University:
Boston University
Course:
CAS MA 511 | Introduction to Analysis I
Academic year:

2023
Views:

177

Pages:

17
Author:

5CelestialChronicle

TUNING MATLAB FOR BETTER PERFORMANCE Tuning MATLAB for Better Performance 2 Where to Find Performance Gains ?  Serial Performance gain  Due to memory access  Due to caching  Due to vector representations  Due to compiler  Due to other ways  Parallel performance gain is covered in the MATLAB Parallel Computing Toolbox tutorial Tuning MATLAB for Better Performance 3 Performance Issues Related to Memory Access Timing shown are recorded on a Windows PC running R2011a in 2012. The numbers are highly dependent on processor and MATLAB version. 4 Tuning MATLAB for Better Performance How Does MATLAB Allocate Arrays ? Each MATLAB array is allocated in contiguous address space. What happens if you don’t preallocate array x ? for i=1:100000 x(i) = i; end To satisfy contiguous memory placement rule, x may need to be moved from one memory segment to another many times during iteration process. Memory Address Array Element 1 x(1) … ... 2000 x(1) 2001 x(2) 2002 x(1) 2003 x(2) 2004 x(3) ... ... 10004 x(1) 10005 x(2) 10006 x(3) 10007 x(4) Tuning MATLAB for Better Performance 5 Always preallocate array before using it  Preallocating array to its maximum size prevents all intermediate array movement and copying described. >> A=zeros(n,m); % initialize A to 0 >> A(n,m)=0; % or touch largest element  If maximum size is not known apriori, estimate with upperbound. Remove unused memory after. >> >> >> >> A=rand(100,100); % . . . % if final size is 60x40, remove unused portion A(61:end,:)=[]; A(:,41:end)=[]; 6 Tuning MATLAB for Better Performance Example  For efficiency considerations, MATLAB arrays are allocated in contiguous memory space. Arrays follow column-major rule.  Preallocate array to avoid data movement. Bad: Good: clear x; n=5000; tic for i=1:n x(i) = i^2; end toc Wallclock time = 0.00046 seconds clear x; n=5000; x = zeros(n, 1); tic for i=1:n x(i) = i^2; end toc Wallclock time = 0.00004 seconds not_allocate.m allocate.m The timing data are recorded on older cluster. The actual times on your computer may vary depending on the processor. Tuning MATLAB for Better Performance 7 Lazy Copy MATLAB uses pass-by-reference if passed array is used without changes; a copy will be made if the array is modified. MATLAB calls it “lazy copy.” Example: function y = lazyCopy(A, x, b, change) If change, A(2,3) = 23; end % forces a local copy of a y = A*x + b; % use x and b directly from calling program pause(2) % keep memory longer to see it in Task Manager On Windows, use Task Manager to monitor memory allocation history. >> n = 5000; A = rand(n); x = rand(n,1); b = rand(n,1); >> y = lazyCopy(A, x, b, 0); % no copy; pass by reference >> y = lazyCopy(A, x, b, 1); % copy; pass by value Tuning MATLAB for Better Performance Performance Issues Related to Caching 8 Code Tuning and Optimization 9 Cache • Cache is a small chunk of fast memory between the main memory and the registers registers primary cache secondary cache main memory Code Tuning and Optimization 10 Cache (2) • If variables are fetched from cache, code will run faster since cache memory is much faster than main memory • Variables are moved from main memory to cache stages Code Tuning and Optimization 11 Cache (3) • Why not just make the main memory out of the same stuff as cache? • Expensive • Runs hot • This was actually done in Cray computers • Liquid cooling system • Currently, special clusters (e.g., XSEDE.org cluster) available with very substantial flash main memory for I/O-bound applications Code Tuning and Optimization 12 Cache (4) • Cache hit • Required variable is in cache • Cache miss • Required variable not in cache • If cache is full, something in there must be thrown out (sent back to main memory) to make room • Want to minimize number of cache misses Code Tuning and Optimization Cache (5) “mini” cache holds 2 lines, 4 words each x(1) x(9) x(2) x(10) x(3) x(8) Main memory … x(7) a b … x(4) x(5) x(6) for i=1:10 x(i) = i; end 13 Code Tuning and Optimization Cache (6) • will ignore i for simplicity • need x(1), not in cache  cache miss • load line from memory into cache • next 3 loop indices result in cache hits x(1) x(2) x(3) x(4) x(1) x(2) x(3) x(8) a b … x(7) x(9) x(10) … x(4) x(5) x(6) for i=1:10 x(i) = i; end 14 Code Tuning and Optimization Cache (7) • need x(5), not in cache  cache miss • load line from memory into cache • free ride next 3 loop indices  cache hits x(1) x(5) x(2) x(6) x(3) x(7) x(4) x(8) x(1) x(9) x(2) x(10) x(3) x(8) … x(7) a b … x(4) x(5) x(6) for i=1:10 x(i) = i; end 15 Code Tuning and Optimization Cache (8) • need x(9), not in cache --> cache miss • load line from memory into cache • no room in cache! • replace old line x(9) x(5) x(10) x(6) a b x(7) x(8) x(1) x(9) x(2) x(10) x(3) x(8) … x(7) a b … x(4) x(5) x(6) for i=1:10 x(i) = i; end 16 Code Tuning and Optimization Cache (9) • Multidimensional array is stored in column-major order: x(1,1) x(2,1) x(3,1) . . x(1,2) x(2,2) x(3,2) . . 17