WIP: Operator determinants #21
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…se). It was dropping the first and last elements along the first axis every time, instead of along the axis being concatenated.
The primary data stored by this class is a list of eigenvalues, so this should be easy. For some reason it's broken for all but trivial cases. I can get the determinant to be one for diagonal correlations, but this is not the primary class for diagonal operators, especially not ones proportional to the identity matrix. I have no idea why this doesn't work. This may be enough for the purposes of this package, since it's usually only off by 50% or so, but I really don't like calling the result a `determinant`.
DWesl
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Non-cyclic homogeneous correlations are still broken. I still can't figure out how to get those working.
…se). It was dropping the first and last elements along the first axis every time, instead of along the axis being concatenated.
The primary data stored by this class is a list of eigenvalues, so this should be easy. For some reason it's broken for all but trivial cases. I can get the determinant to be one for diagonal correlations, but this is not the primary class for diagonal operators, especially not ones proportional to the identity matrix. I have no idea why this doesn't work. This may be enough for the purposes of this package, since it's usually only off by 50% or so, but I really don't like calling the result a `determinant`.
Non-cyclic homogeneous correlations are still broken. I still can't figure out how to get those working.
Gets tox to try it again.
…n apreriodic tests. At this point just under half of the aperiodic tests are broken. Some of them are close and would pass if I required only three-decimal precision, others differ by an order of magnitude.
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This works with the spectral operators on periodic domains. I cannot get this to work for spectral operators on non-periodic domains. There does not appear to be any literature on the subject of determinants of Toeplitz and block Toeplitz operators, although there are suggestions that the determinants can be calculated by means of Levinson-Durbin recursion, somewhat as a side product of solving the linear system. |
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An additional complication: many applications will have different correlation lengths for land and ocean, or will optimize only the one or the other. In either case, the easy way to do that sets many standard deviations to zero, which forces the determinant to zero. Making this useful requires embedding and restriction operators to embed either the land or ocean points within the rectangular domain, apply the transforms, then pull out only the land or ocean points to pass to the next section of the program. If optimizing only net fluxes for land and ocean, a separate operator to rearrange fluxes from a grid so that land fluxes are next to each other, as are ocean fluxes. If optimizing GPP and Reco separately, or fossil fuel and biogenic fluxes separately, being able to rearrange a net flux map to separate the ocean and land fluxes is less useful. |
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Description
Try to provide determinants for the various linear operators.
Motivation and Context
I would like to optimize the correlation length parameters as well as the mean fluxes. This requires the full likelihood, in particular, the determinant of the covariance matrix. I can't calculate that at the moment. This takes a few steps toward calculating those
How Has This Been Tested?
I check the determinants of some operators against
numpy.linalg.det(op.dot(np.eye(*op.shape))).The Fourier operators are causing problems.
Types of changes
Checklist: