from snap import *
from cvxpy import *
import math
import multiprocessing
import numpy
from scipy.sparse import lil_matrix
import sys
import time
import __builtin__
import code
# File format: One edge per line, written as "srcID dstID"
# Commented lines that start with '#' are ignored
# Returns a TGraphVX object with the designated edges and nodes
def LoadEdgeList(Filename):
gvx = TGraphVX()
nids = set()
infile = open(Filename, 'r')
with open(Filename) as infile:
for line in infile:
if line.startswith('#'): continue
[src, dst] = line.split()
if int(src) not in nids:
gvx.AddNode(int(src))
nids.add(int(src))
if int(dst) not in nids:
gvx.AddNode(int(dst))
nids.add(int(dst))
gvx.AddEdge(int(src), int(dst))
return gvx
# TGraphVX inherits from the TUNGraph object defined by Snap.py
class TGraphVX(TUNGraph):
__default_objective = norm(0)
__default_constraints = []
# Data Structures
# ---------------
# node_objectives = {int NId : CVXPY Expression}
# node_constraints = {int NId : [CVXPY Constraint]}
# edge_objectives = {(int NId1, int NId2) : CVXPY Expression}
# edge_constraints = {(int NId1, int NId2) : [CVXPY Constraint]}
# all_variables = set(CVXPY Variable)
#
# ADMM-Specific Structures
# ------------------------
# node_variables = {int NId :
# [(CVXPY Variable id, CVXPY Variable name, CVXPY Variable, offset)]}
# node_values = {int NId : numpy array}
# node_values points to the numpy array containing the value of the entire
# variable space corresponding to then node. Use the offset to get the
# value for a specific variable.
#
# Constructor
# If Graph is a Snap.py graph, initializes a SnapVX graph with the same
# nodes and edges.
def __init__(self, Graph=None):
# Initialize data structures
self.node_objectives = {}
self.node_variables = {}
self.node_constraints = {}
self.edge_objectives = {}
self.edge_constraints = {}
self.node_values = {}
self.all_variables = set()
self.status = None
self.value = None
# Initialize superclass
nodes = 0
edges = 0
if Graph != None:
nodes = Graph.GetNodes()
edges = Graph.GetEdges()
TUNGraph.__init__(self, nodes, edges)
# Support for constructor with Snap.py graph argument
if Graph != None:
for ni in Graph.Nodes():
self.AddNode(ni.GetId())
for ei in Graph.Edges():
self.AddEdge(ei.GetSrcNId(), ei.GetDstNId())
# Simple iterator to iterator over all nodes in graph. Similar in
# functionality to Nodes() iterator of PUNGraph in Snap.py.
def Nodes(self):
ni = TUNGraph.BegNI(self)
for i in xrange(TUNGraph.GetNodes(self)):
yield ni
ni.Next()
# Simple iterator to iterator over all edge in graph. Similar in
# functionality to Edges() iterator of PUNGraph in Snap.py.
def Edges(self):
ei = TUNGraph.BegEI(self)
for i in xrange(TUNGraph.GetEdges(self)):
yield ei
ei.Next()
# Adds objectives together to form one collective CVXPY Problem.
# Option of specifying Maximize() or the default Minimize().
# Graph status and value properties will also be set.
# Individual variable values can be retrieved using GetNodeValue().
# Option to use serial version or distributed ADMM.
# maxIters optional parameter: Maximum iterations for distributed ADMM.
def Solve(self, M=Minimize, UseADMM=True, NumProcessors=0, Rho=1.0,
MaxIters=250, EpsAbs=0.01, EpsRel=0.01, Verbose=False,
UseClustering = False, ClusterSize = 1000 ):
global m_func
m_func = M
# Use ADMM if the appropriate parameter is specified and if there
# are edges in the graph.
#if __builtin__.len(SuperNodes) > 0:
if UseClustering and ClusterSize > 0:
SuperNodes = self.__ClusterGraph(ClusterSize)
self.__SolveClusterADMM(M,UseADMM,SuperNodes, NumProcessors, Rho, MaxIters,\
EpsAbs, EpsRel, Verbose)
return
if UseADMM and self.GetEdges() != 0:
self.__SolveADMM(NumProcessors, Rho, MaxIters, EpsAbs, EpsRel,
Verbose)
return
if Verbose:
print 'Serial ADMM'
objective = 0
constraints = []
# Add all node objectives and constraints
for ni in self.Nodes():
nid = ni.GetId()
objective += self.node_objectives[nid]
constraints += self.node_constraints[nid]
# Add all edge objectives and constraints
for ei in self.Edges():
etup = self.__GetEdgeTup(ei.GetSrcNId(), ei.GetDstNId())
objective += self.edge_objectives[etup]
constraints += self.edge_constraints[etup]
# Solve CVXPY Problem
objective = m_func(objective)
problem = Problem(objective, constraints)
try:
problem.solve()
except SolverError:
problem.solve(solver=SCS)
if problem.status in [INFEASIBLE_INACCURATE, UNBOUNDED_INACCURATE]:
problem.solve(solver=SCS)
# Set TGraphVX status and value to match CVXPY
self.status = problem.status
self.value = problem.value
# Insert into hash to support ADMM structures and GetNodeValue()
for ni in self.Nodes():
nid = ni.GetId()
variables = self.node_variables[nid]
value = None
for (varID, varName, var, offset) in variables:
if var.size[0] == 1:
val = numpy.array([var.value])
else:
