Inverse (integrated) gradient

Vectorized & fully sparse 1-d, 2-d, & 3-d integrated gradients

Description

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.

Acknowledgements

Inverse Gradient inspired this file.

This file inspired Piv Mat 3.02.

• MATLAB release: MATLAB 7.0.1 (R14SP1)

[Martyn]

There is a bug in intgrad3 where the parameter checks in lines 84 to 96 check nargin against values that are -1 of the correct value, ie on line 84 (nargin<3) should be (nargin<4), etc.

[garima]

I have tried your tool but it perhaps fails in case of functions with singularities..like (x+iy)...plz chek and update...

[Uland Wong]

 

[F Moisy]

Thank you for this excellent tool. Should be included in Matlab.

[John D'Errico]

Sergei,
I caught the bug in the example usage for the release I submitted this morning. Good point too about author and creation dates. I'll add them to all my files. Thanks, John

[Sergei Koptenko]

Rating =1 must be substantiated according to the ?Guidelines for Reviewing a Submission?- (provide specific information on what you like and dislike about the submission, use examples to illustrate your point... etc..). I would suggest to File Review Team to remove all ratings=1 that do not have specific critique as irrelevant and misleading.

Now, the specific critique :-)
1) help files are good, however they lack information about author and creation date.
2) minor -in intgrad2 help section function is called intgrad