Finding the full width half maximum of a peak

Question

I have been trying to figure out the full width half maximum (FWHM) of the the blue peak (see image). The green peak and the magenta peak combined make up the blue peak. I h

Answer 1

Here is a nice little function using the spline approach.

from scipy.interpolate import splrep, sproot, splev

class MultiplePeaks(Exception): pass
class NoPeaksFound(Exception): pass

def fwhm(x, y, k=10):
    """
    Determine full-with-half-maximum of a peaked set of points, x and y.

    Assumes that there is only one peak present in the datasset.  The function
    uses a spline interpolation of order k.
    """

    half_max = amax(y)/2.0
    s = splrep(x, y - half_max, k=k)
    roots = sproot(s)

    if len(roots) > 2:
        raise MultiplePeaks("The dataset appears to have multiple peaks, and "
                "thus the FWHM can't be determined.")
    elif len(roots) < 2:
        raise NoPeaksFound("No proper peaks were found in the data set; likely "
                "the dataset is flat (e.g. all zeros).")
    else:
        return abs(roots[1] - roots[0])