This PR resolves an issue unearthed whilst writing the proofs up of the FS algorithm. Demidenko (2013) had given the derivative with respect to vech(D_k) by:
dl/dvech(D_k)=DupMat^+_k*dl/dvec(D_k)
When in fact, as Turkington (2013) gives it, the derivative is:
dl/dvech(D_k)=DupMat'_k*dl/dvec(D_k)
I believe Turkington as writing out the matrix mutliplication we can see clearly that this is just a restatement of the law of total derivatives. When I implemented this in the code it made surprisingly little difference to results but the code ran faster and the ghost overflow/covergence issues experienced before have vanished.
This PR resolves an issue unearthed whilst writing the proofs up of the FS algorithm. Demidenko (2013) had given the derivative with respect to vech(D_k) by:
dl/dvech(D_k)=DupMat^+_k*dl/dvec(D_k)
When in fact, as Turkington (2013) gives it, the derivative is:
dl/dvech(D_k)=DupMat'_k*dl/dvec(D_k)
I believe Turkington as writing out the matrix mutliplication we can see clearly that this is just a restatement of the law of total derivatives. When I implemented this in the code it made surprisingly little difference to results but the code ran faster and the ghost overflow/covergence issues experienced before have vanished.