Matlab：如何在2D矢量集上矢量化嵌套循环 [英] Matlab: How to vectorize a nested loop over a 2D set of vectors

问题描述

我有以下形式的函数：

function Out = DecideIfAPixelIsWithinAnEllipsoidalClass(pixel,means,VarianceCovarianceMatrix)  
   ellipsoid = (pixel-means)'*(VarianceCovarianceMatrix^(-1))*(pixel-means);  
   if ellipsoid <= 1
      Out = 1;
   else
      Out = 0;
   end
end  

我正在使用matlab进行遥感过程想要对LandSatTM图像进行分类。这张图片有7个波段，是2048 * 2048.所以我将它们存储在3个2068 * 2048 * 7矩阵中。这个函数意味着先前使用类的样本计算的7 * 1矩阵在一个名为ExtractStatisticalParameters和VarianceCovarianceMatrix的函数中，你看到的是一个7 * 7矩阵：

I am doing remote-sensing processes with matlab and I want to classify a LandSatTM images.This picture has 7 bands and is 2048*2048.So I stored them in 3 dimentinal 2048*2048*7 matrix.in this function means is a 7*1 matrix calculated earlier using the sample of the class in a function named ExtractStatisticalParameters and VarianceCovarianceMatrix is a 7*7 matrix in fact you see that:

ellipsoid = (pixel-means)'*(VarianceCovarianceMatrix^(-1))*(pixel-means);  

是椭圆体的等式。我的问题是每次你可以传递一个像素（它是一个7 * 1向量，其中每一行是分隔波段中像素的值），因此我需要写一个这样的循环：

is the equation of an ellipsoid.My problem is that each time you can pass a single pixel(it is a 7*1 vector where each row is the value of the pixel in a seperated band) to this function so I need to write a loop like this:

for k1=1:2048  
   for k2=1:2048  
      pixel(:,1)=image(k1,k2,:); 
      Out = DecideIfAPixelIsWithinAnEllipsoidalClass(pixel,means,VarianceCovarianceMatrix);  
   end  
end  

你知道它需要很多时间和精力系统。你建议我一种减少系统压力的方法吗？

and you know it will take alot of time and energy of the system.Can you suggest me a way to reduce the pressure applied on the systam?

推荐答案

无需循环！

pMinusMean = bsxfun( @minus, reshape( image, [], 7 ), means' ); %//' subtract means from all pixes
iCv = inv( arianceCovarianceMatrix );
ell = sum( (pMinusMean * iCv ) .* pminusMean, 2 ); % note the .* the second time!
Out = reshape( ell <= 1, size(image(:,:,1)) ); % out is 2048-by-2048 logical image

更新：

在下面评论中的（有点激烈的）辩论之后，我添加了一个由 Rody Oldenhuis ：

pMinusMean = bsxfun( @minus, reshape( image, [], 7 ), means' ); %//' subtract means from all pixes
ell = sum( (pMinusMean / varianceCovarianceMatrix ) .* pminusMean, 2 ); % note the .* the second time!
Out = reshape( ell <= 1, size(image(:,:,1)) );

此更改的关键问题是Matlab的 inv（）使用最佳 > mldivide 和 mrdivide （运营商 / 和 \ ）而不是。

The key issue in this change is that Matlab's inv() is poorly implemented and it is best to use mldivide and mrdivide (operators / and \) instead.

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