Complete newbie with hopefully simple matrix division question - not answered elsewhere that I could find

Hi everyone,

I am very inexperienced with Matlab (moving to Matlab from Excel because I'm starting to have complicated matrix problems to solve). I have a 17 x 17 matrix that I want to do a division operation on in which I divide each element in the matrix by every other element in the matrix.

I can build it up one matrix at a time, like this...

a = [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17] b = [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17] and so on through c,d,e,f,g,h,i,j,k,l,m,n,o,p,q

a_result = [a(1)/a(1), a(1)/a(2), a(1)/a(3), a(1)/a(4), a(1)/a(5), a(1)/a(6), a(1)/a(7), a(1)/a(8), a(1)/a(9), a(1)/a(10), a(1)/a(11), a(1)/a(12), a(1)/a(13), a(1)/a(14), a(1)/a(15), a(1)/a(16), a(1)/a(17);a(2)/a(1), a(2)/a(2), a(2)/a(3), a(2)/a(4), a(2)/a(5), a(2)/a(6), a(2)/a(7), a(2)/a(8), a(2)/a(9), a(2)/a(10), a(2)/a(11), a(2)/a(12), a(2)/a(13), a(2)/a(14), a(2)/a(15), a(2)/a(16), a(2)/a(17) ... ; a(1)/b(1), a(1)/b(2), a(1)/b(3)

-and so on until I have a matrix of 289 x 17 elements, then do over for vectors b-q...

b_result = [b(1)/a(1), b(1)/a(2), b(1)/a(3), b(1)/a(4), b(1)/a(5), b(1)/a(6), b(1)/a(7), b(1)/a(8), b(1)/a(9), b(1)/a(10), b(1)/a(11), b(1)/a(12), b(1)/b(13), b(1)/a(14), b(1)/a(15), b(1)/a(16), b(1)/a(17);b(2)/b(1), b(2)/b(2), b(2)/b(3), b(2)/b(4), b(2)/b(5), b(2)/b(6), b(2)/b(7), b(2)/b(8), b(2)/a(9), b(2)/b(10), b(2)/b(11), b(2)/b(12), b(2)/b(13), b(2)/b(14), b(2)/b(15), b(2)/b(16), b(2)/b(17)...

then consolidate the 17 matrices into one mega-matrix so that I can do comparative operations on them with 5 other similarly constructed mega-matrices.

...but it looks like a seriously tedious way to do something that probably Matlab can do easily in some way that I don't know. I tried the element-wise operator (./) but I can't work out how to use it in this situation.

Any thoughts?

Thanks, Sabrina

Answer 1

[KSSV]

a = [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17] ;
b = [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17]  ;
A = repmat(a',1,17) ;
%%divide
A1 = A./a ;
A2 = A./b ;
iwant = [A1 ; A2] ;

[Sabrina]

Thank you very much for your quick response. It will take me a little while to work with your answer and my problem but I'll come back later to let you know how I went. In the meantime I appreciate you giving me a much better way to work with my problem! Thanks!

Update: The repmat function does the job, thanks. Although to get the figures I expect I needed to change the divide command to A1 = A./A'. Still working on it ... more later.

Answer 2

[Guillaume]

A note on terminology that will make it easier for you to get understood when asking question, an array is an n-dimension bunch a numbers. A matrix is a 2-dimension array, and a vector is a 1-d dimensional array. So what you've shown in your examples, we tend to call them vectors.

What you want looks very similar to a kronecker tensor product except you want a division instead of a multiplication. Not a problem, just invert your vector (memberwise):

A = 1:17;
a_result = kron(A, 1./A);
a_result = reshape(A, numel(A), []).';  %if you want to arrange it as in your question