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from typing import Optional, Tuple
import torch
from torch_harmonics.quadrature import clenshaw_curtiss_weights, legendre_gauss_weights, lobatto_weights
from .primitives import compute_split_shapes, reduce_from_azimuth_region, reduce_from_polar_region, split_tensor_along_dim
from .utils import azimuth_group_rank, azimuth_group_size, polar_group_rank, polar_group_size
[docs]
class DistributedQuadratureS2(torch.nn.Module):
r"""
Distributed scalar quadrature on :math:`S^2` for integrating spherical fields on a
latitude/longitude grid, with data and weights split across polar and
azimuth communicator groups.
.. seealso::
:class:`torch_harmonics.QuadratureS2`
Serial counterpart with full mathematical description and parameter
documentation.
Parameters
----------
img_shape : Tuple[int]
Spatial grid shape ``(nlat, nlon)``.
grid : str, optional
Quadrature grid type (``"equiangular"``, ``"legendre-gauss"``,
``"lobatto"``, ``"equiangular-trapezoidal"``), by default ``"equiangular"``.
normalize : bool, optional
If ``True``, divides weights by ``4π`` to return an average instead of
an integral, by default ``False``.
Returns
-------
torch.Tensor
Tensor of shape ``(..., channels)`` containing the global integral over
the last two spatial dimensions (reduced across communicator groups).
Raises
------
ValueError
If an unknown ``grid`` type is provided.
"""
def __init__(self, img_shape: Tuple[int], grid: Optional[str] = "equiangular", normalize: Optional[bool] = False):
super().__init__()
# copy input
self.grid = grid
self.img_shape = img_shape
self.normalize = normalize
# get the comms grid:
self.comm_size_polar = polar_group_size()
self.comm_rank_polar = polar_group_rank()
self.comm_size_azimuth = azimuth_group_size()
self.comm_rank_azimuth = azimuth_group_rank()
if self.grid == "legendre-gauss":
_, weights = legendre_gauss_weights(img_shape[0], -1, 1)
dlambda = 2 * torch.pi / img_shape[1]
quad_weight = dlambda * weights.unsqueeze(1)
quad_weight = quad_weight.tile(1, img_shape[1])
elif self.grid == "lobatto":
_, weights = lobatto_weights(img_shape[0], -1, 1)
dlambda = 2 * torch.pi / img_shape[1]
quad_weight = dlambda * weights.unsqueeze(1)
quad_weight = quad_weight.tile(1, img_shape[1])
elif self.grid == "equiangular":
_, weights = clenshaw_curtiss_weights(img_shape[0], -1, 1)
dlambda = 2 * torch.pi / img_shape[1]
quad_weight = dlambda * weights.unsqueeze(1)
quad_weight = quad_weight.tile(1, img_shape[1])
else:
raise (ValueError("Unknown quadrature mode"))
# apply normalization
if normalize:
quad_weight = quad_weight / (4.0 * torch.pi)
# store lat and lon shapes:
self.lat_shapes = compute_split_shapes(img_shape[0], self.comm_size_polar)
self.lon_shapes = compute_split_shapes(img_shape[1], self.comm_size_azimuth)
# make it contiguous
quad_weight = quad_weight.contiguous().reshape(1, 1, *img_shape)
# split across latitude and longitude
if self.comm_size_polar > 1:
quad_weight = split_tensor_along_dim(quad_weight, dim=-2, num_chunks=self.comm_size_polar)[self.comm_rank_polar]
if self.comm_size_azimuth > 1:
quad_weight = split_tensor_along_dim(quad_weight, dim=-1, num_chunks=self.comm_size_azimuth)[self.comm_rank_azimuth]
# cast to fp32
quad_weight = quad_weight.to(torch.float32).contiguous()
# register buffer
self.register_buffer("quad_weight", quad_weight, persistent=False)
def forward(self, x: torch.Tensor) -> torch.Tensor:
# integrate over last two axes only:
quad = torch.sum(x * self.quad_weight, dim=(-2, -1))
if self.comm_size_polar > 1:
quad = reduce_from_polar_region(quad)
if self.comm_size_azimuth > 1:
quad = reduce_from_azimuth_region(quad)
return quad
