def gaussian_smear(self, r):
        """
        Applies an isotropic Gaussian smear of width (standard deviation) r to
        the potential field. This is necessary to avoid finding paths through
        narrow minima or nodes that may exist in the field (although any
        potential or charge distribution generated from GGA should be
        relatively smooth anyway). The smearing obeys periodic
        boundary conditions at the edges of the cell.

        :param r - Smearing width in cartesian coordinates, in the same units
            as the structure lattice vectors
        """
        # Since scaling factor in fractional coords is not isotropic, have to
        # have different radii in 3 directions
        a_lat = self.__s.lattice.a
        b_lat = self.__s.lattice.b
        c_lat = self.__s.lattice.c

        # Conversion factors for discretization of v
        v_dim = self.__v.shape
        r_frac = (r / a_lat, r / b_lat, r / c_lat)
        r_disc = (int(math.ceil(r_frac[0] * v_dim[0])),
                  int(math.ceil(r_frac[1] * v_dim[1])),
                  int(math.ceil(r_frac[2] * v_dim[2])))

        # Apply smearing
        # Gaussian filter
        gauss_dist = np.zeros(
            (r_disc[0] * 4 + 1, r_disc[1] * 4 + 1, r_disc[2] * 4 + 1))
        for g_a in np.arange(-2.0 * r_disc[0], 2.0 * r_disc[0] + 1, 1.0):
            for g_b in np.arange(-2.0 * r_disc[1], 2.0 * r_disc[1] + 1, 1.0):
                for g_c in np.arange(-2.0 * r_disc[2], 2.0 * r_disc[2] + 1,
                                     1.0):
                    g = np.array(
                        [g_a / v_dim[0], g_b / v_dim[1], g_c / v_dim[2]]).T
                    gauss_dist[int(g_a + r_disc[0])][int(g_b + r_disc[1])][
                        int(g_c + r_disc[2])] = la.norm(
                        np.dot(self.__s.lattice.matrix, g)) / r
        gauss = scipy.stats.norm.pdf(gauss_dist)
        gauss = gauss / np.sum(gauss, dtype=float)
        padded_v = np.pad(self.__v, (
        (r_disc[0], r_disc[0]), (r_disc[1], r_disc[1]), (r_disc[2], r_disc[2])),
                          mode='wrap')
        smeared_v = scipy.signal.convolve(padded_v, gauss, mode='valid')
        self.__v = smeared_v
def gaussian_smear ( self , r ) : a_lat = self . __s . lattice . a b_lat = self . __s . lattice . b c_lat = self . __s . lattice . c v_dim = self . __v . shape r_frac = ( r / a_lat , r / b_lat , r / c_lat ) r_disc = ( int ( math . ceil ( r_frac [ 0 ] * v_dim [ 0 ] ) ) , int ( math . ceil ( r_frac [ 1 ] * v_dim [ 1 ] ) ) , int ( math . ceil ( r_frac [ 2 ] * v_dim [ 2 ] ) ) ) gauss_dist = np . zeros ( ( r_disc [ 0 ] * 4 + 1 , r_disc [ 1 ] * 4 + 1 , r_disc [ 2 ] * 4 + 1 ) ) for g_a in np . arange ( - 2.0 * r_disc [ 0 ] , 2.0 * r_disc [ 0 ] + 1 , 1.0 ) : for g_b in np . arange ( - 2.0 * r_disc [ 1 ] , 2.0 * r_disc [ 1 ] + 1 , 1.0 ) : for g_c in np . arange ( - 2.0 * r_disc [ 2 ] , 2.0 * r_disc [ 2 ] + 1 , 1.0 ) : g = np . array ( [ g_a / v_dim [ 0 ] , g_b / v_dim [ 1 ] , g_c / v_dim [ 2 ] ] ) . T gauss_dist [ int ( g_a + r_disc [ 0 ] ) ] [ int ( g_b + r_disc [ 1 ] ) ] [ int ( g_c + r_disc [ 2 ] ) ] = la . norm ( np . dot ( self . __s . lattice . matrix , g ) ) / r gauss = scipy . stats . norm . pdf ( gauss_dist ) gauss = gauss / np . sum ( gauss , dtype = float ) padded_v = np . pad ( self . __v , ( ( r_disc [ 0 ] , r_disc [ 0 ] ) , ( r_disc [ 1 ] , r_disc [ 1 ] ) , ( r_disc [ 2 ] , r_disc [ 2 ] ) ) , mode = 'wrap' ) smeared_v = scipy . signal . convolve ( padded_v , gauss , mode = 'valid' ) self . __v = smeared_v
Applies an isotropic Gaussian smear of width (standard deviation) r to
        the potential field. This is necessary to avoid finding paths through
        narrow minima or nodes that may exist in the field (although any
        potential or charge distribution generated from GGA should be
        relatively smooth anyway). The smearing obeys periodic
        boundary conditions at the edges of the cell.

        :param r - Smearing width in cartesian coordinates, in the same units
            as the structure lattice vectors