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[Lapack] QR in Lapack


On Sep 28, 2012, at 1:31 PM, Roy P Koomullil 
<rkoomul@Domain.Removed<mailto:rkoomul@Domain.Removed>> wrote:

My matrix size is approx. 14x9 and I need to compute this many times.  For this 
purpose, which API did you suggest, DGEQRF or  DGEQR2?

DGEQR2 without too much hesitation. This said LAPACK is not that efficient for 
this small matrices.
It is hard to do better than LAPACK but rewriting everything and stripping all 
the nice things from LAPACK (checks, etc.) and tuning for 14x9 is possible.
This is really some hard work and I am not sure this is worth it. I am no 
expert in this kind of work. This is essentially computer science,
code tuning. I do not think this is worth it.

I have quick question on using LAPACK for least square calculations.  I have a 
system of equations A x  = b, where A is matrix with dimension M by N, x is a 
vector with dimension N and b is a vector of size M. M is always greater than 
N.  So, I have an over determined system.  I wanted to solve this as a least 
square problem and calculate x=Db, where D is matrix with dimension N by M.  I 
am looking for numerical values of D rather than direct solution of x, so that 
I can use store it for some other computations.  Could you please suggest an 
efficient way of calculating D using LAPACK?

OK ? I think you want is to compute D the pseudo-inverse of A.
(You are not very clear, finding D s.t x = Db does not define D uniquely.)
We do not have a routine to compute the pseudo inverse.
I have posts on the LAPACK forum about this.
http://icl.cs.utk.edu/lapack-forum/viewtopic.php?f=5&t=2712
http://icl.cs.utk.edu/lapack-forum/viewtopic.php?f=5&t=160

Also I am not sure what you want to do but doing DGEQRF once and then 
repeatedly solving with the QR factorization is not that bad of a solution.
I am not sure we have a  routine for this ? We probably should ...

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