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Mathematica results different on different computers !

  • To: mathgroup at smc.vnet.net
  • Subject: [mg125534] Mathematica results different on different computers !
  • From: Nabeel Butt <nabeel.butt at gmail.com>
  • Date: Sun, 18 Mar 2012 02:40:03 -0500 (EST)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com

Hi Guys ...
     I run a piece of code on two different computers (different hardwares)
and I get different results.I think its something to do with overflow or
different precision on systems ? Personally I think my laptop with an
inferior hardware is giving me correct results. The code does involve some
simulation but running the simulation gives the same result on one
particular computer but different for different computers ! You can run and
tell me what answers you are getting ....Thanks in advance....and my code
is below :
\[Lambda] = 0.05;
\[Mu] = 0.05;
T = 1;
nn = 4;
\[CapitalDelta]T = T/nn;
m1 = 0.08;
\[Sigma]1 = 0.2;
m2 = 0.14;
\[Sigma]2 = 0.8;
\[Rho] = 0.1;
mean1 = (m1 - (\[Sigma]1^2)/2)*\[CapitalDelta]T;
var1 = (\[Sigma]1^2)*\[CapitalDelta]T;
rmean1 = E^(mean1 + 1/2 var1);
rvar1 = ((E^var1 - 1) E^(2*mean1 + var1));
mean2 = (m2 - (\[Sigma]2^2)/2)*\[CapitalDelta]T;
var2 = (\[Sigma]2^2)*\[CapitalDelta]T;
rmean2 = E^(mean2 + 1/2 var2);
rvar2 = ((E^var2 - 1) E^(2*mean2 + var2));
b1 = {rk1l = 0.001, rk1u = (rmean1 + 5*Sqrt[rvar1])};
b2 = {rk2l = 0.001, rk2u = (rmean2 + 5*Sqrt[rvar2])};

dl = (rk1u - rk1l)/Num;
dk = (rk2u - rk2l)/Num;
\[ScriptCapitalD] =
  TransformedDistribution[
   Exp[ {u, v}], {u, v} \[Distributed]
    MultinormalDistribution[{(m1 - (\[Sigma]1^2)/
          2)*\[CapitalDelta]T, (m2 - (\[Sigma]2^2)/
          2)*\[CapitalDelta]T}, {{\[Sigma]1^2*\[CapitalDelta]T, \
\[Rho]*\[Sigma]1*\[Sigma]2*\[CapitalDelta]T}, {\[Rho]*\[Sigma]1*\
\[Sigma]2*\[CapitalDelta]T, \[Sigma]2^2*\[CapitalDelta]T}}]];
data = Parallelize[RandomVariate[\[ScriptCapitalD], 10^5]];
ParallelEvaluate[data];


bndry3[Num_, data_] :=
  Module[{UU, M, \[Lambda], \[Mu], \[CapitalDelta]T, s, m, \[Sigma],
    mean, var, rmean, rvar, rkl, rku, dr, ddist, rvals, pvals, amin,
    amax, da, tlist, JN, some, blist, tlist1, tlist2, sol1, sol2,
    templist, l, points, pu, pl, dp, a, b, c, zi, Nm, Nz, Na, zW,
    m1, \[Sigma]1, m2, \[Sigma]2, \[Rho], mean1, var1, rmean1, rvar1,
    mean2, var2, rmean2, rvar2, b1, b2, dl, dk, xvals, yvals, rk1l,
    rk1u, rk2l, rk2u, \[ScriptCapitalD]1, dist, \[ScriptCapitalD],
    prob, JJ},

