MATLAB 矩阵预分配比动态矩阵扩展慢 [英] MATLAB Matrix Preallocation Slower Than Dynamic Matrix Expansion

问题描述

在循环的每次迭代中，我都在计算一个 MATLAB 矩阵.这些矩阵都必须连接在一起以创建一个最终矩阵.在进入循环之前我知道这个最终矩阵的维度，所以我虽然使用zeros"函数预分配矩阵比初始化一个空数组要快，然后在我的循环的每次迭代中简单地附加子数组.奇怪的是，当我预分配时，我的程序运行速度要慢得多.这是代码(只有第一行和最后一行不同):

In each iteration of a loop, I am calculating a MATLAB matrix. These matrices all must be concatenated together to create one final matrix. I know the dimensions of this final matrix before entering the loop, so I though preallocating the matrix using the 'zeros' function would be faster than initializing an empty array then simply appending the subarrays in each iteration of my loop. Oddly, my program runs MUCH slower when I preallocate. Here is the code (Only the first and last lines differ):

这很慢:

w_cuda = zeros(w_rows, w_cols, f_cols);

for j=0:num_groups-1

    % gets # of rows & cols in W. The last group is a special
    % case because it may have fewer than max_row_size rows
    if (j == num_groups-1 && mod(w_rows, max_row_size) ~= 0)
        num_rows_sub = w_rows - (max_row_size * j);    
    else
        num_rows_sub = max_row_size;
    end;

    % calculate correct W and f matrices
    start_index = (max_row_size * j) + 1;
    end_index = start_index + num_rows_sub - 1;

    w_sub = W(start_index:end_index,:);
    f_sub = filterBank(start_index:end_index,:);

    % Obtain sub-matrix
    w_cuda_sub = nopack_cu(w_sub,f_sub);

    % Incorporate sub-matrix into final matrix
    w_cuda(start_index:end_index,:,:) = w_cuda_sub;

end

这很快:

w_cuda = [];

for j=0:num_groups-1

    % gets # of rows & cols in W. The last group is a special
    % case because it may have fewer than max_row_size rows
    if (j == num_groups-1 && mod(w_rows, max_row_size) ~= 0)
        num_rows_sub = w_rows - (max_row_size * j);    
    else
        num_rows_sub = max_row_size;
    end;

    % calculate correct W and f matrices
    start_index = (max_row_size * j) + 1;
    end_index = start_index + num_rows_sub - 1;

    w_sub = W(start_index:end_index,:);
    f_sub = filterBank(start_index:end_index,:);

    % Obtain sub-matrix
    w_cuda_sub = nopack_cu(w_sub,f_sub);

    % Incorporate sub-matrix into final matrix
    w_cuda = [w_cuda; w_cuda_sub];

end

至于其他可能有用的信息——我的矩阵是 3D 的，其中的数字很复杂.与往常一样，我们不胜感激.

As far as other potentially useful information--my matrix is 3D, and the numbers within it are complex. As always, any insight is appreciated.

推荐答案

我一直认为预分配对于任何数组大小都更快，但从未实际测试过.因此，我通过附加和预分配方法使用 1000 次迭代对从 1x1x3 到 20x20x3 的各种数组大小的填充进行了一个简单的测试.代码如下:

I have always assumed preallocation is faster for any array size and never actually tested it. So, I did a simple test timing the population of various array sizes from 1x1x3 up to 20x20x3 using 1000 iterations by both appending and preallocation methods. Here's the code:

arraySize = 1:20;
numIteration = 1000;

timeAppend = zeros(length(arraySize), 1);
timePreAllocate = zeros(length(arraySize), 1);

for ii = 1:length(arraySize); 
    w = [];
    tic;
    for jj = 1:numIteration
        w = [w; rand(arraySize(ii), arraySize(ii), 3)];
    end
    timeAppend(ii) = toc;
end; 

for ii = 1:length(arraySize); 
    w = zeros(arraySize(ii) * numIteration, arraySize(ii), 3);
    tic;
    for jj = 1:numIteration
        indexStart = (jj - 1) * arraySize(ii) + 1;
        indexStop = indexStart + arraySize(ii) - 1;
        w(indexStart:indexStop,:,:) = rand(arraySize(ii), arraySize(ii), 3);
    end
    timePreAllocate(ii) = toc;
end; 

figure;
axes;
plot(timeAppend);
hold on;
plot(timePreAllocate, 'r');
legend('Append', 'Preallocate');

这是(如预期的)结果:

And here are the (as expected) results:

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