Python module#

Summary#

`powerfit.Limit`()	Small helper class to keep track of the lower and upper limits of a data set.
`powerfit.powerlaw`(xdata, ydata[, yerr, ...])	Fit a powerlaw \(y = c x^b\) by a linear fitting of \(\ln y = \ln c + b \ln x\).
`powerfit.exp`(xdata, ydata[, yerr, ...])	Fit an exponential \(y = c \exp(b x)\) by linear fitting of :math`ln y = ln c + b x`.
`powerfit.log`(xdata, ydata[, yerr])	Fit a logarithm \(y = a + b \ln x\).
`powerfit.linear`(xdata, ydata[, yerr, ...])	Fit a linear function \(y = a + b x\).

Details#

class powerfit.Limit#

Small helper class to keep track of the lower and upper limits of a data set.

For example:

lim = Limit()

for data in data_set:
    lim += data

print(lim.lower, lim.upper)

powerfit.evaluate_exp(x: ArrayLike, prefactor: float, exponent: float, **kwargs)#

Evaluate an exponential \(y = c \exp(b x)\)

Parameters:

x – Data points along \(x\).
prefactor – Prefactor \(c\).
exponent – Exponent \(b\).

Returns:

The evaluated exponential.

powerfit.evaluate_linear(x: ArrayLike, offset: float, slope: float, **kwargs)#

Evaluate a linear function \(y = a + b x\) at x.

Parameters:

x – Data points along \(x\).
offset – Offset \(a\).
slope – Slope \(b\).

Returns:

The evaluated linear function.

powerfit.evaluate_powerlaw(x: ArrayLike, prefactor: float, exponent: float, **kwargs)#

Evaluate a powerlaw \(y = c x^b\) at x.

Parameters:

x – Data points along \(x\).
prefactor – Prefactor \(c\).
exponent – Exponent \(b\).

Returns:

The evaluated powerlaw.

powerfit.exp(xdata: ArrayLike, ydata: ArrayLike, yerr: ArrayLike = None, yerr_mode: str = 'differentials', absolute_sigma: bool = True, prefactor: float = None, exponent: float = None) → dict#

Fit an exponential \(y = c \exp(b x)\) by linear fitting of :math`ln y = ln c + b x`. This function does not support more customised operation like fitting an offset, but custom code can be easily written by copy/pasting from here.

Warning

If this function is used to plot the fit, beware that the fit is plotted using just two data-points if the axis is set to semilogy-scale (as the fit will be a straight line on that scale).

Different modes are available to treat yerr:

"differentials": assume that yerr << ydata, such that

\[\begin{split}z &\equiv \ln y \\ \delta z &= \left| \frac{\partial z}{\partial y} \right| \delta y \\ \delta z &= \frac{\delta y}{y}\end{split}\]

See also

scipy.optimize.curve_fit

Parameters:

xdata – Data points along the x-axis.
ydata – Data points along the y-axis.
yerr – Error-bar for ydata.
absolute_sigma – Treat (the effective) yerr as absolute error.
offset – Offset \(a\) (fitted if not specified).
slope – Slope \(b\) (fitted if not specified).

Returns:

The fit details as a dictionary:

offset: (Fitted) offset :math:`a`.
slope: (Fitted) slope :math:`b`.
offset_error: Estimated error of offset.
slope_error: Estimated error of slope.
pcov: Covariance of fit.

powerfit.log(xdata: ArrayLike, ydata: ArrayLike, yerr: ArrayLike = None, **kwargs) → dict#: Fit a logarithm \(y = a + b \ln x\). See documentation of linear().

powerfit.powerlaw(xdata: ArrayLike, ydata: ArrayLike, yerr: ArrayLike = None, yerr_mode: str = 'differentials', absolute_sigma: bool = True, prefactor: float = None, exponent: float = None, cutoff_upper: int = 0, cutoff_lower: int = False) → dict#

Fit a powerlaw \(y = c x^b\) by a linear fitting of \(\ln y = \ln c + b \ln x\).

Note

This function does not support more customised operation like fitting an offset, but custom code can be easily written by copy/pasting from here.

Warning

If this function is used to plot the fit, beware that the fit is plotted using just two data-points if the axis is set to log-log scale (as the fit will be a straight line on that scale).

Different modes are available to treat an error estimate (yerr) in ydata:

"differentials": assume that yerr << ydata, such that

\[\begin{split}z &\equiv \ln y \\ \delta z &= \left| \frac{\partial z}{\partial y} \right| \delta y \\ \delta z &= \frac{\delta y}{y}\end{split}\]