Used Fit Models¶

The currently implemented fit models are builtin models from lmfit. To understand what the parameters stand for in the actual equations, you can have a look at the documentation given for the models themselves.

Exponential curve¶

class ExponentialModel(independent_vars=['x'], prefix='', nan_policy='raise', **kwargs)[source]¶

A model based on an exponential decay function (see https://en.wikipedia.org/wiki/Exponential_decay) with two Parameters: amplitude ( $A$ ), and decay ( $\tau$ ), in:

$f(x; A, \tau) = A e^{-x/\tau}$

Parameters

independent_vars (['x']) – Arguments to func that are independent variables.
prefix (str, optional) – String to prepend to parameter names, needed to add two Models that have parameter names in common.
nan_policy (str, optional) – How to handle NaN and missing values in data. Must be one of: ‘raise’ (default), ‘propagate’, or ‘omit’. See Notes below.
**kwargs (optional) – Keyword arguments to pass to Model.

Notes

1. nan_policy sets what to do when a NaN or missing value is seen in the data. Should be one of:

‘raise’ : Raise a ValueError (default)

‘propagate’ : do nothing

‘omit’ : drop missing data

Logistic curve¶

class StepModel(independent_vars=['x'], prefix='', nan_policy='raise', form='linear', **kwargs)[source]¶

A model based on a Step function, with three Parameters: amplitude ( $A$ ), center ( $\mu$ ) and sigma ( $\sigma$ ).

There are four choices for form:

linear (the default)
atan or arctan for an arc-tangent function
erf for an error function
logistic for a logistic function (see https://en.wikipedia.org/wiki/Logistic_function)

The step function starts with a value 0, and ends with a value of $A$ rising to $A/2$ at $\mu$ , with $\sigma$ setting the characteristic width. The functional forms are defined as:

$\begin{eqnarray*} & f(x; A, \mu, \sigma, {\mathrm{form={}'linear{}'}}) & = A \min{[1, \max{(0, \alpha)}]} \\ & f(x; A, \mu, \sigma, {\mathrm{form={}'arctan{}'}}) & = A [1/2 + \arctan{(\alpha)}/{\pi}] \\ & f(x; A, \mu, \sigma, {\mathrm{form={}'erf{}'}}) & = A [1 + {\operatorname{erf}}(\alpha)]/2 \\ & f(x; A, \mu, \sigma, {\mathrm{form={}'logistic{}'}})& = A [1 - \frac{1}{1 + e^{\alpha}} ] \end{eqnarray*}$

where $\alpha = (x - \mu)/{\sigma}$ .

Parameters

independent_vars (['x']) – Arguments to func that are independent variables.
prefix (str, optional) – String to prepend to parameter names, needed to add two Models that have parameter names in common.
nan_policy (str, optional) – How to handle NaN and missing values in data. Must be one of: ‘raise’ (default), ‘propagate’, or ‘omit’. See Notes below.
**kwargs (optional) – Keyword arguments to pass to Model.

Notes

1. nan_policy sets what to do when a NaN or missing value is seen in the data. Should be one of:

‘raise’ : Raise a ValueError (default)

‘propagate’ : do nothing

‘omit’ : drop missing data