45 lines
733 B
Python
45 lines
733 B
Python
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import numpy as np
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def decompose(M):
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n = len(M)
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U = M.copy()
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L = np.identity(n)
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for i in range(0, n - 1):
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for j in range(i + 1, n):
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L[j, i] = U[j, i] / U[i, i]
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U[j, i:n] -= L[j, i] * U[i, i:n]
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assert np.allclose(M, L@U)
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return L, U
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def solve_lower(m, v):
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x = np.zeros(len(v))
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for i in range(0, len(v)):
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x[i] = (v[i] - m[i, :i] @ x[:i]) / m[i, i]
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assert np.allclose(m@x, v)
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return x
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def solve_upper(m, v):
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x = np.zeros(len(v))
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for i in reversed(range(0, len(m))):
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x[i] = (v[i] - m[i, i+1:] @ x[i+1:]) / m[i, i]
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assert np.allclose(m@x, v)
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return x
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def solve(m, v):
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L, U = decompose(m)
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x = solve_upper(U, solve_lower(L, v))
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assert np.allclose(m@x, v)
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return x
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