Data.differential_evolution

Data.differential_evolution(model, xcol=None, ycol=None, p0=None, sigma=None, **kargs)

Fit model to the data using a differential evolution algorithm.

Parameters:

  • model (lmfit.Model) – An instance of an lmfit.Model that represents the model to be fitted to the data

  • xcol (index or None) – Columns to be used for the x data for the fitting. If not givem defaults to the Stoner.Core.DataFile.setas x column

  • ycol (index or None) – Columns to be used for the y data for the fitting. If not givem defaults to the Stoner.Core.DataFile.setas y column

Keyword Arguments:

  • p0 (list, tuple, array or callable) – A vector of initial parameter values to try. See the notes in Stoner.Data.curve_fit() for more details.

  • sigma (index) – The index of the column with the y-error bars

  • bounds (callable) – A callable object that evaluates true if a row is to be included. Should be of the form f(x,y)

  • result (bool) – Determines whether the fitted data should be added into the DataFile object. If result is True then the last column will be used. If result is a string or an integer then it is used as a column index. Default to None for not adding fitted data

  • replace (bool) – Inidcatesa whether the fitted data replaces existing data or is inserted as a new column (default False)

  • header (string or None) – If this is a string then it is used as the name of the fitted data. (default None)

  • scale_covar (bool) – whether to automatically scale covariance matrix (leastsq only)

  • output (str, default "fit") – Specify what to return.

Returns:

( various ) –

The return value is determined by the output parameter. Options are
  • ”fit” just the lmfit.model.ModelFit instance that contains all relevant

    information about the fit.

  • ”row” just a one dimensional numpy array of the fit parameters interleaved with their

    uncertainties

  • ”full” a tuple of the fit instance and the row.

  • ”data” a copy of the Stoner.Core.DataFile object with the fit recorded in the

    emtadata and optionally as a column of data.

This function is essentially a wrapper around the scipy.optimize.differential_evolution() function that presents the same interface as the other Stoner package curve fitting functions. The parent function, however, does not provide the variance-covariance matrix to estimate the fitting errors. To work around this, this function does the initial fit with the differential evolution, but then uses that to give a starting vector to a call to scipy.optimize.curve_fit() to calculate the covariance matrix.

See also

Example

"""Simple use of lmfit to fit data."""
from numpy import linspace, exp, random

from Stoner import Data

random.seed(12345)  # Ensure consistent random numbers!
# Make some data
x = linspace(0, 10.0, 101)
y = 2 + 4 * exp(-x / 1.7) + random.normal(scale=0.2, size=101)

d = Data(x, y, column_headers=["Time", "Signal"], setas="xy")

func = lambda x, A, B, C: A + B * exp(-x / C)


# Do the fitting and plot the result
fit = d.differential_evolution(
    func,
    result=True,
    header="Fit",
    A=1,
    B=1,
    C=1,
    prefix="Model",
    residuals=True,
)

# Reset labels
d.labels = []

# Make nice two panel plot layout
ax = d.subplot2grid((3, 1), (2, 0))
d.setas = "x..y"
d.plot(fmt="g+")
d.title = ""

ax = d.subplot2grid((3, 1), (0, 0), rowspan=2)
d.setas = "xyy"
d.plot(fmt=["r.", "b-"])
d.xticklabels = [[]]
d.xlabel = ""

# Annotate plot with fitting parameters
d.annotate_fit(func, prefix="Model", x=0.7, y=0.3, fontdict={"size": "x-small"})
text = r"$y=A+Be^{-x/C}$" + "\n\n"
d.text(7.2, 3.9, text, fontdict={"size": "x-small"})
d.title = "Differential Evolution  Fit"

(png, hires.png, pdf)

../_images/diffev1.png