geometry.py

"""Classes and procedures related to neuronal geometry and distance calculation."""

import logging, math
import numpy as np
import rbf
from mpi4py import MPI
from neural_geometry.alphavol import alpha_shape
from neural_geometry.rbf_surface import RBFSurface
from neural_geometry.rbf_volume import RBFVolume

## This logger will inherit its setting from its root logger
logger = logging.getLogger('%s' % __name__)


def viewitems(obj, **kwargs):
    """
    Function for iterating over dictionary items with the same set-like
    behaviour on Py2.7 as on Py3.

    Passes kwargs to method."""
    func = getattr(obj, "viewitems", None)
    if func is None:
        func = obj.items
    return func(**kwargs)


def rotate2d(theta):
    """
    Returns the 2D rotation matrix associated with counterclockwise rotation around the origin
    by theta radians.
    """
    c, s = np.cos(theta), np.sin(theta)
    rot = np.array(((c, -s), (s, c)))
    return rot


def rotate3d(axis, theta):
    """
    Returns the 3D rotation matrix associated with counterclockwise rotation about
    the given axis by theta radians.
    """
    axis = np.asarray(axis)
    axis = axis / math.sqrt(np.dot(axis, axis))
    a = math.cos(theta / 2.0)
    b, c, d = -axis * math.sin(theta / 2.0)
    aa, bb, cc, dd = a * a, b * b, c * c, d * d
    bc, ad, ac, ab, bd, cd = b * c, a * d, a * c, a * b, b * d, c * d
    return np.array([[aa + bb - cc - dd, 2 * (bc + ad), 2 * (bd - ac)],
                     [2 * (bc - ad), aa + cc - bb - dd, 2 * (cd + ab)],
                     [2 * (bd + ac), 2 * (cd - ab), aa + dd - bb - cc]])


def make_rotate3d(rotate):
    """Creates a rotation matrix based on angles in degrees."""
    rot = None
    for i in range(0, 3):
        if rotate[i] != 0.:
            a = float(np.deg2rad(rotate[i]))
            rot = rotate3d([1 if i == j else 0 for j in range(0, 3)], a)

    return rot


def transform_volume(transform, u, v, l, rotate=None):
    """Transform to Euclidean volume."""

    u = np.array([u]).reshape(-1, )
    v = np.array([v]).reshape(-1, )
    l = np.array([l]).reshape(-1, )

    if rotate is not None:
        rot = make_rotate3d(rotate)
    else:
        rot = None

    x, y, z = transform(u, v, l)

    pts = np.array([x, y, z]).reshape(3, u.size)

    if rot is not None:
        xyz = np.dot(rot, pts).T
    else:
        xyz = pts.T

    return xyz

def get_layer_extents(layer_extents, layer):
    min_u, max_u = 0.0, 0.0
    min_v, max_v = 0.0, 0.0
    min_l, max_l = 0.0, 0.0
    for current_layer, extent in viewitems(layer_extents):
        if current_layer == layer:
            min_u, max_u = extent[0][0], extent[1][0]
            min_v, max_v = extent[0][1], extent[1][1]
            min_l, max_l = extent[0][2], extent[1][2]
    return ((min_u, max_u), (min_v, max_v), (min_l, max_l))

    
def get_total_extents(layer_extents):

    min_u = float('inf')
    max_u = 0.0

    min_v = float('inf')
    max_v = 0.0

    min_l = float('inf')
    max_l = 0.0

    for layer, extent in viewitems(layer_extents):
        min_u = min(extent[0][0], min_u)
        min_v = min(extent[0][1], min_v)
        min_l = min(extent[0][2], min_l)
        max_u = max(extent[1][0], max_u)
        max_v = max(extent[1][1], max_v)
        max_l = max(extent[1][2], max_l)

    return ((min_u, max_u), (min_v, max_v), (min_l, max_l))


