Example #1
0
 def __init__(self, config):
     super(History, self).__init__()
     self.config = config
     self.evals = 0
     self.minSolution = None
     self.minScore = np.inf
     self.maxSolution = None
     self.maxScore = -np.inf
     self._empty = True
     if not hasattr(self, 'cache'):
         self.cache = LRUCache()  # 10,000 items by default
     self.updates = 0
     #how often to print generation report
     self.printEvery = config.printEvery or 1000000000000L
     self.attrs = set([
         "evals", "minSolution", "minScore", "maxScore", "attrs",
         "minSolution", "maxSolution", "_empty", "cache", "updates",
         "printEvery", "useCache"
     ])
Example #2
0
 def __init__(self, config):
     super(History, self).__init__()
     self.config = config
     self.evals = 0
     self.minSolution = None
     self.minScore = np.inf
     self.maxSolution = None
     self.maxScore = -np.inf 
     self._empty = True
     if not hasattr(self, 'cache'):
         self.cache = LRUCache() # 10,000 items by default
     self.updates = 0
     #how often to print generation report
     self.printEvery = config.printEvery or 1000000000000L 
     self.attrs = set(["evals","minSolution","minScore","maxScore","attrs",
                       "minSolution", "maxSolution","_empty","cache",
                       "updates","printEvery", "useCache"])
Example #3
0
class BayesianDirichletScorer(object):
    def __init__(self):
        self.cache = {}
        self.varCache = LRUCache()

    def matchesPrior(self, data, configuration):
        return 1.0

    def matches(self, data, config):
        """count number of instances of configuration in data"""
        cnt = 0L
        for x in data:
            if config <= x:
                cnt += 1
        return cnt

    def __call__(self, network, data):
        network.computeEdgeStatistics()
        total = 0.0
        total -= network.edgeRatio * len(data) * 10
        for variable in network.variables:
            varKey = str(variable.index) + str(variable.parents)
            if self.varCache.has_key(varKey):
                total += self.varCache[varKey]
                continue
            start = total
            for configuration in variable.configurations():
                prior = self.matchesPrior(data, configuration)
                total += gammaln(prior)
                total -= gammaln(prior + self.matches(data, configuration))
                for val in variable.values():
                    priorVal = self.matchesPrior(data, configuration + val)
                    total -= gammaln(priorVal)
                    total += gammaln(priorVal +
                                     self.matches(data, configuration + val))

            self.varCache[varKey] = total - start
        return total / len(data)
Example #4
0
class BayesianDirichletScorer(object):
    def __init__(self):
        self.cache = {}
        self.varCache = LRUCache()

    def matchesPrior(self, data, configuration):
        return 1.0

    def matches(self, data, config):
        """count number of instances of configuration in data"""
        cnt = 0L
        for x in data:
            if config <= x:
                cnt += 1
        return cnt

    def __call__(self, network, data):
        network.computeEdgeStatistics()
        total = 0.0
        total -= network.edgeRatio * len(data) * 10
        for variable in network.variables:
            varKey = str(variable.index) + str(variable.parents)
            if self.varCache.has_key(varKey):
                total += self.varCache[varKey]
                continue
            start = total
            for configuration in variable.configurations():
                prior = self.matchesPrior(data, configuration)
                total += gammaln(prior)
                total -= gammaln(prior + self.matches(data, configuration))
                for val in variable.values():
                    priorVal = self.matchesPrior(data, configuration + val)
                    total -= gammaln(priorVal)
                    total += gammaln(priorVal + self.matches(data, configuration + val))

            self.varCache[varKey] = total - start
        return total / len(data)
Example #5
0
 def __init__(self):
     self.cache = {}
     self.varCache = LRUCache()
Example #6
0
 def __init__(self):
     self.cache = {}
     self.varCache = LRUCache()
Example #7
0
class BayesNet(Distribution):
    counter = 0
    created = 0
    config = Config(numVariables=None,
                    branchFactor=10,
                    variableGenerator=BayesVariable,
                    structureGenerator=GreedyStructureSearch(
                        10, BayesianInformationCriterion()),
                    sampler=DAGSampler(),
                    randomizer=lambda net: None)
    densityCache = LRUCache()
    weightCache = LRUCache()
    likelihoodCache = LRUCache()

    def __init__(self, **kwargs):
        config = BayesNet.config.merge(Config(**kwargs))
        super(BayesNet, self).__init__(**config.__properties__)
        self.numVariables = self.config.numVariables
        self.variableGenerator = self.config.variableGenerator
        self.structureGenerator = self.config.structureGenerator
        self.randomizer = self.config.randomizer
        self.sampler = self.config.sampler

