def get_polydisp_pts_wts(kfki, sigkf, dist_type='gaussian', nkpts=3):
    """
    Calculates a set of Gauss quadrature points & weights for polydisperse
    light.

    Returns a list of points and weights of the final wavevector's distri-
    bution, in units of the initial wavevector.

    Parameters
    ----------
        kfki : Float
            The mean of the polydisperse outgoing wavevectors.
        sigkf : Float
            The standard dev. of the polydisperse outgoing wavevectors.
        dist_type : {`gaussian`, `gamma`}, optional
            The distribution, gaussian or gamma, of the wavevectors.
            Default is `gaussian`
        nkpts : Int, optional
            The number of quadrature points to use. Default is 3
    Returns
    -------
        kfkipts : numpy.ndarray
            The Gauss quadrature points at which to calculate kfki.
        wts : numpy.ndarray
            The associated Gauss quadrature weights.
    """
    if dist_type.lower() == 'gaussian':
        pts, wts = np.polynomial.hermite.hermgauss(nkpts)
        kfkipts = np.abs(kfki + sigkf*np.sqrt(2)*pts)
    elif dist_type.lower() == 'laguerre' or dist_type.lower() == 'gamma':
        k_scale = sigkf**2/kfki
        associated_order = kfki**2/sigkf**2 - 1
        #Associated Laguerre with alpha >~170 becomes numerically unstable, so:
        max_order=150
        if associated_order > max_order or associated_order < (-1+1e-3):
            warnings.warn('Numerically unstable sigk, clipping', RuntimeWarning)
            associated_order = np.clip(associated_order, -1+1e-3, max_order)
        kfkipts, wts = la_roots(nkpts, associated_order)
        kfkipts *= k_scale
    else:
        raise ValueError('dist_type must be either gaussian or laguerre')
    return kfkipts, wts/wts.sum()
def get_polydisp_pts_wts(kfki, sigkf, dist_type='gaussian', nkpts=3):
    """
    Calculates a set of Gauss quadrature points & weights for polydisperse
    light.

    Returns a list of points and weights of the final wavevector's distri-
    bution, in units of the initial wavevector.

    Parameters
    ----------
        kfki : Float
            The mean of the polydisperse outgoing wavevectors.
        sigkf : Float
            The standard dev. of the polydisperse outgoing wavevectors.
        dist_type : {`gaussian`, `gamma`}, optional
            The distribution, gaussian or gamma, of the wavevectors.
            Default is `gaussian`
        nkpts : Int, optional
            The number of quadrature points to use. Default is 3
    Returns
    -------
        kfkipts : numpy.ndarray
            The Gauss quadrature points at which to calculate kfki.
        wts : numpy.ndarray
            The associated Gauss quadrature weights.
    """
    if dist_type.lower() == 'gaussian':
        pts, wts = np.polynomial.hermite.hermgauss(nkpts)
        kfkipts = np.abs(kfki + sigkf*np.sqrt(2)*pts)
    elif dist_type.lower() == 'laguerre' or dist_type.lower() == 'gamma':
        k_scale = sigkf**2/kfki
        associated_order = kfki**2/sigkf**2 - 1
        #Associated Laguerre with alpha >~170 becomes numerically unstable, so:
        max_order=150
        if associated_order > max_order or associated_order < (-1+1e-3):
            warnings.warn('Numerically unstable sigk, clipping', RuntimeWarning)
            associated_order = np.clip(associated_order, -1+1e-3, max_order)
        kfkipts, wts = la_roots(nkpts, associated_order)
        kfkipts *= k_scale
    else:
        raise ValueError('dist_type must be either gaussian or laguerre')
    return kfkipts, wts/wts.sum()
def get_polydisp_pts_wts ( kfki , sigkf , dist_type = 'gaussian' , nkpts = 3 ) : if dist_type . lower ( ) == 'gaussian' : pts , wts = np . polynomial . hermite . hermgauss ( nkpts ) kfkipts = np . abs ( kfki + sigkf * np . sqrt ( 2 ) * pts ) elif dist_type . lower ( ) == 'laguerre' or dist_type . lower ( ) == 'gamma' : k_scale = sigkf ** 2 / kfki associated_order = kfki ** 2 / sigkf ** 2 - 1 #Associated Laguerre with alpha >~170 becomes numerically unstable, so: max_order = 150 if associated_order > max_order or associated_order < ( - 1 + 1e-3 ) : warnings . warn ( 'Numerically unstable sigk, clipping' , RuntimeWarning ) associated_order = np . clip ( associated_order , - 1 + 1e-3 , max_order ) kfkipts , wts = la_roots ( nkpts , associated_order ) kfkipts *= k_scale else : raise ValueError ( 'dist_type must be either gaussian or laguerre' ) return kfkipts , wts / wts . sum ( )
Calculates a set of Gauss quadrature points & weights for polydisperse
    light.

    Returns a list of points and weights of the final wavevector's distri-
    bution, in units of the initial wavevector.

    Parameters
    ----------
        kfki : Float
            The mean of the polydisperse outgoing wavevectors.
        sigkf : Float
            The standard dev. of the polydisperse outgoing wavevectors.
        dist_type : {`gaussian`, `gamma`}, optional
            The distribution, gaussian or gamma, of the wavevectors.
            Default is `gaussian`
        nkpts : Int, optional
            The number of quadrature points to use. Default is 3
    Returns
    -------
        kfkipts : numpy.ndarray
            The Gauss quadrature points at which to calculate kfki.
        wts : numpy.ndarray
            The associated Gauss quadrature weights.
Calculates a set of Gauss quadrature points & weights for polydisperse light .