University:
Boston University
Course:
MET CS 201 | Introduction to Programming
Academic year:

2021
Views:

54

Pages:

20
Author:

Cyncuncewc3b4

TUNING MATLAB FOR BETTER PERFORMANCE Tuning MATLAB for Better Performance 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 Performance Issues Related to Memory Access 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 ? x = 1; for i=2:4 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 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)=[]; % delete 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: n=5000; tic for i=1:n x(i) = i^2; end toc Wallclock time = 0.00046 seconds 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 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 Code Tuning and Optimization 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 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 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 (on XSEDE.org) available with very substantial flash main memory for I/O-bound applications Code Tuning and Optimization 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 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 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 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 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) . . Tuning MATLAB for Better Performance For-loop Order  Best if inner-most loop is for array left-most index, etc. (column- major) Bad: Good: n=5000; x = zeros(n); for i = 1:n % rows for j = 1:n % columns x(i,j) = i+(j-1)*n; end end n=5000; x = zeros(n); for j = 1:n % columns for i = 1:n % rows x(i,j) = i+(j-1)*n; end end Wallclock time = 0.88 seconds Wallclock time = 0.48 seconds forij.m forji.m  For a multi-dimensional array, x(i,j), the 1D representation of the same array, x(k), follows column-wise order and inherently possesses the contiguous property Tuning MATLAB for Better Performance Compute In-place  Compute and save array in-place improves performance and reduces memory usage Bad: Good: x = rand(5000); tic y = x.^2; toc x = rand(5000); tic x = x.^2; toc Wallclock time = 0.30 seconds Wallclock time = 0.11 seconds not_inplace.m inplace.m Caveat: May not be worthwhile if it involves data type or size changes … Code Tuning and Optimization Bad: Good: for i=1:N x = 10; . . end x = 10; for i=1:N . . end Better performance to use vector than loops