        self.variables = []
        for i in xrange(self.numVariables):
            self.variables.append(self.variableGenerator(i, self.config))
        self.decay = 1
        self.dirty = False
        self.acyclic = True
        self.edges = []
        self.edgeRatio = 0.0
        self.edgeTuples = None
        self.cacheKeys = dict([(v.index, v.cacheKey) for v in self.variables])
        self.edgeMap = {}
        self.binary = zeros(len(self.variables)**2)
        self.deferred = False
        self.deferredWeights = False
        self.edgeRep = None
        self.densityStored = None
        self.cacheHits = 0
        self.cacheTries = 0
        self.changed = {}
        self.last = {}
        self.__class__.counter += 1
        self.__class__.created += 1

    def __del__(self):
        for variable in self.variables:
            del variable
        self.__class__.counter -= 1

    def __copy__(self):
        return self.__class__.parse(str(self), self.config)

    @checkDeferred
    def get(self, index):
        for var in self.variables:
            if var.index == index:
                return var
        return None

    @checkDeferred
    def sort(self):
        self.variables = sorted(self.variables, key=lambda x: len(x.parents))
        visited = {}
        skipped = {}
        #print "before: ", [v.index for v in self.variables]
        vars = LinkedList()
        for var in self.variables:
            vars.append(var)
        current = vars.first
        while current is not None:
            v = current.value
            advance = True
            for idx, p in v.parents.iteritems():
                if not visited.has_key(idx):
                    before = current.before
                    vars.remove(current)
                    vars.append(v)
                    if before is not None:
                        current = before.after
                    advance = False
                    skipped[v.index] = True
                    break
            if not advance and skipped.has_key(current.value.index):
                break
            if advance:
                current = current.after
                skipped = {}
                visited[v.index] = True
            #print i, visited, v.index, v.parents
        current = vars.first
        self.variables = []
        while current is not None:
            self.variables.append(current.value)
            current = current.after
        #print "after: ", [v.index for v in self.variables]
        return len(skipped) == 0

    @checkDeferred
    def decompose(self):
        acyclic = self.sort()
        #self.variables is now ordered in a way to allow sampling
        clusters = []
        for var in self.variables:
            # is the parent in one of the clusters?
            member = False
            for c in clusters:
                for v in c:
                    if var.parents.has_key(v):
                        member = True
                        break
                if member:
                    c.append(var.index)
                    break
            if not member:
                clusters.append([var.index])
        return clusters

    @checkDeferredWeights
    def distribution(self, index, x):
        var = None
        for v in self.variables:
            if v.index == index:
                var = v
        return var.distribution(x)

    @checkDeferredWeights
    def randomize(self):
        return self.randomizer(self)

    @checkDeferredWeights
    def conditionalLikelihood(self, index, data):
        sum = 0.0
        var = None
        for v in self.variables:
            if v.index == index:
                var = v
                break
        for x in data:
            key = self.cacheKeys[var.index]
            key += str(x[var.index])
            if not BayesNet.densityCache.has_key(key):
                BayesNet.densityCache[key] = var.density(x)
            sum += log(BayesNet.densityCache[key])
        return sum

    @checkDeferredWeights
    def likelihood(self, data):
        prod = 0.0
        for v in self.variables:
            vprod = 0.0
            for x in data:
                key = self.cacheKeys[v.index]
                key += str(x[v.index])
                if not BayesNet.densityCache.has_key(key):
                    BayesNet.densityCache[key] = v.density(x)
                vprod += log(BayesNet.densityCache[key])
            if isinstance(vprod, np.ndarray):
                vprod = vprod[0]
            self.last[v.index] = vprod
            prod += vprod
        self.densityStored = prod
        return prod

    @checkDeferredWeights
    def likelihoodChanged(self, data, storeChange=False):
        diff = 0.0
        olddiff = 0.0
        total = 0.0
        for v in self.variables:
            if self.changed.has_key(v.index) and self.changed[v.index]:
                inner = 0.0
                for x in data:
                    key = self.cacheKeys[v.index]
                    key += str(x[v.index])
                    if not BayesNet.densityCache.has_key(key):
                        BayesNet.densityCache[key] = v.density(x)
                    inner += log(BayesNet.densityCache[key])
                total += inner
                if storeChange:
                    self.last[v.index] = inner
            else:
                total += self.last[v.index]
        return total

