Eliminate rows in a matrix that have matching & different values

I have a matrix that looks like this:

    2.0000   15.0000    1.0000   11.2427
    2.0000   15.0000    1.0000   15.9927
    4.0000   15.0000    1.0000   17.4080
    5.0000   15.0000    1.0000   11.8038
    6.0000   15.0000    1.0000   11.5288
    7.0000   15.0000    1.0000   11.3480
    8.0000   15.0000    1.0000   11.1031
    9.0000   15.0000    1.0000   11.2669
   11.0000   15.0000    1.0000   11.4250
   11.0000   15.0000    1.0000   11.8218
   12.0000   15.0000    1.0000   11.3909

And I want to remove entire rows on two conditions:

1. Two rows have the same value in the first column (e.g. 2.0000=2.0000, 11.0000=11.0000)

2. The row with the larger value in the fourth column is removed (e.g. 11.2427 < 15.9927, 11.4250 < 11.8218)

So in the matrix above rows 2 and 10 would be removed, leaving me with

    2.0000   15.0000    1.0000   11.2427
    4.0000   15.0000    1.0000   17.4080
    5.0000   15.0000    1.0000   11.8038
    6.0000   15.0000    1.0000   11.5288
    7.0000   15.0000    1.0000   11.3480
    8.0000   15.0000    1.0000   11.1031
    9.0000   15.0000    1.0000   11.2669
   11.0000   15.0000    1.0000   11.4250
   12.0000   15.0000    1.0000   11.3909

Such that the first column has no duplicates - it is totally unique. Any ideas?

Answer 1

[Akira Agata]

Assuming your matrix is A, the following code returns what you want as B.

B = sortrows(A,[1 4]);
idx = [false; diff(B(:,1)) == 0];
B(idx,:) = [];