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MATLAB *P

MATLAB *P. Alan Edelman MIT Lab for Computer Science March 30, 2001. Joint work with Parry Husbands, C. Isbell, S. Kubo, T. Wen. Already a MATLAB fan?. Then no need to justify why a parallel MATLAB would be cool! Especially one that allows software reuse.

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MATLAB *P

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  1. MATLAB*P Alan Edelman MIT Lab for Computer Science March 30, 2001 Joint work with Parry Husbands, C. Isbell, S. Kubo, T. Wen

  2. Already a MATLAB fan? • Then no need to justify why a parallel MATLAB would be cool! • Especially one that allows software reuse. • Especially one for large matrices! • Research topic: how can we do this? Not a MATLAB fan? • Probably you’ve never used MATLAB!

  3. Eigenvalue Records Made Easy >>a=randn(12000*p); >>tic;e=eig(a);toc “68 minutes” 64 processors on T3E

  4. MATLAB*P in action >> a=randn(512,512*p); a2=ones(512*p,512); m=sprand(10000,1000*p,0.01); >> whose Your variables are: Name Size Bytes Class a 512 x 512p 1048576 ddense array a2 512p x 512 1048576 ddense array m 10000 x 1000p 810176 dsparse array Grand total is 624560 elements using 2907328 bytes >> b=inv(a); c=a*b; c(1:3,1:3) ans = 1.0000 0.0000 -0.0000 -0.0000 1.0000 0.0000 0.0000 -0.0000 1.0000 >> e=eig(a);plot(e,’*’);axis([-30 30 -30 30]);axis(’square’) >> [u,s,v]=svds(m,5);s’ ans = 7.7153 7.7342 7.7447 7.7831 16.9842 >> id=eye(1000*p);x=cumsum(id,1);y=cumsum(x,1); >> imagesc(y+y’)

  5. MATLAB*P in action Parallelism through Polymorphism!!! >> a=randn(512,512*p); a2=ones(512*p,512); m=sprand(10000,1000*p,0.01); >> whose Your variables are: Name Size Bytes Class a 512 x 512p 1048576 ddense array a2 512p x 512 1048576 ddense array m 10000 x 1000p 810176 dsparse array Grand total is 624560 elements using 2907328 bytes >> b=inv(a); c=a*b; c(1:3,1:3) ans = 1.0000 0.0000 -0.0000 -0.0000 1.0000 0.0000 0.0000 -0.0000 1.0000 >> e=eig(a);plot(e,’*’);axis([-30 30 -30 30]);axis(’square’) >> [u,s,v]=svds(m,5);s’ ans = 7.7153 7.7342 7.7447 7.7831 16.9842 >> id=eye(1000*p);x=cumsum(id,1);y=cumsum(x,1); >> imagesc(y+y’)

  6. Parallel Problems Server Matlab MATLAB*P Classes & Methods The Product • Parallel Problems Server • Number crunching • MATLAB*P • Interactive benefits

  7. The Parallel Problems Server • Standalone program encapsulating data and algorithms (NetSolve (UTK), MatPar (NASA JPL), PSI (UT Austin)) • Dense and sparse matrices indexed by ids • Row and column distributed in single or double precision • Functions indexed by strings • Written in MPI (portability & functionality) • Handles extremely large datasets • Client communication protocol • Extensible via package system (for functionality and optimisation)

  8. Extensibility S3L Libraries ScaLAPACK Computational &Interface Routines mathfun.cc s3l.cc scalapack.cc Packages(dynamically loaded) mathfun.pp s3l.pp scalapack.pp Server Matlab Matlab Scripts

  9. MATLAB*P: Delivering the Benefits • Uses MATLAB’s classes and objects • No source code changes! • New classes • ddense and dsparse • Distributed dense and sparse matrices • Only matrix ids and sizes are stored in Matlab • Operator overloading gives transparency • layout • Enables further integration by allowing re-use of Matlab code

  10. Code Reuse example • MATLAB’s hilb routinehilb(n)=nxn Hilbert matrixh(i,j)=1/(i+j-1) 1) We want this to work! >>hilb(1000*p); >>type hilb function H=hilb(n) J=1:n;J=J(ones(n,1),:); I=J’; E=ones(n,n); H=E./(I+J-1); 2)This must be parallel: 3) So that this can be parallel

  11. The magic of layout variables • p=layout(1) • Specify parallelism:randn(100*p,100) or ones(100,100*p) • More importantly, allows propagation of parallelism through code: • >> a=randn(1000*p,1000);>> [m,n]=size(a);>> m 1000p>> b=ones(3*m,n); • b is now a parallel object!

  12. Nick Higham’s Toolbox >> a=clement(100*p) a = ddense object: 100-by-100 >> a2=clement(100); >> norm(a-a2,’fro’) ans = 0 >> b=fiedler(500*p) % b(i,j)=abs(i-j); b = ddense object: 500-by-500 >> c=inv(b); >> imagesc(b); >> imagesc(c); Nearly 70% of the functions work without modification.

