Talk:Gauss-Jordan matrix inversion
what's wrong (with REXX)?
My REXX algorithm works nicely most of the time. But sometimes it fails. E.g., with this matrix:
3 1 8 9 6 6 2 8 10 1 5 7 2 10 3 3 2 7 7 9 3 5 6 1 1
The first elimination sets a.2.2=0 and how could this become 1 furtheron? Help! Thanks!! --Walter Pachl 08:52, 3 November 2018 (UTC)
I don't see your failure, a.2.2 becomes zero and stays a zero.
Also, where it says "Main diagonal has all ones" isn't true.
With:
a= 3 1 8 9 6 6 2 8 10 1 5 7 2 10 3 3 2 7 7 9 3 5 6 1 1
- Output:
show 1 The given matrix
3 1 8 9 6 1 0 0 0 0
6 2 8 10 1 0 1 0 0 0
5 7 2 10 3 0 0 1 0 0
3 2 7 7 9 0 0 0 1 0
3 5 6 1 1 0 0 0 0 1
show 2 1
3 1 8 9 6 1 0 0 0 0
0 0 -4 -4 -11/2 -1 1/2 0 0 0
0 16/5 -34/5 -3 -21/5 -1 0 3/5 0 0
0 1 -1 -2 3 -1 0 0 1 0
0 4 -2 -8 -5 -1 0 0 0 1
show 2 2
3 1 8 9 6 1 0 0 0 0
0 0 -4 -4 -11/2 -1 1/2 0 0 0
0 0 4 4 11/2 1 -1/2 0 0 0
0 0 4 4 11/2 1 -1/2 0 0 0
0 0 4 4 11/2 1 -1/2 0 0 0
show 2 3
3 1 8 9 6 1 0 0 0 0
0 0 -4 -4 -11/2 -1 1/2 0 0 0
0 0 4 4 11/2 1 -1/2 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
show 2 4
3 1 8 9 6 1 0 0 0 0
0 0 -4 -4 -11/2 -1 1/2 0 0 0
0 0 4 4 11/2 1 -1/2 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
Lower part has all zeros
show 3
3 1 8 9 6 1 0 0 0 0
0 0 -4 -4 -11/2 -1 1/2 0 0 0
0 0 4 4 11/2 1 -1/2 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
show 4 5
3 1 8 9 6 1 0 0 0 0
0 0 -4 -4 -11/2 -1 1/2 0 0 0
0 0 4 4 11/2 1 -1/2 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
show 4 4
3 1 8 9 6 1 0 0 0 0
0 0 -4 -4 -11/2 -1 1/2 0 0 0
0 0 4 4 11/2 1 -1/2 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
show 4 3
3 1 0 1 -5 -1 1 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 4 4 11/2 1 -1/2 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
show 4 2
3 1 0 1 -5 -1 1 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 4 4 11/2 1 -1/2 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
Upper half has all zeros
show 5
1 1/3 0 1/3 -5/3 -1/3 1/3 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 1 1 11/8 1/4 -1/8 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
Main diagonal has all ones
show 6 The inverse matrix
-1/3 1/3 0 0 0
0 0 0 0 0
1/4 -1/8 0 0 0
0 0 0 0 0
0 0 0 0 0
The product of input and inverse matrix
1 1/3 0 1/3 -5/3
0 0 0 0 0
0 0 1 1 11/8
0 0 0 0 0
0 0 0 0 0
I would add the statement (at least for now):
signal on noValue
as you have a piece of dead code (possibly a debugging leftover?):
ss=sigl
-- Gerard Schildberger (talk) 09:25, 3 November 2018 (UTC)
- The problem is that the inverse matrix cannot be computed this way. Any other way? --Walter Pachl 09:35, 3 November 2018 (UTC)