val = numpy.array(var.value).reshape(-1,)
if value is None:
value = val
else:
value = numpy.concatenate((value, val))
self.node_values[nid] = value
"""Function to solve cluster wise optimization problem"""
def __SolveClusterADMM(self,M,UseADMM,superNodes,numProcessors, rho_param,
maxIters, eps_abs, eps_rel,verbose):
#initialize an empty supergraph
supergraph = TGraphVX()
nidToSuperidMap = {}
edgeToClusterTupMap = {}
for snid in xrange(__builtin__.len(superNodes)):
for nid in superNodes[snid]:
nidToSuperidMap[nid] = snid
"""collect the entities for the supergraph. a supernode is a subgraph. a superedge
is a representation of a graph cut"""
superEdgeObjectives = {}
superEdgeConstraints = {}
superNodeObjectives = {}
superNodeConstraints = {}
superNodeVariables = {}
superNodeValues = {}
varToSuperVarMap = {}
"""traverse through the list of edges and add each edge's constraint and objective to
either the supernode to which it belongs or the superedge which connects the ends
of the supernodes to which it belongs"""
for ei in self.Edges():
etup = self.__GetEdgeTup(ei.GetSrcNId(), ei.GetDstNId())
supersrcnid,superdstnid = nidToSuperidMap[etup[0]],nidToSuperidMap[etup[1]]
if supersrcnid != superdstnid: #the edge is a part of the cut
if supersrcnid > superdstnid:
supersrcnid,superdstnid = superdstnid,supersrcnid
if (supersrcnid,superdstnid) not in superEdgeConstraints:
superEdgeConstraints[(supersrcnid,superdstnid)] = self.edge_constraints[etup]
superEdgeObjectives[(supersrcnid,superdstnid)] = self.edge_objectives[etup]
else:
superEdgeConstraints[(supersrcnid,superdstnid)] += self.edge_constraints[etup]
superEdgeObjectives[(supersrcnid,superdstnid)] += self.edge_objectives[etup]
else: #the edge is a part of some supernode
if supersrcnid not in superNodeConstraints:
superNodeConstraints[supersrcnid] = self.edge_constraints[etup]
superNodeObjectives[supersrcnid] = self.edge_objectives[etup]
else:
superNodeConstraints[supersrcnid] += self.edge_constraints[etup]
superNodeObjectives[supersrcnid] += self.edge_objectives[etup]
for ni in self.Nodes():
nid = ni.GetId()
supernid = nidToSuperidMap[nid]
value = None
for (varID, varName, var, offset) in self.node_variables[nid]:
if var.size[0] == 1:
val = numpy.array([var.value])
else:
val = numpy.array(var.value).reshape(-1,)
if not value:
value = val
else:
value = numpy.concatenate((value, val))
if supernid not in superNodeConstraints:
superNodeObjectives[supernid] = self.node_objectives[nid]
superNodeConstraints[supernid] = self.node_constraints[nid]
else:
superNodeObjectives[supernid] += self.node_objectives[nid]
superNodeConstraints[supernid] += self.node_constraints[nid]
for ( varId, varName, var, offset) in self.node_variables[nid]:
superVarName = varName+str(varId)
varToSuperVarMap[(nid,varName)] = (supernid,superVarName)
if supernid not in superNodeVariables:
superNodeVariables[supernid] = [(varId, superVarName, var, offset)]
superNodeValues[supernid] = value
else:
superNodeOffset = sum([superNodeVariables[supernid][k][2].size[0]* \
superNodeVariables[supernid][k][2].size[1]\
for k in xrange(__builtin__.len(superNodeVariables[supernid])) ])
superNodeVariables[supernid] += [(varId, superVarName, var, superNodeOffset)]
superNodeValues[supernid] = numpy.concatenate((superNodeValues[supernid],value))
#add all supernodes to the supergraph
for supernid in superNodeConstraints:
supergraph.AddNode(supernid, superNodeObjectives[supernid], \
superNodeConstraints[supernid])
supergraph.node_variables[supernid] = superNodeVariables[supernid]
supergraph.node_values[supernid] = superNodeValues[supernid]
#add all superedges to the supergraph
for superei in superEdgeConstraints:
superSrcId,superDstId = superei
supergraph.AddEdge(superSrcId, superDstId, None,\
superEdgeObjectives[superei],\
superEdgeConstraints[superei])
#call solver for this supergraph
if UseADMM and supergraph.GetEdges() != 0:
supergraph.__SolveADMM(numProcessors, rho_param, maxIters, eps_abs, eps_rel, verbose)
else:
supergraph.Solve(M, False, numProcessors, rho_param, maxIters, eps_abs, eps_rel, verbose,
UseClustering=False)
self.status = supergraph.status
self.value = supergraph.value
for ni in self.Nodes():
nid = ni.GetId()
snid = nidToSuperidMap[nid]
self.node_values[nid] = []
for ( varId, varName, var, offset) in self.node_variables[nid]:
superVarName = varToSuperVarMap[(nid,varName)]
self.node_values[nid] = numpy.concatenate((self.node_values[nid],\
supergraph.GetNodeValue(snid, superVarName[1])))
# Implementation of distributed ADMM
# Uses a global value of rho_param for rho
# Will run for a maximum of maxIters iterations
def __SolveADMM(self, numProcessors, rho_param, maxIters, eps_abs, eps_rel,
verbose):
global node_vals, edge_z_vals, edge_u_vals, rho
global getValue, rho_update_func
if numProcessors <= 0:
num_processors = multiprocessing.cpu_count()