def uvl_in_bounds(uvl_coords, layer_extents, pop_layers):
    for layer, count in viewitems(pop_layers):
        if count > 0:
            min_extent = layer_extents[layer][0]
            max_extent = layer_extents[layer][1]
            result = (uvl_coords[0] < (max_extent[0] + 0.001)) and \
                     (uvl_coords[0] > (min_extent[0] - 0.001)) and \
                     (uvl_coords[1] < (max_extent[1] + 0.001)) and \
                     (uvl_coords[1] > (min_extent[1] - 0.001)) and \
                     (uvl_coords[2] < (max_extent[2] + 0.001)) and \
                     (uvl_coords[2] > (min_extent[2] - 0.001))
            if result:
                return True
    return False

def make_alpha_shape(vol, alpha_radius=120.):
            
    logger.info("Constructing volume triangulation...")

    tri = vol.create_triangulation()

    logger.info("Constructing alpha shape...")

    alpha = alpha_shape([], alpha_radius, tri=tri)
    
    return alpha

def save_alpha_shape(file_path, dataset_path, alpha_shape):
    import h5py
    f = h5py.File(file_path)
    grp = f.create_group(dataset_path)
    grp['points'] = alpha_shape.points
    grp['simplices'] = alpha_shape.simplices
    grp['bounds'] = alpha_shape.bounds
    f.close()

def load_alpha_shape(file_path, dataset_path):
    import h5py
    f = h5py.File(file_path)
    alpha_shape = None
    if dataset_path in f:
        points = f[dataset_path]['points'][:]
        simplices = f[dataset_path]['simplices'][:]
        bounds = f[dataset_path]['bounds'][:]
        alpha_shape = dentate.alphavol.AlphaShape(points, simplices, bounds)
    f.close()
    return alpha_shape

def euclidean_distance(a, b):
    """Row-wise euclidean distance.
    a, b are row vectors of points.
    """
    return np.sqrt(np.sum((a - b) ** 2, axis=1))


def make_uvl_distance(vol, xyz_coords, rotate=None):
    f = lambda u, v, l: euclidean_distance(vol(u, v, l, rotate=rotate), xyz_coords)
    return f


def optimize_inverse_uvl_coords(vol, xyz_coords, rotate, layer_extents, pop_layers, optiter=100):
    import dlib
    f_uvl_distance = make_uvl_distance(vol, xyz_coords,rotate=rotate)
    for layer, count in viewitems(pop_layers):
        if count > 0:
            min_extent = layer_extents[layer][0]
            max_extent = layer_extents[layer][1]
            uvl_coords,dist = dlib.find_min_global(f_uvl_distance, min_extent, max_extent, optiter)
            if uvl_in_bounds(uvl_coords, layer_extents, { layer: count }):
                return uvl_coords
    return None


def generate_nodes(alpha, nsample, nodeitr):
    from rbf.pde.nodes import min_energy_nodes
    from rbf.pde.geometry import contains

    N = nsample * 2  # total number of nodes
    node_count = 0
    itr = nodeitr

    vert = alpha.points
    smp = np.asarray(alpha.bounds, dtype=np.int64)

    while node_count < nsample:
        logger.info("Generating %i nodes (%i iterations)..." % (N, itr))
        # create N quasi-uniformly distributed nodes
        out = min_energy_nodes(N, (vert, smp), iterations=itr)
        nodes = out[0]

        # remove nodes outside of the domain
        in_nodes = nodes[contains(nodes, vert, smp)]

        node_count = len(in_nodes)
        N = int(1.5 * N)

    logger.info("%i interior nodes generated (%i iterations)" % (node_count, itr))

    xyz_coords = in_nodes.reshape(-1, 3)
    
    return xyz_coords
    


def get_volume_distances(ip_vol, origin_spec=None, nsample=1000, alpha_radius=120., nodeitr=20, comm=None):
    """Computes arc-distances along the dimensions of an `RBFVolume` instance.

