This function provides an alternative way to optimize the projection index, by moving along a geodesic path.
1 
start 
The Starting Projection for the optimization. 
index 
The Projection Index function. Typically generated by a
call to the 
n 
The number of new bases to try at every stage of the
optimization. Needs to be an array of the same length as

bases 
The number of new bases desired. Actual number generated may be lesser if optimization stalls. 
This function provides an alternative way to optimize the projection index. It moves the index along geodesic paths between randomly generated nearby matrices, in hopes of uncovering peaks of the index function. By experience, one can say that it can often reveal structure missed by Simulated Annealing optimization.
A list of basis matrices, of length bases
or shorter (if
the optimization stalls).
Mohit Dayal
Colon
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