def chisquare(dist, fit_result, data, bins=None, range=None):
"""
Perform a Chi^2 test for goodness of fit.
Tests the H0 hypothesis if the distances between fit result and
data are compatible with random fluctuations.
Args:
dist: A mle.Distribution instance
fit_result: The solution dict, returned by the Distribution.fit method
data: The data used in Distribution.fit
bins: Number of bins for the histogram (default: 1+log2(N))
range: Range for the histogram (default: min(data), max(data))
Returns:
chisquare: the test statistic, chi^2/ndf
p-value: the p-value, probability that differences between dist
and data are compatible with random fluctuation
"""
variables = dist.get_vars()
if len(variables) > 1:
raise ValueError("This is a 1d only chisquare test")
var = variables[0]
# rule of thumb for number if bins if not provided
if bins is None:
bins = _np.ceil(2*len(data[var.name])**(1.0/3.0))
entries, edges = _np.histogram(data[var.name], bins=bins, range=range)
# get expected frequencies from the cdf
cdf = dist.cdf(edges, **fit_result["x"])
exp_entries = _np.round(len(data[var.name]) * (cdf[1:] - cdf[:-1]))
# use only bins where more then 4 entries are expected
mask = exp_entries >= 5
chisq, pvalue = _chisquare(entries[mask],
exp_entries[mask],
ddof=len(fit_result["x"])
)
chisq = chisq/(_np.sum(mask) - len(fit_result["x"]) - 1)
return chisq, pvalue
def calculatePeakDisplacements(intensityProfiles, peakFitSettings, progressReporter = None, pInitial = None, **curveFitKwargs):
"""
Fits an ODM FitFunction to the target Series of intensity profiles.
Parameters
----------
intensityProfiles : pandas.Series of 1D numpy.ndarray
A series of intensityProfiles that will be curve fit
peakFitSettings : ODAFitSettings instance
The curve fit settings to use for curve fitting
progressReporter : ProgressReporter instance
The ProgressReporter to use for displaying progress information.
A StdOutProgressReporter is used by default.
curveFitKwargs : Keyword arguments that will be passed to the curve_fit
function (scipy.optimization).
Returns
-------
A dataframe with the calculated displacements that has the same index as the input
intensity profile Series.
"""
if not progressReporter:
progressReporter = _StdOutProgressReporter()
fitFunction = peakFitSettings.fitFunction
index=intensityProfiles.index
if pInitial is not None:
p0 = pInitial
else:
templateProfile = peakFitSettings.referenceIntensityProfile if peakFitSettings.referenceIntensityProfile is not None else intensityProfiles.iloc[0]
estimatesDict = fitFunction.estimateInitialParameters(templateProfile, **peakFitSettings.estimatorValuesDict)
p0 = estimatesDict.values()
xmin = peakFitSettings.xminBound
xmax = peakFitSettings.xmaxBound
xdata = _np.arange(len(intensityProfiles.iloc[0]))[xmin:xmax]
progress = 0.0
total = len(index)
curveFitResults = total*[None]
for i in range(total):
ydata = intensityProfiles.iloc[i][xmin:xmax]
popt,pcov = _curve_fit(fitFunction,\
xdata = xdata,\
ydata = ydata,\
p0 = p0,**curveFitKwargs)
p0 = popt
curveFitResult = {}
curveFitResult['popt'] = popt
curveFitResult['pcov'] = pcov
curveFitResult['chiSquare'] = _chisquare(ydata,fitFunction(xdata,*popt))[0]
curveFitResult['curveFitResult'] = attrdict.AttrDict(curveFitResult)
curveFitResult['displacement'] = fitFunction.getDisplacement(*popt)
curveFitResults[i] = curveFitResult
progress += 1
progressReporter.progress(progress / total * 100)
df = _pd.DataFrame(index=index,data=curveFitResults)
progressReporter.done()
return df
