S is diagonal matrix of singular values?

Hi

I did {U,S,V)=svd(A)

when A is mxn

results: U is mxm, V is nxn, S is mxn (n> m)

S should be a diagonal matrix of singular values, the m singular values are diagonal location.

How ever, I use fprinf print ths S in a file as

fprintf(fids,[repmat('%8.4f\t',1,size(S,2)) '\n'],S);

Then I read this using a fotran code as

do k = 1, m

read(1,*) (s(k,j) j=1,n)

enddo

I found the singular values are not in diagonal. If this is corect, the U and V must re-agranged based on singular values, from large down to smaller. Why this did not in matlab. if not, what is the wrong with fprintf or svd. How we can make S to be realy a diagonal matrix?

Thanks

MK

Answer 1

[Christine Tobler]

MATLAB (and Fortran) store matrices in a column-first ordering, while in your file, you want to save numbers in a row-first order. The fprintf command passes the numbers of S in based on linear indexing into S:

>> S
S =
    3.8795         0         0
         0    1.4585         0
         0         0    0.3144
         0         0         0
>> fprintf([repmat('%8.4f\t',1,size(S,2)) '\n'],S)
  3.8795	  0.0000	  0.0000	
  0.0000	  0.0000	  1.4585	
  0.0000	  0.0000	  0.0000	
  0.0000	  0.3144	  0.0000	

Passing the transpose of S in fixes the issue:

>> fprintf([repmat('%8.4f\t',1,size(S,2)) '\n'],S')
  3.8795	  0.0000	  0.0000	
  0.0000	  1.4585	  0.0000	
  0.0000	  0.0000	  0.3144	
  0.0000	  0.0000	  0.0000	

You can also do this more directly using the writematrix command:

>> writematrix(S, 'S.txt')
>> type S.txt
3.87951723431537,0,0
0,1.4585169755725,0
0,0,0.31437233188791
0,0,0