/
dot.py
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/
dot.py
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from ..core import Basic, Expr
__all__ = 'dotprint',
default_styles = [(Basic, {'color': 'blue', 'shape': 'ellipse'}),
(Expr, {'color': 'black'})]
def styleof(expr, styles=default_styles):
"""Merge style dictionaries in order.
>>> styles = [(Basic, {'color': 'blue', 'shape': 'ellipse'}),
... (Expr, {'color': 'black'})]
>>> styleof(Basic(1), styles)
{'color': 'blue', 'shape': 'ellipse'}
>>> styleof(x + 1, styles) # this is an Expr
{'color': 'black', 'shape': 'ellipse'}
"""
style = {}
for typ, sty in styles:
if isinstance(expr, typ):
style.update(sty)
return style
def attrprint(d, delimiter=', '):
"""Print a dictionary of attributes.
>>> print(attrprint({'color': 'blue', 'shape': 'ellipse'}))
"color"="blue", "shape"="ellipse"
"""
return delimiter.join('"%s"="%s"' % item for item in sorted(d.items()))
def dotnode(expr, styles=default_styles, labelfunc=str, pos=(), repeat=True):
"""String defining a node.
>>> print(dotnode(x))
"Symbol('x')_()" ["color"="black", "label"="x", "shape"="ellipse"];
"""
style = styleof(expr, styles)
if isinstance(expr, Basic) and not expr.is_Atom:
label = str(expr.__class__.__name__)
else:
label = labelfunc(expr)
style['label'] = label
expr_str = repr(expr)
if repeat:
expr_str += '_%s' % str(pos)
return f'"{expr_str}" [{attrprint(style)}];'
def dotedges(expr, atom=lambda x: not isinstance(x, Basic), pos=(), repeat=True):
"""List of strings for all expr->expr.arg pairs.
>>> for e in dotedges(x+2):
... print(e)
"Add(Symbol('x'), Integer(2))_()" -> "Integer(2)_(0,)";
"Add(Symbol('x'), Integer(2))_()" -> "Symbol('x')_(1,)";
See Also
========
dotprint
"""
if atom(expr):
return []
else:
expr_str = repr(expr)
arg_strs = [repr(arg) for arg in expr.args]
if repeat:
expr_str += '_%s' % str(pos)
arg_strs = [arg_str + '_%s' % str(pos + (i,)) for i, arg_str in enumerate(arg_strs)]
return [f'"{expr_str}" -> "{arg_str}";' for arg_str in arg_strs]
template = \
"""digraph{
# Graph style
%(graphstyle)s
#########
# Nodes #
#########
%(nodes)s
#########
# Edges #
#########
%(edges)s
}"""
graphstyle = {'rankdir': 'TD', 'ordering': 'out', 'bgcolor': 'transparent'}
def dotprint(expr, styles=default_styles,
atom=lambda x: not isinstance(x, Basic),
maxdepth=None, repeat=True, labelfunc=str, **kwargs):
"""
DOT description of a Diofant expression tree
Options are
``styles``: Styles for different classes. The default is::
[(Basic, {'color': 'blue', 'shape': 'ellipse'}),
(Expr, {'color': 'black'})]``
``atom``: Function used to determine if an arg is an atom. The default is
``lambda x: not isinstance(x, Basic)``. Another good choice is
``lambda x: not x.args``.
``maxdepth``: The maximum depth. The default is None, meaning no limit.
``repeat``: Whether to different nodes for separate common subexpressions.
The default is True. For example, for ``x + x*y`` with
``repeat=True``, it will have two nodes for ``x`` and with
``repeat=False``, it will have one (warning: even if it appears
twice in the same object, like Pow(x, x), it will still only appear
only once. Hence, with repeat=False, the number of arrows out of an
object might not equal the number of args it has).
``labelfunc``: How to label leaf nodes. The default is ``str``. Another
good option is ``repr``. For example with ``str``, the leaf nodes
of ``x + 1`` are labeled, ``x`` and ``1``. With ``repr``, they
are labeled ``Symbol('x')`` and ``Integer(1)``.
Additional keyword arguments are included as styles for the graph.
Examples
========
>>> print(dotprint(x + 2))
digraph{
<BLANKLINE>
# Graph style
"bgcolor"="transparent"
"ordering"="out"
"rankdir"="TD"
<BLANKLINE>
#########
# Nodes #
#########
<BLANKLINE>
"Add(Symbol('x'), Integer(2))_()" ["color"="black", "label"="Add", "shape"="ellipse"];
"Integer(2)_(0,)" ["color"="black", "label"="2", "shape"="ellipse"];
"Symbol('x')_(1,)" ["color"="black", "label"="x", "shape"="ellipse"];
<BLANKLINE>
#########
# Edges #
#########
<BLANKLINE>
"Add(Symbol('x'), Integer(2))_()" -> "Integer(2)_(0,)";
"Add(Symbol('x'), Integer(2))_()" -> "Symbol('x')_(1,)";
}
"""
# repeat works by adding a signature tuple to the end of each node for its
# position in the graph. For example, for expr = Add(x, Pow(x, 2)), the x in the
# Pow will have the tuple (1, 0), meaning it is expr.args[1].args[0].
graphstyle.update(kwargs)
nodes = []
edges = []
def traverse(e, depth, pos=()):
nodes.append(dotnode(e, styles, labelfunc=labelfunc, pos=pos, repeat=repeat))
if maxdepth and depth >= maxdepth:
return
edges.extend(dotedges(e, atom=atom, pos=pos, repeat=repeat))
[traverse(arg, depth+1, pos + (i,)) for i, arg in enumerate(e.args) if not atom(arg)]
traverse(expr, 0)
return template % {'graphstyle': attrprint(graphstyle, delimiter='\n'),
'nodes': '\n'.join(nodes),
'edges': '\n'.join(edges)}