else:
num_processors = numProcessors
rho = rho_param
if verbose:
print 'Distributed ADMM (%d processors)' % num_processors
# Organize information for each node in helper node_info structure
node_info = {}
# Keeps track of the current offset necessary into the shared node
# values Array
length = 0
for ni in self.Nodes():
nid = ni.GetId()
deg = ni.GetDeg()
obj = self.node_objectives[nid]
variables = self.node_variables[nid]
con = self.node_constraints[nid]
neighbors = [ni.GetNbrNId(j) for j in xrange(deg)]
# Node's constraints include those imposed by edges
for neighborId in neighbors:
etup = self.__GetEdgeTup(nid, neighborId)
econ = self.edge_constraints[etup]
con += econ
# Calculate sum of dimensions of all Variables for this node
size = sum([var.size[0] for (varID, varName, var, offset) in variables])
# Nearly complete information package for this node
node_info[nid] = (nid, obj, variables, con, length, size, deg,\
neighbors)
length += size
node_vals = multiprocessing.Array('d', [0.0] * length)
x_length = length
# Organize information for each node in final edge_list structure and
# also helper edge_info structure
edge_list = []
edge_info = {}
# Keeps track of the current offset necessary into the shared edge
# values Arrays
length = 0
for ei in self.Edges():
etup = self.__GetEdgeTup(ei.GetSrcNId(), ei.GetDstNId())
obj = self.edge_objectives[etup]
con = self.edge_constraints[etup]
con += self.node_constraints[etup[0]] +\
self.node_constraints[etup[1]]
# Get information for each endpoint node
info_i = node_info[etup[0]]
info_j = node_info[etup[1]]
ind_zij = length
ind_uij = length
length += info_i[X_LEN]
ind_zji = length
ind_uji = length
length += info_j[X_LEN]
# Information package for this edge
tup = (etup, obj, con,\
info_i[X_VARS], info_i[X_LEN], info_i[X_IND], ind_zij, ind_uij,\
info_j[X_VARS], info_j[X_LEN], info_j[X_IND], ind_zji, ind_uji)
edge_list.append(tup)
edge_info[etup] = tup
edge_z_vals = multiprocessing.Array('d', [0.0] * length)
edge_u_vals = multiprocessing.Array('d', [0.0] * length)
z_length = length
# Populate sparse matrix A.
# A has dimensions (p, n), where p is the length of the stacked vector
# of node variables, and n is the length of the stacked z vector of
# edge variables.
# Each row of A has one 1. There is a 1 at (i,j) if z_i = x_j.
A = lil_matrix((z_length, x_length), dtype=numpy.int8)
for ei in self.Edges():
etup = self.__GetEdgeTup(ei.GetSrcNId(), ei.GetDstNId())
info_edge = edge_info[etup]
info_i = node_info[etup[0]]
info_j = node_info[etup[1]]
for offset in xrange(info_i[X_LEN]):
row = info_edge[Z_ZIJIND] + offset
col = info_i[X_IND] + offset
A[row, col] = 1
for offset in xrange(info_j[X_LEN]):
row = info_edge[Z_ZJIIND] + offset
col = info_j[X_IND] + offset
A[row, col] = 1
A_tr = A.transpose()
# Create final node_list structure by adding on information for
# node neighbors
node_list = []
for nid, info in node_info.iteritems():
entry = [nid, info[X_OBJ], info[X_VARS], info[X_CON], info[X_IND],\
info[X_LEN], info[X_DEG]]
# Append information about z- and u-value indices for each
# node neighbor
for i in xrange(info[X_DEG]):
neighborId = info[X_NEIGHBORS][i]
indices = (Z_ZIJIND, Z_UIJIND) if nid < neighborId else\
(Z_ZJIIND, Z_UJIIND)
einfo = edge_info[self.__GetEdgeTup(nid, neighborId)]
entry.append(einfo[indices[0]])
entry.append(einfo[indices[1]])
node_list.append(entry)
pool = multiprocessing.Pool(num_processors)
num_iterations = 0
z_old = getValue(edge_z_vals, 0, z_length)
# Proceed until convergence criteria are achieved or the maximum
# number of iterations has passed
while num_iterations <= maxIters:
# Check convergence criteria
if num_iterations != 0:
x = getValue(node_vals, 0, x_length)
z = getValue(edge_z_vals, 0, z_length)
u = getValue(edge_u_vals, 0, z_length)
# Determine if algorithm should stop. Retrieve primal and dual
# residuals and thresholds
stop, res_pri, e_pri, res_dual, e_dual =\
self.__CheckConvergence(A, A_tr, x, z, z_old, u, rho,\
x_length, z_length,
eps_abs, eps_rel, verbose)
if stop: break
z_old = z
# Update rho and scale u-values
rho_new = rho_update_func(rho, res_pri, e_pri, res_dual, e_dual)
scale = float(rho) / rho_new
edge_u_vals[:] = [i * scale for i in edge_u_vals]
rho = rho_new
num_iterations += 1
if verbose:
# Debugging information prints current iteration #
print 'Iteration %d' % num_iterations
pool.map(ADMM_x, node_list)
pool.map(ADMM_z, edge_list)
pool.map(ADMM_u, edge_list)
pool.close()
pool.join()
# Insert into hash to support GetNodeValue()
for entry in node_list:
nid = entry[X_NID]
index = entry[X_IND]
size = entry[X_LEN]
self.node_values[nid] = getValue(node_vals, index, size)
# Set TGraphVX status and value to match CVXPY
if num_iterations <= maxIters:
self.status = 'Optimal'
else:
self.status = 'Incomplete: max iterations reached'
