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MathGroup Archive 2005

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NMinimice and NumberQ

  • To: mathgroup at smc.vnet.net
  • Subject: [mg62093] NMinimice and NumberQ
  • From: "Guillermo Sanchez" <guillermosanchezleon at hotmail.com>
  • Date: Fri, 11 Nov 2005 02:51:56 -0500 (EST)
  • Reply-to: guillermo at usal.es
  • Sender: owner-wri-mathgroup at wolfram.com

Dear group
(*First evaluate these expressions, don't worry it contents )

ff1[{f2_, inp2_:inp, p2_:p, tiemp_:t}, inp1_, p1_, t0_, a_, var_, n_, 
opts___] :=
Module[{modelo, dd, ddd, tt, ff, i, j, g, X, sigma, invsigma, m, deter, bb},
Subscript[d, 0] = t0; modelo[inp_, p_, t1_] = f2 /. {inp2 -> inp, inp -> p2 
-> p,
tiemp -> t1}; g[t_] = Simplify[{D[modelo[inp, p, t], inp], D[modelo[inp, p, 
t], p]}
/. {inp -> inp1, p -> p1}]; tt = Table[Subscript[t, i], {i, 0, n}]; dd =
Table[Subscript[d, i], {i, n}]; ddd = FoldList[Plus, Subscript[d, 0], dd]; X 
=
(g[#1] &amp; ) /@ tt /. Thread[tt -> ddd]; ff[i_, j_] := Which[i == j, 1, i 
< j,
E^((-a)*Sum[Subscript[d, k], {k, i, j - 1}]), i > j, 
E^((-a)*Sum[Subscript[d, k],
{k, j, i - 1}])]; sigma = var*Array[ff, {n + 1, n + 1}]; invsigma = 
Inverse[sigma];
m = Transpose[X] . invsigma . X; m];

m1 = ff1[{1.12*E^(-0.04*p - 0.12*t)*inp + 0.7*E^(-1.09*p - 0.0012*t)*inp +
1.2*E^(-0.58*p - 0.0001*t)*inp}, 100000, 5, 0.5, 1, 1, 2];

dd = Table[Subscript[d, i], {i, 3}];

(*My questions start here *)

(*I apply the below function to obtain {d1, ..., di, ..dn} by minimization.
It works find but I wish increase the speed.*)

deter[x_/;VectorQ[x,NumberQ]]:=Det[m1/. Thread[dd\[Rule]x]] ;

NMinimize[{-deter[dd],Thread[dd>1]},dd];//Timing

(* In this example the above function only spents a few seconds, however in 
real
problem it spent a few minutes. I was looking for a faster way. I realize 
that the
below expression usually (no always) spent the halt of the time but I need 
build it
each time depending on the number of di, for this reason it is not 
applicable inside
a package where the number of di can be chose by the user.*)



deter1[d1_?NumberQ,d2_?NumberQ ,d3_?NumberQ ]:=Det[m1/. 
Thread[dd\[Rule]{d1,d2,
d3}]] ;NMinimize[{-deter1[d1,d2,d3],Thread[{d1,d2, d3}>1]},{d1,d2, 
d3}];//Timing



(* Note that in the below expression I only introduce a curly braces and the 
time of
computation increases almost the double. Why? *)



deter2[{d1_?NumberQ,d2_?NumberQ ,d3_?NumberQ }]:=Det[m1/. 
Thread[dd\[Rule]{d1,d2,
d3}]] ;NMinimize[{-deter2[{d1,d2, d3}],Thread[{d1,d2, d3}>1]},{d1,d2, 
d3}];//Timing

(* Any help for enhance deter[x_/;VectorQ[x,NumberQ]] *)

Guillermo



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