Inverse (integrated) gradient

Vectorized & fully sparse 1-d, 2-d, & 3-d integrated gradients
5.7K Downloads
Updated 2 Jan 2013

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The inverse of the gradient function. I've provided versions that work on 1-d vectors, or 2-d or 3-d arrays. In the 1-d case I offer 5 different methods, from cumtrapz, and an integrated cubic spline, plus several finite difference methods.

In higher dimensions, only a finite difference/linear algebra solution is provided, but it is fully vectorized and fully sparse in its approach. In 2-d and 3-d, if the gradients are inconsistent, then a least squares solution is generated.

(I'll enhance the 2-d and 3d tools if there is any interest. Currently they are set to be 2nd order methods on uniform grids.)

Please notify me of any bugs.

Cite As

John D'Errico (2024). Inverse (integrated) gradient (https://www.mathworks.com/matlabcentral/fileexchange/9734-inverse-integrated-gradient), MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R14SP1
Compatible with any release
Platform Compatibility
Windows macOS Linux
Categories
Find more on Numerical Integration and Differential Equations in Help Center and MATLAB Answers
Acknowledgements

Inspired by: Inverse Gradient

Inspired: PIVMat 4.20

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Version Published Release Notes
1.1.0.0

Fixed bug for complex inputs

1.0.0.0

Upgrades to the 1-d cumulative integration code, for both accuracy and speed in the finite difference methods.