Constructing matrix out of submatrices
- To: mathgroup at smc.vnet.net
- Subject: [mg113776] Constructing matrix out of submatrices
- From: Sebastian Schmitt <sschmitt at physi.uni-heidelberg.de>
- Date: Fri, 12 Nov 2010 05:26:54 -0500 (EST)
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