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71 lines
2.1 KiB
Python
71 lines
2.1 KiB
Python
import numpy as np
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from scipy.sparse.linalg import cg
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def generate_random_matrix_and_vector(size):
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A = np.random.uniform(-1, 1, (size, size))
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A = np.dot(A.T, A) + np.eye(size) * size # dodanie `size` do przekątnej zwiększa wartości własne -> obejście problemu z overflow
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b = np.random.uniform(-1, 1, size)
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return A, b
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def richardson(A, b, x0=None, max_iterations=1000, tol=1e-5):
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if x0 is None:
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x0 = np.zeros_like(b, dtype=float)
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x = np.array(x0, dtype=float)
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n = len(b)
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eigenvalues = np.linalg.eigvals(A)
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lambda_min = np.min(eigenvalues)
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lambda_max = np.max(eigenvalues)
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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(max_iterations):
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Ax = np.dot(A, x)
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residual = b - Ax
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if np.linalg.norm(residual) < tol:
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print('Convergence achieved.')
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return x
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x = x + omega * residual
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print('Maximum number of iterations reached without convergence.')
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return x
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def run_tests():
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test_sizes = [2, 3, 4, 5, 10, 20, 50, 100]
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tolerance = 1e-5
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for n in test_sizes:
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print(f"\nRunning test for n = {n}")
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A, b = generate_random_matrix_and_vector(n)
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# print("\nMatrix A:")
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# print(A)
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# print("\nVector b:")
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# print(b)
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solution_richardson = richardson(A, b, max_iterations=10000000, tol=1e-7)
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print("Richardson Method Solution:", solution_richardson)
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solution_cg, info = cg(A, b)
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if info == 0:
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print("SciPy Conjugate Gradient solution:", solution_cg)
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else:
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print("SciPy Conjugate Gradient did not converge.")
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difference = np.linalg.norm(solution_richardson - solution_cg)
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print(f"Difference between Richardson and CG solutions: {difference:.8f}")
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if difference < tolerance:
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print("The solutions are effectively the same.")
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else:
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print("The solutions are different!")
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run_tests()
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