Fm = Fmat(m, -1, 1, tseq.dt)
def step(x, t, dt):
assert dt == tseq.dt
return x @ Fm.T
f = {'m': m, 'model': step, 'jacob': Fm, 'noise': 0}
# In the animation, it can sometimes/somewhat occur
# that the truth is outside 3*sigma !!!
# Yet this is not so implausible because sinusoidal_sample()
# yields (multivariate) uniform (random numbers) -- not Gaussian.
wnum = 25
X0 = RV(func=lambda N: sqrt(5) / 10 * sinusoidal_sample(m, wnum, N))
def yplot(y):
lh = plt.plot(jj, y, 'g*', MarkerSize=8)[0]
plt.pause(0.8)
return lh
h = partial_direct_obs_setup(m, jj)
h['noise'] = 0.01
h['plot'] = yplot
other = {'name': os.path.relpath(__file__, 'mods/')}
setup = TwinSetup(f, h, tseq, X0, **other)
################### Noise setup ###################
# Instead of sampling model noise from sinusoidal_sample(),
# we will replicate it below by a covariance matrix approach.
# But, for strict equivalence, one would have to use
# uniform (i.e. not Gaussian) random numbers.
wnumQ = 25
sample_filename = 'data/samples/LA_Q_wnum' + str(wnumQ) + '.npz'
try:
# Load pre-generated
L = np.load(sample_filename)['Left']
except FileNotFoundError:
# First-time use
print('Generating a sample from which to initialize experiments.')
NQ = 20000 # Must have NQ > (2*wnumQ+1)
A = sinusoidal_sample(m,wnumQ,NQ)
A = 1/10 * anom(A)[0] / sqrt(NQ)
Q = A.T @ A
U,s,_ = tsvd(Q)
L = U*sqrt(s)
np.savez(sample_filename, Left=L)
X0 = GaussRV(C=CovMat(sqrt(5)*L,'Left'))
################### Forward model ###################
damp = 0.98;
Fm = Fmat(m,-1,1,tseq.dt)
def step(x,t,dt):
assert dt == tseq.dt
return x @ Fm.T
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,
'jacob': Fm,
'noise': 0
}
# In the animation, it can sometimes/somewhat occur
# that the truth is outside 3*sigma !!!
# Yet this is not so implausible because sinusoidal_sample()
# yields (multivariate) uniform (random numbers) -- not Gaussian.
wnum = 25
X0 = RV(M=Nx, func = lambda N: sqrt(5)/10 * sinusoidal_sample(Nx,wnum,N))
Obs = partial_direct_Obs(Nx,jj)
Obs['noise'] = 0.01
HMM = HiddenMarkovModel(Dyn,Obs,tseq,X0,LP=LPs(jj))
####################
# Suggested tuning
####################
# config = EnKF('PertObs',N=100,infl=1.02)
################### Noise setup ###################
# Instead of sampling model noise from sinusoidal_sample(),
# we will replicate it below by a covariance matrix approach.
# But, for strict equivalence, one would have to use
# uniform (i.e. not Gaussian) random numbers.
wnumQ = 25
sample_filename = 'data/samples/LA_Q_wnum' + str(wnumQ) + '.npz'
try:
# Load pre-generated
L = np.load(sample_filename)['Left']
except FileNotFoundError:
# First-time use
print('Generating a sample from which to initialize experiments.')
NQ = 20000 # Must have NQ > (2*wnumQ+1)
A = sinusoidal_sample(Nx, wnumQ, NQ)
A = 1 / 10 * center(A)[0] / sqrt(NQ)
Q = A.T @ A
U, s, _ = tsvd(Q)
L = U * sqrt(s)
np.savez(sample_filename, Left=L)
X0 = GaussRV(C=CovMat(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