remove non-unique columns even if the sign has changed

I have a 76x16 matrix. Some of the data is repeated and I want to remove repeated columns, which I have tried to do below. However, the numbers are the same but the sign has changed, e.g. columns 8 and 14 are the same data but the signs are reversed (where 8 is +ve, 14 is -ve etc), which my code doesn't acocunt for. The +ve/-ve matters so I cant just abs() the dataset.

I want to keep the first occurence of the repeated columns, where I should be left with 6 columns of data. Can anybody help?

mlag= unique(newca1.','rows','stable').'
mlag(:,max(mlag) == 0) = [];

Answer 1

[Les Beckham]

Perhaps this?

load newca.mat
[~, icol, ~] = unique(abs(newca1).', 'rows', 'stable')

icol = 7×1

1 2 3 4 7 8 12

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mlag = newca1(:,icol)

mlag = 76×7

0 0 0 0 0 0.1250 0 0 0 0 0 0 0.1111 0 0 0 0 0 0 0.1000 0 0 0.0909 0.0909 0.0909 0.0909 0.0909 0 0 0.1667 0.1667 0.1667 0.0833 0.0833 0 0 0.1538 0.1538 0.2308 0.0769 0.0769 0 0 0.3571 0.0714 0.3571 -0.2143 0.1429 0.2857 0 0.1333 0.0667 0.3333 0 0.3333 0.2667 0 0.1333 0.0667 0.3333 -0.0667 0.3333 0.2667 0 0.1333 0.0667 0.2667 -0.0667 0.3333 0.2667

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[LC]

Thank you!

[Les Beckham]

You are quite welcome.

Answer 2

[Steven Lord]

Make a copy of newca1, let's call it M. Multiply each column of M whose first element is negative by -1. This way if you think of your columns as vectors, they're all pointing "right" (towards +Inf along the x axis, if this were a 2-dimensional problem.) Call unique on M and ask not only for the unique rows but also the indices of the unique rows. Use the indices to extract the corresponding columns of newca1.