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import numpy as np
def generate_orthogonal_matrix(n, id_num):
"""Deterministic orthogonal matrix for given ID and dimension."""
rng = np.random.RandomState(id_num * 17 + 42)
A = rng.randn(n, n)
Q, _ = np.linalg.qr(A)
if np.linalg.det(Q) < 0:
Q[:, 0] = -Q[:, 0]
return Q
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