Check and eliminate rows based on conditions 2

Hi. I have a matrix as below. I need help to code this problem.

A =

        [1.0000   -0.1367    0.0366    0.2431    0.1541    0.2263    0.3913   -0.1903
       -0.1367    1.0000   -0.3278   -0.1718   -0.3803   -0.1378   -0.0839    0.2210
        0.0366   -0.3278    1.0000    0.2087    0.4730    0.2077    0.0717   -0.1989
        0.2431   -0.1718    0.2087    1.0000    0.2513    0.3382    0.5135   -0.3838
        0.1541   -0.3803    0.4730    0.2513    1.0000    0.1547    0.0867   -0.1398
        0.2263   -0.1378    0.2077    0.3382    0.1547    1.0000    0.5096   -0.4888]

1. Therefore, I have to check every row in third column.

2. For every row in third column, I have to ensure that all previous rows have more value than current row value. If any previous row value in third column is less than current value, that previous row will be eliminated. Else, previous row will maintain.

3. For matrix A, as result, all rows except row 3, 5, and 6 will eliminate. End result after check and eliminate will produce matrix B as below.

A =

        0.0366   -0.3278    1.0000    0.2087    0.4730    0.2077    0.0717   -0.1989  
        0.1541   -0.3803    0.4730    0.2513    1.0000    0.1547    0.0867   -0.1398
        0.2263   -0.1378    0.2077    0.3382    0.1547    1.0000    0.5096   -0.4888

[Image Analyst]

"For every row in third column, I have to ensure that all previous rows have more value than current row value. If any previous row value in third column is less than current value, that previous row will be eliminated." <=== that is contradictory. The second sentence contradicts the first. Previous rows NEED to be less than the current row or else the third column will not monotonically increase. If you REMOVE the previous row, you are no longer guaranteed that each row will be more than the above row.

[yue ishida]

actually, that's the point of this algorithm...

Answer 1

[Andrei Bobrov]

[~,ii] = sort(A(:,3),'descend');

for MATLAB >= R2016b

out = A(ii(all(tril(ii < ii')==0,2)),:);

for MATLAB <= R2016a

out = A(ii(all(tril(bsxfun(@lt,ii(:),ii(:)'))==0,2)),:);