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75 lines
2.3 KiB
Python
75 lines
2.3 KiB
Python
#!/usr/bin/env python3
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"""
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sdta_smn_portability.py — SMN Portability Simulator for the SDTA Framework
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Computes the portability coefficient η = ||Π_D A Π_D†||_F / ||A||_F
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for a given constraint matrix, predicting how much of the problem's
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structure can be captured in the degenerate (ZIM-Sidon) subspace.
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This is a reference implementation of the SDTA portability screen.
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See 6-Documentation/docs/specs/sdta_spec.md §4 for the formal definition.
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Usage:
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python3 sdta_smn_portability.py # default 8x8 test
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python3 sdta_smn_portability.py instance.npy # load from file
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"""
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import numpy as np
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import sys
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def compute_smn(A: np.ndarray) -> float:
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"""Semantic mass: average absolute correlation between constraint pairs.
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Proxy for constraint interlocking. High SMN = low portability."""
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n = A.shape[0]
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smn = 0.0
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count = 0
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for i in range(n):
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for j in range(i + 1, n):
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smn += abs(A[i, j] * A[j, i])
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count += 1
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return smn / max(count, 1)
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def zim_sidon_rotate(A: np.ndarray, k: int):
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"""Rotate A into the k-dimensional Sidon-degenerate subspace.
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Returns: (A_D, A_res, eta) where:
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A_D = projection onto top-k singular subspace
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A_res = residual = A - A_D
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eta = portability coefficient = ||A_D||_F / ||A||_F
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"""
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n = A.shape[0]
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U, s, Vt = np.linalg.svd(A, full_matrices=False)
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k_actual = min(k, n)
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A_D = U[:, :k_actual] @ np.diag(s[:k_actual]) @ Vt[:k_actual, :]
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A_res = A - A_D
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norm_A = np.linalg.norm(A, 'fro')
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norm_AD = np.linalg.norm(A_D, 'fro')
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eta = norm_AD / norm_A if norm_A > 0 else 0.0
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return A_D, A_res, eta
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def main():
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if len(sys.argv) < 2:
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# Default test: 8x8 symmetric random matrix
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n = 8
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np.random.seed(42)
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A = np.random.randn(n, n) * 0.5
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A = (A + A.T) / 2
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else:
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A = np.load(sys.argv[1])
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smn = compute_smn(A)
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k = A.shape[0] // 2
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A_D, A_res, eta = zim_sidon_rotate(A, k)
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print(f"Problem size: {A.shape[0]}x{A.shape[0]}")
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print(f"SMN (semantic mass): {smn:.4f}")
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print(f"Portability eta: {eta:.4f}")
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print(f"Original search space: 2^{A.shape[0]} = {2**A.shape[0]}")
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residual_bits = A.shape[0] * (1 - eta)
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print(f"Residual search space: 2^{residual_bits:.2f} = {int(2**residual_bits)}")
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if __name__ == "__main__":
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main()
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