DIFFERENT

An alternative to GRADIENT for non-uniform grids.

Description

GRADIENT approximates derivatives using centered difference quotients.
This is not very accurate for non-uniform grids, where differences
are not properly centered.

DIFFERENT uses the scheme: Forward + Backward - Centered difference quotients.
This is more accurate for non-uniform grids. For uniform grids the schemes are
equivalent. Interval endpoints are always treated differently.

DIFFERENT is at least a factor 2 faster than GRADIENT.

• MATLAB release: MATLAB 7.10 (2010a)

[Jan Simon]

H1 line, detailed help text, examples, "See also" line, name of the author. The function accepts arrays and the dimension to operate on can be specified. The inputs are checked. The calculations are correct, vectorized and fast.
This submission is useful and usable and earns 5 stars.

For large arrays the creation of temporary arrays consumes much time. I've published a C-Mex function for the 2nd order gradient calculation without the need of temporary arrays, which is 12 times faster: http://www.mathworks.com/matlabcentral/fileexchange/29887-dgradient
And see Robert Canfield's evergreen central_difference: http://www.mathworks.com/matlabcentral/fileexchange/12

[Jonas Lundgren]

Thank you Jan for your comments. A faster version will soon be available.