MATLAB Central Newsreader - Contracting Matrices

Contracting Matrices

Philosophaie — Sat, 27 Dec 2008 16:25:03 -0500

I have a 4x4x4x4 matrices. I want to contract one of the indices and make a 4x4x4 matrix. The original matrix has both co and contra- varient components. Here is a excerpt from my code:

    for j=1:4
        for k=1:4
           for i=1:4
            Ricci(j,k)=Ricci(j,k)+Riemann(j,k,i,i)
        end
    end
end

Re: Contracting Matrices

Roger Stafford — Sat, 27 Dec 2008 17:23:02 -0500

"Philosophaie" <ertlejack@sbcglobal.net> wrote in message <gj5ksv$1mq$1@fred.mathworks.com>...
> I have a 4x4x4x4 matrices. I want to contract one of the indices and make a 4x4x4 matrix. The original matrix has both co and contra- varient components. Here is a excerpt from my code:
>
> for j=1:4
> for k=1:4
> for i=1:4
> Ricci(j,k)=Ricci(j,k)+Riemann(j,k,i,i)
> end
> end
> end

Try:

temp = reshape(Riemann,4,4,[],1);
Ricci = squeeze(sum(temp(:,:,1:4+1:4*4,1),3));

However it produces a 4x4 size, not 4x4x4.

Roger Stafford

Re: Contracting Matrices

Philosophaie — Sat, 27 Dec 2008 18:49:01 -0500

> temp = reshape(Riemann,4,4,[],1);
> Ricci = squeeze(sum(temp(:,:,1:4+1:4*4,1),3));
> disp(Ricci(:,:))
this produces a 1x4 matrix

What am I doing wrong?

Re: Contracting Matrices

Roger Stafford — Sat, 27 Dec 2008 21:06:01 -0500

"Philosophaie" <ertlejack@sbcglobal.net> wrote in message <gj5tat$jb2$1@fred.mathworks.com>...
> > temp = reshape(Riemann,4,4,[],1);
> > Ricci = squeeze(sum(temp(:,:,1:4+1:4*4,1),3));
> > disp(Ricci(:,:))
> this produces a 1x4 matrix
> What am I doing wrong?

I would suggest doing the 'size' operator at each stage. You should get these results:

size(Riemann) --> [4 4 4 4]
size(temp) --> [4 4 16 1]
size(temp(:,:,1:4+1:4*4,1)) --> [4 4 4 1]
size(sum(temp(:,:,1:4+1:4*4,1),3)) --> [4 4 1 1]
size(Ricci) --> [4 4]

Where does yours differ from this?

Roger Stafford

Re: Contracting Matrices

Philosophaie — Sat, 27 Dec 2008 21:32:01 -0500

"Roger Stafford" <ellieandrogerxyzzy@mindspring.com.invalid> wrote in message <gj65bp$dhc$1@fred.mathworks.com>...
> "Philosophaie" <ertlejack@sbcglobal.net> wrote in message <gj5tat$jb2$1@fred.mathworks.com>...
> > > temp = reshape(Riemann,4,4,[],1);
> > > Ricci = squeeze(sum(temp(:,:,1:4+1:4*4,1),3));
> > > disp(Ricci(:,:))
> > this produces a 1x4 matrix
> > What am I doing wrong?
>
> I would suggest doing the 'size' operator at each stage. You should get these results:
>
> size(Riemann) --> [4 4 4 4]
> size(temp) --> [4 4 16 1]
> size(temp(:,:,1:4+1:4*4,1)) --> [4 4 4 1]
> size(sum(temp(:,:,1:4+1:4*4,1),3)) --> [4 4 1 1]
> size(Ricci) --> [4 4]

My results were:
size(Riemann) --> [4 4 4 4]
size(temp) --> [4 4 16]
size(sum(temp(:,:,1:4+1:4*4,1),3)) --> [4 1]
size(Ricci) --> [4 1]

What does the "3" do in the sum command. Where am I going wrong?

Re: Contracting Matrices

Roger Stafford — Sat, 27 Dec 2008 22:27:01 -0500

"Philosophaie" <ertlejack@sbcglobal.net> wrote in message <gj66sh$dfj$1@fred.mathworks.com>...
> ......
> My results were:
> size(Riemann) --> [4 4 4 4]
> size(temp) --> [4 4 16]
> size(sum(temp(:,:,1:4+1:4*4,1),3)) --> [4 1]
> size(Ricci) --> [4 1]
>
> What does the "3" do in the sum command. Where am I going wrong?

  If my understanding is correct, 'reshape' of a [4 4 4 4] array should have given you [4 4 16 1], not [4 4 16].

  What did you get for size(temp(:,:,1:4+1:4*4,1))? It should have been [4 4 4 1] or with the above result [4 4 4]. Given the above [4 4 16] result, the expression temp(:,:,1:4+1:4*4,1) should have given an error. Did it?

  In any case, the 'sum' action should have been along the third dimension and left you with a size of [4 4 1] or at worst [4 4]. It looks as though your 'sum' paid no attention to the '3' parameter, which directs summation to that third dimension. There should also have been an error indicated for the presence of the parameter '3' if your 'sum' wasn't recognizing a second parameter.

  I have no way of accounting for your results. What version of matlab did you use?

Roger Stafford

Re: Contracting Matrices

Bruno Luong — Sun, 28 Dec 2008 09:20:03 -0500

"Roger Stafford" <ellieandrogerxyzzy@mindspring.com.invalid> wrote in message <gj6a3l$nt3$1@fred.mathworks.com>...

>
> What did you get for size(temp(:,:,1:4+1:4*4,1))? It should have been [4 4 4 1] or with the above result [4 4 4]. Given the above [4 4 16] result, the expression temp(:,:,1:4+1:4*4,1) should have given an error. Did it?
>

Roger,

singleton in the last dimension is automatically removed by Matlab.

m x n x p x 1 array is exactly like m x n x p array.

Bruno

Re: Contracting Matrices

Steven Lord — Mon, 29 Dec 2008 03:35:24 -0500

"Roger Stafford" <ellieandrogerxyzzy@mindspring.com.invalid> wrote in
message news:gj65bp$dhc$1@fred.mathworks.com...
> "Philosophaie" <ertlejack@sbcglobal.net> wrote in message
> <gj5tat$jb2$1@fred.mathworks.com>...
>> > temp = reshape(Riemann,4,4,[],1);
>> > Ricci = squeeze(sum(temp(:,:,1:4+1:4*4,1),3));
>> > disp(Ricci(:,:))
>> this produces a 1x4 matrix
>> What am I doing wrong?
>
> I would suggest doing the 'size' operator at each stage. You should get
> these results:
>
> size(Riemann) --> [4 4 4 4]
> size(temp) --> [4 4 16 1]

Since SIZE drops trailing singleton dimensions, size(temp) should be [4 4
16]. Similarly, for the lines below, the trailing 1 is dropped.

*snip*

--
Steve Lord
slord@mathworks.com