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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.

       }}} P {{{       

       }}} Q {{{       

       }}} M {{{          

       }}} a {{{       

       }}} b {{{       

       }}} N {{{          

       }}} c {{{       

       }}} d {{{       

       }}} C1 {{{       

       }}} C2 {{{       

       }}} P {{{       

       }}} p {{{       

       }}} q {{{       

       }}} Q {{{       

       }}} r {{{       

       }}} s {{{       

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)

...

• See how to multiply matrices using Map/Reduce