Refactor the graph layout code, and add interface with graphviz

[nthiery]

Latest version of the patch on:
http://combinat.sagemath.org/hgwebdir.cgi/patches/file/tip/trac_7004-graphviz-nt.patch
and followups

Using the graphviz interface requires graphviz to be installed on the
machine, as well as a dot2tex spkg which can be installed with:

sage -f http://sage.math.washington.edu/home/nthiery/dot2tex-2.8.7-dev.spkg

From the patch description:

• Refactors the graph layout code:

• Add a new main graph.layout() method, to be called by plot, plot3d, latex, graph_editor, ...

• The various graph layout algorithms spread over the graph code are systematically reorganized into as many layout methods that can be called from layout():

• graph.layout_circular()

• graph.layout_spring()

• graph.layout_tree()

• graph.layout_ranked()

• graph.layout_acyclic()

• graph.layout_planar()

• graph.layout_default()

• Extends the graphviz_string method (latex labels) and refactors its logic to make it simpler for subclasses

• Slightly simplifies the handling of default values for graph.latex_options

• Visible user change: graph_editor, plot3d, ... all accept the same layout options.

• Implements an interface to dot2tex/graphviz:

• Define a new layout method .layout_graphviz() implemented by calling dot2tex and graphviz

• Implement an alternative implementation of latex for graphs by delegating all the work to dot2tex (GraphLatex.dot2tex_picture)

• Makes some fixes to the poset code:

  • __repr__ -> _repr_
  • _latex_ by calling latex on the internal element

• Moved the level_sets method from HasseDiagram to DirectedGraph Reimplemented to support properly non acyclic graph. It should be quite faster (it just goes through the graph, without modifying it).

TODO, for this ticket or a later one:

• Double check all the logic to make sure it is backward compatible

  • Done for the latex part (Rob)

• What should be the default layout algorithm?

  • Planar layout when the graph is planar (not yet: the planar
    layout is not that nice looking; postponed for later when
    planar+spring will be implemented)
  • acyclic if acyclic
  • spring otherwise

• The spring option for ranked layouts does not work nicely:

     sage: G = posets.IntegerPartitions(5).hasse_diagram()
     sage: G = DiGraph({1:(2,3), 2:[4], 3:[4]})            # alternative example
     sage: G.plot(layout="acyclic_dummy", spring = True)

to be compared with:

      sage: G.plot(layout="acyclic_dummy")
      sage: G.plot(layout="spring")

Thinking twice about it, this seems to be inherent. See the comments in the code.

• Find a better name for acyclic_dummy. Once the spring layout will be functional, this could be set to the default value, and the layout renamed to acyclic_spring.

• Choose a good option name for the direction of growth of acyclic layout, an a good default value. Merge this with the option for tree layout (tree_orientation).

  • orientation = "up" (as for tree) ?
  • rankdir = "BT" (as in graphviz)?

• A lot of code is doing things very similar to dot2tex. Maybe things could be merged.

• Implement the various options for both latex constructions (tikz or dot2tex)

• Implement the default layout of standard graphs using a default_layout method rather than at construction time.

CC: @sagetrac-sage-combinat @nathanncohen @rlmill

Component: graph theory

Keywords: graph layout, graphviz, acyclic

Author: Nicolas M. Thiéry

Reviewer: Vincent Delecroix

Merged: sage-4.4.1.alpha2

Issue created by migration from https://trac.sagemath.org/ticket/7004

[nthiery]

Description changed:

--- 
+++ 
@@ -1,4 +1,4 @@
-Experimental patch on:  http://combinat.sagemath.org/hgwebdir.cgi/patches/file/tip/graphviz-nt.patch
+Experimental patch on:  http://combinat.sagemath.org/hgwebdir.cgi/patches/file/tip/trac_7004-graphviz-nt.patch
 
 From the patch description:
 

[nthiery]

Description changed:

--- 
+++ 
@@ -1,4 +1,8 @@
 Experimental patch on:  http://combinat.sagemath.org/hgwebdir.cgi/patches/file/tip/trac_7004-graphviz-nt.patch
+
+This also requires graphviz and a dot2tex spkg available from: 
+
+http://sage.math.washington.edu/home/nthiery/dot2tex-0.2.spkg
 
 From the patch description:
 

[nthiery]

Description changed:

--- 
+++ 
@@ -2,7 +2,7 @@
 
 This also requires graphviz and a dot2tex spkg available from: 
 
-http://sage.math.washington.edu/home/nthiery/dot2tex-0.2.spkg
+http://sage.math.washington.edu/home/nthiery/dot2tex-2.8.6.spkg
 
 From the patch description:
 
@@ -23,17 +23,20 @@
 
 TODO:
 
+- make layout(layout="bla") automatically lookup _layout_bla, so that subclasses can define new layout algorithms (e.g. acyclic for directed graphs).
+
 - Add an optional default_layout method that subclasses could
   override (like for the Petersen graph, ...). This would be better
   for them than to systematically construct the layout at
   construction time.
 
