MATLAB Tutorial Series
Tuning MATLAB for Better Performance
Kadin Tseng
Scientific Computing and Visualization, IS&T
Boston University
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Topics Covered
1. Performance Issues
1.1 Memory Allocations
1.2 Vector Representations
1.3 Compiler
1.4 Other Considerations
2. Multiprocessing with MATLAB
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1. Performance Issues
1.1
1.2
1.3
1.4
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Memory Access
Vector Representations
Compiler
Other Considerations
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1.1 Memory Access
Memory access patterns often affect computational
performance. Some effective ways to enhance
performance in MATLAB :
 Allocate array memory before using it
 For-loops Ordering
 Compute and save array in-place where applicable.
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How Does MATLAB Allocate Arrays ?
 MATLAB arrays are allocated in contiguous address space.
Memory Array
Address element
Without pre-allocation
x = 1;
for i=2:4
x(i) = i;
end
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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)
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How … Arrays ? Examples
 MATLAB arrays are allocated in contiguous address space.
 Pre-allocate arrays enhance performance significantly.
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
The timing data are recorded on Katana. The actual times may
vary depending on the processor.
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Passing Arrays Into A Function
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.” Consider the following example:
function y = lazyCopy(A, x, b, change)
If change, A(2,3) = 23; end
% change 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, can 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);
>> y = lazyCopy(A, x, b, 1);
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For-loop Ordering
 Best if inner-most loop is for array left-most index, etc. (columnmajor)
 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
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
for i=1:n*n
x(i) = i;
end
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x = 1:n*n;
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Compute In-place
 Compute and save array in-place improves performance (and
reduce memory usage)
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
Caveat:
May not be worthwhile if it involves data type or size change …
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Other Considerations
 Generally, better to use function instead of script
 m-file
 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.
 Physical memory is much faster than virtual mem.
 Avoid passing large matrices to a function and modifying only a
handful of elements.
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Other Considerations (cont’d)
 load and save are efficient to handle whole data file; textscan is
more memory-efficient to extract text meeting specific criteria.
 Don’t reassign array that results in change of data type or shape.
 Limit m-files size and complexity.
 Computationally intensive jobs often require large memory …
 Structure of array more memory-efficient than array of structures.
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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

(93 GB on some Katana nodes)
 Minimize memory usage. (Details to follow …)
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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=5000; A = zeros(n); A(3,2) = 1; B = ones(n);
>> C = A*B;
>> As = sparse(A);
>> Cs = As*B; % it can save time for low density
>> A2 = sparse(n,n); A2(3,2) = 1;
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Minimize Memory Usage (Cont’d)
 Use “matlab –nojvm …” saves lots of memory – if warranted
 Memory usage query
For Unix:
Katana% top
For Windows:
>> m = feature('memstats'); % largest contiguous free block
Use MS Windows Task Manager to monitor memory allocation.
 Distribute memory among multiprocessors via MATLAB
Parallel Computing Toolbox.
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Special Functions for Real Numbers
MATLAB provides a few functions for processing real,
noncomplex, data specifically. These functions are more
efficient than their generic versions:
 realpow – power for real numbers
 realsqrt – square root for real numbers
 reallog – logarithm for real numbers
 realmin/realmax – min/max for real numbers
n = 1000; x = 1:n;
x = x.^2;
tic
x = sqrt(x);
toc
n = 1000; x = 1:n;
x = x.^2;
tic
x = realsqrt(x);
toc
Wallclock time = 0.00022 seconds
Wallclock time = 0.00004 seconds
• isreal reports whether the array is real
• single/double converts data to single-/double-precision
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Vector Operations
 MATLAB is designed for vector and matrix operations. The use of
for-loop, in general, can be expensive, especially if the loop count
is large or nested.
 Without array pre-allocation, its size extension in a for-loop is
costly as shown before.
 From a performance standpoint, in general, vector representation
should be used in place of for-loops.
i = 0;
for t = 0:.01:100
i = i + 1;
y(i) = sin(t);
end
t = 0:.01:100;
y = sin(t);
Wallclock time = 0.1069 seconds
Wallclock time = 0.0007 seconds
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Vector Operations of Arrays
>> A = magic(3) % define a 3x3 matrix A
A=
8 1 6
3 5 7
4 9 2
>> B = A^2;
% B = A * A;
>> C = A + B;
>> b = 1:3
% define b as a 1x3 row vector
b=
1 2 3
>> [A, b']
% add b transpose as a 4th column to A
ans =
8 1 6 1
3 5 7 2
4 9 2 3
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Vector Operations
>> [A; b]
% add b as a 4th row to A
ans =
8 1 6
3 5 7
4 9 2
1 2 3
>> A = zeros(3)
% zeros generates 3*3 array of 0’s
A=
0 0 0
0 0 0
0 0 0
>> B = 2*ones(2,3) % ones generates 2 * 3 array of 1’s
B=
2 2 2
2 2 2
Alternatively,
>> B = repmat(2,2,3) % matrix replication
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Vector Operations
>> y = (1:5)’;
>> n = 3;
>> B = y(:, ones(1,n))
% B = y(:, [1 1 1]) or B=[y y y]
B=
1 1 1
2 2 2
3 3 3
4 4 4
5 5 5
Again, B can be generated via repmat as
>> B = repmat(y, 1, 3);
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Vector Operations
>> A = magic(3)
A=
8 1 6
3 5 7
4 9 2
>> B = A(:, [1 3 2]) % switch 2nd and third columns of A
B=
8 6 1
3 7 5
4 2 9
>> A(:, 2) = [ ] % delete second column of A
A=
8 6
3 7
4 2
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Vector Operation Example
n = 3000; x = zeros(n);
for j=1:n
for i=1:n
x(i,j) = i+(j-1)*n;
x(i,j) = x(i,j)^2;
end
end
n = 3000;
i = (1:n) ';
I = repmat(i,1,n); % replicate along j
x = I + (I'-1)*n;
x = x.^2;
Wallclock time = 0.128 seconds
Wallclock time = 0.127 seconds
Notes on the vector form of the computations :
•
To eliminate the for-loops, all values of i and j must be made available at
once. The ones or repmat utilities can be used to replicate rows or
columns. In this special case, J = I' is used to save computations and
memory.
•
Often, there are trade-offs between efficiency and memory using the vector
form. Here, the creation of I adds to the memory and compute time.
However, as more works can be leveraged against I, efficiency improves.
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Functions Useful in Vectorizing
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Function
Description
all
Test to see if all elements are of a prescribed value
any
Test to see if any element is of a prescribed value
zeros
Create array of zeroes
ones
Create array of ones
repmat
Replicate and tile an array
find
Find indices and values of nonzero elements
diff
Find differences and approximate derivatives
squeeze
Remove singleton dimensions from an array
prod
Find product of array elements
sum
Find the sum of array elements
cumsum
Find cumulative sum
shiftdim
Shift array dimensions
logical
Convert numeric values to logical
sort
Sort array elements in ascending /descending order
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Laplace Equation
Laplace Equation:
u u
 2 0
2
x y
2
2
(1)
Boundary Conditions:
u ( x,0)  sin (x)
0 x1
u ( x,1)  sin (x)e
u (0, y)  u (1, y)  0
x
0 x1
(2)
0 y1
Analytical solution:
u( x, y)  sin (x)e  xy
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0  x  1; 0  y  1
(3)
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Discrete Laplace Equation
Discretize Equation (1) by centered-difference yields:
uin, 1
j 
uin1,j  uin1,j  ui,jn 1  ui,jn 1
4
i  1,2, ,m; j  1,2, ,m
(4)
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
(5)
 u n(ix, jy )
For simplicity, we take
x   y 
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m1
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Computational Domain
y, j
u(x,1)  sin(x)e x
x, i
u(1,y)  0
u(0,y)  0
u(x,0)  sin(x)
uin, j 1