  13. MATLAB*P vs. NetSolve • Differing goals: • MATLAB*P - transparency, code reuse • NetSolve - resource management, load balancing Server #1 MATLAB Agent MATLAB Server Server #2 x=A\b; x=netsolve(‘solve’,A,b);

  14. Iterative methods • Find x=A\b when you don’t have A! • Tested MATLAB’s pcg.m and gmres.m. They worked without modification • Performed better with some modification (that also improved the serial code): • Use dot(a,b) instead of a’*b • Sample the residual less frequently

  15. Automatic Polymorphism Directives Rewriting Parallelism through Polymorphism • Parallelism delivered through MATLAB classes and operator overloading • Extensibility • Minimal user-visible changes • Support for interactive environments • Disadvantage: Can’t infer parallelism from language constructs (e.g. for loops) Programmer Effort

  16. Performance Summary • Get performance of libraries! • Complex operations on large matrices do very well • Elementwise code fares poorly 2 procs. DEC Alpha Matlab MATLAB*Pm=moler(2000) 343s 29schol(m) 52s 14s

  17. IRLAB • Building term/document and query matrices handled by standalone C programs • Everything else is written in MATLAB: • Viewing documents • Retrieval schemes • Evaluation

  18. Support for PDEs • Specify domains and equations à la PDE toolbox • Find solution quickly in parallel on server • Use domain decomposition (KeLP) transparently

  19. New button!

  20. New button!

  21. cumulvs? Parallelism for “Workgroups” >>whose a 512x512p ddense array b 512p512 ddense array MATLAB*P AVS, VTK, Mathematica, MAPLE?, ...

  22. Conclusion • MATLAB*P provides users with: • Convenience • Interactivity and familiar syntax • Reliability • Few changes to existing system • Expressiveness • MATLAB’s data parallel syntax • Compatibility • Can easily interface to libraries • MATLAB code executed in parallel • Access to MATLAB’s environment

  23. MATLAB*P in action Parallelism through Polymorphism!!! >> a=randn(512,512*p); a2=ones(512*p,512); m=sprand(10000,1000*p,0.01); >> whose Your variables are: Name Size Bytes Class a 512 x 512p 1048576 ddense array a2 512p x 512 1048576 ddense array m 10000 x 1000p 810176 dsparse array Grand total is 624560 elements using 2907328 bytes >> b=inv(a); c=a*b; c(1:3,1:3) ans = 1.0000 0.0000 -0.0000 -0.0000 1.0000 0.0000 0.0000 -0.0000 1.0000 >> e=eig(a);plot(e,’*’);axis([-30 30 -30 30]);axis(’square’) >> [u,s,v]=svds(m,5);s’ ans = 7.7153 7.7342 7.7447 7.7831 16.9842 >> id=eye(1000*p);x=cumsum(id,1);y=cumsum(x,1); >> imagesc(y+y’)

  24. MATLAB*P in action Parallelism through Polymorphism!!! >> a=randn(512,512*p); a2=ones(512*p,512); m=sprand(10000,1000*p,0.01); >> whose Your variables are: Name Size Bytes Class a 512 x 512p 1048576 ddense array a2 512p x 512 1048576 ddense array m 10000 x 1000p 810176 dsparse array Grand total is 624560 elements using 2907328 bytes >> b=inv(a); c=a*b; c(1:3,1:3) ans = 1.0000 0.0000 -0.0000 -0.0000 1.0000 0.0000 0.0000 -0.0000 1.0000 >> e=eig(a);plot(e,’*’);axis([-30 30 -30 30]);axis(’square’) >> [u,s,v]=svds(m,5);s’ ans = 7.7153 7.7342 7.7447 7.7831 16.9842 >> id=eye(1000*p);x=cumsum(id,1);y=cumsum(x,1); >> imagesc(y+y’)

  25. MATLAB*P uses • Teaching Scientific Computing • A PGAPack (Parallel Genetic Algorithms) toolbox • Implementing fast cshifts, eoshifts, and sections • A Bezier Curve and Surface package • A Binary Image Processing package • Large Scale Information Retrieval • Ocean Modeling • Machine Learning

  26. What’s the point? • What benefits? (think MATLAB) • Ease of use and interactivity • Ease of development of applications • Lots of functionality available • Visualisation The benefits of interactive tools can beenjoyed in supercomputer installationswithout an appreciable loss in performance

  27. MATLAB*P in action >> a=randn(512,512*p); a2=ones(512*p,512); m=sprand(10000,1000*p,0.01); >> whose Your variables are: Name Size Bytes Class a 512 x 512p 1048576 ddense array a2 512p x 512 1048576 ddense array m 10000 x 1000p 810176 dsparse array Grand total is 624560 elements using 2907328 bytes >> b=inv(a); c=a*b; c(1:3,1:3) ans = 1.0000 0.0000 -0.0000 -0.0000 1.0000 0.0000 0.0000 -0.0000 1.0000 >> e=eig(a);plot(e,’*’);axis([-30 30 -30 30]);axis(’square’) >> [u,s,v]=svds(m,5);s’ ans = 7.7153 7.7342 7.7447 7.7831 16.9842 >> id=eye(1000*p);x=cumsum(id,1);y=cumsum(x,1); >> imagesc(y+y’)

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