Currently, the only use of FD is to double check the derivatives computed
either by hand-written code or (more frequently) by automatic differentiation.
However, only multiprecision number types allow to really be sure that the
rounding/cut off errors of FD do not hide subtle errors.

Unfortunately, this patch doesn't go all the way.  It now won't run with 'double'
anymore.  Also, user code needs to be modified in small but inelegant ways
(e.g., no 'std::' prefixes for math functions).  Since the FD tests don't
have to be run every day that's okay for now.

[[Imported from SVN: r9884]]

[[Imported from SVN: r9849]]

This used to be in the base class as default implementations, but I think
it is nicer to have it in a derived class.  In particular, this will
eventually allow to do the FD approximation with high-precision number types.

[[Imported from SVN: r9842]]

Because the gradient is needed anyway when computing the Hesse matrix.
Not computing it separately a second time shaves off about 8% wall time
of each iteration.

[[Imported from SVN: r9555]]

ADOL-C doesn't play nice with OpenMP.  Hence we have to disable
the latter for the time being.

[[Imported from SVN: r9446]]

[[Imported from SVN: r9421]]

[[Imported from SVN: r9391]]

[[Imported from SVN: r9390]]

[[Imported from SVN: r9294]]

[[Imported from SVN: r9284]]

the ones with i<=j.  The rest follows from symmetry of
the Hessian.

Needless to say, this makes the Hessian assembly quite
a bit faster.

[[Imported from SVN: r8587]]

The speed increase cause by the patch is, alas, hardly measurable.

[[Imported from SVN: r8360]]

[[Imported from SVN: r7837]]

[[Imported from SVN: r7611]]

and barycentric coordinates.  This is easy because we know the
number of element corners at compile time (I currently don't
see support for non-simplex elements at all).  This saves 
time, but not much: about 1%.

[[Imported from SVN: r7550]]

[[Imported from SVN: r7426]]

[[Imported from SVN: r7424]]

remove projection onto tangent space.  Is the variations are all tangent to the manifold you don't actually need it

[[Imported from SVN: r7422]]

[[Imported from SVN: r7391]]

[[Imported from SVN: r7390]]

Be smarter about when to compute what.  This speeds up assembly of the Hessian for harmonic maps from R^3 to S^2 by a factor of 3

[[Imported from SVN: r7389]]

[[Imported from SVN: r7388]]

Remove class specializations.  The old implementation for the UnitVector class will handle all cases

[[Imported from SVN: r7380]]

[[Imported from SVN: r7379]]

[[Imported from SVN: r7378]]

[[Imported from SVN: r7374]]

Remove a few specializations.  From now on we will assume that all target spaces can be parametrized by some sort of global embedding.  I don't see a case coming where that is not general enough

[[Imported from SVN: r7373]]

[[Imported from SVN: r7338]]

[[Imported from SVN: r7312]]

[[Imported from SVN: r7176]]

[[Imported from SVN: r7174]]

[[Imported from SVN: r7089]]

[[Imported from SVN: r6718]]

[[Imported from SVN: r6499]]

[[Imported from SVN: r6452]]

[[Imported from SVN: r6209]]

[[Imported from SVN: r5996]]

[[Imported from SVN: r5995]]

[[Imported from SVN: r5994]]

[[Imported from SVN: r5992]]