# S is diagonal matrix of singular values?

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Minkang Cheng on 6 Nov 2020
Answered: Christine Tobler on 6 Nov 2020
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
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

Christine Tobler on 6 Nov 2020
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