How to expand a MxM matrix with replicates of itself and drop some of the rows and cols periodically?

Question

How can I expand a 2d-matrix with dimensions x,x (e.g. mat = {{ 1, 2 }, { 3, 4 }}) with replicates of mat into matTimes100 with dimensions 100*x,100*x? I tried Join[ mat, mat, mat, <97>, 2 ] which works nicely and would give me dimensions 100*x,x. However, I do not want to manually insert mat 100 times into Join[].

How to do that automatically? Join[ Table[ mat, { 1, 100 } ], 2 ] does not work, since it delivers Join[{mat, mat, mat, <97>}, 2 ].

EDIT:

On request, I try to clarify my question. In addition, I try to figure out, what exactly I'm trying to do.

Let's assume a MxM Matrix with M = 3:

mat={{1, 2, 3}, {4, 5, 6}, {7, 8, 9}};
Reverse@mat//TableForm

Now I would like to make a larger NxN matrix out of it with some of the rows and cols dropped in a periodic manner. I tried to visualize my purpose. In the MWE below I choose num = 2 with N = M + num * ( M - 1 ). The dropped rows/cols are indicated by the blue lines.

Thanks for your hints!!

Answer 1

I like this one:

ArrayFlatten[Table[mat, 100, 100]]

Answer 2

Here is one way to do it, using Fold

newmat = Fold[Join[#1, #2, 2] &, mat, ConstantArray[mat, 100]];
MatrixForm@newmat

Another method, using ArrayReshape and Transpose

ArrayReshape[Transpose[ConstantArray[mat, 100]], {2, 200}]

Another method using ArrayPad

ArrayPad[mat, {{0, 0}, {0, 200}}, mat]

Answer 3

PadRight[#, {10, 10} Dimensions[#], "Periodic"] & @ {{1, 2}, {3, 4}}

Answer 4

f1 = Drop[ArrayFlatten[ConstantArray[Reverse@#, {#2, #2}]], 3;; ;;3, 4;; ;;3] &

f2 = Drop[KroneckerProduct[ConstantArray[1, {#2 , #2}], Reverse@ #], 3;; ;;3, 4;; ;;3] &


mat = {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}};
n = 5;
f1[mat,n] // MatrixForm

f1[mat, n] == f2[mat, n]

True

Answer 5

You can simply use Band

dim = Length[mat]
SparseArray[(Band[{dim # - 1, dim # - 1}] -> mat) & /@ Range[3]];
% // MatrixForm

$\left( \begin{array}{cccccc} 1 & 2 & 0 & 0 & 0 & 0 \\ 3 & 4 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 2 & 0 & 0 \\ 0 & 0 & 3 & 4 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 0 & 3 & 4 \\ \end{array} \right)$

you can do the same thing with Outer also

Outer[Times, IdentityMatrix[3], mat] // ArrayFlatten;
% // MatrixForm

You can modify the first argument depending on how you want to replicate your matrix. For example if want to get Kuba's answer replace IdentityMatrix[3] by ConstantArray[1, {3, 3}].

If you want to put your matrix row wise, then use Band[{1, dim # - 1}].

dim = Length[mat]
SparseArray[(Band[{1, dim # - 1}] -> mat) & /@ Range[3]];
% // MatrixForm

$\left( \begin{array}{cccccc} 1 & 2 & 1 & 2 & 1 & 2 \\ 3 & 4 & 3 & 4 & 3 & 4 \\ \end{array} \right)$