n
n
uin1,j  uin1,j  ui,j
 1  ui,j 1
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i  1,2,  ,m;
j  1,2,  ,m
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Five-point Finite-Difference Stencil
Interior cells.
x
Where solution of the Laplace
equation is sought.
x o x
x
(i, j)
Exterior cells.
Green cells denote cells where
homogeneous boundary
conditions are imposed while
non-homogeneous boundary
conditions are colored in blue.
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x
x o x
x
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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 = del + sum(sum(abs(up-u(i,j))));
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More efficient way ?
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Solution Contour Plot
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SOR Update Function
m
Matrix size
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Wallclock
ssor2Dij
Wallclock
ssor2Dji
Wallclock
ssor2Dv
for loops reverse loops
vector
128
1.01
0.98
0.26
256
8.07
7.64
1.60
512
65.81
60.49
11.27
1024
594.91
495.92
189.05
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Integration Example
• An integration of the cosine function between 0 and π/2
• Integration scheme is mid-point rule for simplicity.
• Several parallel methods will be demonstrated.
p
b
n
 cos(x)dx   
a
i 1 j 1
Worker 1
aij  h
aij
 n

h
 cos(aij  2 )h
cos(x)dx 

i 1 
 j 1
p

mid-point of increment
Worker 2
cos(x)
h
Worker 3
a = 0; b = pi/2; % range
m = 8; % # of increments
h = (b-a)/m; % increment
p = numlabs;
n = m/p; % inc. / worker
ai = a + (i-1)*n*h;
aij = ai + (j-1)*h;
Worker 4
x=a
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x=b
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Integration Example — the Kernel
n
function intOut = Integral(fct, a, b, n)
%function intOut = Integral(fct, a, b, n)
% performs mid-point rule integration of "fct"
% fct -- integrand (cos, sin, etc.)
% a -- starting point of the range of integration
% b –- end point of the range of integration
% n -- number of increments
% Usage example: >> Integral(@cos, 0, pi/2, 500)

