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Strange result in math.inv() function #1109

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opened this Issue May 24, 2018 · 7 comments

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isma4444 commented May 24, 2018

 Somehow I get different results using the inverse of matrices with python and with math.js Original matrix: ``````A = 6.123233995736766e-17 1 0 788 -1 6.123233995736766e-17 0 692 0 0 1 0 0 0 0 1 `````` The result by using math.js ``````math.inv(A)= 0 -1 0 0 1 6.123233995736766e-17 0 -788 0 0 1 0 0 0 0 1 `````` Using python: `````` [[ 6.123234e-17 -1.000000e+00 -0.000000e+00 6.920000e+02] [ 1.000000e+00 6.123234e-17 0.000000e+00 -7.880000e+02] [ 0.000000e+00 0.000000e+00 1.000000e+00 0.000000e+00] [ 0.000000e+00 0.000000e+00 0.000000e+00 1.000000e+00]] `````` The element (0,3) is different and by a big margin.
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harrysarson commented May 24, 2018

 For reference in MATLAB I get the same as python: `````` 6.12323399573677e-17 -1 0 692 1 6.12323399573677e-17 0 -788 0 0 1 0 0 0 0 1 `````` The matrix `A` is very nearly singular with is causing these problems. I dunno if these errors can be avoided or not. @isma4444 what does `Ainv = math.inv(A); math.inv(Ai)` give?
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ericman314 commented May 24, 2018

 Changing element (0,0) to exactly 0 results in the `inv(A)` giving the correct inverse. I suspect this is not an issue with a singular matrix but an actual bug related to some conditional check equating that element to 0 during gaussian elimination or something like that. I'm intrigued and interested in finding the bug but I won't be able to get to it for a day or two, likely.

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ericman314 commented May 25, 2018

 I managed to implement a Gauss-Jordan elimination with full pivoting in `inv.js` which solves this issue. Unfortunately, I shamelessly copied the algorithm from Numerical Recipes in C so we probably can't include it in math.js. I will need to study the algorithm and try to reproduce it from memory.
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josdejong commented May 26, 2018

 Thanks for looking into this Eric. Maybe there is an open source implementation of the Gauss-Jordan elimination that you could port, like from Octave or so?
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harrysarson commented May 26, 2018

 numpy must have something aswell, might be worth a look

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ericman314 commented May 28, 2018 • edited

 Thanks, those are indeed good resources. But it ended up being simple enough to add pivoting to the current implementation; see PR #1114.
Owner

josdejong commented May 29, 2018

 This issue is fixed now in v4.4.1. Thanks again Eric!

josdejong closed this May 29, 2018

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