    Parameters
    ----------
    ip_vol : RBFVolume
        An interpolated volume instance of class RBFVolume.
    origin_coords : array(float)
        Origin point to use for distance computation.
    nsample : int
        Number of points to sample inside the volume.
    alpha_radius : float
        Parameter for creation of alpha volume that encloses the
        RBFVolume. Smaller values improve the quality of alpha volume,
        but increase the time for sampling points inside the volume.
    nodeitr : int 
        Number of iterations for distributing sampled points inside the volume.
    comm : MPIComm (optional)
        mpi4py MPI communicator: if provided, node generation and distance computation will be performed in parallel
    Returns
    -------
    (Y1, X1, ... , YN, XN) where N is the number of dimensions of the volume.
    X : array of coordinates
        The sampled coordinates.
    Y : array of distances
        The arc-distance from the starting index of the coordinate space to the corresponding coordinates in X.

    """

    size = 1
    rank = 0
    if comm is not None:
        rank = comm.rank
        size = comm.size

    uvl_coords=None
    origin_extent=None
    origin_ranges=None
    origin_pos_um=None
    if rank == 0:
        boundary_uvl_coords = np.array([[ip_vol.u[0], ip_vol.v[0], ip_vol.l[0]],
                                        [ip_vol.u[0], ip_vol.v[-1], ip_vol.l[0]],
                                        [ip_vol.u[-1], ip_vol.v[0], ip_vol.l[0]],
                                        [ip_vol.u[-1], ip_vol.v[-1], ip_vol.l[0]],
                                        [ip_vol.u[0], ip_vol.v[0], ip_vol.l[-1]],
                                        [ip_vol.u[0], ip_vol.v[-1], ip_vol.l[-1]],
                                        [ip_vol.u[-1], ip_vol.v[0], ip_vol.l[-1]],
                                        [ip_vol.u[-1], ip_vol.v[-1], ip_vol.l[-1]]])

        resample = 10
        span_U, span_V, span_L = ip_vol._resample_uvl(resample, resample, resample)

        if origin_spec is None:
            origin_coords = np.asarray([np.median(span_U), np.median(span_V), np.max(span_L)])
        else:
            origin_coords = np.asarray([origin_spec['U'](span_U), origin_spec['V'](span_V), origin_spec['L'](span_L)])
            
        logger.info('Origin coordinates: %f %f %f' % (origin_coords[0], origin_coords[1], origin_coords[2]))

        pos, extents = ip_vol.point_position(origin_coords[0], origin_coords[1], origin_coords[2])

        origin_pos = pos[0]
        origin_extent = extents[0]
        origin_pos_um = (origin_pos[0] * origin_extent[0], origin_pos[1] * origin_extent[1])
        origin_ranges = ((-(origin_pos[0] * origin_extent[0]), (1.0 - origin_pos[0]) * origin_extent[0]),
                        (-(origin_pos[1] * origin_extent[1]), (1.0 - origin_pos[1]) * origin_extent[1]))

        logger.info(
            'Origin position: %f %f extent: %f %f' % (origin_pos[0], origin_pos[1], origin_extent[0], origin_extent[1]))
        logger.info('Origin ranges: %f : %f %f : %f' % (
        origin_ranges[0][0], origin_ranges[0][1], origin_ranges[1][0], origin_ranges[1][1]))

        logger.info("Creating volume triangulation...")
        tri = ip_vol.create_triangulation()

        logger.info("Constructing alpha shape...")
        alpha = alpha_shape([], alpha_radius, tri=tri)
    
        xyz_coords = generate_nodes(alpha, nsample, nodeitr)

        logger.info('Inverse interpolation of UVL coordinates...')
        uvl_coords_interp = ip_vol.inverse(xyz_coords)
        xyz_coords_interp = ip_vol(uvl_coords_interp[:, 0], uvl_coords_interp[:, 1], uvl_coords_interp[:, 2],
                                   mesh=False).reshape(3, -1).T

        xyz_error_interp = np.abs(np.subtract(xyz_coords, xyz_coords_interp))

        node_uvl_coords = uvl_coords_interp
        uvl_coords = np.vstack([boundary_uvl_coords, node_uvl_coords])

    comm.barrier()
    if comm is not None:
        uvl_coords = comm.bcast(uvl_coords, root=0)
        origin_extent, origin_pos_um, origin_ranges = comm.bcast((origin_extent, origin_pos_um, origin_ranges), root=0)

    if rank == 0:
        logger.info('Computing volume distances...')
        
