def inferFlow(self, lhsMode):
""" Infer flow of information in the clause, by populating a VarInfo
object for each variable and a GoalInfo object for each goal.
Information flows from the lhs's input variable, to the output
variable through predicates which map inputs to outputs.
"""
# (re)populate the varDict and goalDict structures for a rule
self.varDict = {}
self.goalDict = {}
# lhs goal is is special - it connects to input/outputs of the predicate
gin = self.goalDict[0] = GoalInfo(0)
gin.mode = lhsMode
#for lhs, infer inputs/outputs from the known mode
for i in range(self.rule.lhs.arity):
v = self.rule.lhs.args[i]
vin = self.varDict[v] = VarInfo(v)
assert parser.isVariableAtom(
v
), 'arguments to defined predicate %s cannot be a constant' % str(
rule.lhs)
if gin.mode.isInput(i):
gin.inputs.add(v) #input to predicate means output of lhs
vin.outputOf = 0
else:
gin.outputs.add(v) #input to predicate means input to lhs
vin.inputTo.add(0)
# for rhs goals, use inputs/outputs to infer mode
for j in range(1, len(self.goals)):
gin = self.goalDict[j] = GoalInfo(j)
goal = self.goals[j]
for i in range(goal.arity):
v = goal.args[i]
if parser.isVariableAtom(v):
if v not in self.varDict: self.varDict[v] = VarInfo(v)
vin = self.varDict[v]
if vin.outputOf != None:
# not first occurrence, so it's an input to this goal
gin.inputs.add(v)
vin.inputTo.add(j)
else:
gin.outputs.add(v)
vin.outputOf = j
#validate - lhs has exactly one output, which must be bound somewhere
lhsGin = self.goalDict[0]
assert len(
lhsGin.outputs
) == 1, 'lhs must have exactly one output but outputs are ' + str(
lhsGin.outputs)
y = only(lhsGin.outputs)
self.varDict[y] != None, 'lhs output variable "%s" not bound' % y
def inferFlow(self):
""" Infer flow of information in the clause, by populating a VarInfo
object for each variable and a GoalInfo object for each goal.
Information flows from the lhs's input variable, to the output
variable through predicates which map inputs to outputs.
"""
# populate the varDict and goalDict structures for a rule
self.varDict = {}
self.goalDict = {}
#for lhs, infer inputs/outputs from the known mode
gin = self.goalDict[0] = GoalInfo(0)
gin.mode = self.lhsMode
for i in range(self.rule.lhs.arity):
v = self.rule.lhs.args[i]
if v not in self.varDict:
self.varDict[v] = VarInfo(v)
else:
assert False,'same variable cannot appear twice in a rule lhs'
vin = self.varDict[v]
assert parser.isVariableAtom(v), 'arguments to defined predicate %s cannot be a constant' % str(self.rule.lhs)
if gin.mode.isInput(i):
gin.inputs.add(v) #input to predicate means output of lhs
vin.outputOf = 0
else:
gin.outputs.add(v) #input to predicate means input to lhs
vin.inputTo.add(0)
# for rhs goals, use inputs/outputs to infer mode
for j in range(1,len(self.goals)):
gin = self.goalDict[j] = GoalInfo(j)
goal = self.goals[j]
for i in range(goal.arity):
v = goal.args[i]
if parser.isVariableAtom(v):
if v not in self.varDict: self.varDict[v] = VarInfo(v)
vin = self.varDict[v]
if vin.outputOf!=None:
# not first occurrence, so it's an input to this goal
gin.inputs.add(v)
vin.inputTo.add(j)
else:
gin.outputs.add(v)
vin.outputOf = j
#validate - lhs has exactly one output, which must be bound somewhere
lhsGin = self.goalDict[0]
#TODO: changed here
# print 'len(lhsGin.outputs)=%d' % (len(lhsGin.outputs))
assert len(lhsGin.outputs)==1, 'lhs mode '+str(self.lhsMode)+' and lhs has >1 output: outputs '+str(lhsGin.outputs)+' for rule '+str(self.rule)
y = only(lhsGin.outputs)
self.varDict[y]!=None,'lhs output variable "%s" not bound' % y
def inferFlow(self,lhsMode):
""" Infer flow of information in the clause, by populating a VarInfo
object for each variable and a GoalInfo object for each goal.
