TriSolve

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Unformatted text preview: Administrivia: October 5, 2009 Administrivia: October 5, 2009 • Homework 1 due Wednesday • Reading in Davis: • Skim section 6.1 (the fill bounds will make more sense next week) • Read section 6.2, and chapter 4 through 4.3 • A few copies of Davis are available (at a discount) from Roxanne in HFH 5102. Compressed Sparse Matrix Storage Compressed Sparse Matrix Storage • Full storage: • 2-dimensional array. • (nrows*ncols) memory. 31 53 59 41 26 31 41 59 26 53 1 3 2 3 1 • Sparse storage: • Compressed storage by columns (CSC). • Three 1-dimensional arrays. • (2*nzs + ncols + 1) memory. • Similarly, CSR. 1 3 5 6 value: row: colstart: Matrix – Matrix Multiplication: C = A * B Matrix – Matrix Multiplication: C = A * B C(:, :) = 0; for i = 1:n for j = 1:n for k = 1:n C(i, j) = C(i, j) + A(i, k) * B(k, j); • The n 3 scalar updates can be done in any order. • Six possible algorithms: ijk, ikj, jik, jki, kij, kji (lots more if you think about blocking for cache). • Goal is O(nonzero flops) time for sparse A, B, C. • Even time = O(n 2 ) is too slow! CSC Sparse Matrix Multiplication with SPA CSC Sparse Matrix Multiplication with SPA B = x C A for j = 1:n C(:, j) = A * B(:, j) SPA gather scatter/ accumulate All matrix columns and vectors are stored compressed except the SPA. The Landscape of Sparse Ax=b Solvers...
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