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# SPDX-FileCopyrightText: Copyright (c) 2022 The torch-harmonics Authors. All rights reserved.
# SPDX-License-Identifier: BSD-3-Clause
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from typing import List, Tuple, Union, Optional
import math
import torch
import torch.nn as nn
from torch_harmonics.quadrature import _precompute_latitudes, _precompute_longitudes
from torch_harmonics.distributed import polar_group_size, azimuth_group_size, distributed_transpose_azimuth, distributed_transpose_polar
from torch_harmonics.distributed import reduce_from_azimuth_region, copy_to_azimuth_region
from torch_harmonics.distributed import polar_group_rank, azimuth_group_rank
from torch_harmonics.distributed import compute_split_shapes
class DistributedResampleS2(nn.Module):
"""
Distributed resampling module for spherical data on the 2-sphere.
This module performs distributed resampling of spherical data across multiple processes,
supporting both upscaling and downscaling operations. The data is distributed across
polar and azimuthal directions, and the module handles the necessary communication
and interpolation operations.
Parameters
-----------
nlat_in : int
Number of input latitude points
nlon_in : int
Number of input longitude points
nlat_out : int
Number of output latitude points
nlon_out : int
Number of output longitude points
grid_in : str, optional
Input grid type, by default "equiangular"
grid_out : str, optional
Output grid type, by default "equiangular"
mode : str, optional
Interpolation mode ("bilinear" or "bilinear-spherical"), by default "bilinear"
"""
def __init__(
self,
nlat_in: int,
nlon_in: int,
nlat_out: int,
nlon_out: int,
grid_in: Optional[str] = "equiangular",
grid_out: Optional[str] = "equiangular",
mode: Optional[str] = "bilinear",
):
super().__init__()
# currently only bilinear is supported
if mode in ["bilinear", "bilinear-spherical"]:
self.mode = mode
else:
raise NotImplementedError(f"unknown interpolation mode {mode}")
self.nlat_in, self.nlon_in = nlat_in, nlon_in
self.nlat_out, self.nlon_out = nlat_out, nlon_out
self.grid_in = grid_in
self.grid_out = grid_out
# 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()
# compute splits: is this correct even when expanding the poles?
self.lat_in_shapes = compute_split_shapes(self.nlat_in, self.comm_size_polar)
self.lon_in_shapes = compute_split_shapes(self.nlon_in, self.comm_size_azimuth)
self.lat_out_shapes = compute_split_shapes(self.nlat_out, self.comm_size_polar)
self.lon_out_shapes = compute_split_shapes(self.nlon_out, self.comm_size_azimuth)
# for upscaling the latitudes we will use interpolation
self.lats_in, _ = _precompute_latitudes(nlat_in, grid=grid_in)
self.lons_in = _precompute_longitudes(nlon_in)
self.lats_out, _ = _precompute_latitudes(nlat_out, grid=grid_out)
self.lons_out = _precompute_longitudes(nlon_out)
# in the case where some points lie outside of the range spanned by lats_in,
# we need to expand the solution to the poles before interpolating
self.expand_poles = (self.lats_out > self.lats_in[-1]).any() or (self.lats_out < self.lats_in[0]).any()
if self.expand_poles:
self.lats_in = torch.cat([torch.tensor([0.], dtype=torch.float64),
self.lats_in,
torch.tensor([math.pi], dtype=torch.float64)]).contiguous()
# prepare the interpolation by computing indices to the left and right of each output latitude
lat_idx = torch.searchsorted(self.lats_in, self.lats_out, side="right") - 1
# make sure that we properly treat the last point if they coincide with the pole
lat_idx = torch.where(self.lats_out == self.lats_in[-1], lat_idx - 1, lat_idx)
# lat_idx = np.where(self.lats_out > self.lats_in[-1], lat_idx - 1, lat_idx)
# lat_idx = np.where(self.lats_out < self.lats_in[0], 0, lat_idx)
# compute the interpolation weights along the latitude
lat_weights = ((self.lats_out - self.lats_in[lat_idx]) / torch.diff(self.lats_in)[lat_idx]).to(torch.float32)
lat_weights = lat_weights.unsqueeze(-1)
# register buffers
self.register_buffer("lat_idx", lat_idx, persistent=False)
self.register_buffer("lat_weights", lat_weights, persistent=False)
# get left and right indices but this time make sure periodicity in the longitude is handled
lon_idx_left = torch.searchsorted(self.lons_in, self.lons_out, side="right") - 1
lon_idx_right = torch.where(self.lons_out >= self.lons_in[-1], torch.zeros_like(lon_idx_left), lon_idx_left + 1)
# get the difference
diff = self.lons_in[lon_idx_right] - self.lons_in[lon_idx_left]
diff = torch.where(diff < 0.0, diff + 2 * math.pi, diff)
lon_weights = ((self.lons_out - self.lons_in[lon_idx_left]) / diff).to(torch.float32)
# register buffers
self.register_buffer("lon_idx_left", lon_idx_left, persistent=False)
self.register_buffer("lon_idx_right", lon_idx_right, persistent=False)
self.register_buffer("lon_weights", lon_weights, persistent=False)
self.skip_resampling = (nlon_in == nlon_out) and (nlat_in == nlat_out) and (grid_in == grid_out)
def extra_repr(self):
return f"in_shape={(self.nlat_in, self.nlon_in)}, out_shape={(self.nlat_out, self.nlon_out)}"
def _upscale_longitudes(self, x: torch.Tensor):
"""Upscale the longitude dimension using interpolation."""
