distributed_resample.py

# coding=utf-8

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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):
    r"""
    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):
        r"""
        Pretty print module
        """
        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.
        
        Parameters
        -----------
        x : torch.Tensor
            Input tensor with shape (..., nlat, nlon)
            
        Returns
        -------
        torch.Tensor
            Upscaled tensor in the longitude dimension
        """
        # 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.
        
        Parameters
        -----------
        x : torch.Tensor
            Input tensor with shape (..., nlat, nlon)
            
        Returns
        -------
        torch.Tensor
            Tensor with expanded pole values
        """
        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.
        
        Parameters
        -----------
        x : torch.Tensor
            Input tensor with shape (..., nlat, nlon)
            
        Returns
        -------
        torch.Tensor
            Upscaled tensor in the latitude dimension
        """
        # 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