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CSE5304—Project Proposal Parallel Matrix Multiplication

CSE5304—Project Proposal Parallel Matrix Multiplication. Tian Mi. Cannon's algorithm. // assume s = sqrt(p) is an integer forall i=0 to s-1 // skew A left-circular-shift row i of A by i // so that A(i,j) overwritten by A(i,(j+i)mod s) forall i=0 to s-1 // skew B

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CSE5304—Project Proposal Parallel Matrix Multiplication

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  1. CSE5304—Project ProposalParallel Matrix Multiplication Tian Mi

  2. Cannon's algorithm • // assume s = sqrt(p) is an integer • forall i=0 to s-1 // skew A • left-circular-shift row i of A by i • // so that A(i,j) overwritten by A(i,(j+i)mod s) • forall i=0 to s-1 // skew B • up-circular-shift column i of B by i • // so that B(i,j) overwritten by B((i+j)mod s), j) • for k=0 to s-1 // sequential • forall i=0 to s-1 and j=0 to s-1 • // all processors in parallel • C(i,j) = C(i,j) + A(i,j)*B(i,j) • left-circular-shift each row of A by 1 • up-circular-shift each column of B by 1

  3. Cannon's algorithm--Example • http://www.vampire.vanderbilt.edu/education-outreach/me343_fall2008/notes/parallelMM_10_09.pdf

  4. N*N matrix with P processors • Divide matrix to multipliable submatrix • Follow Cannon’s algorithm, but addition is submatrix addition, multiplication is submatrix multiplication • A(0,0) ＋/×B(0,0)=

  5. Objectives • Implementation • Sequential program on Cannon’s algorithm • Parallel Cannon’s algorithm • N*N matrix with N*N processors • N*N matrix with P processors • Analysis • Compare the two programs with different input size • Test the parallel program with different number of processors • Running time of both programs • Speed up, efficiency

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