+- Move the layout code out of posets into a _layout_acyclic_spring in directed graphs, and have _layout_acyclic call it if dot2tex is not available.
+
 - Refactor the remaining layout functions (planar, ...) as above
 
 - Double check all the logic to make sure it is backward compatible
 
-- A lot of code is doing things very similar to dot2tex. Maybe things
-  could be merged.
+- A lot of code is doing things very similar to dot2tex. Maybe things could be merged.
 
 - Finish to doctest everything
 

[nthiery]

Description changed:

--- 
+++ 
@@ -2,7 +2,7 @@
 
 This also requires graphviz and a dot2tex spkg available from: 
 
-http://sage.math.washington.edu/home/nthiery/dot2tex-2.8.6.spkg
+http://sage.math.washington.edu/home/nthiery/dot2tex-2.8.7.spkg
 
 From the patch description:
 

[nthiery]

Description changed:

--- 
+++ 
@@ -1,48 +1,89 @@
-Experimental patch on:  http://combinat.sagemath.org/hgwebdir.cgi/patches/file/tip/trac_7004-graphviz-nt.patch
+Latest version of the patch on:  http://combinat.sagemath.org/hgwebdir.cgi/patches/file/tip/trac_7004-graphviz-nt.patch
 
 This also requires graphviz and a dot2tex spkg available from: 
 
 http://sage.math.washington.edu/home/nthiery/dot2tex-2.8.7.spkg
 
 From the patch description:
+- Refactors the graph layout code:
 
-- Refactors the graph layout code, with:
+  - Add a new main graph.layout() method, to be called by plot,
+    plot3d, latex, graph_editor, ...
 
-  - A new main graph.layout() method, to be called by plot, latex, ...
-  - Many layout methods, like graph._layout_circular()
+  - The various graph layout algorithms spread over the graph code
+    are systematically reorganized into as many layout methods that
+    can be called from layout():
+
+     - graph.layout_circular()
+     - graph.layout_spring()
+     - graph.layout_tree()
+     - graph.layout_ranked()
+     - graph.layout_acyclic()
+     - graph.layout_planar()
+     - graph.layout_default()
+
   - Extends the graphviz_string method (latex labels)
-  - Define a new layout method ._layout_acyclic() implemented by
+    and refactors its logic to make it simpler for subclasses
+
+  - Slightly simplifies the handling of default values for
+    graph.latex_options
+
+  - Visible user change: graph_editor, plot3d, ... all accept the
+    same layout options.
+
+- Implements an interface to dot2tex/graphviz:
+
+  - Define a new layout method .layout_graphviz() implemented by
     calling dot2tex and graphviz
+
   - Implement an alternative implementation of latex for graphs
     by delegating all the work to dot2tex (GraphLatex.dot2tex_picture)
-  - Slightly simplifies the handling of default values for graph.latex_options
 
 - Makes some fixes to the poset code:
   - `__repr__` -> `_repr_`
   - `_latex_` by calling latex on the internal element
 
-TODO:
+  - Moved the level_sets method from HasseDiagram to DirectedGraph
+    Reimplemented to support properly non acyclic graph. It should be
+    quite faster (it just goes through the graph, without modifying it).
 
-- make layout(layout="bla") automatically lookup _layout_bla, so that subclasses can define new layout algorithms (e.g. acyclic for directed graphs).
-
-- Add an optional default_layout method that subclasses could
-  override (like for the Petersen graph, ...). This would be better
-  for them than to systematically construct the layout at
-  construction time.
-
-- Move the layout code out of posets into a _layout_acyclic_spring in directed graphs, and have _layout_acyclic call it if dot2tex is not available.
-
-- Refactor the remaining layout functions (planar, ...) as above
+TODO, for this ticket or a later one:
 
 - Double check all the logic to make sure it is backward compatible
 
-- A lot of code is doing things very similar to dot2tex. Maybe things could be merged.
+- graph_editor was using iterations=1000 as default. Was there a
+  reason? If yes, do we want to set this up as default value for all
+  layouts?
 
-- Finish to doctest everything
+- What should be the default layout algorithm?
 
-- Implement the different options for both latex constructions
+   - Planar layout when the graph is planar
+   - acyclic if acyclic
+   - spring otherwise
 
-- Add appropriate # optional comments
+- The spring option for graded layouts does not work. Could someone
+  please debug this?
 
-- Make dot2tex.spkg into an optional sage package
+    sage: G = posets.IntegerPartitions(3).hasse_diagram()
+    sage: G.plot(layout="acyclic_dummy")
+    sage: G.plot(layout="acyclic_dummy", spring = True)
 
+- Find a better name for acyclic_dummy. Once the spring layout will
+  be functional, this could be set to the default value, and the
+  layout renamed to acyclic_spring.
+
+- Choose a good option name for the direction of growth of acyclic
+  layout, an a good default value. Merge this with the option for
+  tree layout (tree_orientation).
+
+  orientation = "up" (as for tree) ?
+  rankdir = "BT" (as in graphviz)?
+
+- A lot of code is doing things very similar to dot2tex. Maybe things
+  could be merged.
+
+- Implement the various options for both latex constructions (tikz or
+  dot2tex)
+
+- Implement the default layout of standard graphs using a
+  default_layout method rather than at construction time.