    ldists_u = []
    ldists_v = []
    obs_uvls = []
    for i, uvl in enumerate(uvl_coords):
        if i % size == rank:
            sample_U = uvl[0]
            sample_V = uvl[1]
            sample_L = uvl[2]
            pos, extent = ip_vol.point_position(sample_U, sample_V, sample_L)

            uvl_pos = pos[0]
            uvl_extent = extent[0]
            
            obs_uvls.append(uvl)
            ldists_u.append(uvl_pos[0] * origin_extent[0] - origin_pos_um[0])
            ldists_v.append(uvl_pos[1] * origin_extent[1] - origin_pos_um[1])

    distances_u = np.asarray(ldists_u, dtype=np.float32)
    distances_v = np.asarray(ldists_v, dtype=np.float32)
    obs_uvl = np.asarray(np.vstack(obs_uvls), dtype=np.float32)
    

    return (origin_ranges, obs_uvl, distances_u, distances_v)


def interp_soma_distances(comm, ip_dist_u, ip_dist_v, soma_coords, layer_extents, population_layers, 
                          interp_chunk_size=1000, populations=None, allgather=False):
    """Interpolates path lengths of cell coordinates along the dimensions of an `RBFVolume` instance.

    Parameters
    ----------
    comm : MPIComm
        mpi4py MPI communicator
    ip_dist_u : RBFInterpolant
        Interpolation function for computing arc distances along the first dimension of the volume.
    ip_dist_v : RBFInterpolant
        Interpolation function for computing arc distances along the second dimension of the volume.
    soma_coords : { population_name : coords_dict }
        A dictionary that maps each cell population name to a dictionary of coordinates. The dictionary of coordinates must have the following type:
          coords_dict : { gid : (u, v, l) }
          where:
          - gid: cell identifier
          - u, v, l: floating point coordinates
    population_layers: { population_name : layers }
        A dictionary of population count per layer
        Argument layers has the following type:
         { layer_name: count }
    allgather: boolean (default: False)
       if True, the results are gathered from all ranks and combined
    Returns
    -------
    A dictionary of the form:

      { population: { gid: (distance_U, distance_V } }

    """

    rank = comm.rank
    size = comm.size

    if populations is None:
        populations = sorted(soma_coords.keys())

    soma_distances = {}
    for pop in populations:
        coords_dict = soma_coords[pop]
        if rank == 0:
            logger.info('Computing soma distances for %d cells from population %s...' % (len(coords_dict), pop))
        count = 0
        local_dist_dict = {}
        pop_layer = population_layers[pop]
        u_obs = []
        v_obs = []
        gids = []
        for gid, coords in viewitems(coords_dict):
            if gid % size == rank:
                soma_u, soma_v, soma_l = coords
                try:
                    assert(uvl_in_bounds(coords, layer_extents, pop_layer))
                except Exception as e:
                    logger.error("gid %i: out of limits error for coordinates: %f %f %f)" % \
                                 (gid, soma_u, soma_v, soma_l))
                    raise e

                u_obs.append(np.array([soma_u, soma_v, soma_l]).ravel())
                v_obs.append(np.array([soma_u, soma_v, soma_l]).ravel())
                gids.append(gid)
        if len(u_obs) > 0:
            u_obs_array = np.vstack(u_obs)
            v_obs_array = np.vstack(v_obs)
            distance_u_obs = ip_dist_u(u_obs_array).reshape(-1, 1)
            distance_v_obs = ip_dist_v(v_obs_array).reshape(-1, 1)
            distance_u = np.mean(distance_u_obs, axis=1)
            distance_v = np.mean(distance_v_obs, axis=1)
            try:
                assert (np.all(np.isfinite(distance_u)))
                assert (np.all(np.isfinite(distance_v)))
            except Exception as e:
                u_nan_idxs = np.where(np.isnan(distance_u))[0]
                v_nan_idxs = np.where(np.isnan(distance_v))[0]
                logger.error('Invalid distances: u: %s; v: %s', str(u_obs_array[u_nan_idxs]),
                             str(v_obs_array[v_nan_idxs]))
                raise e