# do the interpolation
lwgt = self.lon_weights.to(x.dtype)
if self.mode == "bilinear":
x = torch.lerp(x[..., self.lon_idx_left], x[..., self.lon_idx_right], lwgt)
else:
omega = x[..., self.lon_idx_right] - x[..., self.lon_idx_left]
somega = torch.sin(omega)
start_prefac = torch.where(somega > 1e-4, torch.sin((1.0 - lwgt) * omega) / somega, (1.0 - lwgt))
end_prefac = torch.where(somega > 1e-4, torch.sin(lwgt * omega) / somega, lwgt)
x = start_prefac * x[..., self.lon_idx_left] + end_prefac * x[..., self.lon_idx_right]
return x
def _expand_poles(self, x: torch.Tensor):
"""Expand the data to include pole values for interpolation."""
x_north = x[..., 0, :].sum(dim=-1, keepdims=True)
x_south = x[..., -1, :].sum(dim=-1, keepdims=True)
x_count = torch.tensor([x.shape[-1]], dtype=torch.long, device=x.device, requires_grad=False)
if self.comm_size_azimuth > 1:
x_north = reduce_from_azimuth_region(x_north.contiguous())
x_south = reduce_from_azimuth_region(x_south.contiguous())
x_count = reduce_from_azimuth_region(x_count)
x_north = x_north / x_count
x_south = x_south / x_count
if self.comm_size_azimuth > 1:
x_north = copy_to_azimuth_region(x_north)
x_south = copy_to_azimuth_region(x_south)
x = nn.functional.pad(x, pad=[0, 0, 1, 1], mode='constant')
x[..., 0, :] = x_north[...]
x[..., -1, :] = x_south[...]
return x
def _upscale_latitudes(self, x: torch.Tensor):
"""Upscale the latitude dimension using interpolation."""
# do the interpolation
lwgt = self.lat_weights.to(x.dtype)
if self.mode == "bilinear":
x = torch.lerp(x[..., self.lat_idx, :], x[..., self.lat_idx + 1, :], lwgt)
else:
omega = x[..., self.lat_idx + 1, :] - x[..., self.lat_idx, :]
somega = torch.sin(omega)
start_prefac = torch.where(somega > 1e-4, torch.sin((1.0 - lwgt) * omega) / somega, (1.0 - lwgt))
end_prefac = torch.where(somega > 1e-4, torch.sin(lwgt * omega) / somega, lwgt)
x = start_prefac * x[..., self.lat_idx, :] + end_prefac * x[..., self.lat_idx + 1, :]
return x
def forward(self, x: torch.Tensor):
if self.skip_resampling:
return x
# transpose data so that h is local, and channels are split
num_chans = x.shape[-3]
# h and w is split. First we make w local by transposing into channel dim
if self.comm_size_polar > 1:
channels_shapes = compute_split_shapes(num_chans, self.comm_size_polar)
x = distributed_transpose_polar.apply(x, (-3, -2), self.lat_in_shapes)
# expand poles if requested
if self.expand_poles:
x = self._expand_poles(x)
# upscaling
x = self._upscale_latitudes(x)
# now, transpose back
if self.comm_size_polar > 1:
x = distributed_transpose_polar.apply(x, (-2, -3), channels_shapes)
# now, transpose in w:
if self.comm_size_azimuth > 1:
channels_shapes = compute_split_shapes(num_chans, self.comm_size_azimuth)
x = distributed_transpose_azimuth.apply(x, (-3, -1), self.lon_in_shapes)
# upscale
x = self._upscale_longitudes(x)
# transpose back
if self.comm_size_azimuth > 1:
x = distributed_transpose_azimuth.apply(x, (-1, -3), channels_shapes)
return x
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