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Peak Functions¶

The Peak function type, IPeakFunction, is a specialized kind of 1D function. It is used when, for the given function, approximate values of height, fwhm & peak centre can be determined from the function parameters. Their main use is to improve the choosing of starting values for these types of function from the GUI.

The function calculation also only occurs around a given peak radius (defined in Settings->Fitting->CurveFitting menu). Any function values outside this radius are automatically zeroed. The best description here is to walk through defining an example. Here will implement a Gaussian (called PyGaussian so as not interfere with Mantid’s Gaussian).

Parameters & Attributes¶

The parameters & attributes are defined in exactly the same manner as for the IFunction1D case:

from mantid.api import *
import math
import numpy as np

class PyGaussian(IPeakFunction):

    def init(self):
        self.declareParameter("Height")
        self.declareParameter("PeakCentre")
        self.declareParameter("Sigma")
        # We don't use any attributes in this example

FunctionFactory.subscribe(PyGaussian) # Registration is identical

Evaluating the Function & Derivative¶

Function evaluation proceeds in a similar manner to IFunction1D with the exception that the method is now called functionLocal. Python PeakFunctions can also provide an analytical derivative by defining a functionDerivLocal method. This is optional and default is to be calculated numerical derivatives:

def functionLocal(self, xvals):
    height = self.getParameterValue("Height")
    peak_centre = self.getParameterValue("PeakCentre")
    sigma = self.getParameterValue("Sigma")
    weight = math.pow(1./sigma,2)

    offset_sq=np.square(xvals-peak_centre)
    out=height*np.exp(-0.5*offset_sq*weight)
    return out

# the following method is optional
def functionDerivLocal(self, xvals, jacobian):
    height = self.getParameterValue("Height")
    peak_centre = self.getParameterValue("PeakCentre")
    sigma = self.getParameterValue("Sigma")
    weight = math.pow(1./sigma, 2)

    # X index
    i = 0
    for x in xvals:
        diff = x-peak_centre
        exp_term = math.exp(-0.5*diff*diff*weight)
        jacobian.set(i, 0, exp_term)
        jacobian.set(i, 1, diff*height*exp_term*weight)
        # derivative with respect to weight not sigma
        jacobian.set(i, 2, -0.5*diff*diff*height*exp_term)
        i += 1