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  - ensures each Tensor-container operates for the following base types:
    - floatScalar
    - doubleScalar
    - complex

  - adds/improves test applications for each container and base type:
    - constructors
    - member functions
    - global functions
    - global operators

  - misc:
    - silently removes `invariantIII()` for `tensor2D` and `symmTensor2D`
      since the 3rd invariant does not exist for 2x2 matrices
    - fixes `invariantII()` algorithm for `tensor2D` and `symmTensor2D`
    - adds `Cmpt` multiplication to `Vector2D` and `Vector`
    - adds missing access funcs for symmetric containers
    - improves func/header documentations

- make read construct from Istream explicit

BUG: sph(const SymmTensor2D<Cmpt>&)

- had incorrect constant, but the 2D routines still need more attention
 (#1575)

- also support transposed construction when given a set of vectors

- change contiguous from a series of global functions to separate
  templated traits classes:

    - is_contiguous
    - is_contiguous_label
    - is_contiguous_scalar

  The static constexpr 'value' and a constexpr conversion operator
  allow use in template expressions.  The change also makes it much
  easier to define general traits and to inherit from them.

  The is_contiguous_label and is_contiguous_scalar are special traits
  for handling data of homogeneous components of the respective types.

- this adds support for various STL operations including

    * sorting, filling, find min/max element etc.
    * for-range iteration

STYLE: use constexpr for VectorSpace rank

Previously the coordinate system functionality was split between
coordinateSystem and coordinateRotation. The coordinateRotation stored
the rotation tensor and handled all tensor transformations.

The functionality has now been revised and consolidated into the
coordinateSystem classes. The sole purpose of coordinateRotation
is now just to provide a selectable mechanism of how to define the
rotation tensor (eg, axis-angle, euler angles, local axes) for user
input, but after providing the appropriate rotation tensor it has
no further influence on the transformations.

--

The coordinateSystem class now contains an origin and a base rotation
tensor directly and various transformation methods.

  - The origin represents the "shift" for a local coordinate system.

  - The base rotation tensor represents the "tilt" or orientation
    of the local coordinate system in general (eg, for mapping
    positions), but may require position-dependent tensors when
    transforming vectors and tensors.

For some coordinate systems (currently the cylindrical coordinate system),
the rotation tensor required for rotating a vector or tensor is
position-dependent.

The new coordinateSystem and its derivates (cartesian, cylindrical,
indirect) now provide a uniform() method to define if the rotation
tensor is position dependent/independent.

The coordinateSystem transform and invTransform methods are now
available in two-parameter forms for obtaining position-dependent
rotation tensors. Eg,

      ... = cs.transform(globalPt, someVector);

In some cases it can be useful to use query uniform() to avoid
storage of redundant values.

      if (cs.uniform())
      {
          vector xx = cs.transform(someVector);
      }
      else
      {
          List<vector> xx = cs.transform(manyPoints, someVector);
      }

Support transform/invTransform for common data types:
   (scalar, vector, sphericalTensor, symmTensor, tensor).

====================
  Breaking Changes
====================

- These changes to coordinate systems and rotations may represent
  a breaking change for existing user coding.

- Relocating the rotation tensor into coordinateSystem itself means
  that the coordinate system 'R()' method now returns the rotation
  directly instead of the coordinateRotation. The method name 'R()'
  was chosen for consistency with other low-level entities (eg,
  quaternion).

  The following changes will be needed in coding:

      Old:  tensor rot = cs.R().R();
      New:  tensor rot = cs.R();

      Old:  cs.R().transform(...);
      New:  cs.transform(...);

  Accessing the runTime selectable coordinateRotation
  has moved to the rotation() method:

      Old:  Info<< "Rotation input: " << cs.R() << nl;
      New:  Info<< "Rotation input: " << cs.rotation() << nl;

- Naming consistency changes may also cause code to break.

      Old:  transformVector()
      New:  transformPrincipal()

  The old method name transformTensor() now simply becomes transform().

====================
  New methods
====================

For operations requiring caching of the coordinate rotations, the
'R()' method can be used with multiple input points:

       tensorField rots(cs.R(somePoints));

   and later

       Foam::transformList(rots, someVectors);

The rotation() method can also be used to change the rotation tensor
via a new coordinateRotation definition (issue #879).

