a matrix decomposition story

[Michal Wallace]

I had this matrix:

  ] y =. > 1 2 1; 2 3 4; 3 5 2

1 2 1

2 3 4

3 5 2

I used 128!:10 to get the LU decomposition...

But the decomposition was not what I expected:

128!:10 y

┌─────┬───────┐

│0 1 2│1 2 1│

│ │2 _1 2│

│ │3 1 _3│

└─────┴───────┘

So I did this:

   [ 'LU L I U' =. ((1 { 128!:10) , [: (>/~ ; =/~ ; <:/~) i.@#) y

┌───────┬─────┬─────┬─────┐

│1 2 1│0 0 0│1 0 0│1 1 1│

│2 _1 2│1 0 0│0 1 0│0 1 1│

│3 1 _3│1 1 0│0 0 1│0 0 1│

└───────┴─────┴─────┴─────┘

So I could do this:

(I + LU * L) ; (LU * U)

┌─────┬───────┐

│1 0 0│1 2 1│

│2 1 0│0 _1 2│

│3 1 1│0 0 _3│

└─────┴───────┘

But I was sure I could do that tacitly with gerunds.

I couldn't figure it out, so I started writing this email.

But then I learned about m"n and realized I could combine it with m/ !

([: (;`+)/&.|. (1 {:: 128!:10) (*`]`*)"2 (>/~ , =/~ ,: <:/~)@i.@#) y

┌─────┬───────┐

│1 0 0│1 2 1│

│2 1 0│0 _1 2│

│3 1 1│0 0 _3│

└─────┴───────┘

(the end)

[bill lam]

Isn't 128!:10 LUP?

The permutation 0&{ should be significant.

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[Michal Wallace]

Yes. It wasn't actually the decomposition I thought it was. I just got sidetracked trying to do that thing. :D