'for'循环vs矢量化在MATLAB中 [英] 'for' loop vs vectorization in MATLAB

问题描述

我在MATLAB中编写了一些东西，正如所建议的那样，我总是试图使用矢量化。但是最后这个计划很慢。所以我发现在一个地方代码是显着更快的时候使用循环（下面的例子）。

我想知道如果我误解了一些东西或做错了什么，因为在这种情况下性能很重要，而且我不想猜测矢量化或者循环是否会更快。

 ％数据初始化
 
k = 8; 
 n = 2 ^ k + 1; 
 h = 1 /（n-1）; 
 cw = 0.1; 
 
 iter = 10000; 
 
 uloc = zeros（n）; 
 fploc = uloc; 
 uloc（2：end-1,2：end-1）= 1; 
 vloc = uloc; 
 ploc = ones（n）; 
 
 uloc2 = zeros（n）; 
 fploc2 = uloc2; 
 uloc2（2：end-1,2：end-1）= 1; 
 vloc2 = uloc2; 
 ploc2 = ones（n）; 
 
 %%%%%%%%%%%%%%%%%%%%%%% 
％矢量化版本％
 %%%%%%%% %%%%%%%%%%%%%% 
 tic 
 for it = 1：iter 
 il = 2：4; 
 jl = 2：4; 
 fploc（il，jl）= h / 6 *（ -  uloc（il-1，jl-1）+ uloc（il-1，jl）... 
 -2 * uloc （il + 1，jl + 1）... 
。（1 + 1，jl + 1） （il-1，jl）... 
 + vloc（il，jl-1）-vloc（il，jl-1） +1）... 
 + 2 * vloc（il + 1，jl）+ vloc（il + 1，jl + 1））... 
 ... 
 + cw * （il，jl）-ploc（il，jl）+ 4 * ploc（il，jl）... 
 -ploc（il + 1，jl）-ploc （IL，JL + 1））; 
 end 
 toc 
 
 
 %%%%%%%%%%%%%%%%%%%%%% 
％循环版本％
 %%%%%%%%%%%%%%%%%%%%%% 
 tic 
 for it = 1：iter 
 for il = （il-1，j-1）+ uloc2（il-1，jl）2：4 
。 （i + 1，j1）+ uloc2（i1 + 1）+ 1（i + 1） ，j1 + 1）... 
 ... 
 -vloc2（il-1，jl-1）-2 * vloc2（il-1，jl）... 
 + vloc2 （il，jl-1）-vloc2（il，jl + 1）... 
 + 2 * vloc2（il + 1，jl）+ vloc2（il + 1，jl + 1））... 
 ... 
 + cw * h ^ 2 *（ -  ploc2（il-1，jl）-ploc2（il，jl-1）+ 4 * ploc2（il，jl）... 
 -ploc2（il + 1，jl）-ploc2（il，jl + 1））; 
 end 
 end 
 end 
 toc 
  

解决方案在过去的几年中，MATLAB的即时编译器（JIT）已经有了很大的改进。即使你是正确的，一般应该矢量化代码，根据我的经验，这只适用于某些操作和功能，也取决于你的功能处理多少数据。

要找出最好的方法，最好的办法是到分析你的MATLAB代码有和没有向量化。

I was programming something in MATLAB and, as recommended, I am always trying to use vectorization. But in the end the program was quite slow. So I found out that in one place the code is significantly faster when using loops (example below).

I would like to know if I misinterpreted something or did something wrong, because performance is important in this case, and I don't want to keep guessing if vectorization or loops are going to be faster.

% data initialization

k = 8;
n = 2^k+1;
h = 1/(n-1);
cw = 0.1;

iter = 10000;

uloc = zeros(n);
fploc = uloc;
uloc(2:end-1,2:end-1) = 1;
vloc = uloc;
ploc = ones(n);

uloc2 = zeros(n);
fploc2 = uloc2;
uloc2(2:end-1,2:end-1) = 1;
vloc2 = uloc2;
ploc2 = ones(n);

%%%%%%%%%%%%%%%%%%%%%%
% vectorized version %
%%%%%%%%%%%%%%%%%%%%%%
tic
for it=1:iter
    il=2:4;
    jl=2:4;
    fploc(il,jl) = h/6*(-uloc(il-1,jl-1) + uloc(il-1,jl)...
        -2*uloc(il,jl-1)+2*uloc(il,jl+1)...
        -uloc(il+1,jl) + uloc(il+1,jl+1)...
        ...
        -vloc(il-1,jl-1) - 2*vloc(il-1,jl)...
        +vloc(il,jl-1) - vloc(il,jl+1)...
        + 2*vloc(il+1,jl) + vloc(il+1,jl+1))...
        ...
        +cw*h^2*(-ploc(il-1,jl)-ploc(il,jl-1)+4*ploc(il,jl)...
        -ploc(il+1,jl)-ploc(il,jl+1));
end
toc


%%%%%%%%%%%%%%%%%%%%%%
%    loop version    %
%%%%%%%%%%%%%%%%%%%%%%
tic
for it=1:iter
    for il=2:4
        for jl=2:4
            fploc2(il,jl) = h/6*(-uloc2(il-1,jl-1) + uloc2(il-1,jl)...
                -2*uloc2(il,jl-1)+2*uloc2(il,jl+1)...
                -uloc2(il+1,jl) + uloc2(il+1,jl+1)...
                ...
                -vloc2(il-1,jl-1) - 2*vloc2(il-1,jl)...
                +vloc2(il,jl-1) - vloc2(il,jl+1)...
                + 2*vloc2(il+1,jl) + vloc2(il+1,jl+1))...
                ...
                +cw*h^2*(-ploc2(il-1,jl)-ploc2(il,jl-1)+4*ploc2(il,jl)...
                -ploc2(il+1,jl)-ploc2(il,jl+1));
        end
    end
end
toc

解决方案

MATLAB's just in time compiler (JIT) has been improved significantly over the last couple years. And even though you are right that one should generally vectorize code, from my experience this is only true for certain operations and functions and also depends on how much data your functions are handling.

The best way for you to find out what works best, is to profile your MATLAB code with and without vectorization.

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