for i in range(N+1):
Jac[i,i] = 1.
#print 'J is', Jac
#Jac0 = np.copy(Jac) #** ALT AT 26/03 - ADDING THIS VARIABLE TO ALL Jac CALCULATIONS**
dsdx = np.zeros([DM,N+1])
dxds = np.zeros([N+1,DM])
## Running from 0 to 10
for w in range(10):
random = np.zeros(N+1)
#random = np.random.randn(N+1)
x[:,w+1] = mod.lorenz96(x[:,w],random,dt)
dfdx = mod.df(x[:,w])
#######Jac = Jac + dt*(np.dot(dfdx,Jac))
Jac = Jac*(np.exp(dt*dfdx))
print 'Initial Jacs', Jac
##print 'x10 is', x[:,10]
# Main loop
mcn = 0
summation = np.zeros(N+1)
run = 500
count = 1
integ = DM*ns
differ = np.zeros(DM)
scount = 0
x[:, 10] = x[:, 0]
##for t in range(10, run):
for t in range(run):
S[0] = np.transpose(np.dot(H, x[:, t]))
Y[0] = y[:, t]
dsdx[0, :] = H
Jac = Jac0
for n in range(2, DM + 1):
for i in range(1, ns + 1):
tt = t + (i - 1 + (n - 1) * ns)
#random = np.zeros(N)
x[:, tt + 1] = mod.lorenz96(x[:, tt], random, dt)
####f = mod.l95(x[:,tt],dt)
dfdx = mod.df(x[:, tt])
#print 'dfdx', dfdx
Jac = np.dot(dfdx, Jac)
idxs = MO * (n - 2) + MO
S[idxs] = np.transpose(np.dot(H, x[:, tt + 1]))
idxy = t + (n - 1) * ns
Y[idxs] = y[:, idxy]
dsdx[idxs, :] = Jac[0, :]
dxds = np.linalg.pinv(dsdx)
########dxds = np.linalg.pinv(dsdx,rcond=2.22e-16)
dif = Y - S
##for t in range(10, run):
for t in range(run):
####if (t == tobs[mcn]):
if (t == 10):
##ldelay = integ + t
####print 'Initial x10 is', x[:,10]
####print 'Initial dsdx', dsdx
ldelay = integ + mcn*ns
####print 'ldelay', ldelay
for m in range(t,ldelay+1): ## ldelay + 1 really needed or only ldelay is enough? ##
if m == t:
random = np.zeros(N+1)
x[:,m+1] = mod.lorenz96(x[:,m],random,dt)
####print 'Jac', Jac[0,:]
dsdx[scount,:] = Jac[0,:]
dfdx = mod.df(x[:,m])
Jac = Jac + dt*(np.dot(dfdx,Jac))
########Jac = Jac*(np.exp(dt*dfdx))
####print 'Second dsdx', dsdx
scount = scount + 1
else:
random = np.zeros(N+1)
#random = np.random.randn(N+1)
x[:,m+1] = mod.lorenz96(x[:,m],random,dt)
#print 'x is', x[:,m+1]
dfdx = mod.df(x[:,m])
Jac = Jac + dt*(np.dot(dfdx,Jac)) ## SEE IF Jac SHOULD BE FROM TIME 9 TO 10 ##
######Jac = Jac*(np.exp(dt*dfdx))
Jaclast = Jac
newcount = (count+1)*ns
if (m+1 == newcount):
for m in range(2, M + 1):
for i in range(1, int(nTau) + 1):
tt = t + dt * (i - 1 + (m - 1) * nTau)
##Jacsize = D**2
##Jacv = Jac.reshape(Jacsize) # creates an array (Jacsize,)
##Jacvec = Jacv.reshape(Jacsize,1) # creates an array (Jacsize,1)
##dxdt = mod.dxdt(xx,Jacvec,D,dt)
##xtran = mod.rk4(dxdt,dt)
##xx = xtran[0:D]
##print 'n=', n, 'xx at m', m, 'is', xx
##Jact = xtran[D:]
##Jac = Jact.reshape(D,D)
dfdx = mod.df(xx)
