Data.lmfit

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

Wrap the lmfit module fitting.

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") – Specifiy 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 paraeters 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 optinally as a column of data.

Note

If p0 is fed a 2D array, then it assumed that you want to calculate \(\chi^2\) for different starting parameters with some variables fixed. In this mode, fitting is carried out repeatedly with each row representing one attempt with different values of the parameters. In this mode the return value is a 2D array whose rows correspond to the inputs to the rows of p0, the columns are the fitted values of the parameters with an additional column for \(\chi^2\).

Example

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

from Stoner import Data

# 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")

# Do the fitting and plot the result
func = lambda x, A, B, C: A + B * exp(-x / C)
fit = d.lmfit(
    func,
    result=True,
    header="Fit",
    A=1,
    B=1,
    C=1,
    residuals=True,
    output="report",
)

# 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=["ro", "b-"])
d.xticklabels = [[]]
d.xlabel = ""

# Annotate plot with fitting parameters
d.annotate_fit(func, prefix="Model", x=7.2, y=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 = u"Levenberg-Marquardt Fit"

(png, hires.png, pdf)

../_images/lmfit2.png