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Re: Which algorithm does Octave use to invert the following positive sem
From: |
Martin Helm |
Subject: |
Re: Which algorithm does Octave use to invert the following positive semidefinite matrix? |
Date: |
Mon, 4 Apr 2011 17:53:51 +0200 |
User-agent: |
KMail/1.13.6 (Linux/2.6.34.7-0.7-desktop; KDE/4.6.1; x86_64; ; ) |
Am Montag, 4. April 2011, 16:45:28 schrieb Olumide:
> Can someone tell me what algorithm Octave uses to invert the following
> positive semidefinite matrix, that has zeros along its diagonal.
> Matrices of this sort that arise in scattered data interpolation with
> radial basis functions.
>
> [ 0.000000 529.831737 1198.292909 529.831737 1.000000
> 10.000000 0.000000 ]
> [ 529.831737 0.000000 529.831737 1198.292909 1.000000
> 0.000000 10.000000 ]
> [ 1198.292909 529.831737 0.000000 529.831737 1.000000
> -10.000000 0.000000 ]
> [ 529.831737 1198.292909 529.831737 0.000000 1.000000
> 0.000000 -10.000000 ]
> [ 1.000000 1.000000 1.000000 1.000000 0.000000
> 0.000000 0.000000 ]
> [ 10.000000 0.000000 -10.000000 0.000000 0.000000
> 0.000000 0.000000 ]
> [ 0.000000 10.000000 0.000000 -10.000000 0.000000
> 0.000000 0.000000 ]
>
> Whereas the LAPACK routines DPOTRI and DGETRI fail because the matrix
> has zero elements along its diagonal, Octave successfully computes
> the inverts the matrix to be
>
> [ 1.8034e-003 -1.8034e-003 1.8034e-003 -1.8034e-003 2.5000e-001
> 5.0000e-002 -2.2854e-018 ]
> [ -1.8034e-003 1.8034e-003 -1.8034e-003 1.8034e-003 2.5000e-001
> -1.4014e-017 5.0000e-002 ]
> [ 1.8034e-003 -1.8034e-003 1.8034e-003 -1.8034e-003 2.5000e-001
> -5.0000e-002 -1.1356e-017 ]
> [ -1.8034e-003 1.8034e-003 -1.8034e-003 1.8034e-003 2.5000e-001
> -1.2975e-017 -5.0000e-002 ]
> [ 2.5000e-001 2.5000e-001 2.5000e-001 2.5000e-001 -5.6449e+002
> 1.6031e-015 -2.2001e-015 ]
> [ 5.0000e-002 1.5053e-017 -5.0000e-002 1.1470e-017 -1.6031e-015
> 5.9915e+000 2.3211e-016 ]
> [ 1.3878e-017 5.0000e-002 5.8566e-018 -5.0000e-002 1.4668e-015
> -1.6985e-017 5.9915e+000 ]
>
> I've verified that the product of both matrices is the identify
> matrix.
>
> Thanks,
>
> - Olumide
>
Just one question: Why do you think your matrix is positiv semidefinite? It has
positive and negative eigen values!