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Suppose we want to multiply the matrices A and B together to form matrix
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C:
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We will assume all matrices are square - the algorithm can be generalized to deal with rectangular matrices.
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The input matrices, A and B, are decomposed into rectangular sub-blocks.
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If we have N processors we have rows and columns of sub-blocks. This means that N should be a perfect square. (Of course this condition can be relaxed -- it is used for simplicity of discussion)
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One sub-block is assigned to each processor in a grid corresponding to the sub-block structure.
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The algorithm ensures that the output matrix C has the same decomposition as A and B.
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If A B and C are M by M with M2 = N m2 and thus M = m
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Then each processor stores an m by m subblock
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Processors are labelled by a two vector (l,k) l,k = 1 ...
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Secs 228.9