Information flows from the lhs's input variable, to the output
variable through predicates which map inputs to outputs.
"""
# (re)populate the varDict and goalDict structures for a rule
self.varDict = {}
self.goalDict = {}
gin = self.goalDict[-1] = GoalInfo(-1)
gin.mode = lhsMode
gin.rootAncestors.add(-1)
#for lhs, infer inputs/outputs from the known mode
for i in range(self.rule.lhs.arity):
v = self.rule.lhs.args[i]
vin = self.varDict[v] = VarInfo(v)
vin.onehot = lhsMode.isOnehot(i)
if lhsMode.isInput(i):
gin.inputs.add(v)
vin.outputOf = -1
else:
vin.inputTo.add(-1)
gin.outputs.add(v)
# for rhs goals, use inputs/outputs to infer mode
for j in range(len(self.rule.rhs)):
gin = self.goalDict[j] = GoalInfo(j)
for i in range(self.rule.rhs[j].arity):
v = self.rule.rhs[j].args[i]
if parser.isVariableAtom(v):
if v not in self.varDict: self.varDict[v] = VarInfo(v)
vin = self.varDict[v]
if vin.outputOf!=None:
gin.inputs.add(v)
vin.inputTo.add(j)
goalWhichBoundV = vin.outputOf
for a in self.goalDict[goalWhichBoundV].rootAncestors:
gin.rootAncestors.add(a)
else:
gin.outputs.add(v)
vin.outputOf = j
# if no ancestors then this is a root
if not gin.rootAncestors: gin.rootAncestors.add(j)
#validate - lhs has exactly one output, which is either bound
#by a RHS goal or else is a constant
lhsGin = self.goalDict[-1]
assert len(lhsGin.outputs)==1, 'lhs must have exactly one output'
y = only(lhsGin.outputs)
yVin = self.varDict[y]
assert yVin.outputOf!=None or not parser.isVariableAtom(y), 'lhs output variable "%s" not bound' % y
def msgGoal2Var(j,v,depth):
"""Send a message from a goal to a variable. Note goals can have at
most one input and at most one output. This is complex
because there are several cases, depending on if the goal
is LHS on RHS, and if the variable is an input or
output."""
if (j,v) in messages: return messages[(j,v)]
else:
gin = self.goalDict[j]
if TRACE: print '%smsg: %d->%s' % (('| '*depth),j,v)
# The lhs goal, j==0, is the input factor
if j==0 and v in self.goalDict[j].inputs:
#input port -> input variable
assert parser.isVariableAtom(v),'input must be a variable'
return cacheMessage((j,v),v)
elif j==0:
#output port -> output variable
assert False,'illegal message - something is wrong'
elif j>0 and v in self.goalDict[j].outputs:
#message from rhs goal to an output variable of that goal
msgName = 'f_%d_%s' % (j,v)
mode = self.toMode(j)
if not gin.inputs:
# special case - binding a variable to a constant with set(Var,const)
assert matrixdb.isSetMode(mode),'output variables without inputs are only allowed for set/2'
addOp(depth,ops.AssignOnehotToVar(msgName,mode))
return cacheMessage((j,v),msgName)
else:
fx = msgVar2Goal(only(gin.inputs),j,depth+1) #ask for the message forward from the input to goal j
if not gin.definedPred:
addOp(depth,ops.VecMatMulOp(msgName,fx,mode))
else:
addOp(depth,ops.DefinedPredOp(self.tensorlogProg,msgName,fx,mode,self.depth+1))
return cacheMessage((j,v),msgName)
elif j>0 and v in self.goalDict[j].inputs:
#message from rhs goal to an input variable of that goal
gin = self.goalDict[j]
msgName = 'b_%d_%s' % (j,v)
mode = self.toMode(j)
def hasOutputVarUsedElsewhere(gin):
outVar = only(gin.outputs)
return self.varDict[outVar].inputTo
if gin.outputs and hasOutputVarUsedElsewhere(gin):
bx = msgVar2Goal(only(gin.outputs),j,depth+1) #ask for the message backward from the input to goal
addOp(depth,ops.VecMatMulOp(msgName,bx,mode,transpose=True))
return cacheMessage((j,v),msgName)
else:
