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34 lines
1.2 KiB
Python
34 lines
1.2 KiB
Python
from linear_algebra_utils import LinearAlgebraUtils
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from eigenvalue_methods import EigenvalueMethods
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class RichardsonMethod:
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def __init__(self, A, b, x0=None, max_iterations=1000, tol=1e-5):
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self.A = A
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self.b = b
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self.x0 = x0 if x0 is not None else [0.0] * len(b)
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self.max_iterations = max_iterations
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self.tol = tol
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def solve(self):
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x = self.x0[:]
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lambda_min = EigenvalueMethods.inverse_power_method(self.A)
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lambda_max = EigenvalueMethods.power_method(self.A)
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if lambda_min < 0:
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raise ValueError("Matrix A is not positive semi-definite.")
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omega = 2 / (lambda_min + lambda_max)
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for iteration in range(self.max_iterations):
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Ax = LinearAlgebraUtils.matrix_vector_multiply(self.A, x)
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residual = LinearAlgebraUtils.vector_subtraction(self.b, Ax)
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if LinearAlgebraUtils.vector_norm(residual) < self.tol:
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print('Convergence achieved.')
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return x
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x = LinearAlgebraUtils.vector_addition(x, LinearAlgebraUtils.scalar_multiply(omega, residual))
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print('Maximum number of iterations reached without convergence.')
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return x
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