import numpy as np
import json
from datetime import datetime, timezone

def extract_condition_number(matrix):
    """
    Calculates the condition number kappa(A) using SVD.
    kappa = sigma_max / sigma_min.
    High kappa = ill-conditioned matrix (noise dominates signal).
    """
    try:
        S = np.linalg.svd(matrix, compute_uv=False)
        s_max = np.max(S)
        s_min = np.min(S)
        
        if s_min == 0:
            return float('inf'), S
        
        kappa = s_max / s_min
        return kappa, S
    except Exception as e:
        return None, str(e)

def format_somatic_entry(seq, field, val, unit, crit=False):
    """Formats output to Somatic Ledger v1.0 standard."""
    return json.dumps({
        "ts": datetime.now(timezone.utc).isoformat().replace("+00:00", "Z"),
        "seq": seq,
        "field": field,
        "val": float(val),
        "unit": unit,
        "crit": crit
    })

if __name__ == "__main__":
    # Simulate an observation matrix A_hV 
    # (Observations h x Hypotheses V)
    np.random.seed(42)
    # Case 1: Well-conditioned signal
    A_stable = np.random.randn(50, 5) 
    # Case 2: Ill-conditioned (simulating sensor drift or collinearity)
    A_noisy = np.random.randn(50, 5)
    A_noisy[:, -1] = A_noisy[:, 0] * 1e-6 + np.random.randn(50) * 1e-7

    for name, mat in [("stable", A_stable), ("noisy", A_noisy)]:
        kappa, _ = extract_condition_number(mat)
        crit = kappa > 1000 if kappa else False
        print(f"{name}: {format_somatic_entry(1, 'kappa_A_hV', kappa, 'ratio', crit)}")