Geodetic distance on WGS84 earth ellipsoid

In 1975, Vincenty published a rapidly converging algorithm for computing the distance between points on an ellipsoidal earth. The algorithm is precise to within a few millimeters. Since then, his algorithm has since seen significant implementation in geodesy and engineering. After adjusting the algorithm to converge in all cases (the original suffers from convergence failure in a few outlying cases), I have provided it here in MATLAB form. The function itself does not require the Mapping Toolbox, but I have included a (commented-out) code section following the body of the function, which you can use if you have the Mapping Toolbox to compare the accuracy of this algorithm to spherical earth distances. Note that in that toolbox, the Mathworks uses a fast but somewhat less precise method for computing geodetic distances on an ellipsoid. This function will provide rapid, extremely precise results. Please see code comments for references.