#optimize away the message from the output var
# of gin. note that this would be a dense
# all-ones vector.
if gin.outputs:
assert len(gin.outputs)==1, 'need single output from %s' % self.goals[j]
#this variable now is connected to the main chain
self.varDict[only(gin.outputs)].connected = True
addOp(depth,ops.AssignPreimageToVar(msgName,mode))
return cacheMessage((j,v),msgName)
else:
assert False,'unexpected message goal %d -> %s ins %r outs %r' % (j,v,gin.inputs,gin.outputs)
def generateOps(self):
""" Convert the compiled rule to a sequence of matrix ops.
"""
numMainChainGoals = len([j for j in range(len(self.rule.rhs)) if self.goalDict[j].mainChain])
if not numMainChainGoals:
lhsGin = self.goalDict[-1]
#find constraints on the input
#TODO can we have multiple inputs in this case?
x0 = only(lhsGin.inputs)
self.detectSecondaryChainConstraints(x0)
x = self.varDict[x0].constrainedVersion
#generate code to weight the onehot vector for the
#constant output by the score of the input
constOut = only(lhsGin.outputs)
tmpOut = 'weight_%s_by_%s' % (constOut,x0)
self.varDict[constOut].constrainedVersion = tmpOut
self.ops.append(ops.WeightedOnehot(tmpOut,x,constOut))
#execute this code for mainChain goals
for j in range(len(self.rule.rhs)):
gin = self.goalDict[j]
if gin.mainChain:
#TODO compile pair predicates?
x0 = only(gin.inputs)
self.detectSecondaryChainConstraints(x0)
x = self.varDict[x0].constrainedVersion
y = only(gin.outputs)
mode = self.toMode(j)
if not gin.definedPred:
self.ops.append(ops.RightMatMulOp(y,x,mode))
else:
self.ops.append(ops.DefinedPredOp(self.tensorlogProg,y,x,mode,self.depth+1))
# also look for non-mainchain constraints on the final output
# of the chain
for v,vin in self.varDict.items():
if (-1 in vin.inputTo) and parser.isVariableAtom(v):
self.detectSecondaryChainConstraints(v)
def argOnehotMode(x):
if (not parser.isVariableAtom(x)) or self.varDict[x].onehot: return '1'
else: return ''
class BPCompiler(object):
"""Compiles a logical rule + a mode into a sequence of ops.py operations."""
def __init__(self, tensorlogProg, depth, rule):
""" Build a compiler for a rule. The tensorlogProg is used to
recursively compile any intensionally-defined predicates.
The depth is a depth bound.
"""
self.rule = rule
self.tensorlogProg = tensorlogProg
self.depth = depth #used for recursively compiling subpredicates with tensorlogProg
self.ops = [] #operations used for BP
self.output = None #final outputs of the function associated with BP for the mode
self.inputs = None #inputs of the function associated with BP for the mode
self.goals = [
self.rule.lhs
] + self.rule.rhs #for convenience, in looping over lhs and rhs goals
if STRICT: self.validateRuleBeforeAnalysis()
def validateRuleBeforeAnalysis(self):
"""Raises error if the rule doesn't satisfy the assumptions made by
the compiler. Can be run before flow analysis."""
assert self.rule.lhs.arity == 2
for goal in self.rule.rhs:
assert goal.arity == 1 or goal.arity == 2
def compile(self, lhsMode):
"""Top-level analysis routine for a rule.
"""
#infer the information flow for all the variables and goals,
#and store in the varDict/goalDict under vin.outputOf,
#vin.inputTo, gin.outputs, gin.inputs
self.inferFlow(lhsMode)
#recursively call the tensorlog program to compile
#any intensionally-defined subpredicates
self.compileDefinedPredicates()
# generate an operation sequence that implements the BP algorithm
if PRODUCE_OPS:
self.generateOps()
def inferFlow(self, lhsMode):
""" Infer flow of information in the clause, by populating a VarInfo
object for each variable and a GoalInfo object for each goal.
Information flows from the lhs's input variable, to the output
variable through predicates which map inputs to outputs.