j 1
cos(aij  h2 )h
% 0 to pi/2
h = (b – a)/n;
% increment length
intOut = 0.0;
% initialize integral
for j=1:n
% sum integrals
aij = a +(j-1)*h;
% function is evaluated at mid-interval
intOut = intOut + fct(aij+h/2)*h;
end
Vector form of the function:
function intOut = Integral(fct, a, b, n)
h = (b – a)/n;
aij = a + (0:n-1)*h;
intOut = sum(fct(aij+h/2))*h;
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Integration Example — Serial Integration
% serial integration
tic
m = 10000;
a = 0;
b = pi*0.5;
intSerial = Integral(@cos, a, b, m);
toc
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Integration Example Benchmarks
increment
For loop
vector
10000
0.011
0.0002
20000
0.022
0.0004
40000
0.044
0.0008
80000
0.087
0.0016
160000
0.1734
0.0033
320000
0.3488
0.0069
 Timings (seconds) obtained on a quad-core Xeon X5570
 Computation linearly proportional to # of increments.
 FORTRAN and C timings are an order of magnitude faster.
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Compiler
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.
 Many MATLAB general and toolbox licenses are
available. Infrequently, MATLAB access may be
denied if all licenses are checked out. Running a
stand-alone requires NO licenses and no waiting.
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Compiler (Cont’d)
 Some compiled codes may run more efficiently than
m-files because they are not run in interpretive
mode.
 A stand-alone enables you to share it without
revealing the source.
www.bu.edu/tech/research/training/tutorials/matlab/vector/miscs/compiler/
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Compiler (Cont’d)
How to build a standalone executable
>> mcc –o ssor2Dijc –m ssor2Dij
How to run ssor2Dijc on Katana
Katana% run_ssor2Dijc.sh /usr/local/apps/matlab_2009b 256 256
Input arguments
MATLAB root
Details:
• The m-file is ssor2Dij.m
• Input arguments to code are processed as strings by mcc. Convert
with str2num if need be. ssor2Dij.m requires 2 inputs; m, n
if isdeployed, m=str2num(m); end
• Output cannot be returned; either save to file or display on screen.
• The executable is ssor2Dijc
• run_ssor2Dijc.sh is the run script generated by mcc.
• None of SOR codes benefits, in runtime, from mcc.
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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.
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MATLAB profiler
To use profile viewer, DONOT start MATLAB with –nojvm option
>> profile on –detail 'builtin' –timer 'real'
>> % run code to be
Turns on profiler. –detail 'builtin'
>> % profiled here
enables MATLAB builtin functions;
>> %
-timer 'real' reports wallclock time.
>> %
>> profile viewer % view profiling data
>> profile off
% turn off profiler
Profiling example.
>> profile on
>> ssor2Dij % profiling the SOR Laplace solver
>> profile viewer
>> profile off
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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.
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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
>> plot(magic(20))
>> profile viewer
>> p = profile('info');
>> profsave(p, ‘my_profile') % html files in my_profile dir
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Profiling – save as MAT file
Viewing is dynamic; you can change the options. Must be viewed in
the MATLAB environment.
>> profile on
>> plot(magic(20))
>> profile viewer
>> p = profile('info');
>> save myprofiledata p
>> clear p
>> load myprofiledata
>> profview(0,p)
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MATLAB “grammar checker”
 mlint is used to identify coding inconsistencies and make
coding performance improvement recommendations.
 mlint is a standalone utility; it is an option in profile.
 MATLAB editor provides this feature.
 Debug mode can also be invoked through editor.
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Running MATLAB in Command
Line Mode and Batch
Katana% matlab -nodisplay –nosplash –r “n=4, myfile(n); exit”
Add –nojvm to save memory if Java is not required
For batch jobs on Katana, use the above command in the
batch script.
Visit http://www.bu.edu/tech/research/computation/linuxcluster/katana-cluster/runningjobs/ for instructions on running
batch jobs.
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Comment Out Block Of Statements
On occasions, one wants to comment out an entire block of lines.
If you use the MATLAB editor:
• Select statement block with mouse, then
– press Ctrl R keys to insert % to column 1 of each line.
– press Ctrl T keys to remove % on column 1 of each line.
If you use another editor:
• %{
n = 3000;
x = rand(n);
%}
• if 0
n = 3000;
x = rand(n);
end
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Multiprocessing With MATLAB
• Explicit parallel operations
MATLAB Parallel Computing Toolbox Tutorial
www.bu.edu/tech/research/training/tutorials/matlab-pct/
• Implicit parallel operations
– Require shared-memory computer architecture (i.e.,
multicore).
– Feature on by default. Turn it off with
katana% matlab –singleCompThread
– Specify number of threads with maxNumCompThreads
To be deprecated. Still supported on Version 2010b
– Activated by vector operation of applications such as
hyperbolic or trigonometric functions, some LaPACK
routines, Level-3 BLAS.
– See “Implicit Parallelism” section of the above link.
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Useful SCV Info
Please help us do better in the future by participating in a quick
survey: http://scv.bu.edu/survey/spring11tut_survey.html
 SCV home page (http://scv.bu.edu/)
 Resource Applications (https://acct.bu.edu/SCF)
 Help
 Web-based tutorials (http://scv.bu.edu/)

(MPI, OpenMP, MATLAB, IDL, Graphics tools)
 HPC consultations by appointment
 Kadin Tseng (kadin@bu.edu)
 Doug Sondak (sondak@bu.edu)
 help@twister.bu.edu, help@katana.bu.edu
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