如何从 3D 数组的选定列构造矩阵？

Question

我有一个尺寸为 K x M x N 的 3D GPU 阵列 A 和一个长度为 M 的 int 向量 v 并且想要构造 2D GPU 阵列形式

X = [A(:,1,v(1)), A(:,2,v(2)),..., A(:,M,v(M))]（取决于v）

以最省时的方式。由于所有这些都是 GPU 数组，我想知道是否有比预分配 X 和使用明显的 for 循环更快的方法来完成此操作。我的代码需要调用数百万个这样的实例，因此这成为瓶颈。如果重要的话，典型的数量级订单为 K = 350 000, 2<=M<=15, N<=2000。

编辑： 这是我试图改进的原始瓶颈代码的最小工作版本。转换为 3D 数组 A 已被注释掉。根据需要调整数组大小参数。

% generate test data:
K = 4000; M = 2; % N = 100

A_cell = cell(1,M);
s = zeros(1,M,'uint16');
for m=1:M
    s(m) = m*50; % defines some widths for the matrices in the cells
    A_cell{m} = cast(randi([0 1],K,s(m),'gpuArray'),'logical');
end
N = max(s,[],2);

% % A_cell can be replaced by a 3D array A of dimensions K x M x N:
% A = true(K,M,N,'gpuArray');
% for m=1:M
%     A(:,m,1:s(m)) = permute(A_cell{m},[1 3 2]);
% end

% bottleneck code starts here and has M = 2 nested loops:
I_true = true(K,1,'gpuArray');
I_01 = false(K,1,'gpuArray');
I_02 = false(K,1,'gpuArray');

for j_1=1:s(1)
    for j_2=1:s(2)

        v = [j_1,j_2];

        I_tmp = I_true;

        for m=1:M
            I_tmp = I_tmp & A_cell{m}(:,v(m));
        end

        I_02 = I_02 | I_tmp;
    end

    I_01 = I_01 | I_02;
end

Out = gather(I_01);

% A_cell can be replaced by 3D array A above

Answer 1

MATLAB 允许您一次索引多个维度。这允许您给出一个线性索引向量 h，它同时索引第二个和第三个维度：

% Some example data
k=2;
m=3;
n=4;
v=[2,3,1];
A=rand(k,m,n);
X=[A(:,1,v(1)),A(:,2,v(2)),A(:,3,v(3))]
%solution
h=sub2ind([m,n],[1:m],v);
Y=A(:,h)

进一步阅读：Linear indexing, logical indexing, and all that

Answer 2

关于我上面发布的代码，事实证明使用 2D gpuAarray 而不是 3D gpuArray 代替单元格更快。这允许非常直接地选择列和最远内部循环的矢量化。更准确地说：

% generate test data:
K = 4000; M = 2;

A_cell = cell(1,M); % this is given externally
s = zeros(1,M,'uint16');
for m=1:M
    s(m) = m*50; % defines some widths for the matrices in the cells
    A_cell{m} = cast(randi([0 1],K,s(m)),'logical'); % cell2mat doesn't work with cells of gpuArrays
end

% conversion of A_cell into an appropriate 2D array is straightforward:
A_hor = gpuArray(cell2mat(A_cell)); % horizontal concatenation of the cells

% bottleneck code starts here and has M = 2 nested loops:
I_01 = false(K,1,'gpuArray');
I_02 = false(K,1,'gpuArray');

t = [1,s]; t = t(1:M); % vector of the starting indices of the old matrices inside A_hor

for j_1=1:s(1)
    for j_2=1:s(2)

        j = [j_1,j_2];

        k = t-1+j; % vector of the positions of the needed columns

        I_02 = I_02 | all(A_hor(:,k),2);
    end

    I_01 = I_01 | I_02;
end

Out = gather(I_01);

如何从 3D 数组的选定列构造矩阵？

How to construct a matrix from selected columns of a 3D array?

matlab

vectorization

multidimensional-array

gpuarray