We normalize unit vectors again in the constructor and the assignment operator.
This makes sure we never drift away from the unit sphere, and it also allows
us to init unit spheres with any value in R^n and be sure we obtain a unit
vector.  This makes the test pass again.  Leaving the projection out didn't
really make a measurable difference anyway.

[[Imported from SVN: r9574]]

[[Imported from SVN: r9572]]

[[Imported from SVN: r9571]]

[[Imported from SVN: r9563]]

The old implementation used quaternion multiplication to transport
the argument to the Lie algebra, and use the standard formula there.
However, one may as well use the formula for the unit sphere in R^4,
which is much simpler, and also faster.  I fact, this patch gives
a few percent of speedup for the overall code.

[[Imported from SVN: r9562]]

There is one copy which takes FieldVector<T,4> as its second argument.
Since EmbeddedTangentVector ( = Quaternion<T>) derives from FieldVector<T,4>,
that second implementation should work in all cases.

[[Imported from SVN: r9560]]

The methods 

Rotation<T,3> exp(const Rotation<T,3>& p, const EmbeddedTangentVector& v) 

and

otation<T,3> exp(const Rotation<T,3>& p, const Dune::FieldVector<T,4>& v)

do literally the same.  So they should be next to each other in the code.

[[Imported from SVN: r9559]]

This effectively means that we use another prolongation of the distance 
function on M into the surrounding space.  Since the prolongation does not
matter this patch should not change the algorithm behavior.  However, it
shaves off a few norm calculations and division.  I cannot really measure
any difference though.

A possible effect of this is that while all values should remain on the
manifold, they may start to 'drift away' due to numerical artifacts.
So we may have to add an occasional renormalization step eventually.

[[Imported from SVN: r9558]]

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]]

[[Imported from SVN: r9526]]

[[Imported from SVN: r9525]]

and move from GenericReferenceElement to ReferenceElement

[[Imported from SVN: r9524]]

The Weingarten map is block-diagonal for a product space.

[[Imported from SVN: r9517]]

It used to be a compile-term error, but now that we have ADOL-C support
the missing gradient is not a problem anymore.

[[Imported from SVN: r9516]]

[[Imported from SVN: r9510]]

[[Imported from SVN: r9509]]

[[Imported from SVN: r9508]]

This patch brings it back.

[[Imported from SVN: r9477]]

[[Imported from SVN: r9476]]

[[Imported from SVN: r9467]]

[[Imported from SVN: r9451]]

[[Imported from SVN: r9450]]

[[Imported from SVN: r9449]]

[[Imported from SVN: r9448]]

I can't make up my mind whether I want 'ctype' or 'field_type'

[[Imported from SVN: r9447]]

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: r9445]]

When using the classes with ADOL-C, T becomes an 'adouble',
which is a non-trivial type.  However, the convexityField
is constexpr (and with a reason -- otherwise we could write
the initialization together with the declaration), and
constexpr and non-trivial types don't work together.

[[Imported from SVN: r9444]]

[[Imported from SVN: r9443]]

[[Imported from SVN: r9442]]

[[Imported from SVN: r9441]]

And set the inner loop solver verbosity to QUIET

[[Imported from SVN: r9435]]

This number is nowadays infered from the number of transfer operators.

[[Imported from SVN: r9432]]

Since ADOL-C is not multi-threaded we will not be using OpenMP
in the foreseeable future.  And on a single-threaded code the
OpenMP timer and the Dune timer return the same values anyway.

[[Imported from SVN: r9431]]

[[Imported from SVN: r9430]]

Offer setInitialIterate instead

[[Imported from SVN: r9429]]

[[Imported from SVN: r9428]]

Because ADOL-C doesn't like calls to sqrt(0), obviously.
The use of sqrt(x) for small x can be avoided completely
using modified series expansions, because the overall
function exp is differentiable even at x=0.

[[Imported from SVN: r9426]]

Makes for a more precise Hessian matrix when using automatic differentiation.

[[Imported from SVN: r9425]]

[[Imported from SVN: r9424]]