"""
# (re)populate the varDict and goalDict structures for a rule
self.varDict = {}
self.goalDict = {}
# lhs goal is is special - it connects to input/outputs of the predicate
gin = self.goalDict[0] = GoalInfo(0)
gin.mode = lhsMode
#for lhs, infer inputs/outputs from the known mode
for i in range(self.rule.lhs.arity):
v = self.rule.lhs.args[i]
vin = self.varDict[v] = VarInfo(v)
assert parser.isVariableAtom(
v
), 'arguments to defined predicate %s cannot be a constant' % str(
rule.lhs)
if gin.mode.isInput(i):
gin.inputs.add(v) #input to predicate means output of lhs
vin.outputOf = 0
else:
gin.outputs.add(v) #input to predicate means input to lhs
vin.inputTo.add(0)
# for rhs goals, use inputs/outputs to infer mode
for j in range(1, len(self.goals)):
gin = self.goalDict[j] = GoalInfo(j)
goal = self.goals[j]
for i in range(goal.arity):
v = goal.args[i]
if parser.isVariableAtom(v):
if v not in self.varDict: self.varDict[v] = VarInfo(v)
vin = self.varDict[v]
if vin.outputOf != None:
# not first occurrence, so it's an input to this goal
gin.inputs.add(v)
vin.inputTo.add(j)
else:
gin.outputs.add(v)
vin.outputOf = j
#validate - lhs has exactly one output, which must be bound somewhere
lhsGin = self.goalDict[0]
assert len(
lhsGin.outputs
) == 1, 'lhs must have exactly one output but outputs are ' + str(
lhsGin.outputs)
y = only(lhsGin.outputs)
self.varDict[y] != None, 'lhs output variable "%s" not bound' % y
def compileDefinedPredicates(self):
"""Recursively call the tensorlog program to compile
each subpredicate."""
for j in range(1, len(self.goals)):
gin = self.goalDict[j]
mode = self.toMode(j)
if self.tensorlogProg.findPredDef(mode):
gin.definedPred = True
self.tensorlogProg.compile(mode, self.depth + 1)
def toMode(self, j):
"""Return a mode declaration for the j-th goal of the rule"""
goal = self.goals[j]
gin = self.goalDict[j]
def argIOMode(x):
if x in gin.inputs: return 'i'
elif x in gin.outputs: return 'o'
else:
assert x != 'i' and x != 'o' and x != 'i1' and x != 'i2', 'Illegal to use constants i,o,i1,o1 in a program'
return x
return tensorlog.ModeDeclaration(
parser.Goal(goal.functor, [argIOMode(x) for x in goal.args]))
#
# the main belief propagation algorithm
#
def generateOps(self):
"""Emulate BP and emit the sequence of operations needed."""
messages = {} #cached messages
def addOp(depth, op):
"""Add an operation to self.ops, echo if required"""
if TRACE: print '%s+%s' % (('| ' * depth), op)
self.ops.append(op)
def cacheMessage((src, dst), msg):
""" Send a message, caching it if possible
"""
if (src, dst) not in messages:
messages[(src, dst)] = msg
return messages[(src, dst)]
def msgGoal2Var(j, v, depth):
"""Send a message from a goal to a variable. Note goals can have at
most one input and at most one output. This is complex
because there are several cases, depending on if the goal
is LHS on RHS, and if the variable is an input or
output."""
