deerlab.dd_rice3¶

dd_rice3 = <deerlab.model.Model object>¶

Sum of two 3D-Rice distributions model

Parameters:

rarray_like: Distance axis, in nanometers.
location1scalar: 1st Rician location.
spread1scalar: 1st Rician spread.
location2scalar: 2nd Rician location.
spread2scalar: 2nd Rician spread.
location3scalar: 3rd Rician location.
spread3scalar: 3rd Rician spread.
amp2scalar: 2nd Rician amplitude.
amp1scalar: 1st Rician amplitude.
amp3scalar: 3rd Rician amplitude.

Returns:

Pndarray: Distance distribution.

Notes

Parameter List

Name	Lower	Upper	Type	Frozen	Unit	Description
`location1`	1	20	nonlin	No	nm	1st Rician location
`spread1`	0.05	2.5	nonlin	No	nm	1st Rician spread
`location2`	1	20	nonlin	No	nm	2nd Rician location
`spread2`	0.05	2.5	nonlin	No	nm	2nd Rician spread
`location3`	1	20	nonlin	No	nm	3rd Rician location
`spread3`	0.05	2.5	nonlin	No	nm	3rd Rician spread
`amp2`	0	inf	linear	No		2nd Rician amplitude
`amp1`	0	inf	linear	No		1st Rician amplitude
`amp3`	0	inf	linear	No		3rd Rician amplitude

Model

$P(r) = a_1 R(r,\nu_1,\sigma_1) + a_2 R(r,\nu_2,\sigma_2) + a_3 R(r,\nu_3,\sigma_3)$

$R(r,\nu,\sigma) = \frac{\nu^{n/2-1}}{\sigma^2}r^{n/2}\exp\left(-\frac{(r^2+\nu^2)}{2\sigma^2}\right)I_{n/2-1}\left(\frac{r\nu}{\sigma^2} \right)$

where $n=3$ and $I_{n/2-1}(x)$ is the modified Bessel function of the first kind with order $n/2-1$ . This is a three-dimensional non-central chi distribution, the 3D generalization of the 2D Rice distribution.

Examples

Example of the model evaluated at the start values of the parameters:

(Source code, png, hires.png, pdf)