def LmodtestM(lam,i, p):
x0=np.array([56.,100.,760.,35.,9888.])
dx=np.array([5.6,10.,76.,3.5,988.8])
x0h=x0+lam*dx
dxlam=lam*dx
mxdx=DAm.nldalec(x0h,i)[1][i-1]
mx=DAm.nldalec(x0,i)[1][i-1]
M=DAm.ldalec(x0,i)[2]
Mdx=M*np.matrix(dxlam).T
if p=='all':
err=(np.linalg.norm(mxdx-mx))/(np.linalg.norm(Mdx))
else:
err=(np.linalg.norm(mxdx[p]-mx[p]))/(np.linalg.norm(Mdx[p]))
return err #(np.linalg.norm(mxdx))/(np.linalg.norm(Mdx)+np.linalg.norm(mx))
def d2J(X):
Mlist,GPP_diff=DAm.ldalec(X,lenrun)
nlhx=DAm.nldalec(X,lenrun)
X1=[X[0],X[1],X[2],X[3],X[4]]
X0=np.matrix(X1).T
#Figure out Hi's, y and y_err
H=[]
hx=[]
y=[]
y_err=[]
for x in range(lenrun):
temp=[]
temp2=[]
yi=[]
yi_err=[]
obs=False
if d.gpp[x]!=None:
temp.append([GPP_diff[x],0,0,0,0])
temp2.append(nlhx[x,0])
yi=np.append(yi,[d.gpp[x]])
yi_err=np.append(yi_err,[d.gpp_err[x]**2])
obs=True
if d.lf[x]!=None:
temp.append([d.p_5,0,0,0,0])
temp2.append(nlhx[x,1])
yi=np.append(yi,[d.lf[x]])
yi_err=np.append(yi_err,[d.lf_err[x]**2])
obs=True
if d.lw[x]!=None:
temp.append([0,0,d.p_6,0,0])
temp2.append(nlhx[x,2])
yi=np.append(yi,[d.lw[x]])
yi_err=np.append(yi_err,[d.lw_err[x]**2])
obs=True
if d.rt[x]!=None:
temp.append([d.p_2*GPP_diff[x],0,0,d.p_8*d.T[x],d.p_9*d.T[x]])
temp2.append(nlhx[x,3])
yi=np.append(yi,[d.rt[x]])
yi_err=np.append(yi_err,[d.rt_err[x]**2])
obs=True
if d.nee[x]!=None:
temp.append([-(1-d.p_2)*GPP_diff[x],0,0,-d.p_8*d.T[x],-d.p_9*d.T[x]])
temp2.append(nlhx[x,4])
yi=np.append(yi,[d.nee[x]])
yi_err=np.append(yi_err,[d.nee_err[x]**2])
obs=True
if obs==False:
temp.append([0,0,0,0,0])
temp2.append(0)
yi=np.append(yi,0)
yi_err=np.append(yi_err,0)
H.append(np.matrix(np.vstack(temp)))
hx.append(temp2)
y.append(yi)
y_err.append(yi_err)
#yhx=np.matrix((np.hstack(y)-np.hstack(hx))).T
#R=Rmat(np.hstack(y_err))
stacklist=[H[0]] #Creates H hat matrix
for x in xrange(1,lenrun):
stacklist.append(H[x]*Mfac(Mlist,x))
#Hhat=np.matrix(np.vstack(stacklist))
#d2J=B.I+Hhat.T*R.I*Hhat
#Incr=[np.matrix(Rmat(y_err[i])).I*yhx[i] for i in range(0,lenrun,1)]
d2jlist=[0]*lenrun
for i in range(lenrun):
if np.linalg.norm(y_err[i])!=0:
d2jlist[i]=stacklist[i].T*np.matrix(Rmat(y_err[i])).I*stacklist[i]
d2J=B.I+sum(d2jlist)
return d2J
def dJ(X):
Mlist,GPP_diff,M=DAm.ldalec(X,lenrun) #run linear model out list of linear model matrices and value for GPP derivative at each time step
