Smoothly bending power law function of Ryde+98. The width of the bend can be controlled.

sbpl.py

def sbpl(x, norm, lam1, lam2, x0, xbrk, Lambda):
    """Smoothly bending powerlaw

    Parameterization from Ryde99
    https://ui.adsabs.harvard.edu/abs/1999ApL%26C..39..281R/abstract

    Parameters
    ----------
    x: array of independent variable
    xmax: only consider x values up to this value
    norm: normalisation at x0
    lam1: powerlaw slope below xbrk
    lam2: powerlaw slope above xbrk
    xbrk: x value where powerlaw break occurs
    Lambda: width of bend at xbrk
    """
    with np.errstate(over='ignore'):
        q = log(x/xbrk) / Lambda
        qpiv = log(x0/xbrk) / Lambda
        return norm * (x/x0)**((lam1 + lam2 + 2)/2.) * \
            ((exp(q) + exp(-q))/(exp(qpiv) + exp(-qpiv))) ** ((lam2 - lam1)/2. * Lambda) * (x0 / x)