def _compute_laplacian_equiangular(nodes, ratio, laplacian_type="normalized"):
""" Computes laplacian of spherical graph sampled as a HEALpix grid
Parameters
----------
nodes : int
Number of nodes in the graph
ratio : float
width / height
laplacian_type : string
Type of laplacian. Options are {´normalized´, ´combinatorial´}
Returns
-------
laplacian : torch.sparse_coo_tensor
Graph laplacian
"""
dim1, dim2 = equiangular_dimension_unpack(nodes, ratio)
bw = [int(dim1 / 2), int(dim2 / 2)]
G = pygsp.graphs.SphereEquiangular(bandwidth=bw, sampling="SOFT")
G.compute_laplacian(laplacian_type)
laplacian = layers.prepare_laplacian(G.L.astype(np.float32))
return laplacian
def get_equiangular_laplacians(nodes, depth, ratio, laplacian_type):
"""Get the equiangular laplacian list for a certain depth.
Args:
nodes (int): initial number of nodes.
depth (int): the depth of the UNet.
laplacian_type ["combinatorial", "normalized"]: the type of the laplacian.
Returns:
laps (list): increasing list of laplacians
"""
laps = []
pixel_num = nodes
for _ in range(depth):
dim1, dim2 = equiangular_dimension_unpack(pixel_num, ratio)
bw1 = equiangular_bandwidth(dim1)
bw2 = equiangular_bandwidth(dim2)
bw = [bw1, bw2]
G = SphereEquiangular(bandwidth=bw, sampling="SOFT")
G.compute_laplacian(laplacian_type)
laplacian = prepare_laplacian(G.L)
laps.append(laplacian)
return laps[::-1]
def _equiangular_calculator(tensor, ratio):
N, M, F = tensor.size()
dim1, dim2 = equiangular_dimension_unpack(M, ratio)
bw_dim1, bw_dim2 = dim1 / 2, dim2 / 2
tensor = tensor.view(N, dim1, dim2, F)
return tensor, [bw_dim1, bw_dim2]