# self.value = self.GetTotalProblemValue()
# Iterate through all variables and update values.
# Sum all objective values over all nodes and edges.
def GetTotalProblemValue(self):
global getValue
result = 0.0
for ni in self.Nodes():
nid = ni.GetId()
for (varID, varName, var, offset) in self.node_variables[nid]:
var.value = self.GetNodeValue(nid, varName)
for ni in self.Nodes():
result += self.node_objectives[ni.GetId()].value
for ei in self.Edges():
etup = self.__GetEdgeTup(ei.GetSrcNId(), ei.GetDstNId())
result += self.edge_objectives[etup].value
return result
# Returns True if convergence criteria have been satisfied
# eps_abs = eps_rel = 0.01
# r = Ax - z
# s = rho * (A^T)(z - z_old)
# e_pri = sqrt(p) * e_abs + e_rel * max(||Ax||, ||z||)
# e_dual = sqrt(n) * e_abs + e_rel * ||rho * (A^T)u||
# Should stop if (||r|| <= e_pri) and (||s|| <= e_dual)
# Returns (boolean shouldStop, primal residual value, primal threshold,
# dual residual value, dual threshold)
def __CheckConvergence(self, A, A_tr, x, z, z_old, u, rho, p, n,
e_abs, e_rel, verbose):
norm = numpy.linalg.norm
Ax = A.dot(x)
r = Ax - z
s = rho * A_tr.dot(z - z_old)
# Primal and dual thresholds. Add .0001 to prevent the case of 0.
e_pri = math.sqrt(p) * e_abs + e_rel * max(norm(Ax), norm(z)) + .0001
e_dual = math.sqrt(n) * e_abs + e_rel * norm(rho * A_tr.dot(u)) + .0001
# Primal and dual residuals
res_pri = norm(r)
res_dual = norm(s)
if verbose:
# Debugging information to print convergence criteria values
print ' r:', res_pri
print ' e_pri:', e_pri
print ' s:', res_dual
print ' e_dual:', e_dual
stop = (res_pri <= e_pri) and (res_dual <= e_dual)
return (stop, res_pri, e_pri, res_dual, e_dual)
# API to get node Variable value after solving with ADMM.
def GetNodeValue(self, NId, Name):
self.__VerifyNId(NId)
for (varID, varName, var, offset) in self.node_variables[NId]:
if varName == Name:
offset = offset
value = self.node_values[NId]
return value[offset:(offset + var.size[0])]
return None
# Prints value of all node variables to console or file, if given
def PrintSolution(self, Filename=None):
numpy.set_printoptions(linewidth=numpy.inf)
out = sys.stdout if (Filename == None) else open(Filename, 'w+')
out.write('Status: %s\n' % self.status)
out.write('Total Objective: %f\n' % self.value)
for ni in self.Nodes():
nid = ni.GetId()
s = 'Node %d:\n' % nid
out.write(s)
for (varID, varName, var, offset) in self.node_variables[nid]:
val = numpy.transpose(self.GetNodeValue(nid, varName))
s = ' %s %s\n' % (varName, str(val))
out.write(s)
# Helper method to verify existence of an NId.
def __VerifyNId(self, NId):
if not TUNGraph.IsNode(self, NId):
raise Exception('Node %d does not exist.' % NId)
# Helper method to determine if
def __UpdateAllVariables(self, NId, Objective):
if NId in self.node_objectives:
# First, remove the Variables from the old Objective.
old_obj = self.node_objectives[NId]
self.all_variables = self.all_variables - set(old_obj.variables())
# Check that the Variables of the new Objective are not currently
# in other Objectives.
new_variables = set(Objective.variables())
if __builtin__.len(self.all_variables.intersection(new_variables)) != 0:
raise Exception('Objective at NId %d shares a variable.' % NId)
self.all_variables = self.all_variables | new_variables
# Helper method to get CVXPY Variables out of a CVXPY Objective
def __ExtractVariableList(self, Objective):
l = [(var.name(), var) for var in Objective.variables()]
# Sort in ascending order by name
l.sort(key=lambda t: t[0])
l2 = []
offset = 0
for (varName, var) in l:
# Add tuples of the form (id, name, object, offset)
l2.append((var.id, varName, var, offset))
offset += var.size[0]
return l2
# Adds a Node to the TUNGraph and stores the corresponding CVX information.
def AddNode(self, NId, Objective=__default_objective,\
Constraints=__default_constraints):
self.__UpdateAllVariables(NId, Objective)
self.node_objectives[NId] = Objective
self.node_variables[NId] = self.__ExtractVariableList(Objective)
self.node_constraints[NId] = Constraints
return TUNGraph.AddNode(self, NId)
def SetNodeObjective(self, NId, Objective):
self.__VerifyNId(NId)
self.__UpdateAllVariables(NId, Objective)
self.node_objectives[NId] = Objective
self.node_variables[NId] = self.__ExtractVariableList(Objective)
def GetNodeObjective(self, NId):
self.__VerifyNId(NId)
return self.node_objectives[NId]
def SetNodeConstraints(self, NId, Constraints):
self.__VerifyNId(NId)
self.node_constraints[NId] = Constraints
def GetNodeConstraints(self, NId):
self.__VerifyNId(NId)
return self.node_constraints[NId]
# Helper method to get a tuple representing an edge. The smaller NId
# goes first.
def __GetEdgeTup(self, NId1, NId2):
return (NId1, NId2) if NId1 < NId2 else (NId2, NId1)
# Helper method to verify existence of an edge.
def __VerifyEdgeTup(self, ETup):
if not TUNGraph.IsEdge(self, ETup[0], ETup[1]):
raise Exception('Edge {%d,%d} does not exist.' % ETup)
