MATLAB中元胞数组的最小值

Question

我在 MATLAB 中有一个元胞数组，其中包含一些按大小降序排列的矩阵（例如 [512x512 double] [256x256 double] [128x128 double] 等）。

现在我想找到并擦除（变成零）元胞数组总共中矩阵中的 100 个最小元素（而不是单独在每个矩阵中）。例如，最小的元素可能在 128x128 矩阵中，下一个在 512x512 矩阵中，依此类推。

我怎样才能最有效地做到这一点？

下一个是我的超慢代码，用于三个这样的单元格数组 - H、D、V（percent2zero 是从整个单元格数组中擦除的元素百分比的参数）：

details=[H;D;V];
for k=1:3
    numOfLevels=length(details(k,:));
    TotalCoeffs=0;
    minimalInEachLevel=zeros(1,numOfLevels);
    for i=1:numOfLevels
        temp=cell2mat(details(k,i));
        TotalCoeffs=TotalCoeffs+numel(temp);
        minimalInEachLevel(i) = min(min(abs(temp)));
    end
    CoeffsToBeRemoved=percent2zero*TotalCoeffs/100;
    for i=1:CoeffsToBeRemoved
        for j=1:numOfLevels
            temp=cell2mat(details(k,j));
            minimalInEachLevel(j) = min(min(abs(temp)));
        end
        [val,ind]=min(minimalInEachLevel);
        temp=cell2mat(details(k,ind));
        temp(find(abs(temp==val),1))=0;
        details(k,ind)=mat2cell(temp,size(temp,1),size(temp,2));        
    end
end

Answer 1

我可以建议的一件事是将所有矩阵中的每个值放入单个 1D 向量中，对向量进行排序并选择 100 个最小值。使用cellfun 和sort 执行此第一步。这背后的逻辑是，如果我们收集所有矩阵的所有值并将它们放入单个向量中，然后对整个向量进行排序，我们将选择 100 个最小值all together，正如您提到的那样。

找到这 100 个最小值后，您必须遍历每个单元格，然后您可以使用 intersect 查看单元格数组中的每个矩阵中是否有任何与这 100 个最小值相同的元素。您可以使用 intersect 的第二个输出，然后使用它来索引每个单元格并将值设置为 0。因为您正在处理单元格并且每个单元格的大小不同，所以循环是唯一的选择。

想到这样的事情。这是假设details 是一个元胞数组，其中每个元胞都是一个矩阵：

%// Create single 1D vector of all values
vals = cellfun(@(x) reshape(x, [], 1), details, 'uni', 0);
vals = cat(1, vals{:});

%// Sort the UNIQUE values and grab the 100 smallest values
vals = unique(vals);
vals = vals(1:100);

%// Loop through each cell, determine those values that are among
%// the 100 smallest and set to 0
for ii = 1 : numel(details)
    [~,ind,~] = intersect(details{ii}, vals);
    details{ii}(ind) = 0;
end

unique 可以在数组或矩阵中找到唯一值，但也可以对唯一值进行排序。因此，此代码将找到 100 个最小且 唯一 值来处理您的元胞数组。

Answer 2

我一直在摆弄这个，基本上想出了与 rayryeng 相同的东西。想法是将每个矩阵重塑为一维向量，对每个向量进行排序并跟踪原始索引，然后开始将一维向量开头的最小元素归零，使用未排序的一维向量的索引返回到二维矩阵并将这些元素归零。我认为它有点将一维向量视为队列。无论如何，我设计了一个函数，该函数将遵循这个过程，用于包含 3 个矩阵的元胞数组。对于具有任意数量矩阵的元胞数组来说，它并不漂亮、优化或泛化，但我认为改进起来并不那么困难。

function [X] = wipeCellMinima(X,percent2zero)
%wipeCellMinima

x1 = X{1};
x2 = X{2};
x3 = X{3};

l1 = length(x1);
l2 = length(x2);
l3 = length(x3);

%reshape each matrix into a 1D vector and sort them, keeping sorted indices
[q1,I1] = sort(reshape(x1,1,l1^2));
[q2,I2] = sort(reshape(x2,1,l2^2));
[q3,I3] = sort(reshape(x3,1,l3^2));

%total number of elements to be "wiped"
n = fix((l1^2 + l2^2 + l3^2)*percent2zero*0.01); 

i1 = 1;
i2 = 1;
i3 = 1;

%treat the reshaped and sorted matrices kind of like queues
for j = 1:n
    %Find the smallest value indexed in sort1 by i1, in sort2 by i2,
    %and in sort3 by i3.
    [~,idx_min] = min([q1(i1),q2(i2),q3(i3)]);
    if(idx_min == 1)
        %The smallest element in all matrices is the first one in the
        %sorted version of x1. Use it's index in the unsorted version of q1
        %to set the corresponding element in x1 to zero. And increment i1.

        %In the unsorted version of q1, the I1(i1)th element needs to be
        %set to zero. The correct row and column can be extracted from the
        %size of the original matrix x1 and the position of the element in
        %the 1D vector.
        row = mod(I1(i1),l1);
        if(row == 0)
            row = l1;
            col = I1(i1)/l1;
        else
            col = floor(I1(i1)/l1) + 1;
        end
        x1(row,col) = 0;
        i1 = i1 + 1;
    elseif(idx_min == 2)
        row = mod(I2(i2),l2);
        if(row == 0)
            row = l2;
            col = I2(i2)/l2;
        else
            col = floor(I2(i2)/l2) + 1;
        end
        x2(row,col) = 0;
        i2 = i2 + 1;
    else
        row = mod(I3(i3),l3);
        if(row == 0)
            row = l3;
            col = I3(i3)/l3;
        else
            col = floor(I3(i3)/l3) + 1;
        end
        x3(row,col) = 0;
        i3 = i3 + 1;
    end
end

X = {x1,x2,x3};

end

Answer 3

n = sum(cellfun('prodofsize',details),2);
CoeffsToBeRemoved = round(percent2zero/100*n);
for i = 1:size(details,1)
    tmp = cellfun(@(x)x(:),details(i,:),'un',0);
    tmp = sort(abs(vertcat(tmp{:})));
    val = tmp(CoeffsToBeRemoved(i));
    for j = 1:size(details,2)
        details{i,j} = details{i,j}.*(abs(details{i,j})>val);
    end
end