Add support for multiple visibility clustering algorithms.

The original visibility based preconditioning paper and
implementation only used the canonical views algorithm.

This algorithm for large dense graphs can be particularly
expensive. As its worst case complexity is cubic in size
of the graph.

Further, for many uses the SCHUR_JACOBI preconditioner
was both effective enough while being cheap. It however
suffers from a fatal flaw. If the camera parameter blocks
are split between two or more parameter blocks, e.g,
extrinsics and intrinsics. The preconditioner because
it is block diagonal will not capture the interactions
between them.

Using CLUSTER_JACOBI or CLUSTER_TRIDIAGONAL will fix
this problem but as mentioned above this can be quite
expensive depending on the problem.

This change extends the visibility based preconditioner
to allow for multiple clustering algorithms. And adds
a simple thresholded single linkage clustering algorithm
which allows you to construct versions of CLUSTER_JACOBI
and CLUSTER_TRIDIAGONAL preconditioners that are cheap
to construct and are more effective than SCHUR_JACOBI.

Currently the constants controlling the threshold above
which edges are considered in the single linkage algorithm
are not exposed. This would be done in a future change.

Change-Id: I7ddc36790943f24b19c7f08b10694ae9a822f5c9

docs/source/solving.rst

@@ -1147,6 +1147,28 @@ elimination group [LiSaad]_.
    ``CLUSTER_JACOBI`` and ``CLUSTER_TRIDIAGONAL``. See
    :ref:`section-preconditioner` for more details.
 
+.. member:: VisibilityClusteringType Solver::Options::visibility_clustering_type
+
+   Default: ``CANONICAL_VIEWS``
+
+   Type of clustering algorithm to use when constructing a visibility
+   based preconditioner. The original visibility based preconditioning
+   paper and implementation only used the canonical views algorithm.
+
+   This algorithm gives high quality results but for large dense
+   graphs can be particularly expensive. As its worst case complexity
+   is cubic in size of the graph.
+
+   Another option is to use ``SINGLE_LINKAGE`` which is a simple
+   thresholded single linkage clustering algorithm that only pays
+   attention to tightly coupled blocks in the Schur complement. This
+   is a fast algorithm that works well.
+
+   The optimal choice of the clustering algorithm depends on the
+   sparsity structure of the problem, but generally speaking we
+   recommend that you try ``CANONICAL_VIEWS`` first and if it is too
+   expensive try ``SINGLE_LINKAGE``.
+
 .. member:: DenseLinearAlgebraLibrary Solver::Options::dense_linear_algebra_library_type
 
    Default:``EIGEN``
@@ -2020,6 +2042,13 @@ The three arrays will be:
    Type of preconditioner used for solving the trust region step. Only
    meaningful when an iterative linear solver is used.
 
+.. member:: VisibilityClusteringType Solver::Summary::visibility_clustering_type
+
+   Type of clustering algorithm used for visibility based
+   preconditioning. Only meaningful when the
+   :member:`Solver::Summary::preconditioner_type` is
+   ``CLUSTER_JACOBI`` or ``CLUSTER_TRIDIAGONAL``.
+
 .. member:: TrustRegionStrategyType Solver::Summary::trust_region_strategy_type
 
    Type of trust region strategy.