Testing for identical numbers in matrix columns

Hello!

I'm not a stupid, I just want to learn to use MATLAB effectively.

I have a matrix. In my work it is 64x64, for example let's see this one

A =
   1     2     3     4
   2     3     3     4
   6     7     2     4

I want to now, in which columns all numbers are equal. I know how to do it for one column

A = [1,2,3,4; 2,3,3,4; 6,7,2,4];
REZ(1) = all((A(1,1)==A(:,1)));

Of course I can do this operation in cycle, but i think there is method to do it in one line.

If I run

>> X=(1:4);

>> REZ_2(X)=((A(1,X)==(A(:,X))));

It doesn't work, with error

??? Error using ==> eq
Matrix dimensions must agree.

How to solve this problem elegant?

[Andrew Newell]

Konstantin, it's not a stupid question, and it might even pick up a vote or two if you change the title to a more descriptive one (for example, "Which matrix columns have all numbers equal?").

[Andrew Newell]

There you go - one vote already!

Answer 1

[Matt Tearle]

all(~diff(A))

Like Andrew's idea, but a bit neater(?). The not (~) converts the differences to logicals (0 difference -> true). Then all sees if all the differences in a column are 0.

Just for fun, here's another possibility:

all(bsxfun(@eq,A,A(1,:)))

(This actually has one advantage, in that it would work even if A has only one row!)

[Sean de Wolski]

My votes goes to the BSXFUN solution.

[Andrew Newell]

I prefer the ALL version because it's not very interesting to say that each element is equal to itself.

Answer 2

[Jos (10584)]

Nothing shorter than:

~std(A)

[Konstantin]

brilliant!

[Matt Tearle]

Jos wins today's internets

[Oisín Moran]

I know this was 7 years ago but for anyone coming across this now it is not guaranteed to work. For example:

~std(0.9*ones(6,1))

Returns

ans =

   logical

   1

Whereas

~std(0.9*ones(7,1))

Returns

ans =

   logical

   0

[Jan]

@Oisín Moran: You are right:

std(0.9*ones(7,1))
>> 1.1992e-16

A rounding problem. This is not reliable also:

std(A) < 10*eps

The limit must reflect the size of the inputs and the summation to get mean(a), which is required for std is not stable.

Answer 3

[Andrew Newell]

Here is one way:

find(~sum(abs(diff(A))))

The idea is that diff takes the differences between adjacent terms in a column, and if all the elements are the same then sum(abs(diff(A)))=0 (the abs is needed in case positive and negative differences cancel out). Then ~sum(abs(diff(A)))=1 only for columns in which all the elements are equal.

[Konstantin]

Thank you very much!

I love this community)

[MICHAEL MONT-ETON]

Thanks for this solution. I plan on using it in my research into inverse solutions for the groundwater equation- a variant of the Laplace equation. It will be used to determine if a particular row or column in the input array is homogeneous. I will credit Mr.Newell in the code, and in publication.