    @checkDeferredWeights
    def marginal(self, cmpIdx, data):
        var = None
        for v in self.variables:
            if v.index == cmpIdx:
                var = v
                break
        total = 0.0
        for t in data:
            total += var.marginalDensity(t, self)
        return total / len(data)

    @checkDeferredWeights
    def map(self, cmpIdx, data):
        var = None
        for v in self.variables:
            if v.index == cmpIdx:
                var = v
                break
        total = 0.0
        for t in data:
            z = var.map(t)
            if z[cmpIdx] == t[cmpIdx]:
                total += 1.0
        return total / len(data)

    @checkDeferredWeights
    def density(self, x):
        self.computeEdgeStatistics()
        prod = 1.0
        for variable in self.variables:
            key = self.cacheKeys[variable.index]
            key += str(x[variable.index])
            if not BayesNet.densityCache.has_key(key):
                BayesNet.densityCache[key] = variable.density(x)
            #print key, " - ", BayesNet.densityCache[key], " - ", variable.density(x)
            prod *= BayesNet.densityCache[key]
        return prod

    @checkDeferredWeights
    def __call__(self):
        """sample the network"""
        return self.sampler(self)

    @checkDeferredWeights
    def sample(self):
        return self.__call__()

    @checkDeferredWeights
    def batch(self, num):
        return [self.__call__() for i in xrange(num)]

    @checkDeferred
    def numFreeParameters(self):
        total = 0
        for variable in self.variables:
            total += variable.numFreeParameters()
        return total

    @checkDeferred
    def update(self, epoch, data):
        self.computeEdgeStatistics()
        for variable in self.variables:
            self.updateVar(variable, data)

    @checkDeferred
    def updateVar(self, variable, data):
        self.computeEdgeStatistics()
        key = self.cacheKeys[variable.index]
        if not BayesNet.weightCache.has_key(key):
            variable.update(data)
            BayesNet.weightCache[key] = variable.getComputedState()
        else:
            variable.restoreComputedState(BayesNet.weightCache[key])

    @checkDeferred
    def merge(self, other, data):
        return self.structureGenerator.merge(self, other, data)

    @checkDeferred
    def cross(self, other, data):
        return self.structureGenerator.cross(self, other, data)

    @checkDeferred
    def hasEdge(self, frm, t):
        """Whether the network has an edge from the parent with index 'from'
         to the child with index 'to'
         
      """
        return (frm, t) in self.edges
        #try:
        #   toNode = [variable for variable in self.variables if variable.index == t][0]
        #   fromNode = [parent for l,parent in fromNode.parents.iteritems() if parent.index == frm][0]
        #   return True
        #except Exception:
        #   return False

    @checkDeferred
    def isAcyclic(self):
        """Is the network a DAG?"""
        if self.dirty:
            self.computeEdgeStatistics()
        return self.acyclic
        """
      tested = set([])
      for variable in self.variables:
         if len(set(variable.parents) - tested) > 0:
            self.acyclic = False
            return False
         tested = set(list(tested) + [variable])
      self.acyclic = True   
      return True   
      """
        """
      for variable in self.variables:
         if variable in variable.parents:
            return False
            
      tested = set([])
      while len(tested) < len(self.variables):
        added = False
        for variable in self.variables:
            if variable in tested:
               continue
            if len(set(variable.parents) - tested) == 0:
               tested = set(list(tested) + [variable])
               added = True
               break
        if not added:
           return False
      return True
      """

    @checkDeferred
    def structureSearch(self, data):
        return self.structureGenerator.search(self, data)

    @checkDeferredWeights
    def getComputedState(self):
        state = {}
        self.computeEdgeStatistics()
        state['acyclic'] = self.acyclic
        state['edges'] = self.edges
        state['edgeRatio'] = self.edgeRatio
        state['edgeTuples'] = self.edgeTuples
        state['cacheKeys'] = self.cacheKeys
        varstate = {}
        varorder = {}
        for i, v in enumerate(self.variables):
            varstate[v.index] = v.getComputedState()
            varorder[i] = v.index
        state['varstate'] = varstate
        state['varorder'] = varorder
        return state

    def restoreComputedState(self, state):
        self.dirty = False
        self.acyclic = state['acyclic']
        self.edges = state['edges']
        self.edgeRatio = state['edgeRatio']
        self.edgeTuples = state['edgeTuples']
        self.cacheKeys = state['cacheKeys']
        varorder = state['varorder']
        varstate = state['varstate']
        self.variables = sorted(self.variables,
                                key=lambda v: varorder[v.index])
        for v in self.variables:
            v.restoreComputedState(varstate[v.index])