# Adds an Edge to the TUNGraph and stores the corresponding CVX information.
# obj_func is a function which accepts two arguments, a dictionary of
# variables for the source and destination nodes
# { string varName : CVXPY Variable }
# obj_func should return a tuple of (objective, constraints), although
# it will assume a singleton object will be an objective and will use
# the default constraints.
# If obj_func is None, then will use Objective and Constraints, which are
# parameters currently set to defaults.
def AddEdge(self, SrcNId, DstNId, ObjectiveFunc=None,
Objective=__default_objective, Constraints=__default_constraints):
ETup = self.__GetEdgeTup(SrcNId, DstNId)
if ObjectiveFunc != None:
src_vars = self.GetNodeVariables(SrcNId)
dst_vars = self.GetNodeVariables(DstNId)
ret = ObjectiveFunc(src_vars, dst_vars)
if type(ret) is tuple:
# Tuple = assume we have (objective, constraints)
self.edge_objectives[ETup] = ret[0]
self.edge_constraints[ETup] = ret[1]
else:
# Singleton object = assume it is the objective
self.edge_objectives[ETup] = ret
self.edge_constraints[ETup] = self.__default_constraints
else:
self.edge_objectives[ETup] = Objective
self.edge_constraints[ETup] = Constraints
return TUNGraph.AddEdge(self, SrcNId, DstNId)
def SetEdgeObjective(self, SrcNId, DstNId, Objective):
ETup = self.__GetEdgeTup(SrcNId, DstNId)
self.__VerifyEdgeTup(ETup)
self.edge_objectives[ETup] = Objective
def GetEdgeObjective(self, SrcNId, DstNId):
ETup = self.__GetEdgeTup(SrcNId, DstNId)
self.__VerifyEdgeTup(ETup)
return self.edge_objectives[ETup]
def SetEdgeConstraints(self, SrcNId, DstNId, Constraints):
ETup = self.__GetEdgeTup(SrcNId, DstNId)
self.__VerifyEdgeTup(ETup)
self.edge_constraints[ETup] = Constraints
def GetEdgeConstraints(self, SrcNId, DstNId):
ETup = self.__GetEdgeTup(SrcNId, DstNId)
self.__VerifyEdgeTup(ETup)
return self.edge_constraints[ETup]
# Returns a dictionary of all variables corresponding to a node.
# { string name : CVXPY Variable }
# This can be used in place of bulk loading functions to recover necessary
# Variables for an edge.
def GetNodeVariables(self, NId):
self.__VerifyNId(NId)
d = {}
for (varID, varName, var, offset) in self.node_variables[NId]:
d[varName] = var
return d
# Bulk loading for nodes
# ObjFunc is a function which accepts one argument, an array of strings
# parsed from the given CSV filename
# ObjFunc should return a tuple of (objective, constraints), although
# it will assume a singleton object will be an objective
# Optional parameter NodeIDs allows the user to pass in a list specifying,
# in order, the node IDs that correspond to successive rows
# If NodeIDs is None, then the file must have a column denoting the
# node ID for each row. The index of this column (0-indexed) is IdCol.
# If NodeIDs and IdCol are both None, then will iterate over all Nodes, in
# order, as long as the file lasts
def AddNodeObjectives(self, Filename, ObjFunc, NodeIDs=None, IdCol=None):
infile = open(Filename, 'r')
if NodeIDs == None and IdCol == None:
stop = False
for ni in self.Nodes():
nid = ni.GetId()
while True:
line = infile.readline()
if line == '': stop = True
if not line.startswith('#'): break
if stop: break
data = [x.strip() for x in line.split(',')]
ret = ObjFunc(data)
if type(ret) is tuple:
# Tuple = assume we have (objective, constraints)
self.SetNodeObjective(nid, ret[0])
self.SetNodeConstraints(nid, ret[1])
else:
# Singleton object = assume it is the objective
self.SetNodeObjective(nid, ret)
if NodeIDs == None:
for line in infile:
if line.startswith('#'): continue
data = [x.strip() for x in line.split(',')]
ret = ObjFunc(data)
if type(ret) is tuple:
# Tuple = assume we have (objective, constraints)
self.SetNodeObjective(int(data[IdCol]), ret[0])
self.SetNodeConstraints(int(data[IdCol]), ret[1])
else:
# Singleton object = assume it is the objective
self.SetNodeObjective(int(data[IdCol]), ret)
else:
for nid in NodeIDs:
while True:
line = infile.readline()
if line == '':
raise Exception('File %s is too short.' % filename)
if not line.startswith('#'): break
data = [x.strip() for x in line.split(',')]
ret = ObjFunc(data)
if type(ret) is tuple:
# Tuple = assume we have (objective, constraints)
self.SetNodeObjective(nid, ret[0])
self.SetNodeConstraints(nid, ret[1])
else:
# Singleton object = assume it is the objective
self.SetNodeObjective(nid, ret)
infile.close()
