MATLAB矩阵预分配比动态矩阵扩展慢

Question

在循环的每次迭代中，我正在计算MATLAB矩阵。这些矩阵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数，所以我使用'零'函数预先分配矩阵比初始化一个空数组要快，然后在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，我的程序运行得慢得多。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，其中的数字很复杂。与往常一样，任何见解都值得赞赏。

Answer 1

我一直认为预分配对于任何数组大小都更快，并且从未实际测试过它。因此，我通过附加和预分配方法使用1000次迭代对1x1x3到20x20x3的各种数组大小进行了简单的测试计时。这是代码：

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：