if (j, v) in messages: return messages[(j, v)]
else:
gin = self.goalDict[j]
if TRACE: print '%smsg: %d->%s' % (('| ' * depth), j, v)
# The lhs goal, j==0, is the input factor
if j == 0 and v in self.goalDict[j].inputs:
#input port -> input variable
assert parser.isVariableAtom(v), 'input must be a variable'
return cacheMessage((j, v), v)
elif j == 0:
#output port -> output variable
assert False, 'illegal message - something is wrong'
elif j > 0 and v in self.goalDict[j].outputs:
#message from rhs goal to an output variable of that goal
msgName = 'f_%d_%s' % (j, v)
mode = self.toMode(j)
if not gin.inputs:
# special case - binding a variable to a constant with set(Var,const)
assert matrixdb.isSetMode(
mode
), 'output variables without inputs are only allowed for set/2'
addOp(depth, ops.AssignOnehotToVar(msgName, mode))
return cacheMessage((j, v), msgName)
else:
fx = msgVar2Goal(
only(gin.inputs), j, depth + 1
) #ask for the message forward from the input to goal j
if not gin.definedPred:
addOp(depth, ops.VecMatMulOp(msgName, fx, mode))
else:
addOp(
depth,
ops.DefinedPredOp(self.tensorlogProg, msgName,
fx, mode, self.depth + 1))
return cacheMessage((j, v), msgName)
elif j > 0 and v in self.goalDict[j].inputs:
#message from rhs goal to an input variable of that goal
gin = self.goalDict[j]
msgName = 'b_%d_%s' % (j, v)
mode = self.toMode(j)
def hasOutputVarUsedElsewhere(gin):
outVar = only(gin.outputs)
return self.varDict[outVar].inputTo
if gin.outputs and hasOutputVarUsedElsewhere(gin):
bx = msgVar2Goal(
only(gin.outputs), j, depth + 1
) #ask for the message backward from the input to goal
addOp(
depth,
ops.VecMatMulOp(msgName, bx, mode, transpose=True))
return cacheMessage((j, v), msgName)
else:
#optimize away the message from the output var
# of gin. note that this would be a dense
# all-ones vector.
if gin.outputs:
assert len(
gin.outputs
) == 1, 'need single output from %s' % self.goals[j]
#this variable now is connected to the main chain
self.varDict[only(gin.outputs)].connected = True
addOp(depth, ops.AssignPreimageToVar(msgName, mode))
return cacheMessage((j, v), msgName)
else:
assert False, 'unexpected message goal %d -> %s ins %r outs %r' % (
j, v, gin.inputs, gin.outputs)
def msgVar2Goal(v, j, depth):
"""Message from a variable to a goal.
"""
if (v, j) in messages: return messages[(v, j)]
else:
vin = self.varDict[v]
vin.connected = True
gin = self.goalDict[j]
#variables have one outputOf, but possily many inputTo connections
vNeighbors = [
j2 for j2 in [vin.outputOf] + list(vin.inputTo) if j2 != j
]
if TRACE:
print '%smsg from %s to %d, vNeighbors=%r' % (
'| ' * depth, v, j, vNeighbors)
assert len(
vNeighbors
), 'variables should have >1 neighbor but %s has only one: %d' % (
v, j)
#form product of the incoming messages, cleverly not
#generating only the variables we really need
currentProduct = msgGoal2Var(vNeighbors[0], v, depth + 1)
for j2 in vNeighbors[1:]:
nextProd = 'p_%d_%s_%d' % (
j, v, j2) if j2 != vNeighbors[-1] else 'fb_%s' % v
multiplicand = msgGoal2Var(j2, v, depth + 1)
addOp(
depth,
ops.ComponentwiseVecMulOp(nextProd, currentProduct,
multiplicand))
currentProduct = nextProd
return cacheMessage((v, j), currentProduct)
#
# main BP code starts here
#
#generate a message from the output variable to the lhs
outputVar = only(self.goalDict[0].outputs)
outputMsg = msgVar2Goal(outputVar, 0, 1)
#now look for other unconnected variables, and connect them to
#a pseudo-node so they have something to send to. The
#outputMsg above will be weighted by the product of all of
#these messages.
weighters = []
psj = len(self.goals)
self.goals.append(parser.Goal('PSEUDO', []))
self.goalDict[psj] = GoalInfo(psj)
#heuristic - start with the rightmost unconnected variable,
#hoping that it's the end of a chain rooted at the input
for j in reversed(range(1, len(self.goals))):
goalj = self.goals[j]
for i in range(goalj.arity):
v = goalj.args[i]
if parser.isVariableAtom(v) and not self.varDict[v].connected:
#save the message from this unconnected node
weighters.append(msgVar2Goal(v, psj, 1))
#multiply the weighting factors from the unconnected node to
#the outputMsg, again cleverly reusing variable names to keep
#the expression simple.
