dapper.mods.Lorenz96.extras
Extra functionality (not necessary for the EnKF or the particle filter).
1"""Extra functionality (not necessary for the EnKF or the particle filter).""" 2 3import numpy as np 4 5import dapper.tools.liveplotting as LP 6from dapper.mods.integration import integrate_TLM 7 8 9def d2x_dtdx(x): 10 """Tangent linear model (TLM). I.e. the Jacobian of dxdt(x).""" 11 M = len(x) 12 F = np.zeros((M, M)) 13 14 def md(i): 15 return np.mod(i, M) # modulo 16 17 for i in range(M): 18 F[i, i] = -1.0 19 F[i, i - 2] = -x[i - 1] 20 F[i, md(i + 1)] = +x[i - 1] 21 F[i, i - 1] = x[md(i + 1)] - x[i - 2] 22 23 return F 24 25 26# dstep_dx = FD_Jac(step) 27def dstep_dx(x, t, dt): 28 """Compute resolvent (propagator) of the TLM. I.e. the Jacobian of `step(x)`.""" 29 # For L96, method='analytic' >> 'approx' 30 return integrate_TLM(d2x_dtdx(x), dt, method="analytic") 31 32 33# Add some non-default liveplotters 34def LPs(jj=None): 35 return [ 36 (1, LP.spatial1d(jj)), 37 (1, LP.correlations), 38 (0, LP.spectral_errors), 39 (0, LP.phase_particles(True, jj)), 40 (0, LP.sliding_marginals(jj)), 41 ]
def
d2x_dtdx(x):
10def d2x_dtdx(x): 11 """Tangent linear model (TLM). I.e. the Jacobian of dxdt(x).""" 12 M = len(x) 13 F = np.zeros((M, M)) 14 15 def md(i): 16 return np.mod(i, M) # modulo 17 18 for i in range(M): 19 F[i, i] = -1.0 20 F[i, i - 2] = -x[i - 1] 21 F[i, md(i + 1)] = +x[i - 1] 22 F[i, i - 1] = x[md(i + 1)] - x[i - 2] 23 24 return F
Tangent linear model (TLM). I.e. the Jacobian of dxdt(x).
def
dstep_dx(x, t, dt):
28def dstep_dx(x, t, dt): 29 """Compute resolvent (propagator) of the TLM. I.e. the Jacobian of `step(x)`.""" 30 # For L96, method='analytic' >> 'approx' 31 return integrate_TLM(d2x_dtdx(x), dt, method="analytic")
Compute resolvent (propagator) of the TLM. I.e. the Jacobian of step(x).
def
LPs(jj=None):