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.
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.
ArrayReshapehelp? $\endgroup$