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| LU Factorization http://forum.alglib.net/viewtopic.php?f=2&t=492 |
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| Author: | rishka [ Fri Nov 25, 2011 6:39 pm ] |
| Post subject: | LU Factorization |
How can I (succesfully) unpack the information module rmatrixlu returns me in the first argument? I.e. i need the matrices L and U explicitely. |
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| Author: | Sergey.Bochkanov [ Mon Nov 28, 2011 7:20 am ] |
| Post subject: | Re: LU Factorization |
Lower part of the result contains L, upper one contains U. They should be easy to unpack. |
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| Author: | rishka [ Mon Nov 28, 2011 7:49 am ] |
| Post subject: | Re: LU Factorization |
Sure, if this were it. What about the Permutation Matrix (Pivots) and the Decomposition A=P L U? I don't understand the function of the returned pivots in order to construct that Decomposition. |
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| Author: | Sergey.Bochkanov [ Mon Nov 28, 2011 9:05 am ] |
| Post subject: | Re: LU Factorization |
Here is extract from documentation: Quote: A is represented as A = P*L*U, where:
* L is lower unitriangular matrix * U is upper triangular matrix * P = P0*P1*...*PK, K=min(M,N)-1, Pi - permutation matrix for I and Pivots[I] |
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| Author: | rishka [ Mon Nov 28, 2011 9:51 am ] |
| Post subject: | Re: LU Factorization |
It seems we are talking past each other. Please take a look at this example (mycode) LU Decomposition A = L U. A: 2,000000 -1,000000 0,000000 1,000000 0,000000 -1,000000 3,000000 7,000000 -1,000000 The Decomposition of A is L: 0,666667 1,000000 0,000000 0,333333 0,411765 1,000000 1,000000 0,000000 0,000000 U: 3,000000 7,000000 -1,000000 0,000000 -5,666667 0,666667 0,000000 0,000000 -0,941176 Now please consider the output of alglib routine rmatrixlux ---> LUA: 3,0000 7,0000 -1,0000 0,6667 -5,6667 0,6667 0,3333 0,4118 -0,9412 ---> PIVOTS: 2 2 2 Matrix U can easily be extracted. But the construction of L is what is making me a headache when using alglib's rmatrixlu. |
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| Author: | Sergey.Bochkanov [ Mon Nov 28, 2011 11:16 am ] |
| Post subject: | Re: LU Factorization |
L is unitriangular, which means that its diagonal elements are equal to 1.0. In your case L is equal to 1,0000 0,0000 0,0000 0,6667 1,0000 0,0000 0,3333 0,4118 1,0000 |
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| Author: | rishka [ Mon Nov 28, 2011 12:40 pm ] |
| Post subject: | Re: LU Factorization |
Which in this case would mean, that LU != A. And, what about the Pivots? I know i am intrusive, and i am really sorry about that, but i hope to solve this (little) problem with your very appreciated help. |
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