test_convolution.py

# coding=utf-8

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import unittest
from parameterized import parameterized
from functools import partial
import math
import numpy as np
import torch
from torch.autograd import gradcheck
from torch_harmonics import *

from torch_harmonics.quadrature import _precompute_grid, _precompute_latitudes

def _compute_vals_isotropic(r: torch.Tensor, phi: torch.Tensor, nr: int, r_cutoff: float):
    """
    helper routine to compute the values of the isotropic kernel densely
    """

    kernel_size = (nr // 2) + nr % 2
    ikernel = torch.arange(kernel_size).reshape(-1, 1, 1)
    dr = 2 * r_cutoff  / (nr + 1)

    # compute the support
    if nr % 2 == 1:
        ir = ikernel * dr
    else:
        ir = (ikernel + 0.5) * dr

    vals = torch.where(
        ((r - ir).abs() <= dr) & (r <= r_cutoff),
        (1 - (r - ir).abs() / dr),
        0,
    )

    return vals


def _compute_vals_anisotropic(r: torch.Tensor, phi: torch.Tensor, nr: int, nphi: int, r_cutoff: float):
    """
    helper routine to compute the values of the anisotropic kernel densely
    """

    kernel_size = (nr // 2) * nphi + nr % 2
    ikernel = torch.arange(kernel_size).reshape(-1, 1, 1)
    dr = 2 * r_cutoff  / (nr + 1)
    dphi = 2.0 * math.pi / nphi

    # disambiguate even and uneven cases and compute the support
    if nr % 2 == 1:
        ir = ((ikernel - 1) // nphi + 1) * dr
        iphi = ((ikernel - 1) % nphi) * dphi
    else:
        ir = (ikernel // nphi + 0.5) * dr
        iphi = (ikernel % nphi) * dphi

    # compute the value of the filter
    if nr % 2 == 1:
        # find the indices where the rotated position falls into the support of the kernel
        cond_r = ((r - ir).abs() <= dr) & (r <= r_cutoff)
        cond_phi = ((phi - iphi).abs() <= dphi) | ((2 * math.pi - (phi - iphi).abs()) <= dphi)
        r_vals = torch.where(cond_r, (1 - (r - ir).abs() / dr) , 0.0)
        phi_vals = torch.where(cond_phi, (1 - torch.minimum((phi - iphi).abs(), (2 * math.pi - (phi - iphi).abs())) / dphi), 0.0)
        vals = torch.where(ikernel > 0, r_vals * phi_vals, r_vals)
    else:
        # find the indices where the rotated position falls into the support of the kernel
        cond_r = ((r - ir).abs() <= dr) & (r <= r_cutoff)
        cond_phi = ((phi - iphi).abs() <= dphi) | ((2 * math.pi - (phi - iphi).abs()) <= dphi)
        r_vals = torch.where(cond_r, (1 - (r - ir).abs() / dr), 0.0)
        phi_vals = torch.where(cond_phi, (1 - torch.minimum((phi - iphi).abs(), (2 * math.pi - (phi - iphi).abs())) / dphi), 0.0)
        vals = r_vals * phi_vals

        # in the even case, the inner casis functions overlap into areas with a negative areas
        rn = - r
        phin = torch.where(phi + math.pi >= 2*math.pi, phi - math.pi, phi + math.pi)
        cond_rn = ((rn - ir).abs() <= dr) & (rn <= r_cutoff)
        cond_phin = ((phin - iphi).abs() <= dphi) | ((2 * math.pi - (phin - iphi).abs()) <= dphi)
        rn_vals = torch.where(cond_rn, (1 - (rn - ir).abs() / dr), 0.0)
        phin_vals = torch.where(cond_phin, (1 - torch.minimum((phin - iphi).abs(), (2 * math.pi - (phin - iphi).abs())) / dphi), 0.0)
        vals += rn_vals * phin_vals

    return vals

def _normalize_convolution_tensor_dense(psi, quad_weights, transpose_normalization=False, merge_quadrature=False, eps=1e-9):
    """
    Discretely normalizes the convolution tensor.
    """

    kernel_size, nlat_out, nlon_out, nlat_in, nlon_in = psi.shape
    scale_factor = float(nlon_in // nlon_out)

    if transpose_normalization:
        # the normalization is not quite symmetric due to the compressed way psi is stored in the main code
        # look at the normalization code in the actual implementation
        psi_norm = torch.sum(quad_weights.reshape(1, -1, 1, 1, 1) * psi[:,:,:1], dim=(1, 4), keepdim=True) / scale_factor
        if merge_quadrature:
            psi = quad_weights.reshape(1, -1, 1, 1, 1) * psi
    else:
        psi_norm = torch.sum(quad_weights.reshape(1, 1, 1, -1, 1) * psi, dim=(3, 4), keepdim=True)
        if merge_quadrature:
            psi = quad_weights.reshape(1, 1, 1, -1, 1) * psi

