MATLAB 矩阵预分配比动态矩阵扩展慢

Question

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。我在进入循环之前知道这个最终矩阵的维度，所以我虽然使用“零”函数预分配矩阵比初始化一个空数组然后简单地在循环的每次迭代中附加子数组要快。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）：

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

就其他可能有用的信息而言——我的矩阵是 3D 的，其中的数字很复杂。与往常一样，我们感谢您的任何见解。

Answer 1

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，我通过追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简单的测试。代码如下：

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');

以下是（如预期的）结果：