MATLAB: Two different ways of expressing the same logical condition lead to two different results ??

binary functionlogical relationoperator precedencerelational operator

I run two codes with a little difference in the way I express logical conditions, namely:
In code 1: I write : A(k,4) > B(:,2) & B(:,2)> A(k,3) In code 2: I write : A(k,4) > B(:,2) > A(k,3)
But in code 1 I have the expected result and in code 2, i do not.
Here are two full code I used:
Code 1:
clear all clc A=xlsread('criteria.xlsx'); B=xlsread('panel.xlsx');
for i=1:89 for j=1:64 for k=1:3 for h=1:2 mask = B(:,5) == A(i,1) & B(:,4) == A(j,2) & A(k,4) > B(:,2) & B(:,2)> A(k,3) & A(h,5) < B(:,1) < A(h,6);
                x = mean(B(mask,3)); 
                B(mask,5) = x;
                y = std(B(mask,3));
                B(mask,6) = y;
            end
        end
    end
end
xlswrite('panel.xlsx',B)
Code 2:
clear all clc A=xlsread('criteria.xlsx'); B=xlsread('panel.xlsx');
for i=1:89 for j=1:64 for k=1:3 for h=1:2 mask = B(:,5) == A(i,1) & B(:,4) == A(j,2) & A(k,4) > B(:,2) > A(k,3) & A(h,5) < B(:,1) < A(h,6);
                x = mean(B(mask,3)); 
                B(mask,7) = x;    
                y = std(B(mask,3)); 
                B(mask,8) = y;
            end
        end
    end
end
xlswrite('panel.xlsx',B)
In order to see the difference in result, I save the output from code 1 into column 5, 6 and the output from code 2 into column 7, 8 both in file panel.xlsx.
Please run these two codes with two attached excel files and help me, thanks!

Best Answer

The basic problem is that you are attempting two logical relations simultaneously: MATLAB's relational operators are binary operators, so they only support one comparison at once. In summary:
X<A<Y     % is NOT valid for comparing A against X and Y
X<A & A<Y % This compares A with both X and Y
In MATLAB logical relational operators follow the standard rules of operator precedence. Look at this example carefully:
>> 3<4<2
ans =
     1
The output is true, so does this mean that 4<2 ? Of course not, we just have to remember the operator precedence rules, just like in high school. This is evaluated according to those rules as:
>> (3<4)<2
ans =
     1
where
>> 3<4
ans =
     1
So 3<4<2 is actually equivalent to 1<2, which is of course very true:
>> 1<2
ans =
      1
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