       Re: Weird NMinimize behaviour

• To: mathgroup at smc.vnet.net
• Subject: [mg97556] Re: [mg97518] Weird NMinimize behaviour
• From: Filippo Miatto <miatto at gmail.com>
• Date: Sun, 15 Mar 2009 05:27:53 -0500 (EST)
• References: <200903142313.SAA25117@smc.vnet.net> <op.uqs5f8y1tgfoz2@bobbys-imac.local>

```woops sorry i didn't see that!

F2[n1_,k1_,n2_,k2_]:=(-1)^(n1+k1+n2+k2)/(360 \[Pi]^4) (8 \[Pi]^4-60 \
[Pi]^2 Mod[-Subscript[z, k1]+Subscript[z, n1]-Subscript[z,
k2]+Subscript[z, n2],2 \[Pi]]^2+60 \[Pi] Mod[-Subscript[z,
k1]+Subscript[z, n1]-Subscript[z, k2]+Subscript[z, n2],2 \[Pi]]^3-15
Mod[-Subscript[z, k1]+Subscript[z, n1]-Subscript[z, k2]+Subscript[z,
n2],2 \[Pi]]^4)

R2[s_]:=(1-1/\[Pi] Sum[(-1)^(n1+1) Subscript[z, n1],{n1,1,2s-1}])^4

j[s_]:=Sum[F2[n1,k1,n2,k2],{n1,0,2s-1},{k1,0,2s-1},{n2,0,2s-1},
{k2,0,2s-1}]+R2[s]

there is also the condition Subscript[z, 0]=0

For example if I try:

NMaximize[{1/j,0<Subscript[z, 1]<Subscript[z, 2]<Subscript[z,
3]<Subscript[z, 4]<Subscript[z, 5]<Subscript[z, 6]<Subscript[z, 7]<2\
[Pi]},{Subscript[z, 1],Subscript[z, 2],Subscript[z, 3],Subscript[z,
4],Subscript[z, 5],Subscript[z, 6],Subscript[z, 7]}]

I get a result of 23.517 on the mac and a result <23 on windows,
although everything is the same. Now i don't know if the result of my
mac is correct (since the one of windows isn't, and actually the
values should be linear with respect to s, and 23.517 is a little too
low) and i'm sure i can't rely on the win machine to go up and
maximize 1/j[s] for high values of s.
if i could understand the reason of this discrepancy i could possibly
fix things, either in the form of the equations or in the parameters
of NMaximize (or NMinimize).
Thank you
Filippo

On Mar 15, 2009, at 1:39 AM, DrMajorBob wrote:

> =CF=80
>
> ???
>
> Post readable code. Use Edit>Copy As>Plain Text and paste into e-mail.
>
> Bobby
>
> On Sat, 14 Mar 2009 18:13:15 -0500, Filippo Miatto
> <miatto at gmail.com> wrote:
>
>> Dear all,
>> i'm working in the quantum optics group of the university of Leiden,
>> and i use mathematica 7 a lot.
>> we have both windows machines and macs. On a mac i was trying to
>> minimize the function
>>
>> j[s_] := Sum[F2[n1, k1, n2, k2], {n1, 0, 2 s - 1}, {k1, 0, 2 s - 1},
>> {n2, 0,2s - 1}, {k2, 0, 2s - 1}] + R2[s]
>>
>> Where
>> R2[s_] := (1 - 1/=CF=80 Sum[(-1)^(n1 + 1) Subscript[z, n1], {n1, 1,
>> 2 s -
>> 1}])^4
>>
>> and
>> F2[n1_, k1_, n2_, k2_] := (-1)^(n1 + k1 + n2 + k2)/(360 =CF=80^4)
>> (8 =CF=80^4 -
>> 60 =CF=80^2 Mod[-Subscript[z, k1] + Subscript[z, n1] - Subscript[z,
>> k2] +
>> Subscript[z, n2], 2 =CF=80]^2 + 60 =CF=80 Mod[-Subscript[z, k1] +
>> Subscript[z,
>> n1] - Subscript[z, k2] + Subscript[z, n2], 2 =CF=80]^3 -15 Mod[-
>> Subscript[z, k1] + Subscript[z, n1] - Subscript[z, k2] +
>> Subscript[z,
>> n2], 2 =CF=80]^4)
>>
>> (sorry for the mess, on the screen the subscripts simply appear as
>> subscripts...)
>>
>> and i get certain results for s=1,2,3,4,5,etc..
>> on the windows machine though, i get worse results! the version of
>> mathematica is the same, machineprecision value is the same, even
>> the .nb file is the same! (the processor is different: a dualcore2duo
>> on the mac and a quad core xeon on the windows machine)
>> The mac can work well until s=6, the windows machine can go on to
>> greater values, but still giving less good results.
>> Do you have any idea how i can solve this issue?
>> Thank you in advance!
>> Filippo=
>>
>
>
>
> --
> DrMajorBob at bigfoot.com

```

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