# Bulk loading for edges
# If Filename is None:
# ObjFunc is a function which accepts three arguments, a dictionary of
# variables for the source and destination nodes, and an unused param
# { string varName : CVXPY Variable } x2, None
# ObjFunc should return a tuple of (objective, constraints), although
# it will assume a singleton object will be an objective
# If Filename exists:
# ObjFunc is the same, except the third param will be be an array of
# strings parsed from the given CSV filename
# Optional parameter EdgeIDs allows the user to pass in a list specifying,
# in order, the EdgeIDs that correspond to successive rows. An edgeID is
# a tuple of (srcID, dstID).
# If EdgeIDs is None, then the file may have columns denoting the srcID and
# dstID for each row. The indices of these columns are 0-indexed.
# If EdgeIDs and id columns are None, then will iterate through all edges
# in order, as long as the file lasts.
def AddEdgeObjectives(self, ObjFunc, Filename=None, EdgeIDs=None,\
SrcIdCol=None, DstIdCol=None):
if Filename == None:
for ei in self.Edges():
src_id = ei.GetSrcNId()
src_vars = self.GetNodeVariables(src_id)
dst_id = ei.GetDstNId()
dst_vars = self.GetNodeVariables(dst_id)
ret = ObjFunc(src_vars, dst_vars, None)
if type(ret) is tuple:
# Tuple = assume we have (objective, constraints)
self.SetEdgeObjective(src_id, dst_id, ret[0])
self.SetEdgeConstraints(src_id, dst_id, ret[1])
else:
# Singleton object = assume it is the objective
self.SetEdgeObjective(src_id, dst_id, ret)
return
infile = open(Filename, 'r')
if EdgeIDs == None and (SrcIdCol == None or DstIdCol == None):
stop = False
for ei in self.Edges():
src_id = ei.GetSrcNId()
src_vars = self.GetNodeVariables(src_id)
dst_id = ei.GetDstNId()
dst_vars = self.GetNodeVariables(dst_id)
while True:
line = infile.readline()
if line == '': stop = True
if not line.startswith('#'): break
if stop: break
data = [x.strip() for x in line.split(',')]
ret = ObjFunc(src_vars, dst_vars, data)
if type(ret) is tuple:
# Tuple = assume we have (objective, constraints)
self.SetEdgeObjective(src_id, dst_id, ret[0])
self.SetEdgeConstraints(src_id, dst_id, ret[1])
else:
# Singleton object = assume it is the objective
self.SetEdgeObjective(src_id, dst_id, ret)
if EdgeIDs == None:
for line in infile:
if line.startswith('#'): continue
data = [x.strip() for x in line.split(',')]
src_id = int(data[SrcIdCol])
dst_id = int(data[DstIdCol])
src_vars = self.GetNodeVariables(src_id)
dst_vars = self.GetNodeVariables(dst_id)
ret = ObjFunc(src_vars, dst_vars, data)
if type(ret) is tuple:
# Tuple = assume we have (objective, constraints)
self.SetEdgeObjective(src_id, dst_id, ret[0])
self.SetEdgeConstraints(src_id, dst_id, ret[1])
else:
# Singleton object = assume it is the objective
self.SetEdgeObjective(src_id, dst_id, ret)
else:
for edgeID in EdgeIDs:
etup = self.__GetEdgeTup(edgeID[0], edgeID[1])
while True:
line = infile.readline()
if line == '':
raise Exception('File %s is too short.' % Filename)
if not line.startswith('#'): break
data = [x.strip() for x in line.split(',')]
src_vars = self.GetNodeVariables(etup[0])
dst_vars = self.GetNodeVariables(etup[1])
ret = ObjFunc(src_vars, dst_vars, data)
if type(ret) is tuple:
# Tuple = assume we have (objective, constraints)
self.SetEdgeObjective(etup[0], etup[1], ret[0])
self.SetEdgeConstraints(etup[0], etup[1], ret[1])
else:
# Singleton object = assume it is the objective
self.SetEdgeObjective(etup[0], etup[1], ret)
infile.close()
"""return clusters of nodes of the original graph.Each cluster corresponds to
a supernode in the supergraph"""
def __ClusterGraph(self,clusterSize):
#obtain a random shuffle of the nodes
nidArray = [ni.GetId() for ni in self.Nodes()]
numpy.random.shuffle(nidArray)
visitedNode = {}
for nid in nidArray:
visitedNode[nid] = False
superNodes = []
superNode,superNodeSize = [],0
for nid in nidArray:
if not visitedNode[nid]:
oddLevel, evenLevel, isOdd = [],[],True
oddLevel.append(nid)
visitedNode[nid] = True
#do a level order traversal and add nodes to the superNode until the
#size of the supernode variables gets larger than clusterSize
while True:
if isOdd:
if __builtin__.len(oddLevel) > 0:
while __builtin__.len(oddLevel) > 0:
topId = oddLevel.pop(0)
node = TUNGraph.GetNI(self,topId)
varSize = sum([variable[2].size[0]* \
variable[2].size[1]\
for variable in self.node_variables[topId]])
if varSize + superNodeSize <= clusterSize:
superNode.append(topId)
superNodeSize = varSize + superNodeSize
else:
if __builtin__.len(superNode) > 0:
superNodes.append(superNode)
superNodeSize = varSize
superNode = [topId]
neighbors = [node.GetNbrNId(j) \
for j in xrange(node.GetDeg())]
for nbrId in neighbors:
if not visitedNode[nbrId]:
evenLevel.append(nbrId)
visitedNode[nbrId] = True
isOdd = False
#sort the nodes according to their variable size
if __builtin__.len(evenLevel) > 0:
evenLevel.sort(key=lambda nid : sum([variable[2].size[0]* \
variable[2].size[1] for variable \
in self.node_variables[nid]]))
else:
break
else:
if __builtin__.len(evenLevel) > 0:
while __builtin__.len(evenLevel) > 0:
topId = evenLevel.pop(0)
node = TUNGraph.GetNI(self,topId)
varSize = sum([variable[2].size[0]* \
variable[2].size[1]\
for variable in self.node_variables[topId]])
if varSize + superNodeSize <= clusterSize:
superNode.append(topId)
superNodeSize = varSize + superNodeSize
else:
if __builtin__.len(superNode) > 0:
superNodes.append(superNode)
superNodeSize = varSize
superNode = [topId]
neighbors = [node.GetNbrNId(j) \
for j in xrange(node.GetDeg())]
for nbrId in neighbors:
if not visitedNode[nbrId]:
oddLevel.append(nbrId)
visitedNode[nbrId] = True
isOdd = True
#sort the nodes according to their variable size
if __builtin__.len(oddLevel) > 0:
oddLevel.sort(key=lambda nid : sum([variable[2].size[0]* \
variable[2].size[1] for variable \
in self.node_variables[nid]]))
else:
break
if superNode not in superNodes:
superNodes.append(superNode)