The new methods transformPoint/invTransformPoint provide
transformations with an origin offset using Cartesian for both local
and global points. These can be used to determine the local position
based on the origin/rotation without interpreting it as a r-theta-z
value, for example.

================
  Input format
================

- Streamline dictionary input requirements

  * The default type is cartesian.
  * The default rotation type is the commonly used axes rotation
    specification (with e1/e2/3), which is assumed if the 'rotation'
    sub-dictionary does not exist.

    Example,

    Compact specification:

        coordinateSystem
        {
            origin  (0 0 0);
            e2      (0 1 0);
            e3      (0.5 0 0.866025);
        }

    Full specification (also accepts the longer 'coordinateRotation'
    sub-dictionary name):

        coordinateSystem
        {
            type    cartesian;
            origin  (0 0 0);

            rotation
            {
                type    axes;
                e2      (0 1 0);
                e3      (0.5 0 0.866025);
            }
        }

   This simplifies the input for many cases.

- Additional rotation specification 'none' (an identity rotation):

      coordinateSystem
      {
          origin  (0 0 0);
          rotation { type none; }
      }

- Additional rotation specification 'axisAngle', which is similar
  to the -rotate-angle option for transforming points (issue #660).
  For some cases this can be more intuitive.

  For example,

      rotation
      {
          type    axisAngle;
          axis    (0 1 0);
          angle   30;
      }
  vs.
      rotation
      {
          type    axes;
          e2      (0 1 0);
          e3      (0.5 0 0.866025);
      }

- shorter names (or older longer names) for the coordinate rotation
  specification.

     euler         EulerRotation
     starcd        STARCDRotation
     axes          axesRotation

================
  Coding Style
================
- use Foam::coordSystem namespace for categories of coordinate systems
  (cartesian, cylindrical, indirect). This reduces potential name
  clashes and makes a clearer declaration. Eg,

      coordSystem::cartesian csys_;

  The older names (eg, cartesianCS, etc) remain available via typedefs.

- added coordinateRotations namespace for better organization and
  reduce potential name clashes.

- Can now retrieve or set a column/row of a tensor.
  Either compile-time or run-time checks.

  Get
     t.col<1>();   t.col(1);
     t.row<1>();   t.row(1);

  Set
     t.col<1>(vec);   t.col(1,vec);
     t.row<1>(vec);   t.row(1,vec);

  The templated versions are compile-time checked

     t.col<3>();
     t.col<3>(vec);

  The parameter versions are run-time checked

     t.col(3);
     t.col(3,vec);

ENH: provide named access to tensor/tensor inner product as inner()

Provides '(i, j)' element access and general forms of inner and outer
products, transpose etc. for square and rectangular VectorSpaces.

VectorSpaces default to be column-vectors as before whereas row-vectors
may be represented as 1xn MatrixSpaces.  In the future it may be
preferable to create a specializations of VectorSpace for column- and
maybe row-vectors but it would add complexity to MatrixSpace to handle
all the type combinations.

Tensor is now a 3x3 specialization of MatrixSpace.

Sub-block const and non-const access is provided via the
'.block<SubTensor, RowStart, ColStart>()' member functions.  Consistent
sub-block access is also provide for VectorSpace so that columns of
MatrixSpaces may be accessed and substituted.

These new classes will be used to create a more extensive set of
primitive vector and tensor types over the next few weeks.

Henry G. Weller
CFD Direct

Foam::direction is an unsigned type which makes it easier for the
compiler to pickup and report errors in the instantiation of
VectorSpaces and associated types.

src/OpenFOAM/primitives: Moved the standard static data members for vector and tensor types into VectorSpace

This simplifies the code easing maintenance and the addition of other
VectorSpace types.

Add support for constructing VectorSpaces from forms with lower component type,
e.g. Vector<scalar> from Vector<label>

Add support for constructing VectorSpaces from forms with lower component type,
e.g. Vector<scalar> from Vector<label>

This reverts commit c5bea524.

This reverts commit b18f6cc1.

largest and smallest representable values.  Accessible directly and via pTraits.