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Constructing matrix out of submatrices


Hi!

I would like to construct a matrix out of submatrices. I guess this is
straight forward but somehow I couldn't find the correct way in the
documentation. The example that follows is of course simplified. Please
don't take shortcuts.

I start with a zero matrix and a submatrix:

matrix = ConstantArray[0, {3, 3}]
submatrix = {{a, b}, {c, d}}

I want to specificy the upper-left corner in the matrix where the
submatrix should be placed. If the position is {1,1} the result should be:

result = {{a, b, 0}, {c, d, 0}, {0, 0, 0}}

If it is {1,2}:

result = {{0, a, b}, {0, c, d}, {0, 0, 0}}

etc.

ReplacePart together with ArrayFlatten comes close, but the submatrix
does not "override" zeros:

ReplacePart[matrix, {1, 1} -> submatrix] // ArrayFlatten

{{a, b, 0, 0}, {c, d, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}

What are possible solutions?

Thanks,

Sebastian


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