Re: ParallelTable doesn't work, but Table does

• To: mathgroup at smc.vnet.net
• Subject: [mg101774] Re: [mg101689] ParallelTable doesn't work, but Table does
• From: Iván Lazaro <gaminster at gmail.com>
• Date: Thu, 16 Jul 2009 08:22:19 -0400 (EDT)
• References: <200907140937.FAA01989@smc.vnet.net> <4A5CD404.4040301@mit.edu>

```Sorry for the inconvenience; the code below work as is expected with Table.

Num = 4;
Time = 600;
cont = 0;

r[r2_, r3_, r4_] := {1, r2, r3, r4};
A[a12_, a13_, a14_, a21_, a23_, a24_, a31_, a32_, a34_, a41_, a42_,
a43_] := {{1, a12, a13, a14}, {a21, 1, a23, a24}, {a31, a32, 1,
a34}, {a41, a42, a43, 1}};

Variable[] := Flatten[Table[Subscript[x, i][t], {i, 1, Num}]]

JacobianMatrix[funs_List, vars_List] := Outer[D, funs, vars]

CondIni[] := Table[{Subscript[x, i][0] == 0.1*i}, {i, 1, Num}]

Y = Table[{Subscript[x, i][t], Subscript[x, i + 4][t],
Subscript[x, i + 8][t], Subscript[x, i + 12][t]}, {i, 5, 8}];

YI9 = Flatten[
Table[{Subscript[x, i][0] == If[Mod[i, 5] == 0, 1, 0, 0],
Subscript[x, i + 4][0] == If[Mod[i + 4, 5] == 0, 1, 0, 0],
Subscript[x, i + 8][0] == If[Mod[i + 8, 5] == 0, 1, 0, 0],
Subscript[x, i + 12][0] == If[Mod[i + 12, 5] == 0, 1, 0, 0]}, =
{i,
5, 8}]];

YI3 = Flatten[CondIni[]];
Ecua[r2_, r3_, r4_, a12_, a13_, a14_, a21_, a23_, a24_, a31_, a32_,
a34_, a41_, a42_, a43_] :=
Flatten[Table[
r[r2, r3, r4][[i]]*
Subscript[x, i][
t]*(1 - Sum[
A[a12, a13, a14, a21, a23, a24, a31, a32, a34, a41, a42,
a43][[i, j]]*Subscript[x, j][t], {j, 1, Num}]), {i, 1,
Num}]];

Table[J =
JacobianMatrix[
Ecua[r2, r3, r4, a12, a13, a14, a21, a23, a24, a31, a32, a34, a41,
a42, a43], Variable[]];
E1 = Flatten[Transpose[J.Y]];
EQ3 = Table[
D[Subscript[x, i][t], {t, 1}] ==
Ecua[r2, r3, r4, a12, a13, a14, a21, a23, a24, a31, a32, a34, a41,
a42, a43][[i]], {i, 1, 4}];
EQ9 = Table[D[Subscript[x, i][t], {t, 1}] == E1[[i - 4]], {i, 5, 20}=
];
sol = NDSolve[Join[EQ9, EQ3, YI3, YI9],
Table[Subscript[x, i][t], {i, 1, 20}], {t, 0, Time},
MaxSteps -> Infinity, AccuracyGoal -> 2];
u = Table[Random[], {4}];
PhiT = Transpose[
Table[{Subscript[x, i][t], Subscript[x, i + 4][t],
Subscript[x, i + 8][t], Subscript[x, i + 12][t]}, {i, 5,
8}] /. sol /. t -> Time];
ExpLyap = Log[Norm[PhiT.u]]/Time;

If[ExpLyap > 0,
PutAppend[
Join[A[a12, a13, a14, a21, a23, a24, a31, a32, a34, a41, a42, a43],
r[r2, r3, r4], ExpLyap], "File"]],

{a12, 0.01, 0.01, 0.01}, {a13, 0.01, 0.01, 0.01}, {a14, 0.01, 0.01,
0.01}, {a21, 0.01, 0.01, 0.01}, {a23, 0.01, 0.01, 0.01}, {a24, 0.01,
0.01, 0.01}, {a31, 0.01, 0.01, 0.01}, {a32, 0.01, 0.01,
0.01}, {a34, 0.01, 0.01, 0.01}, {a41, 0.01, 0.01, 0.01}, {a42, 0.01,
0.01, 0.01}, {a43, 0.01, 0.01, 0.01}, {r2, 0.01, 0.01, 0.01}, {r3,
0.01, 0.01, 0.01}, {r4, 1.11, 1.21, 0.01}]

2009/7/15 Zach Bj=F8rnson <bjornson at mit.edu>

>  Hi-
>
> I'm a bit confused by this code. There's a syntax error (the final ] on t=
he
> last line doesn't have a matching bracket, nor do those iterators a21...r=
4
> apply to anything as the code is written) somewhere, but I can't tell whe=
re.
> I also can't quite tell what the replacement is for the ParallelTable
> function that you originally posted. I'm guessing it's the Do loop at the
> end. Do you have a version of your code that uses Table (not ParallelTabl=
e)
> instead of Do? When I substituted the ParallelTable code for the Do loop,
> and changed ParallelTable to Table, the code didn't run due to other erro=
rs
> (your equations aren't simplifying). Try to get Table to work first (it o=
nly
