RE: [Lapackpp-devel] Pseudoinverse, Eigenvalues and Eigenvectors

[Jacob \(Jack\) G. <jg...@cs...>]

Hi,

Apparently Lapack has a function named DGETRI for obtaining the inverse of a
function.  Would it be reasonable to create a function called inv() in
LaGenMatDouble that makes use of DGETRI?  (If not somewhere else?).

In addition, I would like to build a pseudoinverse function as well (not
implemented in lapack).  The two options would be to do it according to the
definition pinv(A)=inv(A'A)A', or to do the following (sorry for the matlab
style notation) [U,D,V']=svd(A).  pinv(A)=Vpinv(D)U', where to get pinv(D),
just find the inverse of each non-zero value in the diagonal matrix.

The second way apparently is more computationally efficient, but a loop with
if statements to get the pseudoinverse of D may take longer than using
lapack to calculate the pseudoinverse by definition.

Any thoughts on the above?  

Secondly, if I want to obtain the eigenvalues and eigenvectors of a general
matrix, is DGEEV the correct function to implement?  Should I create a
function to add to EigSlv.cc ? 

Let me know

Jack

> -----Original Message-----
> From: lap...@li... [mailto:lapackpp-devel-
> ad...@li...] On Behalf Of Jacob (Jack) Gryn
> Sent: March 24, 2005 4:54 PM
> To: lap...@li...
> Subject: [Lapackpp-devel] Pseudoinverse, Eigenvalues and Eigenvectors
> 
> Just wondering if there's a fast way to do the following with lapack++ (if
> not, then in LAPACK) to do the following functions:
> 
> a) Pseudoinverse (maybe I should do inv(A'A)A', but inv() needs to be done
> via solving the linear equation AA'=I (is there a faster way to do this?)
> 
> b) Get eigenvectors and eigenvalues of a general matrix?  (or even of a
> symmetric matrix)?
> 
> Let me know
> 
> Thanks
> 
> Jack
> 
> 
> 
> 
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