我一直听说矢量化代码比 MATLAB 中的 for 循环运行得更快。然而，当我尝试向量化 MATLAB 代码时，它似乎运行得更慢。

I used tic and toc来测量时间。我只更改了程序中单个函数的实现。我的矢量化版本运行了47.228801秒，我的 for 循环版本运行了16.962089秒。

另外，在我的主程序中，我使用了大量的 N，N = 1000000数据集的大小是1 301，并且我针对具有相同大小和 N 的不同数据集运行每个版本多次。

为什么矢量化速度慢得多？如何进一步提高速度？

“矢量化”版本

function [RNGSet] = RNGAnal(N,DataSet)
%Creates a random number generated set of numbers to check accuracy overall
%   This function will produce random numbers and normalize a new Data set
%   that is derived from an old data set by multiply random numbers and
%   then dividing by N/2
randData = randint(N,length(DataSet));
tempData = repmat(DataSet,N,1);
RNGSet = randData .* tempData;
RNGSet = sum(RNGSet,1) / (N/2); % sum and normalize by the N
end

“for 循环”版本

function [RNGData] = RNGAnsys(N,Data)
%RNGAnsys This function produces statistical RNG data using a for loop
%   This function will produce RNGData that will be used to plot on another
%   plot that possesses the actual data
multData = zeros(N,length(Data));
for i = 1:length(Data)
    photAbs = randint(N,1); % Create N number of random 0's or 1's
    multData(:,i) = Data(i) * photAbs; % multiply each element in the molar data by the random numbers
end

sumData = sum(multData,1); % sum each individual energy level's data point
RNGData = (sumData/(N/2))'; % divide by n, but account for 0.5 average by n/2
end

矢量化

乍一看 for 循环代码告诉我们，因为photAbs是一个二进制数组，其每一列根据每个元素进行缩放Data，这个二进制特征可以用于矢量化。这在代码中被滥用了 -

function RNGData = RNGAnsys_vect1(N,Data)

%// Get the 2D Matrix of random ones and zeros
photAbsAll = randint(N,numel(Data));

%// Take care of multData internally by summing along the columns of the
%// binary 2D matrix and then multiply each element of it with each scalar 
%// taken from Data by performing elementwise multiplication
sumData = Data.*sum(photAbsAll,1);

%// Divide by n, but account for 0.5 average by n/2
RNGData = (sumData./(N/2))'; %//'

return;

经过分析，瓶颈似乎是随机二进制数组创建部分。因此，按照建议使用更快的随机二进制数组创建器这个智能解决方案 https://stackoverflow.com/a/25042251/3293881，上述函数可以进一步优化，如下所示 -

function RNGData = RNGAnsys_vect2(N,Data)

%// Create a random binary array and sum along the columns on the fly to
%// save on any variable space that would be required otherwise. 
%// Also perform the elementwise multiplication as discussed before.
sumData = Data.*sum(rand(N,numel(Data))<0.5,1);

%// Divide by n, but account for 0.5 average by n/2
RNGData = (sumData./(N/2))'; %//'

return;

使用智能二进制随机数组创建器，也可以优化原始代码，这将用于稍后优化 for 循环和矢量化代码之间的公平基准测试。这里列出了优化的 for 循环代码 -

function RNGData = RNGAnsys_opt1(N,Data)

multData = zeros(N,numel(Data));
for i = 1:numel(Data)

    %// Create N number of random 0's or 1's using a smart approach
    %// Then, multiply each element in the molar data by the random numbers
    multData(:,i) = Data(i) * rand(N,1)<.5; 
end

sumData = sum(multData,1); % sum each individual energy level's data point
RNGData = (sumData/(N/2))'; % divide by n, but account for 0.5 average by n/2
return;

标杆管理

基准测试代码

N = 15000; %// Kept at this value as it going out of memory with higher N's.
           %// Size of dataset is more important anyway as that decides how
           %// well is vectorized code against a for-loop code

DS_arr = [50 100 200 500 800 1500 5000]; %// Dataset sizes
timeall = zeros(2,numel(DS_arr));

for k1 = 1:numel(DS_arr)
    DS = DS_arr(k1);
    Data = rand(1,DS);

    f = @() RNGAnsys_opt1(N,Data);%// Optimized for-loop code
    timeall(1,k1) = timeit(f);
    clear f

    f = @() RNGAnsys_vect2(N,Data);%// Vectorized Code
    timeall(2,k1) = timeit(f);
    clear f
end

%// Display benchmark results
figure,hold on, grid on
plot(DS_arr,timeall(1,:),'-ro')
plot(DS_arr,timeall(2,:),'-kx')
legend('Optimized for-loop code','Vectorized code')
xlabel('Dataset size ->'),ylabel('Time(sec) ->')
avg_speedup = mean(timeall(1,:)./timeall(2,:))
title(['Average Speedup with vectorized code = ' num2str(avg_speedup) 'x'])

Results

结束语

根据我迄今为止的经验MATLAB，for 循环和向量化技术都不适合所有情况，但一切都是针对具体情况的。