[Jprogramming] matrix inverse

[Roger Hui]

No Householder, but the following are available:

Choleski    http://www.jsoftware.com/jwiki/Essays/Choleski_Decomposition
LU          http://www.jsoftware.com/jwiki/Essays/LU_Decomposition
QR          http://www.jsoftware.com/jwiki/Essays/QR_Decomposition
Triangular  http://www.jsoftware.com/jwiki/Essays/Triangular_Matrix_Inverse

These can be used to compute the matrix inverse (among other things).



----- Original Message ----- 
From: "Rob Hodgkinson" <rhodgkin at bigpond.net.au>
To: "'Programming forum'" <programming at jsoftware.com>
Sent: Friday, December 09, 2005 9:24 PM
Subject: RE: [Jprogramming] matrix inverse

Impressive Roger !  Very nice.  Do you have something as succinct that
describes the method using Householder transforms as well ? .../Regards Rob



-----Original Message-----
From: programming-bounces at jsoftware.com
[mailto:programming-bounces at jsoftware.com] On Behalf Of Roger Hui
Sent: Saturday, 10 December 2005 12:53 PM
To: programming at jsoftware.com
Subject: [Jprogramming] matrix inverse

How compactly can you define matrix inverse?

minors =: 1&(|:\.)"2^:2
det    =: -/ .*
adjoint=: [: |: */~@($&1 _1)@# * det at minors
inverse=: adjoint % det

"adjoint" is the classical adjoint.  

"minors" appears on the \. page of the dictionary
and also on the green Jsoftware mug.  It was first 
defined by Ken Iverson.

   x=: 5 5 ?.@$ 10x
   y=: inverse x

   x +/ .* y
1 0 0 0 0
0 1 0 0 0
0 0 1 0 0
0 0 0 1 0
0 0 0 0 1

   x
6 5 9 2 4
9 0 7 0 4
6 8 3 8 1
2 8 0 0 2
1 6 0 4 4
   y
  _9r64   39r256   17r256    35r512  _1r16
 31r768 _59r1024  41r3072  249r2048  _3r64
 37r192  _25r256  _13r768   _29r512  _1r16
_7r1536 _61r2048 511r6144 _593r4096 11r128
  _1r48     5r64  _23r192    _7r128    1r4