random = np.zeros(D)
xx = mod.lorenz96(xx, random, dt)
Jac = Jac + dt * (np.dot(dfdx, Jac))
#print 'xx at m', m, 'is', xx
#dfdx = mod.df(xx)
#print 'dfdx', dfdx
#print 'n=', n, 'xx at m', m, 'is', xx
#####Jac = np.dot(dfdx,Jac)
#print 'Jac', Jac
#########Jacsize = D**2
#########Jacv = Jac.reshape(Jacsize)
#########Jacvec = Jacv.reshape(Jacsize,1)
#########f,Jac = mod.dxdt(xx,Jacvec,D,dt)
#f = dxdt[0:D]
for m in range(2,M+1):
for i in range(1,int(nTau)+1):
tt = t + dt*(i-1+(m-1)*nTau)
##Jacsize = D**2
##Jacv = Jac.reshape(Jacsize) # creates an array (Jacsize,)
##Jacvec = Jacv.reshape(Jacsize,1) # creates an array (Jacsize,1)
##dxdt = mod.dxdt(xx,Jacvec,D,dt)
##xtran = mod.rk4(dxdt,dt)
##xx = xtran[0:D]
##print 'n=', n, 'xx at m', m, 'is', xx
##Jact = xtran[D:]
##Jac = Jact.reshape(D,D)
dfdx = mod.df(xx)
random = np.zeros(D)
xx = mod.lorenz96(xx,random,dt)
Jac = Jac + dt*(np.dot(dfdx,Jac))
#print 'xx at m', m, 'is', xx
#dfdx = mod.df(xx)
#print 'dfdx', dfdx
#print 'n=', n, 'xx at m', m, 'is', xx
#####Jac = np.dot(dfdx,Jac)
#print 'Jac', Jac
#########Jacsize = D**2
#########Jacv = Jac.reshape(Jacsize)
#########Jacvec = Jacv.reshape(Jacsize,1)
#########f,Jac = mod.dxdt(xx,Jacvec,D,dt)
#f = dxdt[0:D]
#####if m == t:
##### random = np.zeros(N+1)
##### x[:,m+1] = mod.lorenz96(x[:,m],random,dt)
##### dsdx[scount,:] = Jac[0,:]
##### dfdx = mod.df(x[:,m])
##### Jac = Jac + dt*(np.dot(dfdx,Jac))
##### scount = scount + 1
#####else:
random = np.zeros(N)
#random = np.random.randn(N+1)
x[:,m+1] = mod.lorenz96(x[:,m],random,dt)
#print 'x size', x[:,m].shape
dfdx = mod.df(x[:,m])
Jacvec = Jac.reshape(jacsize)
#print 'Jacvec size', Jacvec.shape
randJ = np.zeros(jacsize)
Jacstep = mod.lorenz96(Jacvec,randJ,dt)
Jac = Jacstep.reshape(N,N)
#print 'Jac is', Jac
######Jac = Jac + dt*(np.dot(dfdx,Jac))
#####Jac = Jac*(np.exp(dt*dfdx))
#Jaclast = Jac
newcount = (count+1)*ns
if (m+1 == newcount):
dsdx[scount,:] = Jac[0,:]
scount = scount + 1
dxds = np.zeros([N + 1, DM])
count = 0
# Running x with pure Lorenz to calculate the initial S
integ = DM * ns
for t in range(integ + 1):
#random = np.random.randn(N+1)
# Taking off randomness from the model (deterministic in the article) ***** PJ - 19/03 *****
random = np.zeros(N + 1)
x[:, t + 1] = mod.lorenz96(x[:, t], random, dt)
#print 'x at', t, 'is', x[:,t+1]
# Calculating dF/dx, J, dS/dx for the first 100 steps
dfdx = mod.df(
x[:, t]
) # CORRECTION MADE:1st dfdx to be calculated shall be from x[:0] ** Me - 22/04**
#print 'dfdx', dfdx
Jac = Jac + dt * (np.dot(dfdx, Jac))
#print 'Jac is', Jac
