solving equation system

[Ben C]

On 2006-07-17, TG <girodt at gmail.com> wrote:
>
> Ben C wrote:
>> On 2006-07-17, TG <girodt at gmail.com> wrote:
>> > Hi there.
>> >
>> > Anyone knows how to use numpy / scipy in order to solve this ?
>> >
>> > * A is an array of shape (n,)
>> > * X is a positive float number
>> > * B is an array of shape (n,)
>> > * O is an array of shape (n,) containing only zeros.
>> >
>> > A.X - B = O
>> > min(X)
>>
>> Are we solving for A, B or X?  And what do you mean by min(X)?
>>
>> If we're solving for X there will be many combinations of A and B for
>> which there is no solution.
>
> Sorry for the poor explanation. I'm trying to put it clear now.
>
> i've got A and B. I'm looking for X. I made a mistake in my equation
>:-/
>
> It's more like :
>
> A.X - B >= O

How about this:

from random import *

def solve(A, B):
	return reduce(max, (float(b) / a for a, b in zip(A, B)))

def test():
	A = [random() for i in range(4)]
	B = [random() for i in range(4)]

	x = solve(A, B)

	for a, b in zip(A, B):
		print a, b, a * x - b

test()

This only works if all elements of both A and B are positive.

> Well, maybe it will be much more simple if I explain the underlying
> problem :
>
> I have an array of N dimensions (generally 2).
> - A first calculation gives me a set of integer coordinates inside this
> array, which I will call the point W.

Is this an array of points, or an array of values, that contains only
one point?

> - After several other calculations, I've got a set of coordinates in
> this N dimensional space that are floating values, and not bound to the
> limits of my original N-array. This is the point L.
>
> What I want to do is to translate the point L along the vector LW

Do you mean the vector L - W? (LW is a scalar, assuming dot product).

> in order to get a point L' which coordinates are inside the original
> N-dimensional array. Then it will be easy to get the closest integer
> coordinates from L'.

> I'm not sure this is clear ... pretty hard to talk about maths in
> english.

Not very clear to me I'm afraid!