Thread Subject: Efficient computation: differences of column vectors of matrix

Hi and thanks for the help,

I have a matrix say

A = [a1,b1,c1,d1; a2,b2,c2,d2; a3,b3,c3,d3; a4,b4,c4,d4]

now, I want the differences across the columns as,

B = [(a1-a2),(a1-a3),(a1-a4),(a2-a3),(a2-a4),(a3-a4);
       (b1-b2),(b1-b3),(b1-b4),(b2-b3),(b2-b4),(b3-b4);
       (c1-c2),(c1-c3),(c1-c4),(c2-c3),(c2-c4),(c3-c4);
       (d1-d2),(d1-d3),(d1-d4),(d2-d3),(d2-d4),(d3-d4)]

i would like to do this efficiently in Matlab because, my A =
200*250000 and so, after doing for each of the 200 columns... B matrix
would be 200*199/2= 19,900 * 250000. I would like to know if it could
be done efficiently (since its across columns). if space is a problem,
i can subdivide the matrix, it shouldn't be an issue.


thanks again,
regards,
arun.

arun <aragorn168b@gm%ail.com> wrote in message <cd6f7a80-0651-417d-ac72-88d6b326e1fe@b14g2000yqd.googlegroups.com>...
> Hi and thanks for the help,
>
> I have a matrix say
>
> A = [a1,b1,c1,d1; a2,b2,c2,d2; a3,b3,c3,d3; a4,b4,c4,d4]
>
> now, I want the differences across the columns as,
>
> B = [(a1-a2),(a1-a3),(a1-a4),(a2-a3),(a2-a4),(a3-a4);
> (b1-b2),(b1-b3),(b1-b4),(b2-b3),(b2-b4),(b3-b4);
> (c1-c2),(c1-c3),(c1-c4),(c2-c3),(c2-c4),(c3-c4);
> (d1-d2),(d1-d3),(d1-d4),(d2-d3),(d2-d4),(d3-d4)]
>
> i would like to do this efficiently in Matlab because, my A =
> 200*250000 and so, after doing for each of the 200 columns... B matrix
> would be 200*199/2= 19,900 * 250000. I would like to know if it could
> be done efficiently (since its across columns). if space is a problem,
> i can subdivide the matrix, it shouldn't be an issue.
>

A=ceil(10*rand(10,4));

J2=nchoosek(1:size(A,2),2);
A(:,J2(:,1))-A(:,J2(:,2))

% Bruno

On Jul 1, 8:31 am, "Bruno Luong" <b.lu...@fogale.findmycountry> wrote:
> arun <aragorn168b@gm%ail.com> wrote in message <cd6f7a80-0651-417d-ac72-88d6b326e...@b14g2000yqd.googlegroups.com>...
> > Hi and thanks for the help,
>
> > I have a matrix say
>
> > A = [a1,b1,c1,d1; a2,b2,c2,d2; a3,b3,c3,d3; a4,b4,c4,d4]
>
> > now, I want the differences across the columns as,
>
> > B = [(a1-a2),(a1-a3),(a1-a4),(a2-a3),(a2-a4),(a3-a4);
> >        (b1-b2),(b1-b3),(b1-b4),(b2-b3),(b2-b4),(b3-b4);
> >        (c1-c2),(c1-c3),(c1-c4),(c2-c3),(c2-c4),(c3-c4);
> >        (d1-d2),(d1-d3),(d1-d4),(d2-d3),(d2-d4),(d3-d4)]
>
> > i would like to do this efficiently in Matlab because, my A =
> > 200*250000 and so, after doing for each of the 200 columns... B matrix
> > would be 200*199/2= 19,900 * 250000. I would like to know if it could
> > be done efficiently (since its across columns). if space is a problem,
> > i can subdivide the matrix, it shouldn't be an issue.
>
> A=ceil(10*rand(10,4));
>
> J2=nchoosek(1:size(A,2),2);
> A(:,J2(:,1))-A(:,J2(:,2))
>
> % Bruno

Hi Bruno,
thank you for your help. But there seems to be a problem.

The J2 matrix seems to generate the indices properly. But, suppose J2
= [1,1,1,2,2,3; 2,3,4,3,4,4] then, A(:,J2(:,1)) will simply choose a
matrix which has the first column repeated three times and 2nd column
repeated 2 times and third column repeated 1 time... I hope I
explained clear enough to understand what hte problem is...
However, thank you. I will also try to work on it.

regards,
arun.

