resample.py

# coding=utf-8

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from typing import List, Tuple, Union, Optional
import math
import numpy as np

import torch
import torch.nn as nn

from torch_harmonics.quadrature import _precompute_latitudes


class ResampleS2(nn.Module):
    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

        # for upscaling the latitudes we will use interpolation
        self.lats_in, _ = _precompute_latitudes(nlat_in, grid=grid_in)
        self.lons_in = np.linspace(0, 2 * math.pi, nlon_in, endpoint=False)
        self.lats_out, _ = _precompute_latitudes(nlat_out, grid=grid_out)
        self.lons_out = np.linspace(0, 2 * math.pi, nlon_out, endpoint=False)

        # 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 = np.insert(self.lats_in, 0, 0.0)
            self.lats_in = np.append(self.lats_in, np.pi)

        # prepare the interpolation by computing indices to the left and right of each output latitude
        lat_idx = np.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 = np.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 = torch.from_numpy((self.lats_out - self.lats_in[lat_idx]) / np.diff(self.lats_in)[lat_idx]).float()
        lat_weights = lat_weights.unsqueeze(-1)

        # convert to tensor
        lat_idx = torch.LongTensor(lat_idx)

        # 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 = np.searchsorted(self.lons_in, self.lons_out, side="right") - 1
        lon_idx_right = np.where(self.lons_out >= self.lons_in[-1], np.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 = np.where(diff < 0.0, diff + 2 * math.pi, diff)
        lon_weights = torch.from_numpy((self.lons_out - self.lons_in[lon_idx_left]) / diff).float()

        # convert to tensor
        lon_idx_left = torch.LongTensor(lon_idx_left)
        lon_idx_right = torch.LongTensor(lon_idx_right)

        # 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)

    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):
        # do the interpolation
        if self.mode == "bilinear":
            x = torch.lerp(x[..., self.lon_idx_left], x[..., self.lon_idx_right], self.lon_weights)
        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 - self.lon_weights) * omega) / somega, (1.0 - self.lon_weights))
            end_prefac = torch.where(somega > 1e-4, torch.sin(self.lon_weights * omega) / somega, self.lon_weights)
            x = start_prefac * x[..., self.lon_idx_left] + end_prefac * x[..., self.lon_idx_right]

        return x

    def _expand_poles(self, x: torch.Tensor):
        repeats = [1 for _ in x.shape]
        repeats[-1] = x.shape[-1]
        x_north = x[..., 0:1, :].mean(dim=-1, keepdim=True).repeat(*repeats)
        x_south = x[..., -1:, :].mean(dim=-1, keepdim=True).repeat(*repeats)
        x = torch.concatenate((x_north, x, x_south), dim=-2)
        return x

    def _upscale_latitudes(self, x: torch.Tensor):
        # do the interpolation
        if self.mode == "bilinear":
            x = torch.lerp(x[..., self.lat_idx, :], x[..., self.lat_idx + 1, :], self.lat_weights)
        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 - self.lat_weights) * omega) / somega, (1.0 - self.lat_weights))
            end_prefac = torch.where(somega > 1e-4, torch.sin(self.lat_weights * omega) / somega, self.lat_weights)
            x = start_prefac * x[..., self.lat_idx, :] + end_prefac * x[..., self.lat_idx + 1, :]

        return x

    def forward(self, x: torch.Tensor):
        if self.expand_poles:
            x = self._expand_poles(x)
        x = self._upscale_latitudes(x)
        x = self._upscale_longitudes(x)
        return x