    return psi / (psi_norm + eps)


def _precompute_convolution_tensor_dense(in_shape, out_shape, kernel_shape, quad_weights, grid_in="equiangular", grid_out="equiangular", theta_cutoff=0.01 * math.pi, transpose_normalization=False, merge_quadrature=False):
    """
    Helper routine to compute the convolution Tensor in a dense fashion
    """

    assert len(in_shape) == 2
    assert len(out_shape) == 2

    quad_weights = quad_weights.reshape(-1, 1)

    if len(kernel_shape) == 1:
        kernel_handle = partial(_compute_vals_isotropic, nr=kernel_shape[0], r_cutoff=theta_cutoff)
        kernel_size = math.ceil( kernel_shape[0] / 2)
    elif len(kernel_shape) == 2:
        kernel_handle = partial(_compute_vals_anisotropic, nr=kernel_shape[0], nphi=kernel_shape[1], r_cutoff=theta_cutoff)
        kernel_size = (kernel_shape[0] // 2) * kernel_shape[1] + kernel_shape[0] % 2
    else:
        raise ValueError("kernel_shape should be either one- or two-dimensional.")

    nlat_in, nlon_in = in_shape
    nlat_out, nlon_out = out_shape

    lats_in, _ = quadrature._precompute_latitudes(nlat_in, grid=grid_in)
    lats_in = torch.from_numpy(lats_in).float()
    lats_out, _ = quadrature._precompute_latitudes(nlat_out, grid=grid_out)
    lats_out = torch.from_numpy(lats_out).float()  # array for accumulating non-zero indices

    # compute the phi differences. We need to make the linspace exclusive to not double the last point
    lons_in = torch.linspace(0, 2 * math.pi, nlon_in + 1)[:-1]
    lons_out = torch.linspace(0, 2 * math.pi, nlon_out + 1)[:-1]

    out = torch.zeros(kernel_size, nlat_out, nlon_out, nlat_in, nlon_in)

    for t in range(nlat_out):
        for p in range(nlon_out):
            alpha = -lats_out[t]
            beta = lons_in - lons_out[p]
            gamma = lats_in.reshape(-1, 1)

            # compute latitude of the rotated position
            z = -torch.cos(beta) * torch.sin(alpha) * torch.sin(gamma) + torch.cos(alpha) * torch.cos(gamma)

            # compute cartesian coordinates of the rotated position
            x = torch.cos(alpha) * torch.cos(beta) * torch.sin(gamma) + torch.cos(gamma) * torch.sin(alpha)
            y = torch.sin(beta) * torch.sin(gamma)

            # normalize instead of clipping to ensure correct range
            norm = torch.sqrt(x * x + y * y + z * z)
            x = x / norm
            y = y / norm
            z = z / norm

            # compute spherical coordinates
            theta = torch.arccos(z)
            phi = torch.arctan2(y, x) + torch.pi

            # find the indices where the rotated position falls into the support of the kernel
            out[:, t, p, :, :] = kernel_handle(theta, phi)

    # take care of normalization
    out = _normalize_convolution_tensor_dense(out, quad_weights=quad_weights, transpose_normalization=transpose_normalization, merge_quadrature=merge_quadrature)

    return out


class TestDiscreteContinuousConvolution(unittest.TestCase):
    def setUp(self):
        if torch.cuda.is_available():
            self.device = torch.device("cuda:0")
            torch.cuda.set_device(self.device.index)
            torch.cuda.manual_seed(333)
        else:
            self.device = torch.device("cpu")

        torch.manual_seed(333)

