SC07MatlabWorkshop12nov2007

# SC07MatlabWorkshop12nov2007 - Parallel Sparse Operations in...

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1   Parallel Sparse Operations in Matlab: Exploring Large Graphs John R. Gilbert University of California at Santa Barbara Aydin Buluc (UCSB) Brad McRae (NCEAS) Steve Reinhardt (Interactive Supercomputing) with thanks to Alan Edelman (MIT & ISC) and Jeremy Kepner (MIT-LL) Support: DOE, NSF, DARPA, SGI, ISC

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2 3D Spectral Coordinates
3 2D Histogram: RMAT Graph

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4 Strongly Connected Components
5 Social Network Analysis in Matlab: 1993 Co-author graph from 1993 Householder symposium

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6 Combinatorial Scientific Computing Emerging large scale, high-performance applications: Web search and information retrieval Knowledge discovery Computational biology Dynamical systems Machine learning Bioinformatics Sparse matrix methods Geometric modeling . . . How will combinatorial methods be used by nonexperts?
7 Outline Infrastructure: Array-based sparse graph computation An application: Computational ecology Some nuts and bolts: Sparse matrix multiplication

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8 Matlab*P A = rand(4000 *p , 4000 *p ); x = randn(4000 *p , 1); y = zeros(size(x)); while norm(x-y) / norm(x) > 1e-11 y = x; x = A*x; x = x / norm(x); end;
9 MATLAB ® Star-P Architecture Ordinary Matlab variables Star-P client manager server manager package manager processor #0 processor #n-1 processor #1 processor #2 processor #3 . . . ScaLAPACK FFTW FPGA interface matrix manager Distributed matrices sort dense/sparse UPC user code MPI user code

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10 P 0 P 1 P 2 P n 59 41 53 26 31 2 3 1 3 1 Each processor stores local vertices & edges in a compressed row structure. Has been scaled to >10 8 vertices, >10 9 edges in interactive session. Distributed Sparse Array Structure 1 2 3 26 53 41 31 59
11 Sparse Array and Matrix Operations dsparse layout, same semantics as ordinary full & sparse Matrix arithmetic: + , max , sum , etc. matrix * matrix

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SC07MatlabWorkshop12nov2007 - Parallel Sparse Operations in...

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