60 lines
1.7 KiB
Python
60 lines
1.7 KiB
Python
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import numpy as np
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from scipy.special import legendre
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from scipy.special import p_roots
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import libsharp
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from numpy.testing import assert_allclose
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def check_legendre_transform(lmax, ntheta):
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l = np.arange(lmax + 1)
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if lmax >= 1:
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sigma = -np.log(1e-3) / lmax / (lmax + 1)
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bl = np.exp(-sigma*l*(l+1))
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bl *= (2 * l + 1)
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else:
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bl = np.asarray([1], dtype=np.double)
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theta = np.linspace(0, np.pi, ntheta, endpoint=True)
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x = np.cos(theta)
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# Compute truth using scipy.special.legendre
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P = np.zeros((ntheta, lmax + 1))
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for l in range(lmax + 1):
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P[:, l] = legendre(l)(x)
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y0 = np.dot(P, bl)
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# double-precision
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y = libsharp.legendre_transform(x, bl)
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assert_allclose(y, y0, rtol=1e-12, atol=1e-12)
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# single-precision
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y32 = libsharp.legendre_transform(x.astype(np.float32), bl)
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assert_allclose(y, y0, rtol=1e-5, atol=1e-5)
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def test_legendre_transform():
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nthetas_to_try = [0, 9, 17, 19] + list(np.random.randint(500, size=20))
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for ntheta in nthetas_to_try:
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for lmax in [0, 1, 2, 3, 20] + list(np.random.randint(50, size=4)):
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yield check_legendre_transform, lmax, ntheta
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def check_legendre_roots(n):
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xs, ws = ([], []) if n == 0 else p_roots(n) # from SciPy
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xl, wl = libsharp.legendre_roots(n)
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assert_allclose(xs, xl, rtol=1e-14, atol=1e-14)
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assert_allclose(ws, wl, rtol=1e-14, atol=1e-14)
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def test_legendre_roots():
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"""
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Test the Legendre root-finding algorithm from libsharp by comparing it with
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the SciPy version.
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"""
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yield check_legendre_roots, 0
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yield check_legendre_roots, 1
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yield check_legendre_roots, 32
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yield check_legendre_roots, 33
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yield check_legendre_roots, 128
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