Singular Matrix

Hello all!

I am trying to do a left hand inversion (using backslash operator) but I get the following message:

Matrix is singular to working precision. RCOND=NaN

What can I do to avoid this and make the operation? The matrix is 1500x1500 and has a lot of zeros...

Thank you.

Answer 1

[William]

The matrix you are working with is not full rank or no independent. This means that some columns or rows within the matrix are functions of others. The best way to figure out which columns or rows are the problems is to delete a row or column and use rank() to see if the number returned is the minimum number of rows or columns. once this is true than you have an independent matrix and the operation should work.

If this doesn't make sense try searching for "Matrix independence" on google

Hope this helps

[Venkat R]

Hi William, I am also facing the same problem. But the rank of my current matrix(278x162) is showing as 162. Now how to find the independent matrix?

regards, Venkat

[Walter Roberson]

Remove any (278-162) rows, leaving 162, and check the rank again.

[Venkat R]

Thank you William But still it doesn't work. Actually I am trying to fit Gaussian mix models to this data. The same code works well for a 2x1000 data ! At one particular stage where cholesky factorization function gives this warning/error. The range of my elements is [0 1]. Any other ideas?

regards, Venkat

[Walter Roberson]

Please expand on "still it doesn't work"

[Venkat R]

Expanding I am using two software packages to compute GMM

1. First one gives (at the Expectation Maximization stage)

Warning: Matrix is singular, close to singular or badly scaled. Results may be inaccurate. RCOND = NaN.

2. The other gives

??? Error using ==> chol Matrix must be positive definite.

Although both the packages work fine for a sample 2x1000 matrix fine.

3. I even tried

 [vec,val] = eig(dscr);
 val(val<0) = eps;
 dscr1 = vec*val*vec';

as mentioned in

http://www.mathworks.com/matlabcentral/newsreader/view_thread/113597

But the same 1) and 2) are continuing

regards,

Venkat

Answer 2

[Panos]

Thank you for your answer William!

The problem was that some rows of the matrix had NaN entries. Consequently, the inverse could not be calculated by MatLab. By using rank I identified them (the result was NaN istead of the minimum rows/columns) and I found a bug to my model. Thanks again!