I would like to generate a $3D$ matrix of dimension $(n1\times n1\times n1)$ compose of $216$ matrix blocks $(n2\times n2\times n2)$. All 216 matrix blocks are subdivided into 4 groups, each one with 54 identical matrices. All matrix elements of each matrix block taking into account each group have the same value, which can be $a, b, c$ or $d$. The position of each block is randomly allocated in the main matrix $(n1\times n1\times n1)$. Figure below represents the proposal.

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Taking into account that the sum of all blocks' volume does not exactly correspond to the volume of the main matrix $(n1\times n1\times n1)$ and the difficulty in adjusting the blocks in the main matrix, null elements can be used to complete the elements in the main matrix.

Below, is a fragment of the code:

n1 = 100;(*dimension of main matrix*)
n2 = 16;(*dimension of block matrix*)
a = 2; b = 3; c = 5; d = 7; (*types of elements contained in each matrix block*)
m = SparseArray[{{i_, j_} -> 0}, {n1, n1, n1}]; (*initial main matrix with null elements*)
m1 = SparseArray[{{i_, j_} -> a}, {n2, n2, n2}]; (*first type of matrix block*)
m2 = SparseArray[{{i_, j_} -> b}, {n2, n2, n2}]; (*second type of matrix block*)
m3 = SparseArray[{{i_, j_} -> c}, {n2, n2, n2}]; (*third type of matrix block*)
m4 = SparseArray[{{i_, j_} -> d}, {n2, n2, n2}]; (*fourth type of matrix block*)
res= ArrayFlatten[];

The idea would be to generate 216 matrix blocks subdivide into four groups of 54 matrices of $m1$, $m2$, $m3$, and $m4$ and allocate them in random positions in the main matrix $m$.

How to do this?

Can anybody help me?

Thank you so much in advance.


1 Answer 1


Maybe this is what you want. This does not use any SparseArrays because the resulting array is just not sparse enough for SparseArray providing any benefit.

k = 6;
A = ArrayReshape[
     ConstantArray[a, Quotient[k^3, 4]],
     ConstantArray[b, Quotient[k^3, 4]],
     ConstantArray[c, Quotient[k^3, 4]],
     ConstantArray[d, Quotient[k^3, 4]]
     ][[PermutationList[RandomPermutation[k^3], k^3]]],
   {k, k, k}
ones = ConstantArray[1, ConstantArray[n2, 3]];
B = ArrayPad[KroneckerProduct[A, ones], ConstantArray[{0, n1 - n2 k}, 3]];

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