vectorization of for loop code
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prod1=zeros(1000,1000);
for n=1:1000;
prod1(n,(1:n))=temp*((n-(1:n)+1).^alpha-(n-(1:n)).^alpha);
end
回答（2 个）
Andrei Bobrov
2017-3-21
编辑：Andrei Bobrov
2017-3-21
nn = 1:n;
z = temp*(nn.^alpha - (nn - 1).^alpha);
prod1 = tril(toeplitz(z));
I assume you want to vectorize this to gain more speed. Then start with simplifying the loop at first:
prod1 = zeros(m, m); % Clean loop
v = temp * diff((0:m) .^ alpha); % Reduce number of calls to ^
for n = 1:m
prod1(n:m, n) = v(1:m-n+1);
end
Some timings:
function SpeedTest
temp = 0.2; % Guessed parameters
alpha = 0.3;
m = 1000;
tic;
for k = 1:10
prod1 = zeros(m, m); % Original loop
for n = 1:m
prod1(n,(1:n))=temp*((n-(1:n)+1).^alpha-(n-(1:n)).^alpha);
end
end
toc
tic;
for k = 1:10
prod1 = zeros(m, m); % Clean loop
v = temp * diff((0:m) .^ alpha); % Reduce number of calls to ^
for n = 1:m
prod1(n:m, n) = v(1:m-n+1);
end
end
toc
tic;
for k = 1:10
nn = 1:n; % Vectorized
z = temp*(nn.^alpha - (nn - 1).^alpha);
prod1 = tril(toeplitz(z));
end
toc
Elapsed time is 1.687053 seconds. % Original
Elapsed time is 0.070619 seconds. % Cleaned loop
Elapsed time is 0.409178 seconds. % Vectorized with TRIL/TOEPLITZ
If run time matters, using a clean loop can be more important then vectorization. The main rules for optimizing loops:
- Avoid repeated calculations
- Process array in column order
- The power operation is expensive. Reduce the calls whenever possible.
Finally: Even if the lean loop is faster, Andrei's suggestion (with the leaner creation of the data) is nicer:
prod1 = tril(toeplitz(temp * diff((0:m) .^ alpha)));
The loop can save seconds of run time, the vectorized version minutes during debugging or expanding the code.
1 个评论
Andrei Bobrov
2017-3-21
编辑：Andrei Bobrov
2017-3-21
+1. Well!
cc = (0:n).^alpha;
k = temp*(cc(2:n+1) - cc(1:n));
prod1 = zeros(n);
for ii = 1:n
prod1(ii:n,ii) = k(1:n - ii + 1);
end
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2017-3-20
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