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list manipulation - Efficient way to combine SparseArray objects?


I have several SparseArray objects, say sa11, sa12, sa21, sa22, which I would like to combine into the equivalent of {{sa11, sa12}, {sa21, sa22}}. As an example, I have :


sa11 = SparseArray[Band[{1, 1}, {4, 4 3}] -> {{ConstantArray[1, 3]}}] 
sa12 = SparseArray[Join[Band[{1, #}, {4, 4 3}] -> 1 & /@ Range[1,  4 3, 4]]]
sa21 = SparseArray[Join[Band[{1, #}, {3, 4 3}] -> 1 & /@ Range[1, 4 3, 3]]] 
sa22 = SparseArray[Band[{1, 1}, {3, 4 3}] -> {{ConstantArray[1, 4]}}]


I am able to generate the big SparseArray with :


sa = SparseArray[Join[{Band[{1, 1}, {4, 4 3}] -> {{ConstantArray[1, 3]}}}, Band[{1,     #},{4, 2 4 3}] -> 1 & /@ Range[4 3 + 1, 2  4 3, 4], Band[{4 + 1, #}, {4 + 3, 4 3}] -> 1 & /@ Range[1, 4 3, 3], {Band[{4 + 1, 4 3 + 1}, {4 + 3, 2 4 3}] -> {{ConstantArray[1, 4]}}}], {4 + 3, 2 4 3}]

Is there an efficient way to achieve this in general ?



Answer



ArrayFlatten[{{sa11, sa12}, {sa21, sa22}}] seems to be what you need. It automatically merges everything into one big SparseArray[].


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