def monteCarloError(self, xdata=None, monteCarlo=None):
"""
Calculates :math:\sigma:math:-confidence regions on the model given some inputs.
From the full covariance matrix (inverse of the Hessian) random
samples are drawn, which are added to the parameters. With this new
set of parameters the model is calculated. This procedure is done
by default, 25 times.
The standard deviation of the models is returned as the error bar.
The calculation of the confidence region is delegated to the class
MonteCarlo. For tweaking of that class can be done outside BaseFitter.
Parameters
----------
xdata : array_like
input data over which to calculate the error bars.
monteCarlo : MonteCarlo
a ready-made MonteCarlo class.
"""
if xdata is None: xdata = self.xdata
if monteCarlo is None:
monteCarlo = MonteCarlo(xdata,
self.model,
self.covariance,
index=self.fitIndex)
return monteCarlo.getError(xdata)
def testMonteCarlo3(self, doplot=False):
print("====== MonteCarlo 3 ===================")
N = 101
x = numpy.arange(N, dtype=float) * 0.1
ran = numpy.random
ran.seed(1235)
noise = ran.standard_normal(N)
ym = x * x + 0.03 * x + 0.05
y1 = ym + 10 * noise
pm = PolynomialModel(2)
ftr = Fitter(x, pm)
pars1 = ftr.fit(y1)
stdv1 = ftr.getStandardDeviations()
print("parameters : ", pars1)
print("std devs : ", stdv1)
print("chisquared : ", ftr.chisq)
lmce = ftr.monteCarloError()
chisq = ftr.chisq
mce = MonteCarlo(x, pm, ftr.covariance)
mce1 = mce.getError()
assertAAE(lmce, mce1)
yfit = pm.result(x)
s2 = numpy.sum(numpy.square((yfit - ym) / lmce))
print(s2, math.sqrt(s2 / N))
integral = numpy.sum(yfit)
s1 = 0
s2 = 0
k = 0
for k in range(1, 100001):
rv = mce.randomVariant(x)
s1 += numpy.sum(rv)
s2 += numpy.sum(numpy.square(rv - yfit))
if k % 10000 == 0:
print("%6d %10.3f %10.3f %10.3f" %
(k, integral, s1 / k, math.sqrt(s2 / k)))
### TBC dont know why the factor 1000 is there. ########
print(abs(integral - s1 / k), math.sqrt(s2 / (k * 1000)))
self.assertTrue(abs(integral - s1 / k) < math.sqrt(s2 / (k * 1000)))
if doplot:
pyplot.plot(x, y1, 'b.')
pyplot.plot(x, ym, 'k-')
pyplot.plot(x, yfit, 'g-')
pyplot.plot(x, yfit + lmce, 'r-')
pyplot.plot(x, yfit - lmce, 'r-')
pyplot.show()
