在矩阵中找到一个临界点 [英] Finding a critical point in matrix

问题描述

我试图在矩阵中找到一个关键点。 index（i，j）处的值应该大于或等于其行中的所有元素，并且小于或等于其列中的所有元素。

下面是我所拥有的（它已关闭但我已经接近）：

  function C = critical（A）
 [nrow ncol] = size（A）; 
 C = []; （A（i，j）> = A（i，1：end））&& amp;& amp;& （A（i，j）≤A（1：end，j））
 C = [C; A（i，j）] 
 end 
 end 
 end 
  

解决方案

使用 bsxfun

 函数[r，c，criP] = critical（A）
 
％//找到每个col的最小值和最大值。 row resptly 
 minI = min（A，[]，1）; 
 maxI = max（A，[]，2）; 
 
％//匹配min&最大为每个col和行resptly 
％//得到元素的索引满足条件
 idx = find（bsxfun（@ eq，A，maxI）& bsxfun（@ eq，A，微型））; 
 
％//从索引中获取相应的值
 criP = A（idx）; 
 
％//同样得到相应的行和col sub 
 [r，c] = ind2sub（size（A），idx）; 
 end 
  

运行示例

r ， c 应该是等长的向量，每个关键点的列子目录。虽然 val 是一个长度相同的向量，给出了临界点本身的值

 >> A 
 
 A = 
 
 3 4 1 1 2 
 2 4 2 1 4 
 4 3 2 1 2 
 3 3 1 1 1 
 2 3 0 2 1 
 
 
>> [r，c，val] =危急（A）
 
r = 
 
 4 
 5 
 
c = 
 
 2 
 2 
 
 val = 
 
 3 
 3 
  

I'm attempting to find a critical point in a matrix. The value at index (i,j) should be greater than or equal to all elements in its row, and less than or equal to all elements in its column.

Here is what I have (it's off but I'm close):

function C = critical(A)
[nrow ncol] = size(A);
C = [];
for i = 1:nrow
    for j = 1:ncol
        if (A(i,j) >= A(i,1:end)) && (A(i,j) <= A(1:end,j))
            C = [C ; A(i,j)]
        end
    end
end

解决方案

Try this vectorised solution using bsxfun

function [ r,c,criP ] = critical( A )

    %// finding the min and max values of each col & row resptly
    minI = min(A,[],1);
    maxI = max(A,[],2);

    %// matching all the values of min & max for each col and row resptly 
    %// getting the indexes of the elements satisfying both the conditions
    idx = find(bsxfun(@eq,A,maxI) & bsxfun(@eq,A,minI));

    %// getting the corresponding values from the indexes
    criP = A(idx);

    %// Also getting corresponding row and col sub
    [r,c] = ind2sub(size(A),idx);
end

Sample Run:

r,c should be a vector of equal length which represents the row and column subs of each Critical point. While val is a vector of same length giving the value of the critical point itself

>> A

A =

 3     4     1     1     2
 2     4     2     1     4
 4     3     2     1     2
 3     3     1     1     1
 2     3     0     2     1


>> [r,c,val] = critical(A)

r =

 4
 5

c =

 2
 2

val =

 3
 3

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