Lecture Note
Tuning Matlab for Better Perfomance (For-loop Order)
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University:
Boston University -
Course:
CAS MA 511 | Introduction to Analysis I Academic year:
2023
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Views:
275
Pages:
19
Author:
5CelestialChronicle
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
Above wall time recorded for R2011a. With R2013a, time difference
is negligible. 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 Code Tuning and Optimization
Bad:
Good:
for i=1:N
x(i) = i;
end
for i=1:N
y(i) = rand();
end
for i=1:N
x(i) = i;
y(i) = rand();
end
Reduces for-loop overhead
More important, improve chances of pipelining
Loop fisssion splits statements into multiple loops Code Tuning and Optimization
Avoid if statements within loops
Bad:
if has overhead
cost and may inhibit
pipelining
for i=1:N
if i == 1
%perform i=1 calculations
else
%perform i>1 calculations
end
end
Good:
%perform i=1 calculations
for i=2:N
%perform i>1 calculations
end Code Tuning and Optimization
Divide is more expensive than multiply
• Intel x86 clock cycles per operation
• add
3-6
• multiply 4-8
• divide
32-45
• Bad:
c = 4;
for i=1:N
x(i)=y(i)/c;
end
• Good:
s = 1/c;
for i=1:N
x(i) = y(i)*s;
end Code Tuning and Optimization
Function Call Overhead
for i=1:N
Bad:
do stuff
myfunc(i);
end
Good:
function myfunc(i)
myfunc2(N);
end
function myfunc2(N)
for i=1:N
do stuff
end
end
Function m-file is precompiled to lower overhead for
repeated usage. Still, there is an overhead .
Caveat: Balance between modularity and performance. Code Tuning and Optimization
Minimize calls to math & arithmetic operations
Bad:
for i=1:N
z(i) = log(x(i)) + log(y(i));
v(i) = x(i) + x(i)^2 + x(i)^3;
end
Good:
for i=1:N
z(i) = log(x(i) * y(i));
v(i) = x(i)*(1+x(i)*(1+x(i)));
end
Processors do mult-add very efficiently; better than ^ and the like. Tuning MATLAB for Better Performance
Special Functions for Real Numbers
MATLAB provides a few functions for processing real number 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
square_root.m
real_square_root.m
isreal reports whether the array is real
single/double converts data to single-, or double-precision Tuning MATLAB for Better Performance
Vector Is Better Than Loops
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 and nested.
Without array pre-allocation, its size extension in a for-loop is costly
as shown before.
When possible, use vector representation instead 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
for_sine.m
vec_sine.m Tuning MATLAB for Better Performance
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 Tuning MATLAB for Better Performance
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 x 3 array of 0’s
A=
0 0 0
0 0 0
0 0 0
>> B = 2*ones(2,3) % ones generates 2 x 3 array of 1’s
B=
2 2 2
2 2 2
Alternatively,
>> B = repmat(2,2,3) % matrix replication Tuning MATLAB for Better Performance
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); Tuning MATLAB for Better Performance
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 Tuning MATLAB for Better Performance
Vector Utility Functions
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 Tuning MATLAB for Better Performance
function in range of 0 to 𝜋/2
• Equals to sum of all rectangles (width times height of bars)
• Integral is area under
b
m
a
i 1
cos( x)dx
a ih
a ( i 1) h
cos(x)
h
m
cos( x )dx cos(a (i 12 )h)h
i 1
; % range
; % # of increments
; % increment
mid-point of increment Tuning MATLAB for Better Performance
% integration with for-loop
tic
m = 100;
a = 0;
% lower limit of integration
b = pi/2;
% upper limit of integration
h = (b – a)/m;
% increment length
integral = 0;
% initialize integral
for i=1:m
x = a+(i-0.5)*h;
% mid-point of increment i
integral = integral + cos(x)*h;
end
toc
h
a
X(1) = a + h/2
b
X(m) = b - h/2 Tuning MATLAB for Better Performance
% integration with vector form
tic
m = 100;
a = 0;
% lower limit of integration
b = pi/2;
% upper limit of integration
h = (b – a)/m;
% increment length
x = a+h/2:h:b-h/2;
% mid-point of m increments
integral = sum(cos(x))*h;
toc
h
a
X(1) = a + h/2
b
X(m) = b - h/2 Tuning MATLAB for Better Performance
Integration Example Benchmarks
increment m
for-loop
Vector
10000
0.00044
0.00017
20000
0.00087
0.00032
40000
0.00176
0.00064
80000
0.00346
0.00130
160000
0.00712
0.00322
320000
0.01434
0.00663
Timings (seconds) obtained on Intel Core i5 3.2 GHz PC
Computational effort linearly proportional to # of increments.
Tuning Matlab for Better Perfomance (For-loop Order)
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