    @checkDeferred
    def computeEdgeStatistics(self):
        if not self.dirty: return
        self.acyclic = self.sort()
        if self.edges is not None: del self.edges
        self.edges = []
        for variable in self.variables:
            for l, variable2 in variable.parents.iteritems():
                self.edges.append((variable2, variable))
        self.edges = sorted(self.edges, key=lambda e: (e[0].index, e[1].index))
        self.edgeRatio = len(self.edges) / (1e-10 + (len(self.variables)**2))
        self.edgeTuples = [(frm.index, to.index) for frm, to in self.edges]
        self.cacheKeys = dict([(v.index, v.cacheKey) for v in self.variables])
        self.dirty = False
        self.densityStored = None

    @checkDeferred
    def getChildren(self, variable):
        children = []
        self.computeEdgeStatistics()
        for variable2 in self.variables:
            if variable2.parents.has_key(variable.index):
                children.append(variable2)
        return children

    @checkDeferred
    def updateVariables(self, data):
        for variable in self.variables:
            variable.update(data)

    @checkDeferred
    def __getitem__(self, index):
        if self.edgeMap.has_key(index):
            return self.edgeMap[index]
        frmidx = index % self.numVariables
        toidx = index / self.numVariables
        for l, v in self.variables[toidx].parents.iteritems():
            if v.index == frmidx:
                self.edgeMap[index] = True
                return True
        self.edgeMap[index] = False
        return False

    def __len__(self):
        return self.numVariables**2

    def __getstate__(self):
        return {
            'v': self.variables,
            'r': self.randomizer,
            's': self.sampler,
            'sg': self.structureGenerator,
        }

    def __setstate__(self, state):
        self.dirty = True
        self.variables = state['v']
        self.numVariables = len(self.variables)
        self.randomizer = state['r']
        self.structureGenerator = state['sg']
        self.sampler = state['s']
        indexMap = {}
        for variable in self.variables:
            indexMap[variable.index] = variable
        for variable in self.variables:
            variable.parents = {}
            for i in variable.parentIndices:
                variable.addParent(indexMap[i])

        self.changed = {}
        self.last = {}
        self.deferred = False
        self.deferredWeights = True
        self.edgeRep = None
        self.edgeMap = {}
        self.edgeTuples = None
        self.edges = None
        self.binary = None
        self.densityStored = None
        self.computeEdgeStatistics()

    @checkDeferred
    def __str__(self):
        """pickle the object"""
        self.computeEdgeStatistics()
        return cPickle.dumps(len(self.variables)) + cPickle.dumps(
            self.edgeTuples)

    def initialize(net):
        for frm, to in net.edgeRep:
            net.variables[to].addParent(net.variables[frm])
        net.dirty = True
        net.deferred = False
        net.edgeRep = None
        net.computeEdgeStatistics()

    @checkDeferred
    def estimate(net):
        for variable in net.variables:
            net.updateVar(variable, net.config.data)
        net.deferredWeights = False

    @classmethod
    def parse(cls, rep, cfg):
        io = StringIO(rep)
        numVars = cPickle.load(io)
        if cfg is None:
            cfg = BayesNet.config
        net = cls(**cfg.__properties__)
        edges = cPickle.load(io)
        net.edgeRep = edges
        net.deferred = True
        net.deferredWeights = True

        return net
Example #8
0
class History(object):
    """A History used to track the progress of an optimization algorithm.
    
    Different algorithms should extend this class in order to define
    the minimal amount of history that needs to be stored in order for the
    algorthm to operate.
    
    """
    useCache = True
    attrs = set()
    sorted = False
    root = True  # whether the current history is the top level root for

    # all histories of this algorithm

    def __init__(self, config):
        super(History, self).__init__()
        self.config = config
        self.evals = 0
        self.minSolution = None
        self.minScore = np.inf
        self.maxSolution = None
        self.maxScore = -np.inf
        self._empty = True
        if not hasattr(self, 'cache'):
            self.cache = LRUCache()  # 10,000 items by default
        self.updates = 0
        #how often to print generation report
        self.printEvery = config.printEvery or 1000000000000L
        self.attrs = set([
            "evals", "minSolution", "minScore", "maxScore", "attrs",
            "minSolution", "maxSolution", "_empty", "cache", "updates",
            "printEvery", "useCache"
        ])

    def __getstate__(self):
        """Used by :class:`CheckpointedHistory`
        and :class:`CheckpointedMultipleHistory` to checkpoint a history
        so it can be rolled back after updates.
        