currentProduct = outputMsg
for msg in weighters:
nextProd = 'w_%s' % outputVar if msg == weighters[
-1] else 'p_%s_%s' % (msg, outputVar)
multiplicand = msg
addOp(0, ops.WeightedVec(nextProd, multiplicand, currentProduct))
currentProduct = nextProd
# save the output and inputs
self.output = currentProduct
self.inputs = list(self.goalDict[0].inputs)
def msgGoal2Var(j, v, depth):
"""Send a message from a goal to a variable. Note goals can have at
most one input and at most one output. This is complex
because there are several cases, depending on if the goal
is LHS on RHS, and if the variable is an input or
output."""
if (j, v) in messages: return messages[(j, v)]
else:
gin = self.goalDict[j]
if TRACE: print '%smsg: %d->%s' % (('| ' * depth), j, v)
# The lhs goal, j==0, is the input factor
if j == 0 and v in self.goalDict[j].inputs:
#input port -> input variable
assert parser.isVariableAtom(v), 'input must be a variable'
return cacheMessage((j, v), v)
elif j == 0:
#output port -> output variable
assert False, 'illegal message - something is wrong'
elif j > 0 and v in self.goalDict[j].outputs:
#message from rhs goal to an output variable of that goal
msgName = 'f_%d_%s' % (j, v)
mode = self.toMode(j)
if not gin.inputs:
# special case - binding a variable to a constant with set(Var,const)
assert matrixdb.isSetMode(
mode
), 'output variables without inputs are only allowed for set/2'
addOp(depth, ops.AssignOnehotToVar(msgName, mode))
return cacheMessage((j, v), msgName)
else:
fx = msgVar2Goal(
only(gin.inputs), j, depth + 1
) #ask for the message forward from the input to goal j
if not gin.definedPred:
addOp(depth, ops.VecMatMulOp(msgName, fx, mode))
else:
addOp(
depth,
ops.DefinedPredOp(self.tensorlogProg, msgName,
fx, mode, self.depth + 1))
return cacheMessage((j, v), msgName)
elif j > 0 and v in self.goalDict[j].inputs:
#message from rhs goal to an input variable of that goal
gin = self.goalDict[j]
msgName = 'b_%d_%s' % (j, v)
mode = self.toMode(j)
def hasOutputVarUsedElsewhere(gin):
outVar = only(gin.outputs)
return self.varDict[outVar].inputTo
if gin.outputs and hasOutputVarUsedElsewhere(gin):
bx = msgVar2Goal(
only(gin.outputs), j, depth + 1
) #ask for the message backward from the input to goal
addOp(
depth,
ops.VecMatMulOp(msgName, bx, mode, transpose=True))
return cacheMessage((j, v), msgName)
else:
#optimize away the message from the output var
# of gin. note that this would be a dense
# all-ones vector.
if gin.outputs:
assert len(
gin.outputs
) == 1, 'need single output from %s' % self.goals[j]
#this variable now is connected to the main chain
self.varDict[only(gin.outputs)].connected = True
addOp(depth, ops.AssignPreimageToVar(msgName, mode))
return cacheMessage((j, v), msgName)
else:
assert False, 'unexpected message goal %d -> %s ins %r outs %r' % (
j, v, gin.inputs, gin.outputs)
def msgGoal2Var(j,v,traceDepth):
"""Send a message from a goal to a variable. Note goals can have at
most one input and at most one output. This is complex
because there are several cases, depending on if the goal
is LHS on RHS, and if the variable is an input or
output."""