return superNodes
## ADMM Global Variables and Functions ##
# By default, the objective function is Minimize().
__default_m_func = Minimize
m_func = __default_m_func
# By default, rho is 1.0. Default rho update is identity function and does not
# depend on primal or dual residuals or thresholds.
__default_rho = 1.0
__default_rho_update_func = lambda rho, res_p, thr_p, res_d, thr_d: rho
rho = __default_rho
# Rho update function takes 5 parameters
# - Old value of rho
# - Primal residual and threshold
# - Dual residual and threshold
rho_update_func = __default_rho_update_func
def SetRho(Rho=None):
global rho
rho = Rho if Rho else __default_rho
# Rho update function should take one parameter: old_rho
# Returns new_rho
# This function will be called at the end of every iteration
def SetRhoUpdateFunc(Func=None):
global rho_update_func
rho_update_func = Func if Func else __default_rho_update_func
# Tuple of indices to identify the information package for each node. Actual
# length of specific package (list) may vary depending on node degree.
# X_NID: Node ID
# X_OBJ: CVXPY Objective
# X_VARS: CVXPY Variables (entry from node_variables structure)
# X_CON: CVXPY Constraints
# X_IND: Starting index into shared node_vals Array
# X_LEN: Total length (sum of dimensions) of all variables
# X_DEG: Number of neighbors
# X_NEIGHBORS: Placeholder for information about each neighbors
# Information for each neighbor is two entries, appended in order.
# Starting index of the corresponding z-value in edge_z_vals. Then for u.
(X_NID, X_OBJ, X_VARS, X_CON, X_IND, X_LEN, X_DEG, X_NEIGHBORS) = range(8)
# Tuple of indices to identify the information package for each edge.
# Z_EID: Edge ID / tuple
# Z_OBJ: CVXPY Objective
# Z_CON: CVXPY Constraints
# Z_[IJ]VARS: CVXPY Variables for Node [ij] (entry from node_variables)
# Z_[IJ]LEN: Total length (sum of dimensions) of all variables for Node [ij]
# Z_X[IJ]IND: Starting index into shared node_vals Array for Node [ij]
# Z_Z[IJ|JI]IND: Starting index into shared edge_z_vals Array for edge [ij|ji]
# Z_U[IJ|JI]IND: Starting index into shared edge_u_vals Array for edge [ij|ji]
(Z_EID, Z_OBJ, Z_CON, Z_IVARS, Z_ILEN, Z_XIIND, Z_ZIJIND, Z_UIJIND,\
Z_JVARS, Z_JLEN, Z_XJIND, Z_ZJIIND, Z_UJIIND) = range(13)
# Contain all x, z, and u values for each node and/or edge in ADMM. Use the
# given starting index and length with getValue() to get individual node values
node_vals = None
edge_z_vals = None
edge_u_vals = None
# Extract a numpy array value from a shared Array.
# Give shared array, starting index, and total length.
def getValue(arr, index, length):
return numpy.array(arr[index:(index + length)])
# Write value of numpy array nparr (with given length) to a shared Array at
# the given starting index.
def writeValue(sharedarr, index, nparr, length):
if length == 1:
nparr = [nparr]
sharedarr[index:(index + length)] = nparr
# Write the values for all of the Variables involved in a given Objective to
# the given shared Array.
# variables should be an entry from the node_values structure.
def writeObjective(sharedarr, index, objective, variables):
for v in objective.variables():
