#!/usr/bin/env python
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"""Calculate radius of gyration of neurites."""

import neurom as nm
from neurom import morphmath as mm
from neurom.core.dataformat import COLS
import numpy as np


def segment_centre_of_mass(seg):
    """Calculate and return centre of mass of a segment.

    C, seg_volalculated as centre of mass of conical frustum"""
    h = mm.segment_length(seg)
    r0 = seg[0][COLS.R]
    r1 = seg[1][COLS.R]
    num = r0 * r0 + 2 * r0 * r1 + 3 * r1 * r1
    denom = 4 * (r0 * r0 + r0 * r1 + r1 * r1)
    centre_of_mass_z_loc = num / denom
    return seg[0][COLS.XYZ] + (centre_of_mass_z_loc / h) * (seg[1][COLS.XYZ] - seg[0][COLS.XYZ])


def neurite_centre_of_mass(neurite):
    """Calculate and return centre of mass of a neurite."""
    centre_of_mass = np.zeros(3)
    total_volume = 0

    seg_vol = np.array(map(mm.segment_volume, nm.iter_segments(neurite)))
    seg_centre_of_mass = np.array(map(segment_centre_of_mass, nm.iter_segments(neurite)))

    # multiply array of scalars with array of arrays
    # http://stackoverflow.com/questions/5795700/multiply-numpy-array-of-scalars-by-array-of-vectors
    seg_centre_of_mass = seg_centre_of_mass * seg_vol[:, np.newaxis]
    centre_of_mass = np.sum(seg_centre_of_mass, axis=0)
    total_volume = np.sum(seg_vol)
    return centre_of_mass / total_volume


def distance_sqr(point, seg):
    """Calculate and return square Euclidian distance from given point to
    centre of mass of given segment."""
    centre_of_mass = segment_centre_of_mass(seg)
    return sum(pow(np.subtract(point, centre_of_mass), 2))


def radius_of_gyration(neurite):
    """Calculate and return radius of gyration of a given neurite."""
    centre_mass = neurite_centre_of_mass(neurite)
    sum_sqr_distance = 0
    N = 0
    dist_sqr = [distance_sqr(centre_mass, s) for s in nm.iter_segments(neurite)]
    sum_sqr_distance = np.sum(dist_sqr)
    N = len(dist_sqr)
    return np.sqrt(sum_sqr_distance / N)


def mean_rad_of_gyration(neurites):
    """Calculate mean radius of gyration for set of neurites."""
    return np.mean([radius_of_gyration(n) for n in neurites])


if __name__ == '__main__':
    #  load a neuron from an SWC file
    filename = 'tests/data/swc/Neuron.swc'
    m = nm.load_morphology(filename)

    # for every neurite, print (number of segments, radius of gyration, neurite type)
    print([(sum(len(s.points) - 1 for s in nrte.iter_sections()),
            radius_of_gyration(nrte), nrte.type) for nrte in m.neurites])

    # print mean radius of gyration per neurite type
    print('Mean radius of gyration for axons: ',
          mean_rad_of_gyration(n for n in m.neurites if n.type == nm.AXON))
    print('Mean radius of gyration for basal dendrites: ',
          mean_rad_of_gyration(n for n in m.neurites if n.type == nm.BASAL_DENDRITE))
    print('Mean radius of gyration for apical dendrites: ',
          mean_rad_of_gyration(n for n in m.neurites
                               if n.type == nm.APICAL_DENDRITE))
