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37 lines
1.5 KiB
Python
37 lines
1.5 KiB
Python
from linear_algebra_utils import LinearAlgebraUtils
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from eigenvalue_methods import EigenvalueMethods
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from matrix_generator import MatrixGenerator
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class RichardsonMethod:
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def __init__(self, A, b, size: int, 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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self.I = MatrixGenerator.generate_identity_matrix(size)
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self.lambda_min = EigenvalueMethods.inverse_power_method(self.A)
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if self.lambda_min < 0:
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raise ValueError("Matrix A is not positive semi-definite.")
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self.lambda_max = EigenvalueMethods.power_method(self.A)
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self.omega = 2 / (self.lambda_min + self.lambda_max)
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def will_converge(self) -> bool:
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wA = LinearAlgebraUtils.matrix_scalar_multiply(self.A, self.omega)
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IMinuswA = LinearAlgebraUtils.matrix_matrix_subtraction(self.I, wA)
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norm = LinearAlgebraUtils.matrix_norm(IMinuswA)
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return norm < 1
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def solve(self):
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x = self.x0[:]
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if not self.will_converge():
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return "Richardson method for those values will NOT converge"
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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_vector_subtraction(self.b, Ax)
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x = LinearAlgebraUtils.vector_vector_addition(x, LinearAlgebraUtils.scalar_matrix_multiply(self.omega, residual))
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return x
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