# inerroi

Computes the inner product on ROI.

## Contents

- Syntax
- Description
- Input Arguments
- Output Arguments
- More About
- References
- See Also
- Code

## Syntax

    i = innerroi(x,y,seti)

## Description

`innerroi(x,y,seti)` computes the inner product on the region of interest from two complex vectors x, y.

## Input Arguments

- x, y : two complex vectors of size seti.nROI^seti.dim (values in region of interest written as a vector).
- seti.dV : area/volume of the infinitesimal element (pixel/voxel) of CD, setGrid.html.

## Output Arguments

i : inner product on ROI, see More About.

## More About

The inner product is, see [1, Sec. 3.6, eq. (33)]:

with for with .

## References

- [1] Florian Bürgel, Kamil S. Kazimierski, and Armin Lechleiter. A sparsity regularization and total variation based computational framework for the inverse medium problem in scattering. Journal of Computational Physics, 339:1-30, 2017. URL: https://doi.org/10.1016/j.jcp.2017.03.011.

## See Also

- innerinv.html
- normroi.html

## Code

    function i = innerroi(x,y,seti)
    i = (y'*x)*seti.dV;
    end