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Root directory contains three sub-directories namely ’Sequential’, ’OpenMP’ and ’MPI’.
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Each subdirectory has source code in the form of ** ’*.c’** file.
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Matrix is generated in a manner that it decomposes into a L and U containing only 1s and 0s.
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To submit jobs for various configurations run ’./submit.sh’ on terminal. This will automatically submit all the jobs in the subdirectory to the general-compute queue of the ccr cluster.
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Outputs are generated in the output.txt file. Sample outputs are included.
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In the corresponding subdirectory run ./plot.sh on the linux terminal to generate a graphical visualization of the output. gnuplot is required to generate graph.
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Graphs are generated as ’Plot.pdf’. Please wait for the job run to finish and outputs to accumulate.
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Gaussian elimination algorithm was implemented that sequentially decomposes the square matrix.
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Algorithm was evaluated on input matrix size of 1000, 5000, 10000, 20000.
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Time taken to decompose the matrix grew exponentially with the increase in size.
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Since, this was a sequential implementation increase in compute nodes won’t do anything.
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Since I was using Gaussian elimination that computes L and U matrices separately, I ran out of memory when matrix size of 50,000 was tried. This implementation makes two copies of the matrix of same size as input.
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Gaussian elimination algorithm was implemented that uses the block wise decomposition in parallel.
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The for loops are parallelized in a manner that blocks of matrices are decomposed by dividing the work among parallel threads.
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Algorithm was evaluated for input matrix of sizes 1000, 5000, 10000, 20000 with a combination of 2, 4, 8, 16, 32 threads executing in parallel.
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On a fixed workload the decompostion was faster when more threads are executing in parallel. The execution was comparatively faster on larger workload due to the fact, parallelism was more effective.
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For a fixed number of cores the time increased exponentially with increase in matrix size.
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The parallelism was ineffective on relatively smaller loads.
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Since I was using Gaussian elimination that computes L and U matrices separately, I ran out of memory when matrix size of 50,000 was tried. This implementation makes two copies of the matrix of same size as input.
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Cyclic distribution was used to accomplish LU factorization of the input square matrix.
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Each node is responsible for computing its own block and broadcast the result to rest of the nodes.
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Algorithm was evaluated for input matrix of sizes 1000, 5000, 10000 with a combination of 8, 16, 32 compute nodes working in parallel.
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For a fixed number of compute nodes the algorithm showed uniform behavior.
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For fixed workload the parallelism was more effective for larger workloads on maximum compute nodes.
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Since, MPI involves communication overhead between different nodes, it was slower as compared to OpenMP.
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As expected sequential algorithm turns out to be the worst performer of the three.
LU factorization algorithm has a great extent of parallelization when scaled appropriately.