def fit_and_plot(cand):
data = cand.profile
n = len(data)
xs = np.linspace(0.0, 1.0, n, endpoint=False)
G = gauss._compute_data(cand)
print "k: %g, log(k): %g" % (G.k, np.log10(G.k))
test_ks = np.logspace(np.log10(G.k)-2, np.log10(G.k)+1, 1e3)
#test_ks = np.exp(np.linspace(np.log(1e-1),np.log(1e3),1e3))
plt.figure(1)
resids = [gauss._rms_residual(k,data) for k in test_ks]
plt.loglog(test_ks,resids,color="green", label="_nolabel_")
#plt.axvline(true_k,color="red", label="true k")
best_k = test_ks[np.argmin(resids)]
plt.axvline(best_k,color="green", label="best k")
plt.axvline(G.k,color="cyan", label="k from fit")
plt.ylabel("RMS of residuals")
plt.xlabel("Value of k used (i.e. held fixed) when fitting")
plt.legend(loc="best")
plt.figure(2)
mue, ae, be = gauss._fit_all_but_k(best_k, data)
#plt.plot(xs, true_prof, color="red", label="true")
plt.plot(xs, data, color="black", label="data")
plt.plot(xs, (ae*utils.vonmises_histogram(best_k,mue,n)+be), color="green", label="exhaustive best fit")
plt.plot(xs, G.histogram(n), color="cyan", label="best fit")
plt.legend(loc="best")
plt.show()
def fake_profile(cand):
# Modify profile data and remove existing gaussian fit
print "create fake profile to fit"
true_k = 8
n = 128
s = 10
a = 10
mu = 0.1
k2 = 30
a2 = 10
mu2 = 0.5
true_prof = a*utils.vonmises_histogram(true_k,mu,n) + a2*utils.vonmises_histogram(k2,mu2,n)
data = true_prof + s*np.random.randn(n)
import copy
modcand = copy.deepcopy(cand)
modcand.profile = data
del modcand.gaussfit
return modcand
def _fit_all_but_k(cls, k, data):
n = len(data)
fft = np.fft.rfft(data)
nup = 16*n
corr = np.fft.irfft(fft*utils.vonmises_coefficient(k, np.arange(len(fft))), nup)
mu = np.argmax(corr)/float(nup)
x = utils.vonmises_histogram(k, mu, n)
data = data - np.mean(data)
x = x - np.mean(x)
a = np.dot(data, x)/np.dot(x, x)
b = np.mean(data) - a*np.mean(x)
return mu, a, b
def _fit_all_but_k(cls, k, data):
n = len(data)
fft = np.fft.rfft(data)
nup = 16 * n
corr = np.fft.irfft(
fft * utils.vonmises_coefficient(k, np.arange(len(fft))), nup)
mu = np.argmax(corr) / float(nup)
x = utils.vonmises_histogram(k, mu, n)
data = data - np.mean(data)
x = x - np.mean(x)
a = np.dot(data, x) / np.dot(x, x)
b = np.mean(data) - a * np.mean(x)
return mu, a, b
def _rms_residual(cls, k, data):
n = len(data)
mu, a, b = cls._fit_all_but_k(k, data)
return np.sqrt(
np.mean((data - (a * utils.vonmises_histogram(k, mu, n) + b))**2))
def histogram(self, n):
return self.a * utils.vonmises_histogram(self.k, self.mu, n) + self.b
def histogram(self, n):
return self.a*utils.vonmises_histogram(self.k, self.mu, n) + self.b
def _rms_residual(cls, k, data):
n = len(data)
mu, a, b = cls._fit_all_but_k(k, data)
return np.sqrt(np.mean((data-(a*utils.vonmises_histogram(k,mu,n)+b))**2))