Editing Openai/693eaf5a-1494-8007-b1e3-00abefb11523 (section)

=== Assistant: Below is a clean, ready-to-run Python script that: ===
Below is a clean, ready-to-run Python script that:
# Takes a 1-D price series
# Computes optimal bin boundaries using maximum entropy / Freedman-Diaconis optimal binning (you can swap in other methods)
# Constructs a tetrahedral volume model
# Maps each bin to a proportional “swath” of the tetrahedral volume
# Reports the % of the total tetrahedral volume that each binned price region occupies

=== <syntaxhighlight lang="python">import numpy as np ===
import pandas as pd

=== ------------------------------------------------------------- ===
=== 1. Load or define your price series ===
=== ------------------------------------------------------------- ===
=== Example placeholder — replace with your actual prices: ===
prices = np.array([101, 100, 102, 105, 108, 107, 109, 115, 117, 120])

=== ------------------------------------------------------------- ===
=== 2. Compute optimal bins (Freedman–Diaconis rule) ===
=== ------------------------------------------------------------- ===
def optimal_bins(data):
    data = np.asarray(data)
    q75, q25 = np.percentile(data, [75 ,25])
    iqr = q75 - q25
    bin_width = 2 '' iqr '' len(data) ''' (-1/3)

    if bin_width == 0:
        return 1

    num_bins = int(np.ceil((data.max() - data.min()) / bin_width))
    return max(num_bins, 1)

num_bins = optimal_bins(prices)
bin_edges = np.linspace(prices.min(), prices.max(), num_bins + 1)

=== ------------------------------------------------------------- ===
=== 3. Bin the data ===
=== ------------------------------------------------------------- ===
bin_counts, _ = np.histogram(prices, bins=bin_edges)
total_points = len(prices)
bin_percentages = bin_counts / total_points

=== ------------------------------------------------------------- ===
=== 4. Tetrahedral geometry ===
=== ------------------------------------------------------------- ===
=== A regular tetrahedron with edge length L has volume: ===
=== V = L^3 / (6√2) ===
L = 1  # normalized tetrahedron
tetra_volume = L'''3 / (6 * np.sqrt(2))

=== Each bin gets a proportional “volume swath” ===
=== swath_volume = (bin_percentage) * (tetra_volume) ===
swath_volumes = bin_percentages * tetra_volume
swath_percentage_of_tetra = swath_volumes / tetra_volume  # equals bin % of total

=== ------------------------------------------------------------- ===
=== 5. Return a structured result ===
=== ------------------------------------------------------------- ===
df = pd.DataFrame({
    "Bin Lower": bin_edges[:-1],
    "Bin Upper": bin_edges[1:],
    "Count": bin_counts,
    "Price % of Total": np.round(bin_percentages * 100, 2),
    "Tetrahedral Volume %": np.round(swath_percentage_of_tetra * 100, 2),
})

print("\nOptimal Binning + Tetrahedral Swath Mapping\n")
print(df.to_string(index=False))
print("\nTotal tetrahedral volume (normalized L=1):", tetra_volume)

</syntaxhighlight>