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()
'for experiment initialization. Generating...')
NQ = 20000 # Must have NQ > (2*wnumQ+1)
A = sinusoidal_sample(Nx, wnumQ, NQ)
A = 1 / 10 * (A - A.mean(0)) / np.sqrt(NQ)
Q = A.T @ A
U, s, _ = tsvd(Q)
L = U * np.sqrt(s)
np.savez(sample_filename, Left=L)
X0 = modelling.GaussRV(C=modelling.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,
'model': lambda x, t, dt: damp * step(x, t, dt),
'linear': lambda x, t, dt: damp * Fm,
'noise': modelling.GaussRV(C=modelling.CovMat(L, 'Left')),
}
HMM = modelling.HiddenMarkovModel(Dyn, Obs, tseq, X0, LP=LPs(jj))
import numpy as np
import dapper.mods as modelling
from dapper.mods.LA import Fmat, sinusoidal_sample
from dapper.mods.Lorenz96 import LPs
Nx = 1000
Ny = 4
jj = modelling.linspace_int(Nx, Ny)
tseq = modelling.Chronology(dt=1, dkObs=5, T=300, BurnIn=-1, Tplot=100)
# WITHOUT explicit matrix (assumes dt == dx/c):
# step = lambda x,t,dt: np.roll(x,1,axis=x.ndim-1)
# WITH:
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,
}
# In the animation, it can sometimes/somewhat occur