        for (i, gid) in enumerate(gids):
            local_dist_dict[gid] = (distance_u[i], distance_v[i])
            if rank == 0:
                logger.info('gid %i: distances: %f %f' % (gid, distance_u[i], distance_v[i]))
        if allgather:
            dist_dicts = comm.allgather(local_dist_dict)
            combined_dist_dict = {}
            for dist_dict in dist_dicts:
                for k, v in viewitems(dist_dict):
                    combined_dist_dict[k] = v
            soma_distances[pop] = combined_dist_dict
        else:
            soma_distances[pop] = local_dist_dict

    return soma_distances

def make_distance_interpolant(comm, geometry_config, make_volume, resolution=[30, 30, 10], nsample=1000):
    from rbf.interpolate import RBFInterpolant

    rank = comm.rank

    layer_extents = geometry_config['Parametric Surface']['Layer Extents']
    (extent_u, extent_v, extent_l) = get_total_extents(layer_extents)

    rotate = geometry_config['Parametric Surface']['Rotation']
    origin = geometry_config['Parametric Surface']['Origin']

    min_u, max_u = extent_u
    min_v, max_v = extent_v
    min_l, max_l = extent_l

    ## This parameter is used to expand the range of L and avoid
    ## situations where the endpoints of L end up outside of the range
    ## of the distance interpolant
    safety = 0.01

    ip_volume = None
    if rank == 0:
        logger.info('Creating volume: min_l = %f max_l = %f...' % (min_l, max_l))
        ip_volume = make_volume((min_u - safety, max_u + safety), \
                                (min_v - safety, max_v + safety), \
                                (min_l - safety, max_l + safety), \
                                resolution=resolution, rotate=rotate)

    ip_volume = comm.bcast(ip_volume, root=0)
        
    interp_sigma = 0.01
    interp_basis = rbf.basis.ga
    interp_order = 1
    
    if rank == 0:
        logger.info('Computing reference distances...')

    vol_dist = get_volume_distances(ip_volume, origin_spec=origin, nsample=nsample, comm=comm)
    (origin_ranges, obs_uvl, dist_u, dist_v) = vol_dist

    if rank == 0:
        logger.info('Done computing reference distances...')
    
    sendcounts = np.array(comm.gather(len(obs_uvl), root=0))
    displs = np.concatenate([np.asarray([0]), np.cumsum(sendcounts)[:-1]])

    obs_uvs = None
    dist_us = None
    dist_vs = None
    if rank == 0:
        obs_uvs = np.zeros((np.sum(sendcounts), 3), dtype=np.float32)
        dist_us = np.zeros(np.sum(sendcounts), dtype=np.float32)
        dist_vs = np.zeros(np.sum(sendcounts), dtype=np.float32)

    uvl_datatype = MPI.FLOAT.Create_contiguous(3).Commit() 
    comm.Gatherv(sendbuf=obs_uvl, recvbuf=(obs_uvs, sendcounts, displs, uvl_datatype), root=0)
    uvl_datatype.Free()
    comm.Gatherv(sendbuf=dist_u, recvbuf=(dist_us, sendcounts, displs, MPI.FLOAT), root=0)
    comm.Gatherv(sendbuf=dist_v, recvbuf=(dist_vs, sendcounts, displs, MPI.FLOAT), root=0)

    ip_dist_u=None
    ip_dist_v=None
    if rank == 0:
        logger.info('Computing U volume distance interpolants...')
        ip_dist_u = RBFInterpolant(obs_uvs, dist_us, order=interp_order, phi=interp_basis, \
                                   sigma=interp_sigma)
        logger.info('Computing V volume distance interpolants...')
        ip_dist_v = RBFInterpolant(obs_uvs, dist_vs, order=interp_order, phi=interp_basis, \
                                   sigma=interp_sigma)

