Numerical Examples

We have provided implementations for the sample problems described.

We present the examples and their verbose outputs. We have included these outputs so the reader can check that his/her copy of the package is executing properly. The user should be running MATLAB (version 5 or compatible) in the following directory:

>> !ls
Fline.m       dgrad.m      grad.m             move.m       sg_min.m
README        dimension.m  gradline.m         nosym.m      sg_newton.m
clamp.m       dtangent.m   invdgrad_CG.m      partition.m  sg_prcg.m
connection.m  examples     invdgrad_MINRES.m  sg_dog.m     tangent.m
dFline.m      finitediff   ip.m               sg_frcg.m

(Note that there may also be the additional subdirectories docs/ or @cell/.)

Each example problem has a subdirectory in the examples subdirectory.

>> !ls examples
jordan      ldatoy      procrustes  simdiag     simschur    tracemin

Each of these subdirectories contains an implementation for $F(Y)$ ($dF(Y)$ and $ddF(Y,H)$), which sets the (global) parameters of $F(Y)$ (this function must be called before any other), a guess function to generate an initial guess, and possibly some auxiliary functions for computing $F(Y)$, related quantities, or instances of a specific problem.

>> !ls examples/ldatoy
F.m           dF.m          guess.m
Kinetic.m     ddF.m         parameters.m
>> !ls examples/jordan
Block.m       dBlock.m      ddF.m         guess.m       post.m
F.m           dF.m          frank.m       parameters.m

We executed the examples in the supported optimization modes ('newton', 'dog', 'frcg', and 'prcg') and the 'euclidean' metric. For different instances of the same problem, different modes might perform best, so the reader should not feel that a particular mode will exhibit superior performance in all instances.