Re: order of singular values

[Jordi Gutiérrez Hermoso]

2011/5/11 nuncio m <address@hidden>:

> 2011/5/11 Jordi Gutiérrez Hermoso <address@hidden>
>>
>> On 10 May 2011 23:39, nuncio m <address@hidden> wrote:
>> > Dear users,
>> >  I am quite confused about the order in which the function writes
>> > the
>> > letf and right singular values from the function
>> > [u,s,v]=svd(x). Will it be in the same order as that of x
>>
>> I don't understand this question. Singular values aren't left or
>> right; singular vectors are. Singular values are ordered by their
>> size, from largest to smallest. The x matrix doesn't have singular
>> values in any particular order; the s diagonal matrix does, from
>> largest to smallest.
>>
>> Does this answer your question, even if I didn't understand it?
>
> The question is indeed confusing, it is not singular values but
> vectors. What I have is a matrix (X) of 20x100, the row number
> corresponds to the observation number, in my case it is the time
> step. and the column nmber is the coordinates of the data, or the
> locations where I collected the data. My aim is to see the coupled
> variability of two such fields. say with another matrix (XX) having
> 20x150 rows and columns. when I get the left and right singular
> matrix, I like to plot it as a spatial map. If I do an SVD on the
> covariance matrix of the above matrices I will have the left
> singular vectors with some columns and row number =100 and right
> singular vector with row number=150. Now when I plot each column
> expecting the same grid(100/150) as that of my original matrix I am
> getting absurd results. THats why I asked whether the order of the
> left/right singular vectors follows the pattern of my data.

As much as I would like to help what I presume to be a fellow
McGillite, the presentation of your problem poses more work and
attention to detail than I currently want to give this. I know that in
general the order of singular vectors is mostly unrelated to whatever
permutation of rows and columns you have in the original matrix, and
you can't say in general "this singular vector corresponds to this row
or column of my original matrix". Perhaps there is something special
about your problem where this is no longer true, but I don't want to
read a 54-page exposition to understand what.

Sorry,
- Jordi G. H.