Writing Fast Matlab Code #6:Inlining Simple Functions
Every time an M-file function is called, the Matlab interpreter incurs some overhead. Additionally, many M-file functions begin with conditional code that checks the input arguments for errors or deter- mines the mode of operation.
Of course, this overhead is negligible for a single function call. It should only be considered when the function being called is an M-file, the function itself is “simple,” that is, implemented with only a few lines, and called frequently from within a loop.
For example, this code calls the M-file function median repeatedly to perform median filtering:
% Apply the median filter of size 5 to signal x y = zeros(size(x)); % Preallocate for k = 3:length(x)−2 y(k) = median(x(k−2:k+2)); end
Given a 2500-sample array for x, the overall run time is 0.42 seconds.
“Inlining a function” means to replace a call to the function with the function code itself. Beware that inlining should not be confused with Matlab’s “inline” function datatype. Studying median.m (type “edit median” on the console) reveals that most of the work is done using the built-in sort function. The median call can be inlined as
% Apply the median filter of size 5 to signal x y = zeros(size(x)); % Preallocate for k = 3:length(x)−2 tmp = sort(x(k−2:k+2)); y(k) = tmp(3); % y(k) = median(x(k−2:k+2)); end
Now the overall run time is 0.047 seconds, nearly 9 times faster. Furthermore, by inlining median, it can be specifically tailored to evaluating 5-sample medians. But this is only an example; if the Signal Processing Toolbox➋ is available, y = medfilt1(x,5) is much faster.
A surprising number of Matlab’s functions are implemented as M-files, of which many can be inlined in just a few lines. In Matlab 5.3 (R11), the following functions are worth inlining:
conv, cross, fft2, fliplr, flipud, ifft, ifft2, ifftn, ind2sub, ismember, linspace, logspace, mean, median, meshgrid, poly, polyval, repmat, roots, rot90, setdiff, setxor, sortrows, std, sub2ind, union, unique, var
The list above is for Matlab R11; some of these functions have since become built-in. Use the which
command or try “edit function name” to determine whether a function is implemented as an M-file.
For example, in Matlab R11 and earlier, ifft was implemented by simply calling fft and conj. If x is a one-dimensional array, y = ifft(x) can be inlined with y = conj(fft(conj(x)))/length(x).
Another example: b = unique(a) can be inlined with
b = sort(a(:)); b( b((1:end−1)') == b((2:end)') ) = [];
While repmat has the generality to operate on matrices, it is often only necessary to tile a vector or just a scalar. To repeat a column vector y over the columns n times,
A = y(:,ones(1,n)); % Equivalent to A = repmat(y,1,n);
To repeat a row vector x over the rows m times,
A = x(ones(1,m),:); % Equivalent to A = repmat(x,m,1);
To repeat a scalar s into an m×n matrix,
A = s(ones(m,n)); % Equivalent to A = repmat(s,m,n);
This method avoids the overhead of calling an M-file function. It is never slower than repmat (critics should note that repmat.m itself uses this method to construct mind and nind). For constructing matrices with constant value, there are other efficient methods, for example, s+zeros(m,n).
Don’t go overboard. Inlining functions is only beneficial when the function is simple and when it is called frequently. Doing it unnecessarily obfuscates the code.
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