compiled function For 2D array can be written as

cf2 = Compile[{{size, Integer}, {s, Integer}}, Block[{m}, m = Table[Table[0, {s}], {size}]], RuntimeAttributes -> {Listable}, Parallelization -> True]

For example, cf2[{1, 2, 3, 4}, {4, 5, 6, 2}]= {{{0, 0, 0, 0}}, {{0, 0, 0, 0, 0}, {0, 0, 0, 0, 0}}, {{0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0}}, {{0, 0}, {0, 0}, {0, 0}, {0, 0}}}

Hi Marco

the matrix is not big, generally (2*120) and is not sparse at the end of the function. In fact, in the rest of the code I've something like this :

For[k0 = 1, k0 <= nB0, k0++, (* 
  Loop over the different values of B0 *)

  For[k1 = 1, k1 <= nB1, k1++, (* 
    Loop over the different values of B1 *)

    MM = M0;

    For[n = 1, n <= npuls, n++, (* Time evolution for 1 spin*)

     MM = Uevol[0.01, t1, t2, B0[[k0]] + offB0, B1[[k1]] + offB1, 
         u[[n, 1]], u[[n, 2]]].MM;
     Mmean[[n, 1]] = 
      Mmean[[n, 1]] + MM[[2]]*B0distrib[[k0]]*B1distrib[[k1]];
     Mmean[[n, 2]] = 
      Mmean[[n, 2]] + MM[[3]]*B0distrib[[k0]]*B1distrib[[k1]];
     ];

    ];];

where Uevol is a function which gives a matrix. I'm doing very basic operations, sums of products of matrices , and I don't need a formal expression. After that this function will be put inside an objective function minimized by NMinimize. (by the way, apparently NMinimize doesn't like Compile functions as it doesn't work with machine-size real numbers...)

cheers Q.A.

Hi Quentin,

this does not answer you question but have you tried optimising that within Mathematica, i.e. without compilation first? Using the Table command is actually quite slow:

Table[0, {40000}, {40000}]; // AbsoluteTiming

takes 43.5 seconds on my computer.

ConstantArray[0, {40000, 40000}]; // AbsoluteTiming

and

Normal[SparseArray[{}, {40000, 40000}]]; // AbsoluteTiming

run about 7.95 seconds. If you can use a SparseArray only it becomes really fast:

SparseArray[{}, {40000, 40000}]; // AbsoluteTiming

Also further calculations on SparseArray are quite fast: 0.000203 seconds.

Cheers,

Marco