def bsVolFitting():
nopts = 11
xs= [90.0,92.0,94.0,96.0,98.0,100.0,102.0,104.0,106.0,108.0,110.0]
nxs = np.array(xs)
f = 100.0
ws= list(map(lambda x: Utils.dnorm(log(x/f)*10.0), xs))
nws = np.array(ws)
t = 0.5
xss = map(lambda x: [f,x,t], xs)
a = 0.3
a0 = 0.1
b = 1.0
r = -0.45
r0=0.05
vv = 2.3
vv0 = 1.0
ts= list(map(lambda x: lsig(f, x, t, a, b, r, vv), xs))
nts = np.array(ts)
inc = 0.0001
b0 = [r0,vv0]
b1up = [r0+inc,vv0]
b1dn = [r0-inc,vv0]
b2up = [r0,vv0+inc]
b2dn = [r0,vv0-inc]
atmsig = Fitter.cubic(nxs, nts, f)
def err(r, vv, x, y):
alpha = alphaFromRhoV1(f, t, atmsig*f, r, vv)
return lsig(f, x, t, alpha, b, r, vv) - y
def derr(r,vv,x,y):
dr=adnumber(r)
dvv=adnumber(vv)
return np.array([err(dr,vv,x,y).d(dr), err(r,dvv,x,y).d(dvv)])
def sumerrs(ps):
return sum(map(lambda x, y, w: w*err(ps[0], ps[1], x, y)**2.0, nxs, nts, nws))
def dsumerrs(ps):
dr = adnumber(ps[0])
dvv = adnumber(ps[1])
return np.array([sumerrs([dr, ps[1]]).d(dr), sumerrs([ps[0], dvv]).d(dvv)])
res = minimize(sumerrs, [-0.1,2.0], tol = 0.0000001, jac=dsumerrs, bounds=[(-1.0,1.0), (0.0,10.0)], method='SLSQP', options={'disp': True})
rout = res.x[0]
vvout = res.x[1]
alphaout = alpha = alphaFromRhoV1(f, t, atmsig*f, rout, vvout)
print('xs = ' + str(nxs))
print('ts = ' + str(nts))
fits = list(map(lambda x, y: lsig(f, x, t, alphaout, b, rout, vvout) , nxs, nts))
print('fit = ' + str(fits))
print('errs(fit) = ' + str(sumerrs([rout, vvout])))
print('errs(act) = ' + str(sumerrs([r,vv])))
plt.plot(xs, fits,xs,ts)
plt.title('Least-squares fit to noisy data')
plt.legend(['Fit', 'Actual'])
plt.show()
return res
def nput(f, x, v, r, t):
if (v <= 0.0) or (t <= 0.0):
vrt = 1e-5
else:
vrt = v * pow(t, 0.5)
return exp(-r * t) * ((x - f) * Utils.pnorm((x - f) / vrt) + vrt * Utils.dnorm((x - f) / vrt))