    @parameterized.expand(
        [
            # regular convolution
            [8, 4, 2, (16, 32), (16, 32), [3], "equiangular", "equiangular", False, 1e-4],
            [8, 4, 2, (16, 32), (8, 16), [5], "equiangular", "equiangular", False, 1e-4],
            [8, 4, 2, (16, 32), (8, 16), [3, 3], "equiangular", "equiangular", False, 1e-4],
            [8, 4, 2, (16, 32), (8, 16), [4, 3], "equiangular", "equiangular", False, 1e-4],
            [8, 4, 2, (16, 24), (8, 8), [3], "equiangular", "equiangular", False, 1e-4],
            [8, 4, 2, (18, 36), (6, 12), [7], "equiangular", "equiangular", False, 1e-4],
            [8, 4, 2, (16, 32), (8, 16), [5], "equiangular", "legendre-gauss", False, 1e-4],
            [8, 4, 2, (16, 32), (8, 16), [5], "legendre-gauss", "equiangular", False, 1e-4],
            [8, 4, 2, (16, 32), (8, 16), [5], "legendre-gauss", "legendre-gauss", False, 1e-4],
            # transpose convolution
            [8, 4, 2, (16, 32), (16, 32), [3], "equiangular", "equiangular", True, 1e-4],
            [8, 4, 2, (8, 16), (16, 32), [5], "equiangular", "equiangular", True, 1e-4],
            [8, 4, 2, (8, 16), (16, 32), [3, 3], "equiangular", "equiangular", True, 1e-4],
            [8, 4, 2, (8, 16), (16, 32), [4, 3], "equiangular", "equiangular", True, 1e-4],
            [8, 4, 2, (8, 8), (16, 24), [3], "equiangular", "equiangular", True, 1e-4],
            [8, 4, 2, (6, 12), (18, 36), [7], "equiangular", "equiangular", True, 1e-4],
            [8, 4, 2, (8, 16), (16, 32), [5], "equiangular", "legendre-gauss", True, 1e-4],
            [8, 4, 2, (8, 16), (16, 32), [5], "legendre-gauss", "equiangular", True, 1e-4],
            [8, 4, 2, (8, 16), (16, 32), [5], "legendre-gauss", "legendre-gauss", True, 1e-4],
        ]
    )
    def test_disco_convolution(
        self,
        batch_size,
        in_channels,
        out_channels,
        in_shape,
        out_shape,
        kernel_shape,
        grid_in,
        grid_out,
        transpose,
        tol,
    ):
        nlat_in, nlon_in = in_shape
        nlat_out, nlon_out = out_shape

        theta_cutoff = (kernel_shape[0] + 1) / 2 * torch.pi / float(nlat_out - 1)

        Conv = DiscreteContinuousConvTransposeS2 if transpose else DiscreteContinuousConvS2
        conv = Conv(
            in_channels,
            out_channels,
            in_shape,
            out_shape,
            kernel_shape,
            groups=1,
            grid_in=grid_in,
            grid_out=grid_out,
            bias=False,
            theta_cutoff=theta_cutoff
        ).to(self.device)

        _, wgl = _precompute_latitudes(nlat_in, grid=grid_in)
        quad_weights = 2.0 * torch.pi * torch.from_numpy(wgl).float().reshape(-1, 1) / nlon_in

        if transpose:
            psi_dense = _precompute_convolution_tensor_dense(out_shape, in_shape, kernel_shape, quad_weights, grid_in=grid_out, grid_out=grid_in, theta_cutoff=theta_cutoff, transpose_normalization=True, merge_quadrature=True).to(self.device)

            psi = torch.sparse_coo_tensor(conv.psi_idx, conv.psi_vals, size=(conv.kernel_size, conv.nlat_in, conv.nlat_out * conv.nlon_out)).to_dense()

            self.assertTrue(torch.allclose(psi, psi_dense[:, :, 0].reshape(-1, nlat_in, nlat_out * nlon_out)))
        else:
            psi_dense = _precompute_convolution_tensor_dense(in_shape, out_shape, kernel_shape, quad_weights, grid_in=grid_in, grid_out=grid_out, theta_cutoff=theta_cutoff, transpose_normalization=False, merge_quadrature=True).to(self.device)

            psi = torch.sparse_coo_tensor(conv.psi_idx, conv.psi_vals, size=(conv.kernel_size, conv.nlat_out, conv.nlat_in * conv.nlon_in)).to_dense()

            self.assertTrue(torch.allclose(psi, psi_dense[:, :, 0].reshape(-1, nlat_out, nlat_in * nlon_in)))

        # create a copy of the weight
        w_ref = torch.empty_like(conv.weight)
        with torch.no_grad():
            w_ref.copy_(conv.weight)
        w_ref.requires_grad = True

        # create an input signal
        x = torch.randn(batch_size, in_channels, *in_shape, device=self.device)

        # FWD and BWD pass
        x.requires_grad = True
        y = conv(x)
        grad_input = torch.randn_like(y)
        y.backward(grad_input)
        x_grad = x.grad.clone()

        # perform the reference computation
        x_ref = x.clone().detach()
        x_ref.requires_grad = True
        if transpose:
            y_ref = torch.einsum("oif,biqr->bofqr", w_ref, x_ref)
            y_ref = torch.einsum("fqrtp,bofqr->botp", psi_dense, y_ref)
        else:
            y_ref = torch.einsum("ftpqr,bcqr->bcftp", psi_dense, x_ref)
            y_ref = torch.einsum("oif,biftp->botp", w_ref, y_ref)
        y_ref.backward(grad_input)
        x_ref_grad = x_ref.grad.clone()

        # compare results
        self.assertTrue(torch.allclose(y, y_ref, rtol=tol, atol=tol))

        # compare
        self.assertTrue(torch.allclose(x_grad, x_ref_grad, rtol=tol, atol=tol))
        self.assertTrue(torch.allclose(conv.weight.grad, w_ref.grad, rtol=tol, atol=tol))


if __name__ == "__main__":
    unittest.main()