4.1 v1 Sparse Vector and Matrix Algebra

Vectors ab b n a t b a1 a 2 a n 2 a i bi

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Unformatted text preview: a n ] 2 = a i bi i =1 b n – Ex: Perform an inner product of the following sparse vectors stored in unordered compact form: ∑ Pos: R1Indx(k): A1(k): 1 1 2.0 2 3 3.0 3 5 4.0 4 9 5.0 R2Indx(k): A2(k): 5 6.0 4 7.0 1 8.0 3 9.0 5 0 6 0 7 0 8 0 9 0 10 0 11 0 12 0 © Copyright 1999 Daniel Tylavsky Sparse Vector & Matrix Algebra • Step 1: Use an expanded pointer array to identify all nonzeros in A1. • Step 2: Using pointer array, compare A2 with A1 and accumulate all non-zero products. Pos: Pos: Pos: R1Indx(k): R1Indx(k): A1(k): A1(k): 3 4 1 2 3 4 1 2 5 9 1 3 5 9 1 3 2.0 3.0 4.0 5.0 2.0 3.0 4.0 5.0 R2Indx(k): R2Indx(k): A2(k): A2(k): 1 3 5 4 5 4 1 3 6.0 7.0 8.0 9.0 6.0 7.0 8.0 9.0 Pointer(k): Pointer(k): Pointer(k): Inner Prod: Inner Prod: 1 1 67.0 40.0 24.0 24.0 0 0 2 2 0 0 5 5 0 0 66 6 00 0 77 7 00 0 88 8 00 0 99 9 00 0 3 3 00 0 00 0 00 0 10 11 10 11 10 11 00 00 0 0 12 12 12 00 0 44 4 • Position pointer array value at location k gives location of index k in array A1. © Copyright 1999 Daniel Tylavsky Sparse Vector & Matrix Algebra – Sparse Matrix Addition • Assumption: Matrices stored in RR(C)U. • Procedure: – Use multiple switch technique to symb...
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