Abstract definition of matrix multiplication
In the following tables, matrix A represents the quantities of the materials P and Q to produce products M and N. Matrix B represents the prices of the materials P and Q of the suppliers C1 and C2.
In this case, the first row of the second column of AB, aq + bs, represents the total cost of the producing product A.
Product\Resource |
}}} P {{{
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}}} Q {{{
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}}} M {{{
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}}} a {{{
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}}} b {{{
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}}} N {{{
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}}} c {{{
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}}} d {{{
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Resource\Company |
}}} C1 {{{
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}}} C2 {{{
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}}} P {{{
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}}} p {{{
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}}} q {{{
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}}} Q {{{
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}}} r {{{
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}}} s {{{
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Blocking for parallelism
Square blocking
The matrix multiplication of the original arrays can be transformed into matrix multiplication of blocks. For example,
C_block(1,1)=A_block(1,1)*B_block(1,1) + A_block(1,2)*B_block(2,1)
+-----+-----+ +-----+-----+ +-----+-----+ | x x | | | --> | --> | | | | | | | x x | | | --> | --> | | ↓ ↓ | | +-----+-----+ = +-----+-----+ * +-----+-----+ | | | | | | | | | | | | | | | | | | ↓ ↓ | | +-----+-----+ +-----+-----+ +-----+-----+