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Not finished yet, but my coding skill isn't good enough to complete this
yet. Contains generalised inversion, which can invert singular or
rectangular matrices, plus basic operations.
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Grassblade wrote:
> Not finished yet, but my coding skill isn't good enough to complete this
> yet. Contains generalised inversion, which can invert singular or
> rectangular matrices, plus basic operations.
Glad I found this, I was about to write my own versions for a current
project. Anyway, I updated your version to fix a few declare/local bugs,
added the 'rowappend' you left as todo, and added a few new useful
functions - Swap rows, Multiply row, Reduced Row Echelon Form, and
Gauss-Jordan Matrix Inversion.
While the Moore-Penrose generalized inversion is versatile, it is quite
slow. The Gauss-Jordan inversion only works on non-singular square
matrices, but is much faster with those. Tests of 10000 iterations of
each for a simple matrix (the example on
http://en.wikipedia.org/wiki/Gauss%E2%80%93Jordan_elimination) showed
that the MPGinverse was a little more than 7.5 times slower than GJinverse.
Actual results:
10000 iterations, 3x3 simple matrix {{2,-1,0},{-1,2,-1},{0,-1,2}}
GJinverse 18.515 cpu-seconds
MPGinverse 141.328 cpu-seconds
If you're still around, and don't see a problem with it, I think this
would be a good addition to the Object Collection with a few updates to
the naming scheme.
CShake
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Download 'matrices.inc.txt' (23 KB)
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