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unixpickle/egg_balance.py

Created November 21, 2021 14:33
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  1. unixpickle created this gist Nov 21, 2021.
    30 changes: 30 additions & 0 deletions egg_balance.py
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    import numpy as np

    rows = 3
    cols = 6

    # Create all 2^(rows*cols) combinations of egg matrices.
    all_combos = np.zeros([1] * (rows * cols + 2), dtype=np.float32)
    for i in range(rows * cols):
    m = np.zeros([2, rows * cols], dtype=np.float32)
    m[1, i] = 1
    m = m.reshape([1 if i != j else 2 for j in range(rows * cols)] + [rows, cols])
    all_combos = all_combos + m
    all_combos = all_combos.reshape([-1, rows, cols])

    # Compute the center of masses
    coords = np.array([[row, col] for row in range(rows) for col in range(cols)])
    unnormalized = np.sum(all_combos.reshape([-1, rows * cols, 1]) * coords, axis=1)
    normalized = unnormalized / np.maximum(1e-5, np.sum(all_combos, axis=(1, 2))[:, None])

    center_dists = np.sum((normalized - [1, 2.5]) ** 2, axis=-1)
    is_center = center_dists < 1e-5
    is_odd = np.round(np.sum(all_combos, axis=(1, 2))).astype(np.int32) % 2 == 1
    print("total centered configs:", np.sum(is_center))
    print("total odd configs:", np.sum(is_odd))
    print("total odd centered configs:", np.sum(np.logical_and(is_center, is_odd)))

    min_odd_idx = np.argmin(center_dists[is_odd])
    min_odd = all_combos[is_odd][min_odd_idx]
    print("most centered odd configuration:")
    print(min_odd)