    origin_ranges = comm.bcast(origin_ranges, root=0)
    ip_dist_u = comm.bcast(ip_dist_u, root=0)
    ip_dist_v = comm.bcast(ip_dist_v, root=0)

    return origin_ranges, ip_dist_u, ip_dist_v
    

def measure_distances(comm, geometry_config, soma_coords, ip_dist, resolution=[30, 30, 10], interp_chunk_size=1000, allgather=False):

    rank = comm.rank

    layer_extents = geometry_config['Parametric Surface']['Layer Extents']
    cell_distribution = geometry_config['Cell Distribution']
    (extent_u, extent_v, extent_l) = get_total_extents(layer_extents)

    rotate = geometry_config['Parametric Surface']['Rotation']
    origin = geometry_config['Parametric Surface']['Origin']

    origin_ranges, ip_dist_u, ip_dist_v = ip_dist
        
    origin_ranges = comm.bcast(origin_ranges, root=0)
    ip_dist_u = comm.bcast(ip_dist_u, root=0)
    ip_dist_v = comm.bcast(ip_dist_v, root=0)
        
    soma_distances = interp_soma_distances(comm, ip_dist_u, ip_dist_v, soma_coords, 
                                           layer_extents, cell_distribution, 
                                           interp_chunk_size=interp_chunk_size, 
                                           allgather=allgather)

    return soma_distances


def measure_distance_extents(comm, geometry_config, volume):

    layer_extents = geometry_config['Parametric Surface']['Layer Extents']

    (extent_u, extent_v, extent_l) = get_total_extents(layer_extents)

    min_u, max_u = extent_u
    min_v, max_v = extent_v
    min_l, max_l = extent_l

    rotate = geometry_config['Parametric Surface']['Rotation']
    origin_spec = geometry_config['Parametric Surface']['Origin']

    span_U = np.linspace(min_u, max_u, num=2000)
    span_V = np.linspace(min_v, max_v, num=1000)
    span_L = np.linspace(min_l, max_l, num=1000)

    if origin_spec is None:
        coord_U = np.median(span_U)
        coord_V = np.median(span_V)
        coord_L = np.median(span_L)
    else:
        coord_U = origin_spec['U'](span_U)
        coord_V = origin_spec['V'](span_V)
        coord_L = origin_spec['L'](span_L)

    span1_U = np.linspace(min_u, coord_U, num=2000)
    span2_U = np.linspace(coord_U, max_u, num=2000)
    span1_V = np.linspace(min_v, coord_V, num=1000)
    span2_V = np.linspace(coord_V, max_v, num=1000)

    u, v, l = np.meshgrid(span1_U, coord_V, coord_L, indexing='ij')
    u1_xyz = volume(u, v, l, rotate=rotate)
    u, v, l = np.meshgrid(span2_U, coord_V, coord_L, indexing='ij')
    u2_xyz = volume(u, v, l, rotate=rotate)
    u_dist_extent = (-np.sum(euclidean_distance(u1_xyz[:-1, :], u1_xyz[1:, :])),
                     np.sum(euclidean_distance(u2_xyz[:-1, :], u2_xyz[1:, :])))

    u, v, l = np.meshgrid(coord_U, span1_V, coord_L, indexing='ij')
    v1_xyz = volume(u, v, l, rotate=rotate)
    u, v, l = np.meshgrid(coord_U, span2_V, coord_L, indexing='ij')
    v2_xyz = volume(u, v, l, rotate=rotate)

    v_dist_extent = (-np.sum(euclidean_distance(v1_xyz[:-1, :], v1_xyz[1:, :])),
                     np.sum(euclidean_distance(v2_xyz[:-1, :], v2_xyz[1:, :])))

    return u_dist_extent, v_dist_extent


def icp_transform(comm, geometry_config, volume, make_surface, soma_coords, projection_ls, population_extents, rotate=None, populations=None,
                  icp_iter=1000, opt_iter=100):
    """
    Uses the iterative closest point (ICP) algorithm of the PCL library to transform soma coordinates onto a surface for a particular L value.
    http://pointclouds.org/documentation/tutorials/iterative_closest_point.php#iterative-closest-point

