numpy-discussion

[Numpy-discussion] Total least squares problem

[Nils W. <nw...@me...>]

Hi,

How do I solve a Total Least Squares problem in Numpy ?
A small example would be appreciated.

The TLS problem assumes an overdetermined set of linear equations
AX = B, where both the data matrix A as well as the observation
matrix B are inaccurate:

Nils

Reference:

R.D.Fierro, G.H. Golub, P.C. Hansen, D.P.O'Leary,
Regularization by truncated total least squares,
SIAM J. Sci. Comput. Vol.18(4) 1997 pp. 1223-1241

Re: [Numpy-discussion] Total least squares problem

[Travis O. <oli...@ee...>]

>
> How do I solve a Total Least Squares problem in Numpy ?
> A small example would be appreciated.
>
> The TLS problem assumes an overdetermined set of linear equations
> AX = B, where both the data matrix A as well as the observation
> matrix B are inaccurate:


X, resids, rank, s = LinearAlgebra.linear_least_squares(A,B)

-Travis

Re: [Numpy-discussion] Total least squares problem

[Nils W. <nw...@me...>]

Travis Oliphant schrieb:
> 
> >
> > How do I solve a Total Least Squares problem in Numpy ?
> > A small example would be appreciated.
> >
> > The TLS problem assumes an overdetermined set of linear equations
> > AX = B, where both the data matrix A as well as the observation
> > matrix B are inaccurate:
> 
> X, resids, rank, s = LinearAlgebra.linear_least_squares(A,B)
> 
> -Travis

Travis,

There is a difference between classical least squares (Numpy)
and TLS (total least squares).
I am attaching a small example for illustration.

Nils

Re: [Numpy-discussion] Total least squares problem

[Konrad H. <hi...@cn...>]

Nils Wagner <nw...@me...> writes:

> There is a difference between classical least squares (Numpy)
> and TLS (total least squares).

Algorithmically speaking it is even a very different problem. I'd say
the only reasonable (i.e. efficient) solution for NumPy is to
implement the TLS algorithm in a C subroutine calling LAPACK routines
for SVD etc.

Konrad.
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Re: [Numpy-discussion] Total least squares problem

[Nils W. <nw...@me...>]

Konrad Hinsen schrieb:
> 
> Nils Wagner <nw...@me...> writes:
> 
> > There is a difference between classical least squares (Numpy)
> > and TLS (total least squares).
> 
> Algorithmically speaking it is even a very different problem. I'd say
> the only reasonable (i.e. efficient) solution for NumPy is to
> implement the TLS algorithm in a C subroutine calling LAPACK routines
> for SVD etc.
> 
> Konrad.
> --
There are two Fortran implementations of the TLS algorithm already
available via
http://www.netlib.org/vanhuffel/      
.
Moreover there is a tool called f2py that generates Python C/API modules
for wrapping Fortran 77/90/95 codes to Python.

Unfortunately I am not very familar with this tool.
 
Therefore I need some advice for this.

Thanks in advance

 Nils
 
  
> -------------------------------------------------------------------------------
> Konrad Hinsen                            | E-Mail: hi...@cn...
> Centre de Biophysique Moleculaire (CNRS) | Tel.: +33-2.38.25.56.24
> Rue Charles Sadron                       | Fax:  +33-2.38.63.15.17
> 45071 Orleans Cedex 2                    | Deutsch/Esperanto/English/
> France                                   | Nederlands/Francais
> -------------------------------------------------------------------------------