dcmri.conc_step#

dcmri.conc_step(J, T, D, t=None, dt=1.0)[source]#

Indicator concentration inside a step system.

See section Step for more detail.

Parameters:

  • J (array_like) – the indicator flux entering the system.

  • T (float) – mean transit time of the system. Any non-negative value is allowed, including \(T=0\) and \(T=\infty\), in which case the compartment is a trap.

  • D (float) – dispersion of the system, or half-width of the step given as a fraction of T. Values must be between 0 (no dispersion) and 1 (maximal dispersion).

  • t (array_like, optional) – the time points of the indicator flux J, in the same units as T. If t=None, the time points are assumed to be uniformly spaced with spacing dt. Defaults to None.

  • dt (float, optional) – spacing between time points for uniformly spaced time points, in the same units as T. This parameter is ignored if t is explicity provided. Defaults to 1.0.

Returns:

Concentration as a 1D array.

Return type:

numpy.ndarray

See also

res_step, prop_step, flux_step

Example

>>> import dcmri as dc
>>> t = [0,5,15,30,60]
>>> J = [1,2,3,3,2]
>>> dc.conc_step(J, 5, 0.5, t)
array([ 0.        ,  6.44736842, 20.19736842, 28.20175439, 21.58625731])