test_sht.py

# coding=utf-8

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

class TestLegendrePolynomials(unittest.TestCase):

    def setUp(self):
        self.cml = lambda m, l : np.sqrt((2*l + 1) / 4 / np.pi) * np.sqrt(math.factorial(l-m) / math.factorial(l+m))
        self.pml = dict()

        # preparing associated Legendre Polynomials (These include the Condon-Shortley phase)
        # for reference see e.g. https://en.wikipedia.org/wiki/Associated_Legendre_polynomials
        self.pml[(0, 0)] = lambda x : np.ones_like(x)
        self.pml[(0, 1)] = lambda x : x
        self.pml[(1, 1)] = lambda x : - np.sqrt(1. - x**2)
        self.pml[(0, 2)] = lambda x : 0.5 * (3*x**2 - 1)
        self.pml[(1, 2)] = lambda x : - 3 * x * np.sqrt(1. - x**2)
        self.pml[(2, 2)] = lambda x : 3 * (1 - x**2)
        self.pml[(0, 3)] = lambda x : 0.5 * (5*x**3 - 3*x)
        self.pml[(1, 3)] = lambda x : 1.5 * (1 - 5*x**2) * np.sqrt(1. - x**2)
        self.pml[(2, 3)] = lambda x : 15 * x * (1 - x**2)
        self.pml[(3, 3)] = lambda x : -15 * np.sqrt(1. - x**2)**3

        self.lmax = self.mmax = 4

        self.tol = 1e-9

    def test_legendre(self):
        print("Testing computation of associated Legendre polynomials")
        from torch_harmonics.legendre import legpoly

        t = np.linspace(0, 1, 100)
        vdm = legpoly(self.mmax, self.lmax, t)

        for l in range(self.lmax):
            for m in range(l+1):
                diff = vdm[m, l] / self.cml(m,l) - self.pml[(m,l)](t)
                self.assertTrue(diff.max() <= self.tol)


class TestSphericalHarmonicTransform(unittest.TestCase):

    def setUp(self):

        if torch.cuda.is_available():
            print("Running test on GPU")
            self.device = torch.device('cuda')
        else:
            print("Running test on CPU")
            self.device = torch.device('cpu')

    @parameterized.expand([
        [256, 512, 32, "ortho",   "equiangular",    1e-9],
        [256, 512, 32, "ortho",   "legendre-gauss", 1e-9],
        [256, 512, 32, "four-pi", "equiangular",    1e-9],
        [256, 512, 32, "four-pi", "legendre-gauss", 1e-9],
        [256, 512, 32, "schmidt", "equiangular",    1e-9],
        [256, 512, 32, "schmidt", "legendre-gauss", 1e-9],
    ])
    def test_sht(self, nlat, nlon, batch_size, norm, grid, tol):
        print(f"Testing real-valued SHT on {nlat}x{nlon} {grid} grid with {norm} normalization")

        testiters = [1, 2, 4, 8, 16]
        if grid == "equiangular":
            mmax = nlat // 2
        else:
            mmax = nlat
        lmax = mmax

        sht = RealSHT(nlat, nlon, mmax=mmax, lmax=lmax, grid=grid, norm=norm).to(self.device)
        isht = InverseRealSHT(nlat, nlon, mmax=mmax, lmax=lmax, grid=grid, norm=norm).to(self.device)

        with torch.no_grad():
            coeffs = torch.zeros(batch_size, lmax, mmax, device=self.device, dtype=torch.complex128)
            coeffs[:, :lmax, :mmax] = torch.randn(batch_size, lmax, mmax, device=self.device, dtype=torch.complex128)
            signal = isht(coeffs)
        
        # testing error accumulation
        for iter in testiters:
            with self.subTest(i = iter):
                print(f"{iter} iterations of batchsize {batch_size}:")

                base = signal

                for _ in range(iter):
                    base = isht(sht(base))
            
                err = torch.mean(torch.norm(base-signal, p='fro', dim=(-1,-2)) / torch.norm(signal, p='fro', dim=(-1,-2)) )
                print(f"final relative error: {err.item()}")
                self.assertTrue(err.item() <= tol)

    @parameterized.expand([
        [12, 24, 2, "ortho",   "equiangular",    1e-5],
        [12, 24, 2, "ortho",   "legendre-gauss", 1e-5],
        [12, 24, 2, "four-pi", "equiangular",    1e-5],
        [12, 24, 2, "four-pi", "legendre-gauss", 1e-5],
        [12, 24, 2, "schmidt", "equiangular",    1e-5],
        [12, 24, 2, "schmidt", "legendre-gauss", 1e-5],
    ])
    def test_sht_grad(self, nlat, nlon, batch_size, norm, grid, tol):
        print(f"Testing gradients of real-valued SHT on {nlat}x{nlon} {grid} grid with {norm} normalization")

        if grid == "equiangular":
            mmax = nlat // 2
        else:
            mmax = nlat
        lmax = mmax

        sht = RealSHT(nlat, nlon, mmax=mmax, lmax=lmax, grid=grid, norm=norm).to(self.device)
        isht = InverseRealSHT(nlat, nlon, mmax=mmax, lmax=lmax, grid=grid, norm=norm).to(self.device)

        with torch.no_grad():
            coeffs = torch.zeros(batch_size, lmax, mmax, device=self.device, dtype=torch.complex128)
            coeffs[:, :lmax, :mmax] = torch.randn(batch_size, lmax, mmax, device=self.device, dtype=torch.complex128)
            signal = isht(coeffs)
        
        input = torch.randn_like(signal, requires_grad=True)
        err_handle = lambda x : torch.mean(torch.norm( isht(sht(x)) - signal , p='fro', dim=(-1,-2)) / torch.norm(signal, p='fro', dim=(-1,-2)) )
        test_result = gradcheck(err_handle, input, eps=1e-6, atol=tol)
        self.assertTrue(test_result)


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