dapper.mods.Lorenz96.frei2013bridging
Settings as in bib.frei2013bridging.
They also cite its use in the following:
bib.bengtsson2003toward, bib.lei2011moment, bib.frei2013mixture.
1"""Settings as in `bib.frei2013bridging`. 2 3They also cite its use in the following: 4 5`bib.bengtsson2003toward`, `bib.lei2011moment`, `bib.frei2013mixture`. 6""" 7 8import numpy as np 9 10import dapper.mods as modelling 11from dapper.mods.Lorenz96 import dstep_dx, step 12from dapper.tools.localization import nd_Id_localization 13 14t = modelling.Chronology(0.05, dto=0.4, T=4**5, BurnIn=20) 15 16Nx = 40 17Dyn = { 18 "M": Nx, 19 "model": step, 20 "linear": dstep_dx, 21 "noise": 0, 22} 23 24X0 = modelling.GaussRV(M=Nx, C=0.001) 25 26jj = 1 + np.arange(0, Nx, 2) 27Obs = modelling.partial_Id_Obs(Nx, jj) 28Obs["noise"] = 0.5 29Obs["localizer"] = nd_Id_localization((Nx,), (2,), jj) 30 31HMM = modelling.HiddenMarkovModel(Dyn, Obs, t, X0) 32 33 34#################### 35# Suggested tuning 36#################### 37# Compare to Table 1 and 3 from frei2013bridging. Note: 38# - N is too large to be very interesting. 39# - We obtain better EnKF scores than they report, 40# and use inflation and sqrt updating, 41# and don't really need localization. 42# from dapper.mods.Lorenz96.frei2013bridging import HMM # rmse.a 43# xps += EnKF_N(N=400,rot=1) # 0.80 44# xps += LETKF( N=400,rot=True,infl=1.01,loc_rad=10/1.82) # 0.79 # short xp. only 45# xps += Var3D() # 2.42 # short xp. only
t =
<Chronology>
- K: 20480
- Ko: 2559
- T: 1024.0
- BurnIn: 20
- dto: 0.4
- dt: 0.05
Nx =
40
Dyn =
{'M': 40, 'model': <function step>, 'linear': <function dstep_dx>, 'noise': 0}
X0 =
GaussRV({
'C': <CovMat>
M: 40
kind: 'diag'
trunc: 1.0
rk: 40
full: (only computing/printing corners)
[[0.001 0. 0. ... 0. 0. 0. ]
[0. 0.001 0. ... 0. 0. 0. ]
[0. 0. 0.001 ... 0. 0. 0. ]
...
[0. 0. 0. ... 0.001 0. 0. ]
[0. 0. 0. ... 0. 0.001 0. ]
[0. 0. 0. ... 0. 0. 0.001]]
diag:
[0.001 0.001 0.001 ... 0.001 0.001 0.001],
'mu': array([0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]),
'M': 40
})
jj =
array([ 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35,
37, 39])
Obs =
{'M': 20, 'model': Direct obs. at [ 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39]
<function partial_Id_Obs.<locals>.model>, 'linear': Constant matrix
[[0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0.
0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0.
0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0.
0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0.
0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1.
0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0.]
[0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0.]
[0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0.]
[0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0.]
[0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1.]]
<function partial_Id_Obs.<locals>.linear>, 'noise': 0.5, 'localizer': <function localization_setup.<locals>.localization_now>}
HMM =
HiddenMarkovModel({
'Dyn':
Operator({
'M': 40,
'model': <function step>,
'noise':
GaussRV({
'mu': array([0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0.]),
'M': 40,
'C': 0
}),
'linear': <function dstep_dx>
}),
'Obs':
<TimeDependentOperator> CONSTANT operator sepcified by .Op1:
Operator({
'M': 20,
'model':
Direct obs. at [ 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29
31 33 35 37 39]
<function partial_Id_Obs.<locals>.model>,
'noise':
GaussRV({
'C': <CovMat>
M: 20
kind: 'diag'
trunc: 1.0
rk: 20
full:
[[0.5 0. 0. 0. 0. 0. 0. 0. 0.
0.
0. 0. 0. 0. 0. 0. 0. 0. 0.
0. ]
[0. 0.5 0. 0. 0. 0. 0. 0. 0.
0.
0. 0. 0. 0. 0. 0. 0. 0. 0.
0. ]
[0. 0. 0.5 0. 0. 0. 0. 0. 0.
0.
0. 0. 0. 0. 0. 0. 0. 0. 0.
0. ]
[0. 0. 0. 0.5 0. 0. 0. 0. 0.
0.
0. 0. 0. 0. 0. 0. 0. 0. 0.
