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## Re: LU Factorizations

 From: Fumihiro CHIBA Subject: Re: LU Factorizations Date: Thu, 13 Mar 2003 00:35:34 +0900

Hello. I found the following description in http://www.netlib.org/lapack/double/dgetrf.f
```
*  DGETRF computes an LU factorization of a general M-by-N matrix A
*  using partial pivoting with row interchanges.
*
*  The factorization has the form
*     A = P * L * U
*  where P is a permutation matrix, L is lower triangular with unit
*  diagonal elements (lower trapezoidal if m > n), and U is upper
*  triangular (upper trapezoidal if m < n).

On 2003.3.12, at 10:36 Asia/Tokyo, Nick Allen wrote:

```
```I have a question about using Octave to determine an LU matrix
factorization.  Straight out of the manual for the "lu" function I run:

[l, u, p] = lu (a)

l =
1.00000  0.00000
0.33333  1.00000

u =
3.00000  4.00000
0.00000  0.66667

p =
0  1
1  0

but if i then do l*u I get:
3  4
1  2

when it should result in the original matrix a, which was:
1  2
3  4

Could someone please explain to me what is going on?  Is this a problem
with Octave, or is it a fault in my basic understanding of LU
factorizations?  By the way I am running Octave 2.1.36 on an ia32 Linux
platform.

Thanks
Nick

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```
```
Fumihiro CHIBA
Tokorozawa, Saitama, Japan

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```