vID = v.id
value = v.value
# Find the tuple in variables with the same ID. Take the offset.
# If no tuple exists, then silently skip.
for (varID, varName, var, offset) in variables:
if varID == vID:
writeValue(sharedarr, index + offset, value, var.size[0])
break
# Proximal operators
def Prox_logdet(S, A, eta):
global rho
d, q = numpy.linalg.eigh(eta*A-S)
q = numpy.matrix(q)
X_var = ( 1/(2*float(eta)) )*q*( numpy.diag(d + numpy.sqrt(numpy.square(d) + (4*eta)*numpy.ones(d.shape))) )*q.T
x_var = X_var[numpy.triu_indices(S.shape[1])] # extract upper triangular part as update variable
return numpy.matrix(x_var).T
def upper2Full(a):
n = int((-1 + numpy.sqrt(1+ 8*a.shape[0]))/2)
A = numpy.zeros([n,n])
A[numpy.triu_indices(n)] = a
temp = A.diagonal()
A = (A + A.T) - numpy.diag(temp)
return A
def ij2symmetric(i,j,size):
return (size * (size + 1))/2 - (size-i)*((size - i + 1))/2 + j - i
# x-update for ADMM for one node
def ADMM_x(entry):
global rho
variables = entry[X_VARS]
#-----------------------Proximal operator ---------------------------
x_update = [] # proximal update for the variable x
if(__builtin__.len(entry[1].args) > 1 ):
# print 'we are in logdet + trace node'
cvxpyMat = entry[1].args[1].args[0].args[0]
numpymat = cvxpyMat.value
mat_shape = ( int( numpymat.shape[1] * ( numpymat.shape[1]+1 )/2.0 ) ,)
a = numpy.zeros(mat_shape)
for i in xrange(entry[X_DEG]):
z_index = X_NEIGHBORS + (2 * i)
u_index = z_index + 1
zi = entry[z_index]
ui = entry[u_index]
for (varID, varName, var, offset) in variables:
z = getValue(edge_z_vals, zi + offset, var.size[0])
u = getValue(edge_u_vals, ui + offset, var.size[0])
a += (z-u)
A = upper2Full(a)
A = A/entry[X_DEG]
eta = 1/float(rho)
x_update = Prox_logdet(numpymat, A, eta)
solution = numpy.array(x_update).T.reshape(-1)
writeValue(node_vals, entry[X_IND] + variables[0][3], solution, variables[0][2].size[0])
else:
x_update = [] # no variable to update for dummy node
return None
# z-update for ADMM for one edge
def ADMM_z(entry, index_penalty = 1):
global rho
rho = float(rho)
#-----------------------Proximal operator ---------------------------
a_ij = [] #
flag = 0
variables_i = entry[Z_IVARS]
for (varID, varName, var, offset) in variables_i:
x_i = getValue(node_vals, entry[Z_XIIND] + offset, var.size[0])
u_ij = getValue(edge_u_vals, entry[Z_UIJIND] + offset, var.size[0])
if flag == 0:
a_ij = (x_i + u_ij)
flag = 1
else:
a_ij += (x_i + u_ij)
lamb = entry[1].args[0].args[0].value
numBlocks = entry[1].args[1].args[0].value
sizeBlocks = entry[1].args[2].args[0].value
probSize = numBlocks*sizeBlocks
z_ij = numpy.zeros(probSize*(probSize+1)/2)
for i in range(numBlocks):
if (i == 0):
#In the A^{(0)} block (the blocks on the diagonal)
for j in range(sizeBlocks):
for k in range(j, sizeBlocks):
elems = numBlocks
lamSum = 0
points = numpy.zeros((elems))
locList = []
for l in range(elems):
(loc1, loc2) = (l*sizeBlocks + j, l*sizeBlocks+k)
locList.append((loc1,loc2))
index = ij2symmetric(loc1, loc2, probSize)
points[l] = a_ij[index]
lamSum = lamSum + lamb[loc1,loc2]
#Calculate soft threshold
#If answer is positive
ansPos = max((rho*numpy.sum(points) - lamSum)/(rho*elems),0)
#If answer is negative
ansNeg = min((rho*numpy.sum(points) + lamSum)/(rho*elems),0)
if (rho*numpy.sum(points) > lamSum):
for locs in locList:
index = ij2symmetric(locs[0], locs[1], probSize)
z_ij[index] = ansPos
elif(rho*numpy.sum(points) < -1*lamSum):
for locs in locList:
index = ij2symmetric(locs[0], locs[1], probSize)
z_ij[index] = ansNeg
else:
for locs in locList:
index = ij2symmetric(locs[0], locs[1], probSize)
z_ij[index] = 0
else:
#Off diagonal blocks
for j in range(sizeBlocks):
for k in range(sizeBlocks):
elems = (2*numBlocks - 2*i)/2
lamSum = 0
points = numpy.zeros((elems))
locList = []
for l in range(elems):
(loc1, loc2) = ((l+i)*sizeBlocks + j, l*sizeBlocks+k)
locList.append((loc2,loc1))
index = ij2symmetric(loc2, loc1, probSize)
points[l] = a_ij[index]
lamSum = lamSum + lamb[loc2,loc1]
#Calculate soft threshold
#If answer is positive
ansPos = max((rho*numpy.sum(points) - lamSum)/(rho*elems),0)
#If answer is negative
ansNeg = min((rho*numpy.sum(points) + lamSum)/(rho*elems),0)
if (rho*numpy.sum(points) > lamSum):
for locs in locList:
index = ij2symmetric(locs[0], locs[1], probSize)
z_ij[index] = ansPos
elif(rho*numpy.sum(points) < -1*lamSum):
for locs in locList:
index = ij2symmetric(locs[0], locs[1], probSize)
z_ij[index] = ansNeg
else:
for locs in locList:
index = ij2symmetric(locs[0], locs[1], probSize)
z_ij[index] = 0
writeValue(edge_z_vals, entry[Z_ZIJIND] + variables_i[0][3], z_ij, variables_i[0][2].size[0])
return None
# u-update for ADMM for one edge
def ADMM_u(entry):
global rho
size_i = entry[Z_ILEN]
uij = getValue(edge_u_vals, entry[Z_UIJIND], size_i) +\
getValue(node_vals, entry[Z_XIIND], size_i) -\
getValue(edge_z_vals, entry[Z_ZIJIND], size_i)
writeValue(edge_u_vals, entry[Z_UIJIND], uij, size_i)
size_j = entry[Z_JLEN]
uji = getValue(edge_u_vals, entry[Z_UJIIND], size_j) +\
getValue(node_vals, entry[Z_XJIND], size_j) -\
getValue(edge_z_vals, entry[Z_ZJIIND], size_j)
writeValue(edge_u_vals, entry[Z_UJIIND], uji, size_j)
return entry
