# How to save (large) data generated from simulations

The following is a simple example of a much larger simulation that I want to run

Define some processes

norTheta[mu_, sigma_] := Random[NormalDistribution[mu, sigma]];
norPi[mu_, sigma_] := Random[NormalDistribution[mu, sigma]];

thetaNext[thetaNow_] :=
thetaNow + (-lambdaTheta*(thetaNow - thetaBar)*deltaT +
sigmaTheta*norTheta[0, 1]*Sqrt[deltaT]);
piNext[piNow_, thetaNow_] :=
piNow + (-lambdaPi*(piNow - thetaNow)*deltaT +
sigmaPi*norPi[0, 1]*Sqrt[deltaT]);


Then define some parameters

lambdaTheta = 0.07;
thetaBar = 0.02;
sigmaTheta = 0.012;
lambdaPi = 1.0;
sigmaPi = 0.0125;


Then simulate the system

steps = 252;
T = 50;
deltaT = 1/steps; // N
Maturity = T*steps;

process = Transpose[NestList[{  piNext[#[[1]], #[[2]]],
thetaNext[#[[2]]]} &,{0.02, 0.02}, Maturity]];


I have two questions: (1) what is the best MMA of repeating the above 10,000 at each loop saving the output 'process' for use later; (2) what is the fastest way of doing this?

Many thanks, Paul

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are you familiar with Do and Compile? or did I misunderstand the question? – acl Oct 29 '12 at 11:18
I'm not sure how Do / Compile helps here. For example, in matlab or C / java, I would loop over the above 'simulate system' block of code saving the output after T = 50 into a cell array. I would then finish by writing this cell array to a file. Is this the way one should do it in MMA ? – Luap Nalehw Oct 29 '12 at 11:49
– Sjoerd C. de Vries Oct 29 '12 at 12:36
For the "write to file" portion of your task, there's Put[]... – J. M. Oct 29 '12 at 12:59
No, not at all. I suggested to collect 10000 runs in a table generated by Table. I even linked to its reference page. Don't know where in my answer I suggested to use Reap/Sow. The table itself could be saved with DumpSave. See also mathematica.stackexchange.com/a/2008/57 and mathematica.stackexchange.com/a/209/57 – Sjoerd C. de Vries Oct 29 '12 at 14:11