   Off[InterpolatingFunction::dmval];
   sll[ll_, elem_] := ll[[Ordering[ll[[All, elem]]]]];
   M = 0.5;
   \[Lambda] = 0.05;
   \[Mu] = 0.05;
   \[CapitalDelta]T = T/nn;
   s = E^(0.05*\[CapitalDelta]T);
   m1 = 0.08;
   \[Sigma]1 = 0.2;
   m2 = 0.14;
   \[Sigma]2 = 0.8;
   \[Rho] = 0.1;
   UU = 7;
   mean1 = (m1 - (\[Sigma]1^2)/2)*\[CapitalDelta]T;
   var1 = (\[Sigma]1^2)*\[CapitalDelta]T;
   rmean1 = E^(mean1 + 1/2 var1);
   rvar1 = ((E^var1 - 1) E^(2*mean1 + var1));
   mean2 = (m2 - (\[Sigma]2^2)/2)*\[CapitalDelta]T;
   var2 = (\[Sigma]2^2)*\[CapitalDelta]T;
   rmean2 = E^(mean2 + 1/2 var2);
   rvar2 = ((E^var2 - 1) E^(2*mean2 + var2));
   b1 = {rk1l = 0.001, rk1u = (rmean1 + 5*Sqrt[rvar1])};
   b2 = {rk2l = 0.001, rk2u = (rmean2 + 5*Sqrt[rvar2])};

   dl = (rk1u - rk1l)/Num;
   dk = (rk2u - rk2l)/Num;
   \[ScriptCapitalD] =
    TransformedDistribution[
     Exp[ {u, v}], {u, v} \[Distributed]
      MultinormalDistribution[{(m1 - (\[Sigma]1^2)/
            2)*\[CapitalDelta]T, (m2 - (\[Sigma]2^2)/
            2)*\[CapitalDelta]T}, {{\[Sigma]1^2*\[CapitalDelta]T, \
\[Rho]*\[Sigma]1*\[Sigma]2*\[CapitalDelta]T}, {\[Rho]*\[Sigma]1*\
\[Sigma]2*\[CapitalDelta]T, \[Sigma]2^2*\[CapitalDelta]T}}]];

   \[ScriptCapitalD]1 = SmoothKernelDistribution[data];

   g[x_, y_] := Evaluate[CDF[\[ScriptCapitalD]1, {x, y}]];


   fx1[r_] := PDF[LogNormalDistribution[mean1, Sqrt[var1]], r];
   fx2[r_] := CDF[LogNormalDistribution[mean1, Sqrt[var1]], r];
   pu = 1;
   pl = 0;
   dp = (pu - pl)/Num;
   gx1[p_] := InverseCDF[LogNormalDistribution[mean1, Sqrt[var1]], p];
   xvals =
    Flatten[{rk1l, Table[gx1[i + dp], {i, pl, pu - 2*dp, dp}], rk1u}];

   fy1[r_] := PDF[LogNormalDistribution[mean2, Sqrt[var2]], r];
   fy2[r_] := CDF[LogNormalDistribution[mean2, Sqrt[var2]], r];
   pu = 1;
   pl = 0;
   dp = (pu - pl)/Num;
   gy1[p_] := InverseCDF[LogNormalDistribution[mean2, Sqrt[var2]], p];
   yvals =
    Flatten[{rk2l, Table[gy1[i + dp], {i, pl, pu - 2*dp, dp}], rk2u}];




   f[x_, y_] := Evaluate[PDF[\[ScriptCapitalD]1, {x, y}]];

   dist =
    Flatten[Table[{prob = (NIntegrate[

          f[x, y], {x, xvals[[i]], xvals[[i + 1]]}, {y, yvals[[j]],
           yvals[[j + 1]]}, AccuracyGoal -> 4]); {NIntegrate[
         x*(f[x, y])/prob
         , {x, xvals[[i]], xvals[[i + 1]]}, {y, yvals[[j]],
          yvals[[j + 1]]}, AccuracyGoal -> 4],
        NIntegrate[
         y*(f[x, y])/(prob), {x, xvals[[i]], xvals[[i + 1]]}, {y,
          yvals[[j]], yvals[[j + 1]]}, AccuracyGoal -> 4]},

       prob}, {i, 1, Num}, {j, 1, Num}], 1];


   amin = N[0.001];
   amax = N[0.999];
   da = 0.01;

