# "interaction" coefficients
A = np.array([
[1, 1.09, 1.52, 0],
[0, 1, 0.44, 1.36],
[2.33, 0, 1, 0.47],
[1.21, 0.51, 0.35, 1]
])
x0 = 0.25*np.ones(Nx)
def dxdt(x):
return (r*x) * (1 - [email protected])
step = dpr.with_rk4(dxdt, autonom=True)
Tplot = 100
def d2x_dtdx(x):
return np.diag(r - r*(A@x)) - (r*x)[:, None]*A
def dstep_dx(x, t, dt):
return integrate_TLM(d2x_dtdx(x), dt, method='approx')
def LP_setup(jj): return LPs(jj, params=dict())
"""Demonstrate the Lorenz two-speed/scale/layer model."""
import numpy as np
from matplotlib import pyplot as plt
import dapper as dpr
from dapper.mods.LorenzUV.lorenz96 import LUV
from dapper.tools.utils import progbar
from dapper.tools.viz import setup_wrapping
nU, J = LUV.nU, LUV.J
dt = 0.005
K = int(4/dt)
step_1 = dpr.with_rk4(LUV.dxdt, autonom=True)
step_K = dpr.with_recursion(step_1, prog='Simulating')
xx = step_K(LUV.x0, K, np.nan, dt)
# Grab parts of state vector
ii, wrapU = setup_wrapping(nU)
jj, wrapV = setup_wrapping(nU*J)
# Animate linear
plt.figure()
lhU = plt.plot(ii, wrapU(xx[-1, :nU]), 'b', lw=3)[0]
lhV = plt.plot(jj/J, wrapV(xx[-1, nU:]), 'g', lw=2)[0]
for k in progbar(range(K), 'Plotting'):
lhU.set_ydata(wrapU(xx[k, :nU]))
lhV.set_ydata(wrapV(xx[k, nU:]))
def step(x0, t0, dt):
physical_step = with_rk4(LUV.dxdt_trunc, autonom=True)
ml_step = model_nn.predict
output = physical_step(
x0, t0, dt) + dt * ml_step(x0[..., np.newaxis]).squeeze()
return output
from dapper.mods.LorenzUV import model_instance
LUV = model_instance(nU=36, J=10, F=10)
nU = LUV.nU
################
# Full
################
t = dpr.Chronology(dt=0.005, dtObs=0.05, T=4**3, BurnIn=6)
Dyn = {
'M': LUV.M,
'model': dpr.with_rk4(LUV.dxdt, autonom=True),
'noise': 0,
'linear': LUV.dstep_dx,
}
X0 = dpr.GaussRV(mu=LUV.x0, C=0.01)
R = 1.0
jj = np.arange(nU)
Obs = dpr.partial_Id_Obs(LUV.M, jj)
Obs['noise'] = R
other = {'name': utils.rel2mods(__file__)+'_full'}
HMM_full = dpr.HiddenMarkovModel(Dyn, Obs, t, X0, **other)
vmax=vdelta)
ax[0].set_ylabel(labels[0])
ax[1].set_ylabel(labels[1])
ax[2].set_ylabel(labels[1][:2] + ' - ' + labels[0][:2])
for i in delta:
fig.colorbar(delta[i], cax=cax[i], orientation='vertical')
return fig, ax
def other():
print()
# trunc HMM (no param)
HMM_trunc = copy.deepcopy(HMM_trunc_dapper)
HMM_trunc.Dyn.model = with_rk4(LUV.dxdt_trunc, autonom=True)
import numpy as np
from dapper import ens_compatible, Id_mat, GaussRV, Operator
#TODO: allow list of index instead of maxind
class Observator:
"""This class handles sparse observations. It allows to create a dapper-compatible observation operators
"""
def __init__(self,
t,
m,
max_ind=None,
std_o=1,
p=None,