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def cholesky(A):
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L = [[0.0] * len(A) for _ in range(len(A))]
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for i, (Ai, Li) in enumerate(zip(A, L)):
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for j, Lj in enumerate(L[:i+1]):
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s = sum(Li[k] * Lj[k] for k in range(j))
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Li[j] = sqrt(Ai[i] - s) if (i == j) else \
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(1.0 / Lj[j] * (Ai[j] - s))
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return L
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