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GPU sparse matrices

Sparse matrices store only nonzero entries. Jarnevon's initial sparse substrate uses two complementary representations.

COO: construction​

COO stores explicit (row, column, value) triples. It is convenient for GPU generation, compaction, concatenation, sorting and canonicalization.

rowIndices    = [0,0,1,2,2]
columnIndices = [0,2,1,0,2]
values        = [10,20,30,40,50]

CSR: row execution​

CSR replaces repeated row IDs with offset-delimited row boundaries:

rowOffsets    = [0,2,3,5]
columnIndices = [0,2,1,0,2]
values        = [10,20,30,40,50]

Row r owns [rowOffsets[r], rowOffsets[r + 1]). Repeated offsets naturally represent empty rows.

This is the same structural idea used by graph adjacency and other offset-delimited GPU data.

Pipeline​

entry generation
      ↓
     COO
      ↓
sort / canonicalize
      ↓
 GPUCOOToCSR
      ↓
     CSR
      ↓
adaptive SpMV
      ↓
CG / PCG / sparse analytics

The representations describe data and shape; conversion and execution remain separate graph operations. The initial value format is float32; indices and offsets are uint32.