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sankey.py
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sankey.py
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"implements Sankey"
import sys
from collections import defaultdict
import numpy as np
from ipywidgets import Layout
from ipysankeywidget import SankeyWidget # pylint: disable=import-error
from .. import ConstraintSet, Model
from .. import GeometricProgram, SequentialGeometricProgram
from ..nomials.math import MonomialEquality
from ..small_classes import Count
from .. import GPCOLORS
INSENSITIVE = 1e-2
def getcolor(value):
"color scheme for sensitivities"
if abs(value) < INSENSITIVE:
return "#cfcfcf"
return GPCOLORS[0 if value < 0 else 1]
class Sankey(object):
"diagrams of sensitivity flow"
def __init__(self, model):
self.links = defaultdict(float)
self.counter = Count()
if isinstance(model, Model):
if model.program is None:
raise ValueError("Model must be solved before a Sankey"
" diagram can be made.")
if isinstance(model.program, GeometricProgram):
model = model.program
elif isinstance(model.program, SequentialGeometricProgram):
model = model.program.gps[-1]
if not isinstance(model, GeometricProgram):
raise ValueError("did not find a GeometricProgram in the `model`"
" argument: try passing a particular GP.")
self.gp = model
self.constr_name = {}
self.nodes = []
self.var_eqs = set()
self._varprops = None
def constrlinks(self, constrset, target=None):
"adds links of a given constraint set to self.links"
if target is None: # set final target
target = getattr(constrset, "name", None) or "Model"
if getattr(constrset, "num", None):
target += ".%i" % constrset.num
for constr in constrset:
if isinstance(constr, ConstraintSet):
if getattr(constr, "name", None):
source = constr.name
source += ".%i" % constr.num if constr.num else ""
# value is negative so that the plot is GPBLU
self.links[source, target] -= constr.relax_sensitivity
self.constrlinks(constr, source)
else:
self.constrlinks(constr, target)
# pylint: disable=invalid-name, too-many-locals, too-many-branches, too-many-statements
def varlinks(self, constrset, key, target=None, printing=True):
"adds links of a given variable in self.gp to self.links"
if target is None: # set final target as the variable itself
value = constrset.v_ss[key] # if it's zero
target = getattr(constrset, "name", None) or "Model"
if getattr(constrset, "num", None):
target += ".%i" % constrset.num
source = str(key)
shortname = (key.str_without(["lineage"])
+ key.unitstr(into=" [%s]", dimless=" [-]"))
self.nodes.append({"id": source, "title": shortname})
self.links[target, source] += value
if key in self.gp.result["sensitivities"]["cost"]:
cost_senss = self.gp.result["sensitivities"]["cost"]
value = -cost_senss[key] # sensitivites flow _from_ cost
self.links[source, "(objective)"] += value
if printing:
print ("(objective) adds %+.3g to the sensitivity"
" of %s" % (-value, key))
print("(objective) is", self.gp.cost, "\n")
for constr in constrset:
if key not in constr.v_ss:
continue
value = constr.v_ss[key]
if isinstance(constr, ConstraintSet):
if getattr(constr, "name", None):
source = constr.name
source += ".%i" % constr.num if constr.num else ""
self.links[source, target] += value
self.varlinks(constr, key, source, printing)
else:
self.varlinks(constr, key, target, printing)
else:
if constr not in self.constr_name:
# use unicode's circled letters for constraint labels
source = chr(self.counter.next()+9398)
self.constr_name[constr] = source
else:
source = self.constr_name[constr]
if printing:
print ("%s adds %+.3g to the overall sensitivity of %s"
% (source, value, key))
print(source, "is", constr.str_without("units"), "\n")
if ((isinstance(constr, MonomialEquality)
or abs(value) >= INSENSITIVE)
and all(len(getattr(p, "hmap", [])) == 1
and p.hmap.keys()[0].values() == [1]
for p in [constr.left, constr.right])):
leftkey = constr.left.hmap.keys()[0].keys()[0]
if key != leftkey:
key2 = leftkey
else:
key2 = constr.right.hmap.keys()[0].keys()[0]
if key2 not in self.var_eqs: # not already been added
self.var_eqs.update([key2, key])
self.varlinks(self.gp[0], key2, printing=printing)
self.nodes.append({"id": source,
"passthrough": constr})
self.links[source, target] += value
# pylint: disable=too-many-arguments
def diagram(self, variables=None, flowright=False, width=900, height=400,
top=0, bottom=0, left=120, right=55, printing=True):
"creates links and an ipython widget to show them"
margins = dict(top=top, bottom=bottom, left=left, right=right)
self.__init__(self.gp)
if not variables:
self.constrlinks(self.gp[0])
else:
if not getattr(variables, "__len__", False):
variables = [variables]
for var in variables:
self.varlinks(self.gp[0], var.key, printing=printing)
# if var_eqs were found, label them on the diagram
lookup = {key: i for i, key in
enumerate(sorted(map(str, self.var_eqs)))}
for node in self.nodes:
if node["id"] in lookup:
# use inverted circled numbers to id the variables...
node["title"] += " " + chr(0x2776+lookup[node["id"]])
elif "passthrough" in node:
cn = node.pop("passthrough")
l_idx = lookup[str(cn.left.hmap.keys()[0].keys()[0])]
r_idx = lookup[str(cn.right.hmap.keys()[0].keys()[0])]
op = {"=": "=", ">=": u"\u2265", "<=": u"\u2264"}[cn.oper]
# ...so that e.g. (1) >= (2) can label the constraints
node["title"] = (node["id"]+u"\u2009"+chr(l_idx+0x2776)
+ op + chr(r_idx+0x2776))
if flowright:
r, l = margins["right"], margins["left"]
margins["left"], margins["right"] = r, l
links = []
maxflow = np.abs(self.links.values()).max()
for (source, target), value in self.links.items():
if not flowright:
source, target = target, source
links.append({"source": source, "target": target,
"value": max(abs(value), maxflow/1e5),
"color": getcolor(value)})
return SankeyWidget(nodes=self.nodes, links=links,
layout=Layout(width=str(width),
height=str(height)),
margins=margins)
@property
def variable_properties(self):
"Gets and caches properties for contained variables"
if not self._varprops:
varprops = {}
var_eqs = set()
for key in self.gp.v_ss:
if key in var_eqs:
continue
self.__init__(self.gp)
self.varlinks(self.gp, key, printing=False)
maxflow = max(self.links.values())
if maxflow > 0.01: # TODO: arbitrary threshold
varprops[key] = {"constraints": self.counter.next(),
"maxflow": maxflow}
var_eqs.update(self.var_eqs)
self.__init__(self.gp)
self._varprops = varprops
return self._varprops
def sorted_by(self, prop, idx, **kwargs):
"chooses a variable by its rank in # of constraints or maximum flow"
key = sorted(self.variable_properties.items(),
key=lambda i: (-i[1][prop], str(i[0])))[idx][0]
return self.diagram(key, **kwargs)