> needs to go through one iteration, not all n iterations), then change it =
to
> ParallelTable.
>
> -Zach
>
>
> On 7/15/2009 10:16 AM, Iv=E1n Lazaro wrote:
>
> This is the almost complete code without parallelization. Thanks for all
>
>
> Num = 4;
> Time = 600;
>
>
> r[r4_] := {1, 1, 1, r4};
> A[a13_, a14_, a23_, a24_, a32_, a34_, a42_,
>    a43_] := {{1, 1, a13, a14}, {1, 1, a23, a24}, {1, a32, 1,
>     a34}, {1, a42, a43, 1}};
>
>
>
> Variable[] := Flatten[Table[Subscript[x, i][t], {i, 1, Num}]]
>
> JacobianMatrix[funs_List, vars_List] := Outer[D, funs, vars]
>
> CondIni[] := Table[{Subscript[x, i][0] == 0.1*i}, {i, 1, Num}]
>
> Y = Table[{Subscript[x, i][t], Subscript[x, i + 4][t],
>     Subscript[x, i + 8][t], Subscript[x, i + 12][t]}, {i, 5, 8}];
>
> YI9 = Flatten[
>    Table[{Subscript[x, i][0] == If[Mod[i, 5] == 0, 1, 0, 0],
>      Subscript[x, i + 4][0] == If[Mod[i + 4, 5] == 0, 1, 0, 0],
>      Subscript[x, i + 8][0] == If[Mod[i + 8, 5] == 0, 1, 0, 0],
>      Subscript[x, i + 12][0] == If[Mod[i + 12, 5] == 0, 1, 0, 0]}=
, {i,
>       5, 8}]];
> YI3 = Flatten[CondIni[]];
> Ecua[r4_, a13_, a14_, a23_, a24_,a32_,
>    a34_, a42_, a43_] :=
>   Flatten[Table[
>     r[r4][[i]]*
>      Subscript[x, i][
>       t]*(1 - Sum[
>         A[a13, a14, a23, a24,a32, a34, a42,
>            a43][[i, j]] *Subscript[x, j][t], {j, 1, Num}]), {i, 1,
>      Num}]] ;
>
>
>
> Do[
>
>
>  J = JacobianMatrix[
>    Ecua[r4_, a13_, a14_, a23_, a24_,a32_,
>    a34_, a42_, a43_], Variable[]];
>
>  E1 = Flatten[Transpose[J.Y]];
>
>  EQ3 = Table[
>    D[Subscript[x, i][t], {t, 1}] ==
>     Ecua[r4_, a13_, a14_, a23_, a24_,a32_,
>    a34_, a42_, a43_][[i]], {i, 1, 4}];
>
>  EQ9 = Table[D[Subscript[x, i][t], {t, 1}] == E1[[i - 4]], {i, 5, 2=
0}];
>
>  sol = NDSolve[Join[EQ9, EQ3, YI3, YI9],
>    Table[Subscript[x, i][t], {i, 1, 20}], {t, 0, Time},
>    MaxSteps -> Infinity, AccuracyGoal -> 2];
>
> PhiT = Table[{Subscript[x, i][t], Subscript[x, i + 4][t],
>        Subscript[x, i + 8][t], Subscript[x, i + 12][t]}, {i, 5,
>        8}] /. sol /. t -> Time];
>
> EL=Log[PhiT]
>
>  If[EL > 0,
>   PutAppend[Join[A[a13, a14, a23, a24,a32, a34, a42,  a43],
>      r[r4], EL],"File"]],
>
>
>  {a13, 0, 2.00, 0.01}, {a14, 0, 2.00, 0.01}, {a23, 0, 2.00, 0.01}, {a24, =
0,
> 2.00,
>   0.01}, {a32, 0, 2.00, 0.01}, {a34, 0, 2.00, 0.01}, {a42, 0, 2.00, 0.01}=
,
> {a43, 0, 2.00,
>   0.01},  {r4, 0.01, 0.50, 0.01}]
>
>
>
> 2009/7/14 Zach Bj=F8rnson <bjornson at mit.edu>
>
>> Hi- Can you send me your notebook so I can play with it, please? -Zach
>>
>> On 7/14/2009 3:45 PM, Iv=E1n Lazaro wrote:
>>
>>> Thanks for the answer.
>>>
>>> I tried that, but did't work.
>>>
>>> A and r, are a 4x4 matrix and a vector, respectivily. Ecua[] simply
>>> construct equations for NDSolve, and Variables[] do the same. JacobianM=
atrix
>>> make the Jacobian of equations given by Ecua, using the variables
>>> Variable[]. EQ3, EQ9, YI3, YI9 are simply defintions of equations to be
>>> given to NDSolve a 3-dimensional system of equations and a 9-dimensiona=
l
>>> respectivly.
>>>
>>> The problem i'm triyng to resolve is very time consuming, so I expected
>>> that parallelizing could make it faster. As an alternative, i tried wit=
h Do
>>> instead of Table (and ParallelDo instead of ParallelTable), but the err=
or
>>> doesn't disapper. The problem seems to be in NDSolve; maybe is not posi=
ble
>>> parallelize many NDSolve solutions, altought they are not related.
>>>
>>
>

```

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