Gradient along a specified dimension
Y = DGradient(X, Dim, Spacing, Method)
X: Real DOUBLE array, any number of dimensions.
Spacing: Scalar or vector of the length SIZE(X, Dim).
Dim: Dimension to operate on.
Optional, default: 1st non-singelton dimension.
Method: String, order of the applied method for unevenly spaced X:
'1stOrder', faster centered differences as in Matlab's GRADIENT.
'2ndOrder', 2nd order accurate centered differences.
On the edges forward and backward difference are used.
Optional, default: '1stOrder'.
Y: Gradient of X, same size as X.
There are a lot of other derivation tools in the FEX. This function is faster (e.g. 25% faster than dqdt and 10 to 16 times faster than Matlab's GRADIENT), works with multi-dim arrays, on a specific dimension only, and can use a 2nd order method for unevenly spaced data.
For vectors or evenly spaced data no temporary memory is needed. Otherwise 1 or 3 temporary vectors of SIZE(X, Dim) are used for the 1st and 2nd order methods.
The C-Mex file must be compiled at first. Pre-compiled files for Win32 can be downloaded at: http://www.n-simon.de/mex
Run the unit-test function uTest_DGradient to check the integrity and measure speed.
Tested: Matlab 6.5, 7.7, 7.8, WinXP, 32bit
Compiler: LCC2.4/3.8, BCC5.5, OWC1.8, MSVC2008
Assumed Compatibility: higher Matlab versions, Mac, Linux, 64bit
Thanks to Robert A. Canfield (central_diff, #12) and Darren Rowland (diffxy, #29312).