初始化非标准值的双精度数组的最快方法

Question

MATLAB 为具有 0 or 1 等常见值的 preallocation/initializing 数组提供函数。然而，如果我们想让数组有一些任意double值，有多种方法可以做到，而且哪一种更可取并不明显。

这个问题并不新鲜 - 之前曾在 this blog post and in this answer 等地方讨论过。然而，经验表明软件（特别是 MATLAB 及其执行引擎）和硬件会随着时间而变化，因此最佳方法可能在不同的系统上会有所不同。不幸的是，上述来源不提供基准测试代码，这可能是回答这个问题的最终（和永恒）方式。

我正在寻找一个我可以运行的基准测试，它将告诉我在我的系统 上使用 的最快方法，考虑到我可能同时使用 "regular" double 数组和 gpuArray double 数组，大小不一。

Answer 1

function allocationBenchmark(arrSz)
if nargin < 1
  arrSz = 1000;
end

%% RAM
t = [];
disp('--------------- Allocations in RAM ---------------')
t(end+1) = timeit(@()v1(arrSz), 1);
t(end+1) = timeit(@()v2(arrSz), 1);
t(end+1) = timeit(@()v3(arrSz), 1);
t(end+1) = timeit(@()v4(arrSz), 1);
t(end+1) = timeit(@()v5(arrSz), 1);
t(end+1) = timeit(@()v6(arrSz), 1);
t(end+1) = timeit(@()v7(arrSz), 1);
t = 1E3 * t; % conversion to msec
disp(t); disp(" ");
[~,I] = min(t);
disp("Conclusion: method #" + I + " is the fastest on the CPU!"); disp(" ");

%% VRAM
if gpuDeviceCount == 0, return; end
t = [];
disp('--------------- Allocations in VRAM --------------')
t(end+1) = NaN; % impossible (?) to run v1 on the gpu
t(end+1) = gputimeit(@()v2gpu(arrSz), 1);
t(end+1) = gputimeit(@()v3gpu(arrSz), 1);
t(end+1) = gputimeit(@()v4gpu(arrSz), 1);
t(end+1) = gputimeit(@()v5gpu(arrSz), 1);
t(end+1) = gputimeit(@()v6gpu(arrSz), 1);
t(end+1) = gputimeit(@()v7gpu(arrSz), 1);
t = 1E3 * t; % conversion to msec
disp(t); disp(" ");
[~,I] = min(t);
disp("Conclusion: method #" + I + " is the fastest on the GPU!");

end

%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% RAM
function out = v1(M)
% Indexing on the undefined matrix with assignment:
out(1:M, 1:M) = pi;
end

function out = v2(M)
% Indexing on the target value using the `ones` function:
scalar = pi;
out = scalar(ones(M));
end

function out = v3(M)
% Using the `zeros` function with addition:
out = zeros(M, M) + pi;
end

function out = v4(M)
% Using the `repmat` function:
out = repmat(pi, [M, M]);
end

function out = v5(M)
% Using the ones function with multiplication:
out = ones(M) .* pi;
end

function out = v6(M)
% Default initialization with full assignment:
out = zeros(M);
out(:) = pi;
end

function out = v7(M)
% Using the `repelem` function:
out = repelem(pi,M,M);
end

%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% VRAM
function out = v2gpu(M)
scalar = gpuArray(pi);
out = scalar(gpuArray.ones(M));
end

function out = v3gpu(M)
out = gpuArray.zeros(M, M) + gpuArray(pi);
end

function out = v4gpu(M)
out = repmat(gpuArray(pi), [M, M]);
end

function out = v5gpu(M)
out = gpuArray.ones(M) .* gpuArray(pi);
end

function out = v6gpu(M)
% Default initialization with full assignment:
out = gpuArray.zeros(M);
out(:) = gpuArray(pi);
end

function out = v7gpu(M)
% Using the `repelem` function:
out = repelem(gpuArray(pi),M,M);
end

运行以上（例如输入 5000）结果如下：

--------------- Allocations in RAM ---------------
  110.4832  328.1685   48.7895   47.9652  108.8930   93.0481   47.9037

Conclusion: method #7 is the fastest on the CPU!

--------------- Allocations in VRAM --------------
       NaN   37.0322   17.9096   14.2873   17.7377   16.1386   16.6330

Conclusion: method #4 is the fastest on the GPU!

...这告诉我们在每种情况下使用的最佳（或等效）方法。

初始化非标准值的双精度数组的最快方法

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