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4.1.2.1 Parallel machines with distributed memory

We want to perform $ \underline{v} = A_{n\times n} \underline{x}$ with a full matrix $ A$. Depending on the distribution of the matrix we have various implementation opportunities on a parallel machine - two of them are investigated in the following.

Variant 1 : Split $ A$ into adjoint blocks of rows and distribute them on the processors. The appropriate subvectors are handled similar.

Figure 4.2: Matrix distributed as block rows
\begin{figure}\unitlength0.05\textwidth \begin{picture}(20,6)(-2,0) \put(0,0){... ... \put(14,3){\line(0,1){1}} \put(15,3){\line(0,1){1}} \end{picture} \end{figure}


\begin{algorithmus} % latex2html id marker 8367 [H] \caption{Parallel Matrix-by-... ...{x} $\ and ''its'' initial subvector~$\underline{x}^{[p]}$. \end{algorithmus}

Variant 1 : If ALL/SMALL>_TO/SMALL>_ALL/SMALL>_SCATTER-call distributes  $ \underline{x}$ to all processes in the beginning, then no communication is required in the remaining operation.

Variant 2 : Split $ A$ into adjoint blocks of columns and distribute them on the processors. In the same way the appropriate subvectors of $ \underline{x}$ are handled.

Figure 4.3: Matrix distributed as block columns
\begin{figure}\unitlength0.05\textwidth \begin{picture}(20,6)(-2,0) \put(0,0){... ...14,6){\line(1,0){0.35}} \put(15,6){\line(-1,0){0.35}} \end{picture} \end{figure}


\begin{algorithmus} % latex2html id marker 8435\caption{Parallel Matrix-by-Vec... ...ach process~$p$\ owns the whole vector~$\underline{v}^{[p]}$. \end{algorithmus}

Applying the Broadcast-Multiply-Roll algorithm (Alg. 4.4) from the next section on the Matrix-by-Vector operation leads to an additional algorithm.

next up previous contents
Next: 4.1.3 Matrix-by-Matrix-operations (BLAS3) Up: 4.1.2 Matrix-by-Vector operations (BLAS2) Previous: 4.1.2 Matrix-by-Vector operations (BLAS2)   Contents
Gundolf Haase 2000-03-20