[var3 /. #]
> ==
> 0.), (Im[var4 /. #] == 0.), (Im[var5 /. #] == 0.)} &]
> dynamics[C1_, C2_, C3_, C4_, C5_] :=
> Select[imagine[
> N[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_, ra1_, ra2_,
> ra3_] /; (c1 == 0. || c2 == 0. || c3 == 0.) := 10^7
> go[C1_?NumberQ, C2_?NumberQ, C3_?NumberQ, C4_?NumberQ, R1_?NumberQ,
> R2_?NumberQ,
> R3_?NumberQ] := (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}] // Timing
>
> NMinimize::Failed to converge to the requested accuracy or
> precision within 100 iterations.
>
> {227.508, {0.0157464, {c1 -> 3.79253*10^-8, c2 -> 0.316349, c3 ->
> 7.93686,
> ra1 -> 0.000436015, ra2 -> 0.000346922, ra3 -> 0.000722034}}}
>
> Note the message about the failure to converge. You can try various
> options of NMinimize to see if you can get a better result.
>
>
> Andrzej Kozlowski
>
> On 26 Jan 2008, at 10:01, Jason S. Kong 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 <kongjs 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
> >
>
>
>
--
Jason S. Kong
Graduate Student, Chen Lab
Department of Chemistry and Chemical Biology
Baker Laboratory, Cornell University
Ithaca, NY, 14853
- References:
- NMinimize Error In Evaluation
- From: "Jason S. Kong" <kongjs@gmail.com>
- NMinimize Error In Evaluation