0. ]
[0. 0. 0. 0. 0.5 0. 0. 0. 0.
0.
0. 0. 0. 0. 0. 0. 0. 0. 0.
0. ]
[0. 0. 0. 0. 0. 0.5 0. 0. 0.
0.
0. 0. 0. 0. 0. 0. 0. 0. 0.
0. ]
[0. 0. 0. 0. 0. 0. 0.5 0. 0.
0.
0. 0. 0. 0. 0. 0. 0. 0. 0.
0. ]
[0. 0. 0. 0. 0. 0. 0. 0.5 0.
0.
0. 0. 0. 0. 0. 0. 0. 0. 0.
0. ]
[0. 0. 0. 0. 0. 0. 0. 0. 0.5
0.
0. 0. 0. 0. 0. 0. 0. 0. 0.
0. ]
[0. 0. 0. 0. 0. 0. 0. 0. 0.
0.5
0. 0. 0. 0. 0. 0. 0. 0. 0.
0. ]
[0. 0. 0. 0. 0. 0. 0. 0. 0.
0.
0.5 0. 0. 0. 0. 0. 0. 0. 0.
0. ]
[0. 0. 0. 0. 0. 0. 0. 0. 0.
0.
0. 0.5 0. 0. 0. 0. 0. 0. 0.
0. ]
[0. 0. 0. 0. 0. 0. 0. 0. 0.
0.
0. 0. 0.5 0. 0. 0. 0. 0. 0.
0. ]
[0. 0. 0. 0. 0. 0. 0. 0. 0.
0.
0. 0. 0. 0.5 0. 0. 0. 0. 0.
0. ]
[0. 0. 0. 0. 0. 0. 0. 0. 0.
0.
0. 0. 0. 0. 0.5 0. 0. 0. 0.
0. ]
[0. 0. 0. 0. 0. 0. 0. 0. 0.
0.
0. 0. 0. 0. 0. 0.5 0. 0. 0.
0. ]
[0. 0. 0. 0. 0. 0. 0. 0. 0.
0.
0. 0. 0. 0. 0. 0. 0.5 0. 0.
0. ]
[0. 0. 0. 0. 0. 0. 0. 0. 0.
0.
0. 0. 0. 0. 0. 0. 0. 0.5 0.
0. ]
[0. 0. 0. 0. 0. 0. 0. 0. 0.
0.
0. 0. 0. 0. 0. 0. 0. 0. 0.5
0. ]
[0. 0. 0. 0. 0. 0. 0. 0. 0.
0.
0. 0. 0. 0. 0. 0. 0. 0. 0.
0.5]]
diag:
[0.5 0.5 0.5 ... 0.5 0.5 0.5],
'mu': array([0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0.]),
'M': 20
}),
'linear':
Constant matrix
[[0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
0. 0. 0. 0. 0.
0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
0. 0. 0. 0. 0.
0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
0. 0. 0. 0. 0.
0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
0. 0. 0. 0. 0.
0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0.
0. 0. 0. 0. 0.
0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0.
0. 0. 0. 0. 0.
0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0.
0. 0. 0. 0. 0.
0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0.
0. 0. 0. 0. 0.
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[0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 0.
0. 0. 0. 0. 0.
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[0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
1. 0. 0. 0. 0.
0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
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0. 0. 1. 0. 0.
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0. 0. 0. 0. 0.
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0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0.]
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0. 0. 0. 0. 0.
0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0.]
[0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
0. 0. 0. 0. 0.
0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0.]
[0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
0. 0. 0. 0. 0.
0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0.]
[0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
0. 0. 0. 0. 0.
0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1.]]
<function partial_Id_Obs.<locals>.linear>,
'localizer':
<function
localization_setup.<locals>.localization_now at
0x7fa23fdb1090>
}),
'tseq':
<Chronology>
- K: 20480
- Ko: 2559
- T: 1024.0
- BurnIn: 20
- dto: 0.4
- dt: 0.05,
'X0':
GaussRV({
'C': <CovMat>
M: 40
kind: 'diag'
trunc: 1.0
rk: 40
full: (only computing/printing corners)
[[0.001 0. 0. ... 0. 0. 0. ]
[0. 0.001 0. ... 0. 0. 0. ]
[0. 0. 0.001 ... 0. 0. 0. ]
...
[0. 0. 0. ... 0.001 0. 0. ]
[0. 0. 0. ... 0. 0.001 0. ]
[0. 0. 0. ... 0. 0. 0.001]]
diag:
[0.001 0.001 0.001 ... 0.001 0.001 0.001],
'mu': array([0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0.]),
'M': 40
}),
'liveplotters': [],
'sectors': {},
'name': 'Lorenz96/frei2013bridging.py'
})