"""Estimtate the Lyapunov spectrum using an ensemble of perturbations."""
# An old version using explicit TLMs can be found in EmblAUS/Lyap_L{63,96}.
import numpy as np
import scipy.linalg as sla
from matplotlib import pyplot as plt
from mpl_tools.fig_layout import freshfig
from numpy.random import randn
import dapper.tools.series as series
import dapper.tools.viz as viz
from dapper.mods import set_seed, with_recursion, with_rk4
from dapper.tools.progressbar import progbar
set_seed(3000)
########################
# Model selection
########################
mod = "L05"
# Lyapunov exponents: [ 1.05 0. -0.01 -1.05]
if mod == "DP":
from dapper.mods.DoublePendulum import step, x0
T = 5e2
dt = 0.005
eps = 0.0002
Nx = len(x0)
N = Nx
"""Prettier, static illustration of Lorenz two-speed/scale/layer model."""
# Sorry for the mess.
if __name__ == "__main__":
import matplotlib as mpl
import numpy as np
from matplotlib import pyplot as plt
import dapper.mods as modelling
from dapper.mods.LorenzUV.lorenz96 import LUV
# Setup
sd0 = modelling.set_seed(4)
# from dapper.mods.LorenzUV.wilks05 import LUV
nU, J = LUV.nU, LUV.J
dt = 0.005
t0 = np.nan
K = int(10/dt)
step_1 = modelling.with_rk4(LUV.dxdt, autonom=True)
step_K = modelling.with_recursion(step_1, prog=1)
x0 = 0.01*np.random.randn(LUV.M)
x0 = step_K(x0, int(2/dt), t0, dt)[-1] # BurnIn
xx = step_K(x0, K, t0, dt)
# Grab parts of state vector
ii = np.arange(nU+1)
jj = np.arange(nU*J+1)
circU = np.mod(ii, nU)
# mpl.rcParams['toolbar'] = 'None'
###########################
# Setup
###########################
PRMS = 'Lorenz'
if PRMS == 'Wilks':
from dapper.mods.LorenzUV.wilks05 import LUV
else:
from dapper.mods.LorenzUV.lorenz96 import LUV
nU = LUV.nU
K = 400
dt = 0.005
t0 = np.nan
modelling.set_seed(30) # 3 5 7 13 15 30
x0 = np.random.randn(LUV.M)
true_step = with_rk4(LUV.dxdt, autonom=True)
model_step = with_rk4(LUV.dxdt_trunc, autonom=True)
true_K = with_recursion(true_step, prog=1)
###########################
# Compute truth trajectory
###########################
x0 = true_K(x0, int(2 / dt), t0, dt)[-1] # BurnIn
xx = true_K(x0, K, t0, dt)
###########################
# Compute unresovled scales
###########################