tests.py

# coding=utf-8

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import unittest
import numpy as np
import torch
from torch_harmonics import *

# try:
#     from tqdm import tqdm
# except:
#     tqdm = lambda x : x

tqdm = lambda x : x

class TestLegendrePolynomials(unittest.TestCase):

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

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

        TOL = 1e-9

        t = np.linspace(0, np.pi, 100)
        pct = precompute_legpoly(self.mmax, self.lmax, t)

        for l in range(self.lmax):
            for m in range(l+1):
                diff = pct[m, l].numpy() / self.cml(m,l) - self.pml[(m,l)](np.cos(t))
                self.assertTrue(diff.max() <= TOL)
        print("done.")


class TestSphericalHarmonicTransform(unittest.TestCase):

    def __init__(self, testname, norm="ortho"):
        super(TestSphericalHarmonicTransform, self).__init__(testname)  # calling the super class init varies for different python versions.  This works for 2.7
        self.norm = norm
    
    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')

        self.batch_size = 128
        self.nlat = 256
        self.nlon = 2*self.nlat

    def test_sht_leggauss(self):
        print(f"Testing real-valued SHT on Legendre-Gauss grid with {self.norm} normalization")

        TOL = 1e-9
        testiters = [1, 2, 4, 8, 16]
        mmax = self.nlat
        lmax = mmax

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

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

                base = signal

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

    def test_sht_equiangular(self):
        print(f"Testing real-valued SHT on equiangular grid with {self.norm} normalization")

        TOL = 1e-1
        testiters = [1, 2, 4, 8]
        mmax = self.nlat // 2
        lmax = mmax

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

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

                base = signal

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


if __name__ == '__main__':
    sht_test_suite = unittest.TestSuite()
    sht_test_suite.addTest(TestLegendrePolynomials('test_legendre'))
    sht_test_suite.addTest(TestSphericalHarmonicTransform('test_sht_leggauss',    norm="ortho"))
    sht_test_suite.addTest(TestSphericalHarmonicTransform('test_sht_equiangular', norm="ortho"))
    sht_test_suite.addTest(TestSphericalHarmonicTransform('test_sht_leggauss',    norm="four-pi"))
    sht_test_suite.addTest(TestSphericalHarmonicTransform('test_sht_equiangular', norm="four-pi"))
    sht_test_suite.addTest(TestSphericalHarmonicTransform('test_sht_leggauss',    norm="schmidt"))
    sht_test_suite.addTest(TestSphericalHarmonicTransform('test_sht_equiangular', norm="schmidt"))
    unittest.TextTestRunner(verbosity=2).run(sht_test_suite)