Talk:Gauss-Jordan matrix inversion
what's wrong (with my REXX program)?
I suggest to change header to: what's wrong with my REXX program?-- Gerard Schildberger (talk) 09:30, 3 November 2018 (UTC)- Done. -- Gerard Schildberger (talk) 17:56, 3 November 2018 (UTC)
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
I used three different REXX interpreters, all yielded the same results.
-- Gerard Schildberger (talk) 09:25, 3 November 2018 (UTC)
- Can any of the other programs handle this input correctly? --Walter Pachl 15:22, 3 November 2018 (UTC)
- I ran it through the Perl 6 implementation and it works and is nominally correct. (If I invert the inverted matrix, I end up with the original.) I added it as another test case. See the last two tests under Gauss-Jordan_matrix_inversion#Perl_6 --Thundergnat (talk) 18:29, 3 November 2018 (UTC)
- Thank you, that helped. I fixed my program for the case that a.2.2=0.
My inverse matrix is the same as Perl 6's
show 6 The inverse matrix -4525/6238 2529/6238 -233/3119 1481/3119 -639/6238 1033/6238 -1075/6238 342/3119 -447/3119 871/6238 1299/6238 -289/6238 -204/3119 -390/3119 739/6238 782/3119 -222/3119 237/3119 -556/3119 -177/3119 -474/3119 -17/3119 -24/3119 688/3119 -140/3119
Generalization of the REXX algorithm for ANY pivot=0 must be worked out (tbd) --Walter Pachl 19:58, 3 November 2018 (UTC)