# Ublas :

Subject: Re: [ublas] Systems of Linear Ecuations
From: oswin krause (oswin.krause_at_[hidden])
Date: 2013-05-02 06:35:55

Hi,

I think my last mail was a bit off topic as an answer to the warnign. Sorry!

This is already implemented in triangular.hpp as inplace_solve. However
the implementation is not complete.

This reminds me that I wanted to send the improved implementation of my
fork back to ublas as I think that it is quite complete. of course there
is no SSE or stuff like that so there is a lot of space to improve. it
is also not a blocked implementation but given the state of the
matrix-matrix multiply this is hardly an efficiency issue. The
implementation however crucially relies on the efficiency of the
matrix-proxies, but if they are slow (in the sparse/packed case) the
proxies should be improved. I have not benchmarked that.

the implementation is attached, namespaces need to be changed. otherwise
everything is there.

Greetings,
Oswin

On 02.05.2013 00:01, Iulian Calciu wrote:
> Hello,
>
> I have nowhere seen a proposal for Systems of Linear Ecuations solving.
> I know they can be solved with LU descomposition for quadratic systems.
>
> Eg:
> Ax = b;
> A = LU with LU transform;
> LUx = b; note Ux = y, then
> Ly = b => y = LTRIS(L, b), then
> Ux = y => x = UTRIS(U, y);
>
> Note: LTRIS and UTRIS are methods for solving triangular lower/upper
> systems of ecuations.
>
> LTRIS
> x = b;
> for i = 1 : n
> for j = 1 : i - 1
> x(i) = x(i) - L(i,j)x(j)
> end
> x(i) = x(i) / L(i,i);
> end
>
> UTRIS:
> x = b;
> for i = n : -1: 1
> for j = i + 1 : n
> x(i) = x(i) - U(i,j)x(j)
> end
> x(i) = x(i) / U(i,i);
> end
>
> Can this thing be proposed in Boost uBLAS?
>
> Thank you,
> Iulian Calciu
>
>
>
>
>
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> Sent to: Oswin.Krause_at_[hidden]