    """

    import dlib, pcl

    rank = comm.rank
    size = comm.size

    if populations is None:
        populations = list(soma_coords.keys())

    srf_resample = 25

    layer_extents = geometry_config['Parametric Surface']['Layer Extents']

    (extent_u, extent_v, extent_l) = get_total_extents(layer_extents)

    min_u, max_u = extent_u
    min_v, max_v = extent_v
    min_l, max_l = extent_l

    ## This parameter is used to expand the range of L and avoid
    ## situations where the endpoints of L end up outside of the range
    ## of the distance interpolant
    safety = 0.01

    extent_u = (min_u - safety, max_u + safety)
    extent_v = (min_v - safety, max_v + safety)

    projection_ptclouds = []
    for obs_l in projection_ls:
        srf = make_surface(extent_u, extent_v, obs_l, rotate=rotate)
        U, V = srf._resample_uv(srf_resample, srf_resample)
        meshpts = srf.ev(U, V)
        projection_ptcloud = pcl.PointCloud()
        projection_ptcloud.from_array(meshpts)
        projection_ptclouds.append(projection_ptcloud)

    soma_coords_dict = {}
    for pop in populations:
        coords_dict = soma_coords[pop]
        if rank == 0:
            logger.info('Computing point transformation for population %s...' % pop)
        count = 0
        xyz_coords = []
        gids = []
        for gid, coords in viewitems(coords_dict):
            if gid % size == rank:
                soma_u, soma_v, soma_l = coords
                xyz_coords.append(volume(soma_u, soma_v, soma_l, rotate=rotate))
                gids.append(gid)
        xyz_pts = np.vstack(xyz_coords)

        cloud_in = pcl.PointCloud()
        cloud_in.from_array(xyz_pts)

        icp = cloud_in.make_IterativeClosestPoint()

        all_est_xyz_coords = []
        all_est_uvl_coords = []
        all_interp_err = []

        for (k, cloud_prj) in enumerate(projection_ls):
            k_est_xyz_coords = np.zeros((len(gids), 3))
            k_est_uvl_coords = np.zeros((len(gids), 3))
            interp_err = np.zeros((len(gids),))
            converged, transf, estimate, fitness = icp.icp(cloud_in, cloud_prj, max_iter=icp_iter)
            logger.info(
                'Transformation of population %s has converged: ' % (pop) + str(converged) + ' score: %f' % (fitness))
            for i, gid in zip(list(range(0, estimate.size)), gids):
                est_xyz_coords = estimate[i]
                k_est_xyz_coords[i, :] = est_xyz_coords
                f_uvl_distance = make_uvl_distance(est_xyz_coords, rotate=rotate)
                uvl_coords, err = dlib.find_min_global(f_uvl_distance, limits[0], limits[1], opt_iter)
                k_est_uvl_coords[i, :] = uvl_coords
                interp_err[i,] = err
                if rank == 0:
                    logger.info('gid %i: u: %f v: %f l: %f' % (gid, uvl_coords[0], uvl_coords[1], uvl_coords[2]))
            all_est_xyz_coords.append(k_est_xyz_coords)
            all_est_uvl_coords.append(k_est_uvl_coords)
            all_interp_err.append(interp_err)

        coords_dict = {}
        for (i, gid) in enumerate(gids):
            coords_dict[gid] = {'X Coordinate': np.asarray([col[i, 0] for col in all_est_xyz_coords], dtype='float32'),
                                'Y Coordinate': np.asarray([col[i, 1] for col in all_est_xyz_coords], dtype='float32'),
                                'Z Coordinate': np.asarray([col[i, 2] for col in all_est_xyz_coords], dtype='float32'),
                                'U Coordinate': np.asarray([col[i, 0] for col in all_est_uvl_coords], dtype='float32'),
                                'V Coordinate': np.asarray([col[i, 1] for col in all_est_uvl_coords], dtype='float32'),
                                'L Coordinate': np.asarray([col[i, 2] for col in all_est_uvl_coords], dtype='float32'),
                                'Interpolation Error': np.asarray([err[i] for err in all_interp_err], dtype='float32')}

