Parallel-Sparse-Matrix-Vector-Multiplication-MPI-CSR-

Project Overview

• Goal: Implement and evaluate Sparse Matrix–Vector multiplication (y = A·x) using MPI with Compressed Sparse Row (CSR) storage.
• Matrix structure: Symmetric, 11-banded (main diagonal ±5).
• Focus: Wall-clock time, speed-up, efficiency, and effective metrics; separation of computation vs communication costs.
• The program logs per-run metrics (e.g., results.txt) for different matrix sizes and core counts.

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Implemented Sections

• CSR Construction
  • fillRowStart – row pointers (row_start)
  • fillColIdx – column indices within ±5 band (col_idx)
  • fillValues – nonzeros (keeps symmetry)
• SpMV Kernel
  • SpMV_Mult(B, C, col_idx, row_start, values, local_rows)
  • For each row i: accumulate values[j] * B[col_idx[j]] over j ∈ [row_start[i], row_start[i+1])
• MPI Parallelization (row partitioning)
  • Nearly even row-wise distribution across ranks
  • Data movement with MPI_Scatterv / MPI_Gatherv
  • Measures total, computation, and communication times
• Recording
  • Appends matrix size, core count, and timing breakdowns to a results file

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Hardware Environment

• CPU: Intel Xeon E5-2680 v4 (28 cores/processor)
• Memory: 126 GB
• Caches: L1 32 KB, L2 256 KB, L3 ~35 MB
• Network: InfiniBand (high bandwidth; comms latency impacts scaling)
• Toolchain: OpenMPI/MPICH, build flags like -O3 -march=native -DNDEBUG

Note: Very large matrices + high core counts may hit memory limits; communication cost becomes dominant as processes increase.

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Performance Summary

• Speed-up: Increases with core count but shows diminishing returns due to communication and synchronization overheads.
• Efficiency: High at low–mid core counts; decreases as communication dominates at larger scales.
• Problem size effect: Larger N improves compute/communication ratio, aiding scalability; memory bandwidth/patterns remain limiting.
• Overall: Row-wise CSR partitioning is simple and effective; best results typically appear at mid-to-high core counts before communication bottlenecks dominate.

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