gin = self.goalDict[j]
if conf.trace: print '%smsg: %d->%s' % (('| '*traceDepth),j,v)
# The lhs goal, j==0, is the input factor
if j==0 and v in self.goalDict[j].inputs:
#input port -> input variable
assert parser.isVariableAtom(v),'input must be a variable'
return v
elif j==0:
#output port -> output variable
assert False,'illegal message - something is wrong'
elif j>0 and v in self.goalDict[j].outputs:
#message from rhs goal to an output variable of that goal
msgName = 'f_%d_%s' % (j,v)
mode = self.toMode(j)
if not gin.inputs:
# special case - binding a variable to a constant with set(Var,const)
assert matrixdb.isAssignMode(mode),\
'output variables without inputs are only allowed for assign/2: %s' % str(self.rule.rhs[gin.index-1])
addOp(ops.AssignOnehotToVar(msgName,mode), traceDepth,j,v)
return msgName
else:
fx = msgVar2Goal(only(gin.inputs),j,traceDepth+1) #ask for the message forward from the input to goal j
if ops.isBuiltinIOOp(mode):
addOp(ops.BuiltInIOOp(msgName,fx,mode), traceDepth,j,v)
elif not gin.definedPred:
addOp(ops.VecMatMulOp(msgName,fx,mode), traceDepth,j,v)
else:
addOp(ops.DefinedPredOp(self.tensorlogProg,msgName,fx,mode,self.depth+1), traceDepth,j,v)
return msgName
elif j>0 and v in self.goalDict[j].inputs:
#message from rhs goal to an input variable of that goal
gin = self.goalDict[j]
msgName = 'b_%d_%s' % (j,v)
mode = self.toMode(j)
def hasOutputVarUsedElsewhere(gin):
outVar = only(gin.outputs)
return self.varDict[outVar].inputTo
if gin.outputs and hasOutputVarUsedElsewhere(gin):
bx = msgVar2Goal(only(gin.outputs),j,traceDepth+1) #ask for the message backward from the input to goal
addOp(ops.VecMatMulOp(msgName,bx,mode,transpose=True), traceDepth,j,v)
return msgName
else:
if gin.outputs:
#optimize away the message from the output
# var of gin, since it would be a dense
# all-ones vector
assert len(gin.outputs)==1, 'need single output from %s' % self.goals[j]
#this variable now is connected to the main chain
self.varDict[only(gin.outputs)].connected = True
assert not ops.isBuiltinIOOp(mode), 'can only use built in io operators where inputs and outputs are used'
assert not gin.definedPred, 'subpredicates must generate an output which is used downstream'
addOp(ops.AssignPreimageToVar(msgName,mode), traceDepth,j,v)
else:
addOp(ops.AssignVectorToVar(msgName,mode), traceDepth,j,v)
return msgName
else:
assert False,'unexpected message goal %d -> %s ins %r outs %r' % (j,v,gin.inputs,gin.outputs)
def generateOps(self):
"""Emulate BP and emit the sequence of operations needed. Instead of
actually constructing a message from src->dst in the course of
BP, what we do instead is emit operations that would construct
the message and assign it a 'variable' named 'foo', and then
return not the message but the variable-name string 'foo'. """
messages = {}
def addOp(op,traceDepth,msgFrom,msgTo):
"""Add an operation to self.ops, echo if required"""
if conf.trace: print '%s+%s' % (('| '*traceDepth),op)
def jToGoal(msg): return str(self.goals[msg]) if type(msg)==type(0) else msg
op.setMessage(jToGoal(msgFrom),jToGoal(msgTo))
self.ops.append(op)
def msgGoal2Var(j,v,traceDepth):
"""Send a message from a goal to a variable. Note goals can have at
most one input and at most one output. This is complex
because there are several cases, depending on if the goal
is LHS on RHS, and if the variable is an input or
output."""
gin = self.goalDict[j]
if conf.trace: print '%smsg: %d->%s' % (('| '*traceDepth),j,v)
# The lhs goal, j==0, is the input factor
if j==0 and v in self.goalDict[j].inputs:
#input port -> input variable
assert parser.isVariableAtom(v),'input must be a variable'
return v
elif j==0:
#output port -> output variable
assert False,'illegal message - something is wrong'
elif j>0 and v in self.goalDict[j].outputs:
#message from rhs goal to an output variable of that goal
msgName = 'f_%d_%s' % (j,v)
mode = self.toMode(j)
if not gin.inputs:
# special case - binding a variable to a constant with set(Var,const)
assert matrixdb.isAssignMode(mode),\