        soma_coords_dict[pop] = coords_dict

    return soma_coords_dict


def test_nodes():
    from rbf.pde.nodes import min_energy_nodes
    from rbf.pde.geometry import contains
    from dentate.alphavol import alpha_shape
    from mayavi import mlab

    obs_u = np.linspace(-0.016 * np.pi, 1.01 * np.pi, 25)
    obs_v = np.linspace(-0.23 * np.pi, 1.425 * np.pi, 25)
    obs_l = np.linspace(-1.0, 1., num=10)

    u, v, l = np.meshgrid(obs_u, obs_v, obs_l, indexing='ij')
    xyz = DG_volume(u, v, l, rotate=[-35., 0., 0.])

    print('Constructing volume...')
    vol = RBFVolume(obs_u, obs_v, obs_l, xyz, order=2)

    print('Constructing volume triangulation...')
    tri = vol.create_triangulation()

    print('Constructing alpha shape...')
    alpha = alpha_shape([], 120., tri=tri)

    # Define the problem domain
    vert = alpha.points
    smp = np.asarray(alpha.bounds, dtype=np.int64)

    N = 10000  # total number of nodes

    # create N quasi-uniformly distributed nodes
    print('Generating nodes...')
    rbf_logger = logging.Logger.manager.loggerDict['rbf.pde.nodes']
    rbf_logger.setLevel(logging.DEBUG)
    out = min_energy_nodes(N, (vert, smp), iterations=10, build_rtree=True)

    nodes = out[0]

    # remove nodes outside of the domain
    in_nodes = nodes[contains(nodes, vert, smp)]

    print('Generated %d interior nodes' % len(in_nodes))

    vol.mplot_surface(color=(0, 1, 0), opacity=0.33, ures=10, vres=10)
    mlab.points3d(*in_nodes.T, color=(1, 1, 0), scale_factor=15.0)

    mlab.show()

    return in_nodes, vol.inverse(in_nodes)


def test_alphavol():
    from mayavi import mlab
    from dentate.alphavol import alpha_shape

    obs_u = np.linspace(-0.016 * np.pi, 1.01 * np.pi, 20)
    obs_v = np.linspace(-0.23 * np.pi, 1.425 * np.pi, 20)
    obs_l = np.linspace(-3.95, 3.2, num=10)

    u, v, l = np.meshgrid(obs_u, obs_v, obs_l, indexing='ij')
    xyz = DG_volume(u, v, l, rotate=[-35., 0., 0.])

    print('Constructing volume...')
    vol = RBFVolume(obs_u, obs_v, obs_l, xyz, order=2)

    print('Constructing volume triangulation...')
    tri = vol.create_triangulation()

    print('Constructing alpha shape...')
    alpha = alpha_shape([], 120., tri=tri)

    vert = alpha.points
    smp = np.asarray(alpha.bounds, dtype=np.int64)

    edges = np.vstack([np.column_stack([smp[:, 0], smp[:, 1]]),
                       np.column_stack([smp[:, 1], smp[:, 2]])])

    x = vert[:, 0]
    y = vert[:, 1]
    z = vert[:, 2]

    start_idx = edges[:, 0]
    end_idx = edges[:, 1]

    vol.mplot_surface(color=(0, 1, 0), opacity=0.33, ures=10, vres=10)
    mlab.quiver3d(x[start_idx],
                  y[start_idx],
                  z[start_idx],
                  x[end_idx] - x[start_idx],
                  y[end_idx] - y[start_idx],
                  z[end_idx] - z[start_idx],
                  mode='2ddash',
                  scale_factor=1)

    mlab.show()


if __name__ == '__main__':
    #     test_alphavol()
    test_nodes()