def test_operator_defaults():
M = 3
op = modelling.Operator(**{"M": M})
assert (op.linear() == np.identity(M)).all()
assert op.model(3) == 3
assert op.model(3, 2, 1) == 3
assert (op.noise.sample(M) == np.zeros(M)).all()
def test_operator_dyn():
"""Simple test using 1D linear advection."""
Nx = 6
tseq = modelling.Chronology(dt=1, dko=5, T=10)
Fm = Fmat(Nx, c=-1, dx=1, dt=tseq.dt)
def step(x, t, dt):
assert dt == tseq.dt
return x @ Fm.T
Dyn = {
"M": Nx,
"model": step,
"linear": lambda x, t, dt: Fm,
"noise": 0,
}
Dyn_op = modelling.Operator(**Dyn)
# Square wave
x = np.array([1, 1, 1, 0, 0, 0])
x1 = Dyn_op(x, tseq.T - 1, tseq.dt)
assert (x1 == np.array([0, 1, 1, 1, 0, 0])).all()
x2 = Dyn_op(x1, tseq.T - 3, 1)
assert (x2 == np.array([0, 0, 1, 1, 1, 0])).all()
x3 = Dyn_op(x2, tseq.T - 4, 1)
assert (x3 == np.array([0, 0, 0, 1, 1, 1])).all()
x4 = Dyn_op(x3, tseq.T - 5, 1)
assert (x4 == np.array([1, 0, 0, 0, 1, 1])).all()
"""Settings from `bib.wiljes2016second`.""" import numpy as np import dapper.mods as modelling from dapper.mods.Lorenz63.sakov2012 import HMM as _HMM from dapper.mods.Lorenz63.sakov2012 import Nx HMM = _HMM.copy() HMM.tseq = modelling.Chronology(0.01, dko=12, T=4**5, BurnIn=4) jj = np.array([0]) Obs = modelling.partial_Id_Obs(Nx, jj) Obs['noise'] = 8 HMM.Obs = modelling.Operator(**Obs) #################### # Suggested tuning #################### # Reproduce benchmarks for NETF and ESRF (here EnKF-N) from left pane of Fig 1. # from dapper.mods.Lorenz63.wiljes2017 import HMM # rmse.a reported by DAPPER / PAPER: # ------------------------------------------------------------------------------ # HMM.tseq.Ko = 10**2 # xps += OptInterp() # 5.4 / N/A # xps += Var3D(xB=0.3) # 3.0 / N/A # xps += EnKF_N(N=5) # 2.68 / N/A # xps += EnKF_N(N=30,rot=True) # 2.52 / 2.5 # xps += LNETF(N=40,rot=True,infl=1.02,Rs=1.0,loc_rad='NA') # 2.61 / ~2.2 # xps += PartFilt(N=35 ,reg=1.4,NER=0.3) # 2.05 / 1.4 * # *: tuning settings not given #
"""Settings from `bib.mandel2016hybrid`."""
import dapper.mods as modelling
from dapper.mods.Lorenz63.sakov2012 import HMM as _HMM
HMM = _HMM.copy()
# HMM.t = modelling.Chronology(0.01,KObs=10**5,BurnIn=500), with dkObs in [5:55].
# But it's pretty safe to shorten the BurnIn and KObs.
HMM.Obs = modelling.Operator(**{
'M': 3,
'model': lambda x, t: x**3,
'noise': 8,
})
# It is unclear whether the model error (cov Q) is used
# just for the DA method, or also for the truth.
def Q(dkObs): return modelling.GaussRV(M=HMM.Nx, C=0.01/(dkObs*HMM.t.dt))
####################
# Suggested tuning
####################
# Compare EnKF scores with those in figure 5 of paper.
# Note: We tune mult. inflation.
# The paper only seems to use Q, probably yielding divergence.
# rmse.a as reported by: DAPPER paper
# --------------------------------------------------------------------------