'output variables without inputs are only allowed for assign/2: %s' % str(self.rule.rhs[gin.index-1])
addOp(ops.AssignOnehotToVar(msgName,mode), traceDepth,j,v)
return msgName
else:
fx = msgVar2Goal(only(gin.inputs),j,traceDepth+1) #ask for the message forward from the input to goal j
if ops.isBuiltinIOOp(mode):
addOp(ops.BuiltInIOOp(msgName,fx,mode), traceDepth,j,v)
elif not gin.definedPred:
addOp(ops.VecMatMulOp(msgName,fx,mode), traceDepth,j,v)
else:
addOp(ops.DefinedPredOp(self.tensorlogProg,msgName,fx,mode,self.depth+1), traceDepth,j,v)
return msgName
elif j>0 and v in self.goalDict[j].inputs:
#message from rhs goal to an input variable of that goal
gin = self.goalDict[j]
msgName = 'b_%d_%s' % (j,v)
mode = self.toMode(j)
def hasOutputVarUsedElsewhere(gin):
outVar = only(gin.outputs)
return self.varDict[outVar].inputTo
if gin.outputs and hasOutputVarUsedElsewhere(gin):
bx = msgVar2Goal(only(gin.outputs),j,traceDepth+1) #ask for the message backward from the input to goal
addOp(ops.VecMatMulOp(msgName,bx,mode,transpose=True), traceDepth,j,v)
return msgName
else:
if gin.outputs:
#optimize away the message from the output
# var of gin, since it would be a dense
# all-ones vector
assert len(gin.outputs)==1, 'need single output from %s' % self.goals[j]
#this variable now is connected to the main chain
self.varDict[only(gin.outputs)].connected = True
assert not ops.isBuiltinIOOp(mode), 'can only use built in io operators where inputs and outputs are used'
assert not gin.definedPred, 'subpredicates must generate an output which is used downstream'
addOp(ops.AssignPreimageToVar(msgName,mode), traceDepth,j,v)
else:
addOp(ops.AssignVectorToVar(msgName,mode), traceDepth,j,v)
return msgName
else:
assert False,'unexpected message goal %d -> %s ins %r outs %r' % (j,v,gin.inputs,gin.outputs)
def msgVar2Goal(v,j,traceDepth):
"""Message from a variable to a goal.
"""
vin = self.varDict[v]
vin.connected = True
gin = self.goalDict[j]
#variables have one outputOf, but possily many inputTo connections
vNeighbors = [j2 for j2 in [vin.outputOf]+list(vin.inputTo) if j2!=j]
if conf.trace: print '%smsg from %s to %d, vNeighbors=%r' % ('| '*traceDepth,v,j,vNeighbors)
assert len(vNeighbors),'variables should have >1 neighbor but %s has only one: %d' % (v,j)
#form product of the incoming messages, cleverly
#generating only the variables we really need
currentProduct = msgGoal2Var(vNeighbors[0],v,traceDepth+1)
for j2 in vNeighbors[1:]:
nextProd = 'p_%d_%s_%d' % (j,v,j2) if j2!=vNeighbors[-1] else 'fb_%s' % v
multiplicand = msgGoal2Var(j2,v,traceDepth+1)
addOp(ops.ComponentwiseVecMulOp(nextProd,currentProduct,multiplicand), traceDepth,v,j)
currentProduct = nextProd
return currentProduct
#
# main BP code starts here
#
#generate a message from the output variable to the lhs
outputVar = only(self.goalDict[0].outputs)
outputMsg = msgVar2Goal(outputVar,0,1)
#now look for other unconnected variables, and connect them to
#a pseudo-node so they have something to send to. The
#outputMsg above will be weighted by the product of all of
#these messages.
weighters = []
psj = len(self.goals)
self.goals.append( parser.Goal('PSEUDO',[]) )
self.goalDict[psj] = GoalInfo(psj)
#heuristic - start with the rightmost unconnected variable,
#hoping that it's the end of a chain rooted at the input,
#which should be quicker to evaluate
for j in reversed(range(1,len(self.goals))):
goalj = self.goals[j]
for i in range(goalj.arity):
v = goalj.args[i]
if parser.isVariableAtom(v) and not self.varDict[v].connected:
#save the message from this unconnected node
weighters.append(msgVar2Goal(v,psj,1))
#multiply the weighting factors from the unconnected node to
#the outputMsg, again cleverly reusing variable names to keep
#the expression simple.
currentProduct = outputMsg
for msg in weighters:
nextProd = 'w_%s' % outputVar if msg==weighters[-1] else 'p_%s_%s' % (msg,outputVar)
multiplicand = msg
addOp(ops.WeightedVec(nextProd,multiplicand,currentProduct),0,msg,'PSEUDO')
currentProduct = nextProd
# save the output and inputs
self.output = currentProduct
self.inputs = list(self.goalDict[0].inputs)