Looping for finding dominating points.

Hi,

I have a matrix with 'n' rows and two columns, say,

f(1,1) f(1,2)

f(2,1) f(2,2)

f(3,1) f(3,2)

f(4,1) f(4,2)

............

f(n,1) f(n,2)

I would like to remove dominating row or rows, and record non-dominating rows as a data file. It would be much appreciated if any one can help me with coding to do that.

Thanks in advance.

Rizvi

[Yu Jiang]

How do you define a 'dominating row'?

[Mohammed Rizvi]

Hi Yu,

Thanks for your reply. Let's say, rows are [f(1,1) f(1,2)] and [f(2,1) f(2,2)].

If f(1,1)>f(2,1) and f(1,2)>f(2,2) then [f(1,1) f(1,2)] dominates [f(2,1) f(2,2)], so discard [f(1,1) f(1,2)].

I have a mathematical logic for n=4 which is as follows;

Step 1

If f(1,1) > f(2,1) & f(1,2)> f(2,2)

‘Go to Step-2’

elseif f(1,1) > f(3,1) & f(1,2)> f(3,2)

‘Go to Step-2’

elseif f(1,1) > f(4,1) & f(1,2)> f(4,2)

‘Go to Step-2’

else print(f(1,1), f(1,2))

Step 2

If f(2,1) > f(3,1) & f(2,2)> f(3,2)

Go to Step-3

elseif f(2,1) > f(4,1) & f(2,2)> f(4,2)

Go to Step-3

else print(f(2,1), f(2,2))

Step 3

If f(3,1) > f(4,1) & f(3,2)> f(4,2)

print(f(4,1), f(4,2))

else print (f(3,1), f(3,2)) & (f(4,1), f(4,2))

Many thanks in advance.

Rizvi

Answer 1

[Roger Stafford]

Mohammed Rizvi, in a forum of this nature you really ought to carefully define a concept such as "dominating points" so as to avoid causing an excess of guessing at what you mean.

I will guess that you mean by a "dominating point", a point in a given 2D set for which a straight line can be drawn that separates that point from all other points in the set. If that is what you mean, you could call on 'convhull'. Call your n x 2 matrix f.

 K = convhull(f(:,1),f(:,2),'simplify',true);
 f(K,:) = [];

This should strip away all "dominating points" of f.

You used the term "looping" in your subject title. I would warn that removing dominating points one at a time can result, if not done properly, in removing too many points, as remaining points that weren't previously dominating points suddenly become dominating ones. It is much better to use a function like 'convhull' which does the job simultaneously (so to speak.)

[Mohammed Rizvi]

Hi Roger,

Many thanks for your reply. As per your advice I have run the following code

f = dlmread('ipopt_r.dat'); [Here data file includes info about rows]

K = convhull(f(:,1),f(:,2),'simplify',true)

 f(K,:) =[]

However, it is not functioning. Could you please see my replies to other commenters. Thanks again for your help.

Cheers, Rizvi

Answer 2

[Image Analyst]

Try this:

% Define rows to remove:
% However they're determined....I don't know, presumably you do.
% For this demo, let's assume you've identified the rows
% and the row numbers are entered into an array.
dominatingRows = [2,3,42,69,123];  % For example...
% Now, remove the dominating rows:
f(dominatingRows, :) = [];

[Mohammed Rizvi]

Hi

Thanks for your reply. Let's say, rows are [f(1,1) f(1,2)] and [f(2,1) f(2,2)].

If f(1,1)>f(2,1) and f(1,2)>f(2,2) then [f(1,1) f(1,2)] dominates [f(2,1) f(2,2)], so discard [f(1,1) f(1,2)].

I have a data file f(n, m) where ‘n’ probably 100 or more and ‘m’ may be 2 or 3. I would like to remove dominating row or rows (definition given above) comparing with other rows. Every time I run the code and get a new data file f, and thus I need to remove dominating rows or points. I have a mathematical logic to do that for n=4 (please see in the Yu's reply), however, I could not write any code in MATLAB to implement it.

Any help would be greatly appreciated.

Cheers,

Rizvi

[Image Analyst]

Now it's clear - would have been great to have given that definition in your original post. Try this:

rows = 30;  % Whatever you want.
columns = 3;  % Whatever you want.
f = rand(rows, columns)  % Create sample data.
df = diff(f) % Calc diff between each row and one below it.
% Find where all 3 differences are positive.
dominatingRows = sum(df>0, 2) == size(df, 2)
% Extract only the non-dominating rows.
out = f(~dominatingRows,:)