4.1 v1 Sparse Vector and Matrix Algebra

# Abx a is sparse b is sparse x is sparse if x is stored

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Unformatted text preview: A is sparse. – b is sparse. – x is sparse? • If x is stored as a sparse vector: – Perform symbolic manipulation. • If x is stored as a dense vector: – No need to perform symbolic manipulation. • Assume: – A and b are store in RR(C)U and CR(C)U, respectively. © Copyright 1999 Daniel Tylavsky Sparse Vector & Matrix Algebra If b is sparse, perform symbolic program segment to get CRO/U. If b is dense, assume b is stored in ordered compact form. Initialize: Switch=0, IR=0 Clear x(k) IR=IR+1 Set pointer to begin/end or row: IBEG=ERPA(IR-1)+1, IEND=ERPA(IR). Accumulate Inner Product and store in sparse x using Inner Product Alg. N IR=N? Y End The End © Copyright 1999 Daniel Tylavsky Sparse Vector & Matrix Algebra – Teams: Use the expanded accumulator technique to add the follow sparse vectors stored in unordered compact form. Pos: R1Indx(k): A1(k): R2Indx(k): A2(k): 0 1 1 1.0 2 3 2.0 3 4 3.0 4 8 4.0 5 6 5.0 2 6.0 3 7.0 4 8.0 7 6 9.0 10.0 6 0 7 0 8 0 9 0 10 0 11 0 12 0 © Copyright 1999 Daniel Tylavsky Sparse Vector & Matrix Algebra – Teams: Use the expanded pointer technique to add the follow sparse vectors stored in unordered compact form. • Step 1: Merge Row Indices – {1,3,4,8,6,2,7} Pos: R1Indx(k): A1(k): R2Indx(k): A2(k): 0 1 1 1.0 2 3 2.0 3 4 3.0 4 8 4.0 5 6 5.0 2 6.0 3 7.0 4 8.0 7 6 9.0 10.0 6 0 7 0 8 0 9 0 10 0 11 0 12 0...
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