if (t == tobs[count]):
#for a in range(DM):
dsdx[count, :] = Jac[0, :]
count = count + 1
#print 'Initial dsdx is', dsdx
# Calculating initial dx/dS (10-100)
#dxds = np.linalg.pinv(dsdx,rcond=1e-16)
dxds = np.linalg.pinv(
dsdx
) #### CHECK IF THE COMPLETE CALCULATION WILL BE NEEDED!!!!!!!!########
x[:,10] = x[:,0]
##for t in range(10, run):
for t in range(run):
S[0] = np.transpose(np.dot(H,x[:,t]))
Y[0] = y[:,t]
dsdx[0,:] = H
Jac = Jac0
for n in range(2,DM+1):
for i in range(1,ns+1):
tt = t + (i-1+(n-1)*ns)
#random = np.zeros(N)
x[:,tt+1] = mod.lorenz96(x[:,tt],random,dt)
####f = mod.l95(x[:,tt],dt)
dfdx = mod.df(x[:,tt])
#print 'dfdx', dfdx
Jac = np.dot(dfdx,Jac)
idxs = MO*(n-2) + MO
S[idxs] = np.transpose(np.dot(H,x[:,tt+1]))
idxy = t + (n-1)*ns
Y[idxs] = y[:,idxy]
dsdx[idxs,:] = Jac[0,:]
dxds = np.linalg.pinv(dsdx)
########dxds = np.linalg.pinv(dsdx,rcond=2.22e-16)
dif = Y - S
#####if m == t:
##### random = np.zeros(N+1)
##### x[:,m+1] = mod.lorenz96(x[:,m],random,dt)
##### dsdx[scount,:] = Jac[0,:]
##### dfdx = mod.df(x[:,m])
##### Jac = Jac + dt*(np.dot(dfdx,Jac))
##### scount = scount + 1
#####else:
random = np.zeros(N)
#random = np.random.randn(N+1)
x[:, m + 1] = mod.lorenz96(x[:, m], random, dt)
#print 'x size', x[:,m].shape
dfdx = mod.df(x[:, m])
Jacvec = Jac.reshape(jacsize)
#print 'Jacvec size', Jacvec.shape
randJ = np.zeros(jacsize)
Jacstep = mod.lorenz96(Jacvec, randJ, dt)
Jac = Jacstep.reshape(N, N)
#print 'Jac is', Jac
######Jac = Jac + dt*(np.dot(dfdx,Jac))
#####Jac = Jac*(np.exp(dt*dfdx))
#Jaclast = Jac
newcount = (count + 1) * ns
if (m + 1 == newcount):
dsdx[scount, :] = Jac[0, :]
scount = scount + 1
dxds = np.zeros([N+1,DM])
count = 0
# Running x with pure Lorenz to calculate the initial S
integ = DM*ns
for t in range(integ+1):
#random = np.random.randn(N+1)
# Taking off randomness from the model (deterministic in the article) ***** PJ - 19/03 *****
random = np.zeros(N+1)
x[:,t+1] = mod.lorenz96(x[:,t],random,dt)
#print 'x at', t, 'is', x[:,t+1]
# Calculating dF/dx, J, dS/dx for the first 100 steps
dfdx = mod.df(x[:,t]) # CORRECTION MADE:1st dfdx to be calculated shall be from x[:0] ** Me - 22/04**
#print 'dfdx', dfdx
Jac = Jac + dt*(np.dot(dfdx,Jac))
#print 'Jac is', Jac
if (t == tobs[count]):
#for a in range(DM):
dsdx [count,:] = Jac[0,:]
count = count + 1
#print 'Initial dsdx is', dsdx
# Calculating initial dx/dS (10-100)
#dxds = np.linalg.pinv(dsdx,rcond=1e-16)
dxds = np.linalg.pinv(dsdx) #### CHECK IF THE COMPLETE CALCULATION WILL BE NEEDED!!!!!!!!########
#print 'dxds', dxds
# Y and S
