silhouette 0.3.0

Silhouette is the Python library for intensity duration modelling in endurance sports.

Silhouette

A Python library for fitting power-duration curves to cycling data. Scikit-learn compatible.

Models

Model	Parameters
TwoParameterRegressor	CP, W'
ThreeParameterRegressor	CP, W', P_max
OmniDurationRegressor	CP, W', P_max, a, tcp_max

Installation

uv add silhouette

Or with pip:

pip install silhouette

Quick start

import numpy as np
from silhouette import OmniDurationRegressor

durations = np.array([5, 10, 30, 60, 120, 300, 600, 1200, 1800, 3600])
power = np.array([1050, 850, 600, 480, 400, 340, 310, 290, 275, 255])

reg = OmniDurationRegressor()
reg.fit(durations.reshape(-1, 1), power)

reg.cp_       # critical power (W)
reg.p_max_    # peak power (W)
reg.w_prime_  # anaerobic work capacity (J)

reg.predict(np.array([[300]]))  # predicted power at 5 minutes

All three models share the same interface. Swap OmniDurationRegressor for TwoParameterRegressor or ThreeParameterRegressor and the code works the same way.

Known parameters

When parameters are already known, use curve directly without fitting:

from silhouette import TwoParameterRegressor

t = np.arange(1, 3601)
power = TwoParameterRegressor.curve(t, cp=250, w_prime=20_000)

Custom bounds

reg = OmniDurationRegressor(
    bounds={"cp": (200, 400), "p_max": (800, 1500)},
    initial_params={"cp": 280},
)

Time to exhaustion

The inverse of the power-duration curve: given a power, how long can it be sustained?

# On a fitted model
tte = reg.predict_inverse(np.array([250, 300, 350]))

# With known parameters
tte = TwoParameterRegressor.curve_inverse(350, cp=250, w_prime=20_000)

References

• Monod, H., & Scherrer, J. (1965). The work capacity of a synergic muscular group. Ergonomics, 8(3), 329-338.
• Morton, R. H. (1996). A 3-parameter critical power model. Ergonomics, 39(4), 611-619.
• Puchowicz, M. J., Baker, J., & Clarke, D. C. (2020). Development and field validation of an omni-domain power-duration model. Journal of Sports Sciences, 38(7), 801-813.