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 *


def _compute_vals_isotropic(theta: torch.Tensor, phi: torch.Tensor, ntheta: int, theta_cutoff: float):
    """
    helper routine to compute the values of the isotropic kernel densely
    """

    # compute the support
    dtheta = (theta_cutoff - 0.0) / ntheta
    ikernel = torch.arange(ntheta).reshape(-1, 1, 1)
    itheta = ikernel * dtheta

    norm_factor = (
        2
        * math.pi
        * (
            1
            - math.cos(theta_cutoff - dtheta)
            + math.cos(theta_cutoff - dtheta)
            + (math.sin(theta_cutoff - dtheta) - math.sin(theta_cutoff)) / dtheta
        )
    )

    vals = torch.where(
        ((theta - itheta).abs() <= dtheta) & (theta <= theta_cutoff),
        (1 - (theta - itheta).abs() / dtheta) / norm_factor,
        0,
    )
    return vals

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

    # compute the support
    dtheta = (theta_cutoff - 0.0) / ntheta
    dphi = 2.0 * math.pi / nphi
    kernel_size = (ntheta-1)*nphi + 1
    ikernel = torch.arange(kernel_size).reshape(-1, 1, 1)
    itheta = ((ikernel - 1) // nphi + 1) * dtheta
    iphi = ((ikernel - 1) % nphi) * dphi

    norm_factor = 2 * math.pi * (1 - math.cos(theta_cutoff - dtheta) + math.cos(theta_cutoff - dtheta) + (math.sin(theta_cutoff - dtheta) - math.sin(theta_cutoff)) / dtheta)

    # find the indices where the rotated position falls into the support of the kernel
    cond_theta = ((theta - itheta).abs() <= dtheta) & (theta <= theta_cutoff)
    cond_phi = ((phi - iphi).abs() <= dphi) | ((2*math.pi - (phi - iphi).abs()) <= dphi)
    theta_vals = torch.where(cond_theta, (1 - (theta - itheta).abs() / dtheta) / norm_factor, 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, theta_vals * phi_vals, theta_vals)
    return vals

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

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

    if len(kernel_shape) == 1:
        kernel_handle = partial(_compute_vals_isotropic, ntheta=kernel_shape[0], theta_cutoff=theta_cutoff)
        kernel_size = kernel_shape[0]
    elif len(kernel_shape) == 2:
        kernel_handle = partial(_compute_vals_anisotropic, ntheta=kernel_shape[0], nphi=kernel_shape[1], theta_cutoff=theta_cutoff)
        kernel_size = (kernel_shape[0]-1)*kernel_shape[1] + 1
    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)

    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), [2   ], "equiangular",    "equiangular",    False, 5e-5],
            [8, 4, 2, (16, 32), ( 8, 16), [3   ], "equiangular",    "equiangular",    False, 5e-5],
            [8, 4, 2, (16, 32), ( 8, 16), [2, 3], "equiangular",    "equiangular",    False, 5e-5],
            [8, 4, 2, (18, 36), ( 6, 12), [4   ], "equiangular",    "equiangular",    False, 5e-5],
            [8, 4, 2, (16, 32), ( 8, 16), [3   ], "equiangular",    "legendre-gauss", False, 5e-5],
            [8, 4, 2, (16, 32), ( 8, 16), [3   ], "legendre-gauss", "equiangular",    False, 5e-5],
            [8, 4, 2, (16, 32), ( 8, 16), [3   ], "legendre-gauss", "legendre-gauss", False, 5e-5],
            # transpose convolution
            [8, 4, 2, (16, 32), (16, 32), [2   ], "equiangular",    "equiangular",    True, 5e-5],
            [8, 4, 2, ( 8, 16), (16, 32), [3   ], "equiangular",    "equiangular",    True, 5e-5],
            [8, 4, 2, ( 8, 16), (16, 32), [2, 3], "equiangular",    "equiangular",    True, 5e-5],
            [8, 4, 2, ( 6, 12), (18, 36), [4   ], "equiangular",    "equiangular",    True, 5e-5],
            [8, 4, 2, ( 8, 16), (16, 32), [3   ], "equiangular",    "legendre-gauss", True, 5e-5],
            [8, 4, 2, ( 8, 16), (16, 32), [3   ], "legendre-gauss", "equiangular",    True, 5e-5],
            [8, 4, 2, ( 8, 16), (16, 32), [3   ], "legendre-gauss", "legendre-gauss", True, 5e-5],
        ]
    )
    def test_disco_convolution(
        self,
        batch_size,
        in_channels,
        out_channels,
        in_shape,
        out_shape,
        kernel_shape,
        grid_in,
        grid_out,
        transpose,
        tol,
    ):
        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,
        ).to(self.device)

        nlat_in, nlon_in = in_shape
        nlat_out, nlon_out = out_shape

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

        if transpose:
            psi_dense = _precompute_convolution_tensor_dense(
                out_shape, in_shape, kernel_shape, grid_in=grid_out, grid_out=grid_in, theta_cutoff=theta_cutoff
            ).to(self.device)
        else:
            psi_dense = _precompute_convolution_tensor_dense(
                in_shape, out_shape, kernel_shape, grid_in=grid_in, grid_out=grid_out, theta_cutoff=theta_cutoff
            ).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 * conv.quad_weights)
        else:
            y_ref = torch.einsum("ftpqr,bcqr->bcftp", psi_dense, x_ref * conv.quad_weights)
            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()