The Matlab Central Package

  http://www.mathworks.com/matlabcentral/fileexchange/50605

provide a native Matlab/Octave implementation of a subset of
GeographicLib.

It is also possible to call the C++ GeographicLib library directly from
Matlab and Octave.  This gives you access to the full range of
GeographicLib's capabilities.

In order to make use of this facility, it is necessary to write some
interface code.  The files in this directory provide a sample of such
interface code.  This example solves the inverse geodesic problem for
ellipsoids with arbitrary flattening.  (The code geoddistance.m does
this as native Matlab code; but it is limited to ellipsoids with a
smaller flattening.)

For full details on how to write the interface code, see

  http://www.mathworks.com/help/matlab/write-cc-mex-files.html

To compile the interface code, start Matlab or Octave and run, e.g.,

  mex -setup
  help geographiclibinterface
  geographiclibinterface
  help geodesicinverse
  geodesicinverse([40.6, -73.8, 51.6, -0.5])
  ans =

     5.1199e+01   1.0782e+02   5.5518e+06

The first command allows you to select the compiler to use (which should
be the same as that used to compile GeographicLib). On Mac OSX and
Matlab R2014b, the setup command is

  mex -setup C++

These routines just offer a simple interface to the corresponding C++
class. Use the help function to get documentation,

  help geodesicinverse

Unfortunately, the help function does not work for compiled functions in
Octave; in this case, just list the .m file, e.g.,

  type geodesicinverse.m