   (*dist/.{{x_Real,y_Real},z_Real}->x+y+z*)
   tlist1 = Parallelize[ParallelEvaluate[
      Off[FindMinimum::reged]];
     ParallelEvaluate[Off[FindMaximum::lstol]]; Table[{a,
       {l =
         Max[templist = {(sol1 = Flatten[Last[NestList[{{#[[1, 1]]/2},

                    Reverse[
                    Last[sll[
                    Flatten[
                    Table[{{\[Xi]}, (Total[(dist /. {{r_Real, S_Real},
                     p_Real} -> (Log[(S + \[Xi] (r -
                    S) + \[Mu] (\[Xi] - a) S)]*p))])}, {\[Xi],
                    If[(#[[2, 2, 1]] - 2*#[[1, 1]]) >=
                    0, (#[[2, 2, 1]] - 2*#[[1, 1]]), 0],
                    If[(#[[2, 2, 1]] + 2*#[[1, 1]]) <=
                    a, (#[[2, 2, 1]] + 2*#[[1, 1]]), a], #[[1, 1]]}],
                    0], 2]]]} & ,
                   {{a/4}, {-100, {a/2}}}, UU]][[2]]])[[1]], (sol2 =
               Flatten[Last[NestList[{{#[[1, 1]]/2},

                    Reverse[
                    Last[sll[
                    Flatten[
                    Table[{{\[Xi]}, (Total[
                    dist /. {{r_Real, S_Real},
                    p_Real} -> (Log[(S + \[Xi] (r -
                    S) - \[Lambda] (\[Xi] - a) S)]*p)])}, {\[Xi],
                    If[(#[[2, 2, 1]] - 2*#[[1, 1]]) >=
                    a, (#[[2, 2, 1]] - 2*#[[1, 1]]), a],
                    If[(#[[2, 2, 1]] + 2*#[[1, 1]]) <= (
                    1 + a*\[Lambda])/(
                    1 + \[Lambda]), (#[[2, 2, 1]] + 2*#[[1, 1]]), (
                    1 + a*\[Lambda])/(1 + \[Lambda])], #[[1, 1]]}],
                    0], 2]]]} & ,
                   {{0.25*((1 + a*\[Lambda])/(1 + \[Lambda]) -
                    a)}, {-100, {0.5*(a + (1 + a*\[Lambda])/(
                    1 + \[Lambda]))}}}, UU]][[2]]])[[1]],
            Total[dist /. {{r_Real, S_Real}, p_Real} ->
               Log[(S + a (r - S))]*p]}],
        If[templist[[3]] == l, 3,
         Flatten[Position[templist, l]][[1]]],
        Piecewise[{{0, templist[[3]] == l}, {sol1[[2]],
           templist[[1]] == l}, {sol2[[2]],
           templist[[2]] == l}}]}}, {a, amin, amax, da}]];
   (*points=Select[tlist,#[[2,2]]==3&]/.{a_,{J_,
   I_,\[CapitalDelta]_}}->a
   Graphics[Point[points],Axes->True]*)
   (*points=Select[Flatten[templist/.{{x_,y_},{z_,w_}}->{{x,y},{w}},
   1],#[[2]][[1]]==3&]/.{{x_,y_},{w_}}->{x,y};*)
   (*points=Select[tlist,#[[2,2]]==3&]/.{x_,{z_,w_}}->x;
   points*)
   JN = Interpolation[tlist1 /. {x_, {z_, w_, y_}} -> {x, z}];
   (*PN=Interpolation[tlist/.{x_,{z_,w_,y_}}->{x,y}];*)
   (*Off[InterpolatingFunction::dmval];*)
   (*Plot[JN[x],{x,0,1}]*)
   some = NestList[(JJ = #[[2]]; {tlist = Parallelize[ParallelEvaluate[
           Off[FindMinimum::reged]];
          ParallelEvaluate[Off[FindMaximum::lstol]];
          ParallelEvaluate[Off[InterpolatingFunction::dmval]];
          Table[(*nlist=(#[[1]]/.{x_,{z_,w_,y_}}->y);*){a,
            {l =
              Max[templist = {(sol1 =
                    Flatten[Last[NestList[{{#[[1, 1]]/2},

