Predefined Parametric Functions of Time

Syntax

result = curvefit.core.functions.fun(t, params)

Arguments

• t (np.array): This is a list or one dimensional numpy.array.

• params (np.array | List[float]): This is either a list, or numpy.array with one or two dimensions. In any case, len(params) == 3. If params is a two dimensional array, params.shape[1] == len(t). We use the notation below for the values in params:

  Notation	Definition
  $\alpha$	params[0]
  $\beta$	params[1]
  $p$	params[2]
  - fun (Callable): the possible values for fun are listed in the subheadings below:

expit

This is the generalized logistic function which is defined by $$\mbox{expit} ( t , \alpha , \beta , p ) = \frac{p}{ 1.0 + \exp [ - \alpha ( t - \beta ) ] }$$

ln_expit

This is the log of the generalized logistic function which is defined by $$\mbox{ln_expit} ( t , \alpha , \beta , p ) = \log \circ \; \mbox{expit} ( t , \alpha , \beta , p )$$

gaussian_cdf

This is the generalized Gaussian cumulative distribution function which is defined by $$\mbox{gaussian_cdf} ( t , \alpha , \beta , p ) = \frac{p}{2} \left[ 1.0 + \frac{2}{\pi} \int_0^{\alpha(t-\beta)} \exp ( - \tau^2 ) d \tau \right]$$

ln_gaussian_cdf

This is the log of the generalized Gaussian cumulative distribution function which is defined by $$\mbox{ln_gaussian_cdf} ( t , \alpha , \beta , p ) = \log \circ \; \mbox{gaussian_cdf} ( t , \alpha , \beta , p )$$

gaussian_pdf

This is the derivative of the generalized Gaussian cumulative distribution function which is defined by $$\mbox{gaussian_pdf} ( t , \alpha , \beta , p ) = \partial_t \; \mbox{gaussian_cdf} ( t , \alpha , \beta , p )$$

ln_gaussian_pdf

This is the log of the derivative of the generalized Gaussian cumulative distribution function which is defined by $$\mbox{ln_gaussian_cdf} ( t , \alpha , \beta , p ) = \log \circ \; \mbox{gaussian_pdf} ( t , \alpha , \beta , p )$$

dgaussian_pdf

This is the second derivative of the generalized Gaussian cumulative distribution function which is defined by $$\mbox{dgaussian_pdf} ( t , \alpha , \beta , p ) = \partial_t \; \mbox{gaussian_pdf} ( t , \alpha , \beta , p )$$

Result

The result is a list or one dimensional numpy.array with len(result) == len(t). If params is a list or one dimensional array

    result[i] = fun(t[i], alpha, beta, p)

If params is a two dimensional array

    result[i] = fun(t[i], alpha[i], beta[i], p[i])

Example

param_time_fun_xam