# [Numpy-discussion] Numpy and iterative procedures

Geoffrey Zhu gzhu@peak6....
Fri Feb 16 10:38:06 CST 2007

```In fact I am not looking for an implementation but a method to update a
vector iteratively when the value of an item of the vector depend partly
on the already updated items and partly depend on the old items.

-----Original Message-----
From: numpy-discussion-bounces@scipy.org
[mailto:numpy-discussion-bounces@scipy.org] On Behalf Of Nils Wagner
Sent: Friday, February 16, 2007 9:19 AM
To: Discussion of Numerical Python
Subject: Re: [Numpy-discussion] Numpy and iterative procedures

> At first glance it doesn't look hard to, at least, avoid looping over
i, by replacing [i] by [:-2], [i+1] by [1:-1] and [i+2] by [2:]. But I
might be wrong. Can you submit the piece of code with at least the most
internal loop?
>
>
I guess he is looking for an implementation of

http://en.wikipedia.org/wiki/Successive_over-relaxation

Nils

> -----Original Message-----
> From:	numpy-discussion-bounces@scipy.org on behalf of Geoffrey Zhu
> Sent:	Thu 15-Feb-07 18:32
> To:	Discussion of Numerical Python
> Cc:
> Subject:	Re: [Numpy-discussion] Numpy and iterative procedures
>
> Thanks Chuck.
>
> I am trying to use Successive Over-relaxation to solve linear
> equations defined by M*v=q.
>
> There are several goals:
>
> 1. Eventually (in production) I need it to be fast.
> 2. I am playing with the guts of the algorithm for now, to see how it
> works. that means i need some control for now.
> 3. Even in production, there is a chance i'd like to have the ability
> to tinker with the algorithm.
>
>
>   _____
>
> From: numpy-discussion-bounces@scipy.org
> [mailto:numpy-discussion-bounces@scipy.org] On Behalf Of Charles R
> Harris
> Sent: Thursday, February 15, 2007 10:11 AM
> To: Discussion of Numerical Python
> Subject: Re: [Numpy-discussion] Numpy and iterative procedures
>
>
>
>
>
> On 2/15/07, Geoffrey Zhu <gzhu@peak6.com> wrote:
>
> 	Hi,
>
> 	I am new to numpy. I'd like to know if it is possible to code
> efficient
> 	iterative procedures with numpy.
>
> 	Specifically, I have the following problem.
>
> 	M is an N*N matrix. Q is a N*1 vector. V is an N*1 vector I am
trying
> to
> 	find iteratively from the initial value V_0. The procedure is
simply
> to
> 	calculate
>
> 	V_{n+1}[i]=3D1/M[I,i]*(q[i]-
> 	(M[i,1]*v_{n+1}[1]+M[I,2]*v_{n+1}[2]+..+M[i,i-1]*v_{n+1}[i-1]) -
> 	(M[I,i+1]*v_{n}[i+1]+M[I,i+2]*v_{n}[i+2]+..+M[I,N]*v_{n}[N]))
>
> 	I do not see that this is something that can esaily be
vectorized, is
> 	it?
>
>
> I think it would be better if you stated what the actual problem is.
Is
> it a differential equation, for instance. That way we can determine
what
> the problem class is and what algorithms are available to solve it.
>
> Chuck
>
>
>
>
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