Example 01 Quickstart

Example 01 Quickstart

dtfit quickstart -- your first fit in a minute.

dtfit fits models that are nonlinear in their parameters (exponential, transcendental, oscillatory, mixed). You bring a model as a small sympy expression string (e.g. "aexp(bt)") and your data; dtfit recovers the parameters and returns a self-describing FittingResult.

Run headless: python examples/01_quickstart.py

Source: packages/dtfit/examples/01_quickstart.py

import numpy as np

from dtfit import Original, fit


def main() -> None:
    rng = np.random.default_rng(0)
    x = np.linspace(0, 3, 200)
    y = 1.4 * np.exp(0.8 * x) + rng.normal(0, 0.15, x.size)

    # 1. A first fit. Everything in the expression except the variable "t" is a
    #    free parameter -- here a and b.
    res = fit("a*exp(b*t)", Original(x, y), "t", basis="legendre")
    print("== fit(basis="legendre"): a*exp(b*t) ==")
    print(res.summary())
    print("params:", {k: round(v, 4) for k, v in res.params.items()})
    # The optimizer's verdict travels with the result: check it before trusting a
    # fit (converged is False on a misspecified model or a bad seed).
    print("converged:", res.converged)

    # 2. Uncertainty: an overdetermined fit carries a parameter covariance, so it
    #    reports standard errors, confidence intervals and a prediction band.
    print("\n== uncertainty ==")
    print("stderr:", {k: round(v, 4) for k, v in res.stderr().items()})
    print("95% CI:", {k: tuple(round(b, 3) for b in ci)
                      for k, ci in res.confidence_intervals().items()})
    xs = np.linspace(x.min(), x.max(), 5)
    y_hat, y_sd = res.predict(xs, return_std=True)
    print("predict(return_std) sd:", np.round(y_sd, 4))

    # opt-in extrapolation guard: predicting past the fitted range is the classic
    # curve-fitting footgun, so warn_extrapolation flags it instead of silently
    # returning a wild value.
    import warnings
    with warnings.catch_warnings(record=True) as caught:
        warnings.simplefilter("always")
        res.predict(np.array([x.max() + 5.0]), warn_extrapolation=True)
    print("extrapolation warned:", bool(caught))

    # 3. Don't want to choose the basis? basis="auto" fits the candidates and
    # keeps whichever leaves the smallest residual over the samples.
    res2 = fit("a*exp(b*t)", Original(x, y), "t", basis="auto")
    print("\n== fit(basis=\"auto\") ==")
    print("params:", {k: round(v, 4) for k, v in res2.params.items()})


if __name__ == "__main__":
    main()

Output (python examples/01_quickstart.py)

== fit(basis="legendre"): a*exp(b*t) ==
FittingResult: a*exp(b*t)
  a = 1.40773 +/- 0.00896
  b = 0.797487 +/- 0.00258
  R^2 = 0.998637
params: {'a': 1.4077, 'b': 0.7975}
converged: True

== uncertainty ==
stderr: {'a': 0.009, 'b': 0.0026}
95% CI: {'a': (1.39, 1.425), 'b': (0.792, 0.803)}
predict(return_std) sd: [0.009  0.0115 0.0128 0.0128 0.0325]
extrapolation warned: True

== fit(basis="auto") ==
params: {'a': 1.4077, 'b': 0.7975}