3d矩阵到2d矩阵matlab [英] 3d Matrix to 2d Matrix matlab
问题描述
我正在使用Matlab R2014a。
I am using Matlab R2014a.
我有一个三维M x N x M矩阵A.我想要一种矢量化方法来提取二维矩阵B来自它，这样对于每个i，j我有
I have a 3-dimensional M x N x M matrix A. I would like a vectorized way to extract a 2 dimensional matrix B from it, such that for each i,j I have
B（i，j）= A（i，j，g（i，j））
B(i,j)=A(i,j,g(i,j))
其中g是大小为M×N的二维索引矩阵，即在{1,2，...，M}中具有整数值。
where g is a 2-dimensional index matrix of size M x N, i.e. with integral values in {1,2,...,M}.
上下文是我将函数A（k，z，k'）表示为三维矩阵，函数g（k，z）表示为2维矩阵，我想计算函数
The context is that I am representing a function A(k,z,k') as a 3-dimensional matrix, the function g(k,z) as a 2-dimensional matrix, and I would like to compute the function
h（k，z）= f（k，z，g（k，z））
h(k,z)=f(k,z,g(k,z))
这似乎是一个简单而常见的尝试，但我真的无法在网上找到任何东西。非常感谢能有所帮助的人！
This seems like a simple and common thing to try to do but I really can't find anything online. Thank you so much to whoever can help!
我的第一个想法是尝试像B = A（：，：，g）或B = A（g）但是毫不奇怪，这些都不起作用。是否有类似的东西？
My first thought was to try something like B = A(:,:,g) or B=A(g) but neither of these works, unsurprisingly. Is there something similar?
推荐答案
你可以使用最好的矢量化工具， bsxfun -
You can employ the best tool for vectorization, bsxfun here -
B = A(bsxfun(@plus,[1:M]',M*(0:N-1)) + M*N*(g-1))
说明：将其分解为两步
步骤1：计算与 A -
bsxfun(@plus,[1:M]',M*(0:N-1))
步骤2：添加包含dim-3索引所需的偏移量由 g 提供，并使用这些索引编入索引以获得我们想要的输出 -
Step #2: Add the offset needed to include the dim-3 indices being supplied by g and index into A with those indices to get our desired output -
A(bsxfun(@plus,[1:M]',M*(0:N-1)) + M*N*(g-1))
基准测试
这里一个快速的基准测试来比较基于 bsxfun 的方法与 ndgrid + sub2ind 的解决方案https://stackoverflow.com/a/27339316/3293881\">路易斯的解决方案， M 和 N as 100 。
Benchmarking
Here's a quick benchmark test to compare this bsxfun based approach against the ndgrid + sub2ind based solution as presented in Luis's solution with M and N as 100.
使用 tic-toc 的基准代码看起来像这样 -
The benchmarking code using tic-toc would look something like this -
M = 100;
N = 100;
A = rand(M,N,M);
g = randi(M,M,N);
num_runs = 5000; %// Number of iterations to run each approach
%// Warm up tic/toc.
for k = 1:50000
tic(); elapsed = toc();
end
disp('-------------------- With BSXFUN')
tic
for iter = 1:num_runs
B1 = A(bsxfun(@plus,[1:M]',M*(0:N-1)) + M*N*(g-1)); %//'
end
toc, clear B1
disp('-------------------- With NDGRID + SUB2IND')
tic
for iter = 1:num_runs
[ii, jj] = ndgrid(1:M, 1:N);
B2 = A(sub2ind([M N M], ii, jj, g));
end
toc
这是运行时结果 -
Here's the runtime results -
-------------------- With BSXFUN
Elapsed time is 2.090230 seconds.
-------------------- With NDGRID + SUB2IND
Elapsed time is 4.133219 seconds.
结论
正如您所见<基于code> bsxfun 的方法非常有效，既可以作为矢量化方法，也可以作为性能良好的方法。
Conclusions
As you can see bsxfun based approach works really well, both as a vectorized approach and good with performance too.
为什么 bsxfun 更好 -
Why is bsxfun better here -
-
bsxfun复制偏移元素并添加它们，即时 strong>。
bsxfundoes replication of offsetted elements and adding them, both on-the-fly.
在另一个解决方案中， ndgrid 在内部对<$ c $进行两次函数调用c> repmat ，从而产生函数调用开销。在下一步， sub2ind 花费时间添加偏移量以获得线性索引，从而带来另一个函数调用开销。
In the other solution, ndgrid internally makes two function calls to repmat, thus incurring the function call overheads. At the next step, sub2ind spends time in adding the offsets to get the linear indices, bringing in another function call overhead.
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