Lecture Note
Tuning Matlab for Better Perfomance (Profiling - Save as MAT File)
-
University:
Boston University -
Course:
CAS MA 511 | Introduction to Analysis I Academic year:
2023
-
Views:
202
Pages:
20
Author:
5CelestialChronicle
Tuning MATLAB for Better Performance
u u
2 0
2
x
y
2
2
Boundary Conditions:
u( x,0 ) sin(x )
0
u( x,1) sin(x )e
u(0, y ) u(1, y ) 0
0
x1
x1
0 y1
Analytical solution:
u( x, y ) sin(x )e y
0 x 1; 0 y 1 Tuning MATLAB for Better Performance
Finite Difference Numerical Discretization
Discretize equation by centered-difference yields:
uin, 1
j
uin1,j uin1,j ui,jn 1 ui,jn 1
4
i 1,2, ,m; j 1,2, ,m
where n and n+1 denote the current and the next time step, respectively,
while
ui,jn u n(xi ,y j )
i 0,1,2, ,m 1; j 0,1,2, ,m 1
u n(ix, jy )
For simplicity, we take
x y
1
m1 Tuning MATLAB for Better Performance
Computational Domain
y, j
u(x,1) sin(x )e
x, i
u(1,y) 0
u(0,y) 0
u(x,0) sin(x)
uin, j 1
n
n
uin1,j uin1,j ui,j
u
1
i,j 1
4
i 1,2, ,m; j 1,2, ,m Tuning MATLAB for Better Performance
Five-point Finite-difference Stencil
Interior cells.
Where solution of the Laplace
equation is sought.
x
x o x
x
Exterior cells.
Green cells denote cells where
homogeneous boundary
conditions are imposed while
non-homogeneous boundary
conditions are colored in blue.
x
x o x
x Tuning MATLAB for Better Performance
SOR Update Function
How to vectorize it ?
1. Remove the for-loops
2. Define i = ib:2:ie;
3. Define j = jb:2:je;
4. Use sum for del
% original code fragment
jb = 2; je = n+1; ib = 3; ie = m+1;
for i=ib:2:ie
for j=jb:2:je
up = ( u(i ,j+1) + u(i+1,j ) + ...
u(i-1,j ) + u(i ,j-1) )*0.25;
u(i,j) = (1.0 - omega)*u(i,j) +omega*up;
del = del + abs(up-u(i,j));
end
end
% equivalent vector code fragment
jb = 2; je = n+1; ib = 3; ie = m+1;
i = ib:2:ie; j = jb:2:je;
up = ( u(i ,j+1) + u(i+1,j ) + ...
u(i-1,j ) + u(i ,j-1) )*0.25;
u(i,j) = (1.0 - omega)*u(i,j) + omega*up;
del = sum(sum(abs(up-u(i,j)))); Tuning MATLAB for Better Performance
Solution Contour Plot Tuning MATLAB for Better Performance
SOR Timing Benchmarks Tuning MATLAB for Better Performance
Summation
For global sum of 2D matrices: sum(sum(A)) or sum(A(:))
Example: which is more efficient ?
A = rand(1000);
tic,sum(sum(A)),toc
tic,sum(A(:)),toc
No appreciable performance difference; latter more compact.
Your application calls for summing a matrix along rows (dim=2)
multiple times (inside a loop). Example:
A = rand(1000);
tic, for t=1:100,sum(A,2);end, toc
MATLAB matrix memory ordering is by column. Better performance if
sum by column. Swap the two indices of A at the outset.
Example: B=A’; tic, for t=1:100, sum(B,1);end, toc (See twosums.m) Tuning MATLAB for Better Performance
Logical Array helpful for Vectorization
Sometimes, logical array is used to retain target array’s shape
Scalar example:
a = rand(4,3);
b =rand(size(a));
c = zeros(size(b));
b(1,3) = 0; b(3,2) = 0;
for j=1:3
for i=1,4
if (b(i,j) ~= 0) then
c(i,j) = a(i,j)/b(i,j);
end
end
end
Vector example:
% e is true (1) for all b not = 0
e = b~=0
e =
1
1
0
1
1
1
1
0
1
1
1
1
c(e) = a(e)./b(e)
% c = 0 ∀ b
= 0
c =
0.9768
2.3896
0.7821
11.3867
1.4940
0.4487
0
0.0400
0
0.0943
0.2180
1.2741 Tuning MATLAB for Better Performance
46
Other Tips
Generally better to use function rather than script
Script m-file is loaded into memory and evaluate one line at a time.
Subsequent uses require reloading.