nlhx=DAm.nldalec(X,lenrun)[0] #run nonlinear model for obs guess output
X1=[X[0],X[1],X[2],X[3],X[4]]
X0=np.matrix(X1).T
#Creates H_i's, y_i's and y_err_i's
H=[] #linear obs operator
hx=[] #h(x)
y=[] #obs
y_err=[] #obs error
for x in range(lenrun):
temp=[]
temp2=[]
yi=[]
yi_err=[]
obs=False
if d.gpp[x]!=None:
temp.append([GPP_diff[x],0,0,0,0])
temp2.append(nlhx[x,0])
yi=np.append(yi,[d.gpp[x]])
yi_err=np.append(yi_err,[d.gpp_err[x]**2])
obs=True
if d.lf[x]!=None:
temp.append([d.p_5,0,0,0,0])
temp2.append(nlhx[x,1])
yi=np.append(yi,[d.lf[x]])
yi_err=np.append(yi_err,[d.lf_err[x]**2])
obs=True
if d.lw[x]!=None:
temp.append([0,0,d.p_6,0,0])
temp2.append(nlhx[x,2])
yi=np.append(yi,[d.lw[x]])
yi_err=np.append(yi_err,[d.lw_err[x]**2])
obs=True
if d.rt[x]!=None:
temp.append([d.p_2*GPP_diff[x],0,0,d.p_8*d.T[x],d.p_9*d.T[x]])
temp2.append(nlhx[x,3])
yi=np.append(yi,[d.rt[x]])
yi_err=np.append(yi_err,[d.rt_err[x]**2])
obs=True
if d.nee[x]!=None:
temp.append([-(1-d.p_2)*GPP_diff[x],0,0,-d.p_8*d.T[x],-d.p_9*d.T[x]])
temp2.append(nlhx[x,4])
yi=np.append(yi,[d.nee[x]])
yi_err=np.append(yi_err,[d.nee_err[x]**2])
obs=True
if d.cf[x]!=None:
temp.append([1,0,0,0,0])
temp2.append(nlhx[x,5])
yi=np.append(yi,[d.cf[x]])
yi_err=np.append(yi_err,[d.cf_err[x]**2])
obs=True
if obs==False:
temp.append([0,0,0,0,0])
temp2.append(0)
yi=np.append(yi,0)
yi_err=np.append(yi_err,0)
H.append(np.matrix(np.vstack(temp)))
hx.append(np.matrix(temp2))
y.append(np.matrix(yi))
y_err.append((yi_err))
yhx=[y[i].T-hx[i].T for i in range(len(y))] #Create y-h(x) incriment
#stacklist1=[H[0]] #Creates H hat matrix
#for x in xrange(1,len(y)):
# stacklist1.append(H[x]*Mfac(Mlist,x))
stacklist2=[H[0].T] #creats M^T*H^T for each time step
for x in xrange(1,len(y)):
stacklist2.append(MfacAdj(Mlist,x)*H[x].T)
#Incr=[stacklist2[i]*np.matrix(Rmat(y_err[i])).I*yhx[i] for i in range(len(y))] #Creates obs incriment
Incr=[]
for i in range(lenrun):
if np.linalg.norm(y_err[i])!=0:
Incr.append(stacklist2[i]*np.matrix(Rmat(y_err[i])).I*yhx[i])
dJ=B.I*(X0-XB) -np.sum(Incr, axis=0) #Cost function first derivative
dJlist=[float(dJ[0]),float(dJ[1]),float(dJ[2]),float(dJ[3]),float(dJ[4])]
return dJ.T #np.array(dJlist)
def Adjtest(i):
Mlist,gppdiff=DAm.ldalec(x0,i)
M=DAC3.Mfac(Mlist,i)
MT=DAC3.MfacAdj(Mlist,i)
t=M*np.matrix(dx).T
return t.T*t, np.matrix(dx)*MT*t
