LUDecompose, LUBacksubstitue in class scalarMatrix
Good Day to All !
While using the scalarMatrix class (/src/OpenFOAM/matrices/scalarMatrix) I tried
the LUDecompose and LUBacksubstitute functions. They work fine but when i tried to compare the results with the MATLAB answers , it seems the decomposed matrix has some special format to store the L and U parts. Here is what I did:
hmm = ((-3 10 -4)
(2 3 10)
(2 6 1))
According to the class documentation LUDecompose will decompose the matrix with pivoting, which in my understanding implies MATLAB command [L,U] = lu(A).
I called hmm.LUDecompose(hmm, pivotIndices), and assuming that the decomposition is saved back in the scalarMatrix hmm , the Info << hmm << endl;
after decomposition gives:
3 3 ((2 6 1)
(-1.5 19 -2.5)
(1 -0.157895 8.60526))
and Info << source << endl; gives the solution
3(0.883792 0.370031 0.0122324)
Now on the other hand using MATLAB one gets:
Thanks for attention
just a quick pointer: Have a look into the ODE solver classes and how scalarMatrix is used there.
Thanks for the tip. I will follow that clue and post back .
a third variant
i tried it in octave for fun...
[l,u,p] = lu(hmm)
and I got this
1.00000 0.00000 0.00000
-0.66667 1.00000 0.00000
-0.66667 0.76316 1.00000
-3.00000 10.00000 -4.00000
0.00000 12.66667 -1.66667
0.00000 0.00000 8.60526
1 0 0
0 0 1
0 1 0
This is what 'help lu' says:
Compute the LU decomposition of A, using subroutines from LAPACK.
you need to understand what pivotIndices is for, which takes the value (2 2 2) in my case.
Have a look into Numerical Recipes (Press et al.).
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