def FDCheckH(self):
""" Finite-difference checker for the objective function Hessian.
For each element in the Hessian, use a five-point stencil in both
parameter indices to compute a finite-difference derivative, and
compare it to the analytic result.
This is meant to be a foolproof checker, so it is pretty slow. We
could write a faster checker if we assumed we had accurate first
derivatives, but it's better to not make that assumption.
The second derivative is computed by double-wrapping the objective
function via the 'wrap2' function.
"""
Adata = self.Objective.Full(self.mvals0,Order=2)['H']
Fdata = np.zeros((self.FF.np,self.FF.np),dtype=float)
printcool("Checking second derivatives by finite difference!\n%-8s%-20s%-20s%13s%13s%13s%13s" \
% ("Index", "Parameter1 ID", "Parameter2 ID", "Analytic","Numerical","Difference","Fractional"),bold=1,color=5)
# Whee, our double-wrapped finite difference second derivative!
def wrap2(mvals0,pidxi,pidxj):
def func1(arg):
mvals = list(mvals0)
mvals[pidxj] += arg
return f1d5p(fdwrap(self.Objective.Full,mvals,pidxi,'X',Order=0),self.h)
return func1
for i in range(self.FF.np):
for j in range(i,self.FF.np):
Fdata[i,j] = f1d5p(wrap2(self.mvals0,i,j),self.h)
Denom = max(abs(Adata[i,j]),abs(Fdata[i,j]))
Denom = Denom > 1e-8 and Denom or 1e-8
D = Adata[i,j] - Fdata[i,j]
Q = (Adata[i,j] - Fdata[i,j])/Denom
cD = abs(D) > 0.5 and "\x1b[1;91m" or (abs(D) > 1e-2 and "\x1b[91m" or (abs(D) > 1e-5 and "\x1b[93m" or "\x1b[92m"))
cQ = abs(Q) > 0.5 and "\x1b[1;91m" or (abs(Q) > 1e-2 and "\x1b[91m" or (abs(Q) > 1e-5 and "\x1b[93m" or "\x1b[92m"))
print "\r %-8i%-20s%-20s% 13.4e% 13.4e%s% 13.4e%s% 13.4e\x1b[0m" \
% (i, self.FF.plist[i][:20], self.FF.plist[j][:20], Adata[i,j], Fdata[i,j], cD, D, cQ, Q)
def func1(arg):
mvals = list(mvals0)
mvals[pidxj] += arg
return f1d5p(fdwrap(self.Objective.Full,mvals,pidxi,'X',Order=0),self.h)