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30 lines
608 B
Python
30 lines
608 B
Python
import numpy as np
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import numpy.linalg as LA
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from afgl.lanczos import lanczos
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"""
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Todo: better test case
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"""
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def test_lanczos_return_correct_solution():
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N = 1000
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M = 999
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eigvals = np.random.uniform(10000, 100000, N)
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Q, _ = LA.qr(np.random.randn(N, N))
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L = Q @ np.diag(eigvals) @ Q.T
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s = np.random.randint(1, 10, N)
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[V, alp, beta] = lanczos(L, s, M)
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T = np.diag(alp) + np.diag(beta, -1) + np.diag(beta, 1)
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x = LA.solve(L, s)
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e_1 = np.zeros(M)
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e_1[0] = 1
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y = (LA.inv(T) @ e_1) * LA.norm(s)
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x_lanczos = V @ y
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assert LA.norm(x - x_lanczos) < 1e-10
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