On Jul 1, 8:31 am, "Bruno Luong" <b.lu...@fogale.findmycountry> wrote:
> arun <aragorn168b@gm%ail.com> wrote in message <cd6f7a80-0651-417d-ac72-88d6b326e...@b14g2000yqd.googlegroups.com>...
> > Hi and thanks for the help,
>
> > I have a matrix say
>
> > A = [a1,b1,c1,d1; a2,b2,c2,d2; a3,b3,c3,d3; a4,b4,c4,d4]
>
> > now, I want the differences across the columns as,
>
> > B = [(a1-a2),(a1-a3),(a1-a4),(a2-a3),(a2-a4),(a3-a4);
> >        (b1-b2),(b1-b3),(b1-b4),(b2-b3),(b2-b4),(b3-b4);
> >        (c1-c2),(c1-c3),(c1-c4),(c2-c3),(c2-c4),(c3-c4);
> >        (d1-d2),(d1-d3),(d1-d4),(d2-d3),(d2-d4),(d3-d4)]
>
> > i would like to do this efficiently in Matlab because, my A =
> > 200*250000 and so, after doing for each of the 200 columns... B matrix
> > would be 200*199/2= 19,900 * 250000. I would like to know if it could
> > be done efficiently (since its across columns). if space is a problem,
> > i can subdivide the matrix, it shouldn't be an issue.
>
> A=ceil(10*rand(10,4));
>
> J2=nchoosek(1:size(A,2),2);
> A(:,J2(:,1))-A(:,J2(:,2))
>
> % Bruno

Hi I just found the modification which works. I just have to check if
it works faster for bigger matrices.
thank you.

its just,
A(J2(:,1),:) - A(J2(:,2),:)

best,
arun.

arun <aragorn168b@gmail.com> wrote in message <63985d2a-adf8-47c9-aaa3-52e0a1cb9ede@37g2000yqp.googlegroups.com>...

>
> its just,
> A(J2(:,1),:) - A(J2(:,2),:)


Unless I'm mistaking, this is NOT what you have described in the example in the post #1. But anyway you seem to know what you want.

Bruno

Hi
I'm also having a similar problem.
I am having two matrices containing 150 size vectors. say A is 5000x150 aand B is 1500x150. I want to find pairwise euclidean distance between vectors of A and B. i.e. I want 5000x1500 matrix.
Is there any efficient way to do it.
If not distance, even absolute difference is fine.
Because at next level these numbers (5000 changes to 25000)also increase and I am encountering OUT of MEMORY or very time consuming problems.
Thanking you very much,


regards,
ramana

"Bruno Luong" <b.luong@fogale.findmycountry> wrote in message <h2fidh$mpl$1@fred.mathworks.com>...
> arun <aragorn168b@gmail.com> wrote in message <63985d2a-adf8-47c9-aaa3-52e0a1cb9ede@37g2000yqp.googlegroups.com>...
>
> >
> > its just,
> > A(J2(:,1),:) - A(J2(:,2),:)
>
>
> Unless I'm mistaking, this is NOT what you have described in the example in the post #1. But anyway you seem to know what you want.
>
> Bruno

"oruganti murthy" <omurthy@yahoo.com> wrote in message <h2fjmr$gdn$1@fred.mathworks.com>...
> Hi
> I'm also having a similar problem.
> I am having two matrices containing 150 size vectors. say A is 5000x150 aand B is 1500x150. I want to find pairwise euclidean distance between vectors of A and B. i.e. I want 5000x1500 matrix.
> Is there any efficient way to do it.
> If not distance, even absolute difference is fine.
> Because at next level these numbers (5000 changes to 25000)also increase and I am encountering OUT of MEMORY or very time consuming problems.
> Thanking you very much,
>

Take a look at function BSXFUN

Bruno

On Jul 1, 2:36 pm, "Bruno Luong" <b.lu...@fogale.findmycountry> wrote:
> "oruganti murthy" <omur...@yahoo.com> wrote in message <h2fjmr$gd...@fred.mathworks.com>...
> > Hi
> > I'm also having a similar problem.
> > I am having two matrices containing 150 size vectors. say A is 5000x150 aand B is 1500x150. I want to find pairwise euclidean distance between vectors of A and B. i.e. I want 5000x1500 matrix.
> > Is there any efficient way to do it.
> > If not distance, even absolutedifferenceis fine.
> > Because at next level these numbers (5000 changes to 25000)also increase and I am encountering OUT of MEMORY or very time consuming problems.
> > Thanking you very much,
>
> Take a look at function BSXFUN
>
> Bruno

Hi Bruno,
yes, my representation of the final matrix was incorrect. thank you,
arun.