def test_1():
d = np.array([.3, 1, 2, 1])
C = dpr.CovMat(d)
assert np.allclose(np.diag(C.full), d)
def test_3():
"""Make sure truncation and sorting works."""
d = np.array([1, 0, 1])
C = dpr.CovMat(d)
assert np.allclose(np.diag(C.full), d)
try:
# Load pre-generated
L = np.load(sample_filename)['Left']
except FileNotFoundError:
# First-time use
print('Did not find sample file', sample_filename,
'for experiment initialization. Generating...')
NQ = 20000 # Must have NQ > (2*wnumQ+1)
A = sinusoidal_sample(Nx, wnumQ, NQ)
A = 1 / 10 * center(A)[0] / np.sqrt(NQ)
Q = A.T @ A
U, s, _ = tsvd(Q)
L = U * np.sqrt(s)
np.savez(sample_filename, Left=L)
X0 = dpr.GaussRV(C=dpr.CovMat(np.sqrt(5) * L, 'Left'))
###################
# Forward model #
###################
damp = 0.98
Fm = Fmat(Nx, -1, 1, tseq.dt)
def step(x, t, dt):
assert dt == tseq.dt
return x @ Fm.T
Dyn = {
'M': Nx,
def test_2():
"""Special case: np.all(d==d[0])"""
d = np.array([1, 1, 1])
C = dpr.CovMat(d)
assert np.allclose(np.diag(C.full), d)
"""Reproduce results from Fig 11 of
M. Bocquet and P. Sakov (2012): 'Combining inflation-free and
iterative ensemble Kalman filters for strongly nonlinear systems'"""
import numpy as np
import dapper as dpr
from dapper.mods.Lorenz63.sakov2012 import HMM
# The only diff to sakov2012 is R:
# bocquet2012 uses 1 and 8, sakov2012 uses 2 (and 8)
HMM.Obs.noise.C = dpr.CovMat(np.eye(3))
HMM.name = HMM.name.replace("sakov", "bocquet")
####################
# Suggested tuning
####################
# from dapper.mods.Lorenz63.bocquet2012 import HMM # rmse.a:
# HMM.t.dkObs = 25
# xps += iEnKS('Sqrt', N=10,infl=1.02,rot=True) # 0.22
# xps += iEnKS('Sqrt', N=3, infl=1.04) # 0.23
# xps += iEnKS('Sqrt', N=3, xN=1.0) # 0.22
#
# HMM.t.dkObs = 5
# xps += iEnKS('Sqrt', N=10,infl=1.02,rot=True) # 0.13
# xps += iEnKS('Sqrt', N=3, infl=1.02) # 0.13
# xps += iEnKS('Sqrt', N=3, xN=1.0) # 0.15
# xps += iEnKS('Sqrt', N=3, xN=2.0) # 0.14
#