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Fix lanczos test.

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Matrix was badly conditioned.
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alberto
2026-03-23 20:21:35 +01:00
parent d89e683110
commit 35bbbc2520
1 changed files with 8 additions and 6 deletions
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tests/test_main.py
+8 -6
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@@ -8,20 +8,22 @@ Todo: better test case
def test_lanczos_return_correct_solution(): def test_lanczos_return_correct_solution():
N = 6 N = 1000
M = 4 M = 999
eigvals = np.random.uniform(10000, 100000, N)
Q, _ = LA.qr(np.random.randn(N, N))
L = Q @ np.diag(eigvals) @ Q.T
A = np.random.randint(1, 10, size=(N, N))
L = (A + A.T) / 2
s = np.random.randint(1, 10, N) s = np.random.randint(1, 10, N)
[V, alp, beta] = lanczos(L, s, M) [V, alp, beta] = lanczos(L, s, M)
T = np.diag(alp) + np.diag(beta, -1) + np.diag(beta, 1) T = np.diag(alp) + np.diag(beta, -1) + np.diag(beta, 1)
x = LA.solve(A, s) x = LA.solve(L, s)
e_1 = np.zeros(M) e_1 = np.zeros(M)
e_1[0] = 1 e_1[0] = 1
y = (LA.inv(T) @ e_1) * LA.norm(s) y = (LA.inv(T) @ e_1) * LA.norm(s)
x_lanczos = V @ y x_lanczos = V @ y
assert LA.norm(x - x_lanczos) < 1e-3 assert LA.norm(x - x_lanczos) < 1e-10