folie.analysis.mfpt_1d¶
- folie.analysis.mfpt_1d(model, x_end: float, x_range, Npoints=500, x_start=None)[source]¶
Compute the mean first passage time from any point x within x_range to x_end, or from x_start to x_end if x_start is defined.
It use numerical integration of the following formula for point from x_range[0] to x_end [1]
\[MFPT(x,x_{end}) = \int_x^{x_{end}} \mathrm{d}y \frac{e^{\beta V(y)}}{D(y)} \int_{x\_range[0]}^y \mathrm{d} z e^{-\beta V(y)}\]and for point from x_end to x_range[1]
\[MFPT(x,x_{end}) = \int^x_{x_{end}} \mathrm{d}y \frac{e^{\beta V(y)}}{D(y)} \int^{x\_range[1]}_y \mathrm{d} z e^{-\beta V(y)}\]- Parameters:
- model:
A fitted overdamped model
- x_end: float
The point to reach
- x_start: float, default to None
If this is not None it return the MFPT from x_start to x_end, otherwise it return the mean first passage from any point within x_range to x_end
- x_range:
A range of integration, It should be big enough to be able to compute the normalisation factor of the steady state probability.
- Npoints: int, default=500
Number of point to use for
References