                    Reverse[
                    Last[sll[
                    Flatten[
                    Table[{{\[Xi]}, (Total[
                    dist /. {{r_Real, S_Real},
                    p_Real} -> (((Log[(S + \[Xi] (r -
                    S) + \[Mu] (\[Xi] - a) S)] +
                    JJ[(\[Xi]*
                    r)/(S + \[Xi] (r - S) + \[Mu] (\[Xi] - a) S)])*
                    p))])}, {\[Xi],
                    If[(#[[2, 2, 1]] - 2*#[[1, 1]]) >=
                    0, (#[[2, 2, 1]] - 2*#[[1, 1]]), 0],
                    If[(#[[2, 2, 1]] + 2*#[[1, 1]]) <=
                    a, (#[[2, 2, 1]] + 2*#[[1, 1]]), a], #[[1, 1]]}],
                    0], 2]]]} & ,
                    {{a/4}, {-100, {a/2}}}, UU]][[2]]])[[1]], (sol2 =
                    Flatten[Last[NestList[{{#[[1, 1]]/2},

                    Reverse[
                    Last[sll[
                    Flatten[
                    Table[{{\[Xi]}, (Total[
                    dist /. {{r_Real, S_Real},
                    p_Real} -> ((Log[(S + \[Xi] (r -
                    S) - \[Lambda] (\[Xi] - a) S)] +
                    JJ[(\[Xi]*
                    r)/(S + \[Xi] (r - S) - \[Lambda] (\[Xi] -
                    a) S)])*p)])}, {\[Xi],
                    If[(#[[2, 2, 1]] - 2*#[[1, 1]]) >=
                    a, (#[[2, 2, 1]] - 2*#[[1, 1]]), a],
                    If[(#[[2, 2, 1]] + 2*#[[1, 1]]) <= (
                    1 + a*\[Lambda])/(
                    1 + \[Lambda]), (#[[2, 2, 1]] + 2*#[[1, 1]]), (
                    1 + a*\[Lambda])/(1 + \[Lambda])], #[[1, 1]]}],
                    0], 2]]]} & ,
                    {{0.25*((1 + a*\[Lambda])/(1 + \[Lambda]) -
                    a)}, {-100, {0.5*(a + (1 + a*\[Lambda])/(
                    1 + \[Lambda]))}}}, UU]][[2]]])[[1]],

                 Total[dist /. {{r_Real, S_Real},
                    p_Real} -> (Log[(S + a (r - S))] +
                    JJ[(a*r)/(a*r + (1 - a) S)])*p]}],
             If[templist[[3]] == l, 3,
              Flatten[Position[templist, l]][[1]]],
             Piecewise[{{0, templist[[3]] == l}, {sol1[[2]],
                templist[[1]] == l}, {sol2[[2]],
                templist[[2]] == l}}]}}, {a, amin, amax, da}]],
        Interpolation[
         tlist /. {x_, {z_, w_, y_}} -> {x, z}]}) &, {tlist1, JN},
     nn - 1]];
stuff = Table[{1/NN, bndry3[NN, data]}, {NN, 4, 7}];
listn[a_] := {#[[1]], #[[2]][[4, 2]][a]} & /@ stuff;
a = 0.5;
g1 = ListPlot[listn[a], PlotStyle -> {Red, PointSize[Large]}]
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Nabeel Butt
UWO,London
Ontario, Canada


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