Function m-file is compiled into a pseudo-code and is loaded on
first application. Subsequent uses of the function will be faster
without reloading.
Function is modular; self cleaning; reusable.
Global variables are expensive; difficult to track.
Don’t reassign array that results in change of data type or shape
Limit m-files size and complexity
Structure of arrays more memory-efficient than array of structures Tuning MATLAB for Better Performance
Memory Management
Maximize memory availability.
32-bit systems < 2 or 3 GB
64-bit systems running 32-bit MATLAB < 4GB
64-bit systems running 64-bit MATLAB < 8TB
(96 GB on some Katana nodes)
Minimize memory usage. (Details to follow …) Tuning MATLAB for Better Performance
Minimize Memory Usage
Use clear, pack or other memory saving means when possible. If
double precision (default) is not required, the use of ‘single’ data type
could save substantial amount of memory. For example,
>> x=ones(10,'single'); y=x+1; % y inherits single from x
Use sparse to reduce memory footprint on sparse matrices
>> n=3000; A = zeros(n); A(3,2) = 1; B = ones(n);
>> tic, C = A*B; toc
% 6 secs
>> As = sparse(A);
>> tic, D = As*B; toc % 0.12 secs; D not sparse
Be aware that array of structures uses more memory than structure of
arrays. (pre-allocation is good practice too for structs!) Tuning MATLAB for Better Performance
Minimize Memory Uage
For batch jobs, use “matlab –nojvm …” saves lots of memory
Memory usage query
For Linux:
scc1% top
For Windows:
>> m = feature('memstats'); % largest contiguous free block
Use MS Windows Task Manager to monitor memory allocation.
On multiprocessor systems, distribute memory among processors Tuning MATLAB for Better Performance
Compilers
mcc is a MATLAB compiler:
It compiles m-files into C codes, object libraries, or
stand-alone executables.
A stand-alone executable generated with mcc can run
on compatible platforms without an installed MATLAB or
a MATLAB license.
On special occasions, MATLAB access may be denied
if all licenses are checked out. Running a stand-alone
requires NO licenses and no waiting.
It is not meant to facilitate any performance gains.
coder ― m-file to C code converter Tuning MATLAB for Better Performance
mcc example
How to build a standalone executable on Windows
>> mcc –o twosums –m twosums
How to run executable on Windows’ Command Promp (dos)
Command prompt:> twosums 3000 2000
Details:
• twosums.m is a function m-file with 2 input arguments
• Input arguments to code are processed as strings by mcc. Convert
with str2double: if isdeployed, N=str2double(N); end
• Output cannot be returned; either save to file or display on screen.
• The executable is twosums.exe Tuning MATLAB for Better Performance
MATLAB Programming Tools
profile - profiler to identify “hot spots” for performance
enhancement.
mlint - for inconsistencies and suspicious constructs in
m-files.
debug - MATLAB debugger.
guide - Graphical User Interface design tool. Tuning MATLAB for Better Performance
MATLAB Profiler
To use profile viewer, DONOT start MATLAB with –nojvm option
>> profile on –detail 'builtin' –timer 'real'
>> serial_integration2 % run code to be profiled
>> profile viewer % view profiling data
Turn on profiler. Time reported
>> profile off
% turn off profiler
in wall clock. Include timings
for built-in functions. Tuning MATLAB for Better Performance
How to Save Profiling Data
Two ways to save profiling data:
1. Save into a directory of HTML files
Viewing is static, i.e., the profiling data displayed correspond to a
prescribed set of options. View with a browser.
2. Saved as a MAT file
Viewing is dynamic; you can change the options. Must be viewed
in the MATLAB environment. Tuning MATLAB for Better Performance
Profiling – save as HTML files
Viewing is static, i.e., the profiling data displayed correspond to a
prescribed set of options. View with a browser.
>> profile on
>> serial_integration2
>> profile viewer
>> p = profile('info');
>> profsave(p, ‘my_profile') % html files in my_profile dir Tuning MATLAB for Better Performance
Profiling – save as MAT file
Viewing is dynamic; you can change the options. Must be viewed in
the MATLAB environment.
>> profile on
>> serial_integration2
>> profile viewer
>> p = profile('info');
>> save myprofiledata p
>> clear p
>> load myprofiledata
>> profview(0,p)
Tuning Matlab for Better Perfomance (Profiling - Save as MAT File)
of 20
Report
Tell us what’s wrong with it:
Thanks, got it!
We will moderate it soon!
Free up your schedule!
Our EduBirdie Experts Are Here for You 24/7! Just fill out a form and let us know how we can assist you.
Take 5 seconds to unlock
Enter your email below and get instant access to your document