        Should return all objects in the history in a dictionary, sensitive
        to the fact that object references may need to be copied.
        
        :returns: A dictionary with the state of the history
        
        """
        state = {}

        for attr in self.attrs:
            val = getattr(self, attr)
            if isinstance(val, list):
                val = [x for x in val]
            state[attr] = val

        state['cfg'] = self.config.__properties__
        return state

    def __setstate__(self, state):
        for attr in self.attrs:
            val = state[attr]
            setattr(self, attr, val)

        import pyec.config
        self.config = pyec.config.Config(**state['cfg'])

    def empty(self):
        """Whether the history has been used or not."""
        return self._empty

    def better(self, score1, score2):
        """Return whether one score is better than another.
        
        Uses ``config.minimize`` to decide whether lesser or greater
        numbers are better.
        
        :param score1: the score in question (floating point number)
        :type score1: ``float``
        :param score2: the score being compared
        :type score2: ``float``
        :returns: whether ``score1`` is better than ``score2``
        """
        if self.config.minimize:
            return score1 < score2
        else:
            return score1 > score2

    def best(self):
        """Get the best solution, whether minimizing or maximizing.
        
        Same as ``optimal``
        
        """
        if self.config.minimize:
            return self.minimal()
        else:
            return self.maximal()

    optimal = best

    def minimal(self):
        """Get the minimal solution and its score.
        
        :returns: A tuple of two item with the solution object first
                  and the score of that item second 
                  
        """
        return self.minSolution, self.minScore

    def maximal(self):
        """Get the maximal solution and its score.
        
        :returns: A tuple of two item with the solution object first
                  and the score of that item second 
                  
        """
        return self.maxSolution, self.maxScore

    def num_evaluations(self):
        """Get the number of function evaluations performed in this 
        history object.
        
        :returns: An integer representing the number of times the fitness
                  function or objective has been evaluated
                  
        """
        return self.evals

    def update(self, population, fitness, space, opt):
        """
         Update the state of the :class:`History` with the latest population 
         and its fitness scores. Subclasses should probably override
         ``internalUpdate`` rather than ``update``, unless they want to
         change how the min/max are tracked.
         
         Returns the history for use in continuations.
         
         If ``population`` is ``None``, then this method does nothing; this
         is so that you can set up a loop like to run an optimizer like::
         
         p = None
         f = lambda x: 
         t = History()
         o = some_optimizer
         s = o.config.space
         for i in xrange(generations):
             p = some_optimizer[t.update(p,f,s,0), f]()
         t.update(p,f,s,o)
          
         :params population: The previous population.
         :type population: list of points in the search domain
         :params fitness: The fitness / cost / objective function
         :type fitness: Any callable object
         :params space: The search domain
         :type space: :class:`Space`
         :params opt: The optimizer reporting this population
         :type opt: :class:`PopulationDistribution`
         :returns: The history (``self``), for continuations
         
        """
        if population is None:
            return

        #self.config.stats.start(repr(self) + "history.update.all")
        self._empty = False
        self.evals += len(population)
        self.updates += 1

        #self.config.stats.start(repr(self) + "history.update.scoreall")
        # score the sample
        pop = population
        scored = [(x, self.score(x, fitness, space)) for x in pop]
        #self.config.stats.stop(repr(self) + "history.update.scoreall")
        #self.config.stats.start(repr(self) + "history.update.findbest")

        if self.root and self.config.observer is not None:
            self.config.observer.report(opt, scored)

        for x, s in scored:
            if s > self.maxScore:
                self.maxScore = s
                self.maxSolution = x

            if s < self.minScore:
                self.minScore = s
                self.minSolution = x
        #self.config.stats.stop(repr(self) + "history.update.findbest")

        if not (self.updates % self.printEvery):
            genmin = min([s for x, s in scored])
            genmax = max([s for x, s in scored])
            genavg = np.average([s for x, s in scored])
            print self.updates, ": min", self.minScore, " max", self.maxScore,
            print " this generation (min, avg, max): ", genmin, genavg, genmax

        #self.config.stats.start(repr(self) + "history.update.internal")
        self.internalUpdate(scored)
        #self.config.stats.stop(repr(self) + "history.update.internal")
        #self.config.stats.stop(repr(self) + "history.update.all")
        return self

    def internalUpdate(self, population):
        """
         Update the state of the :class:`History` with the latest population 
         and its fitness scores. This is an internal call intended for
         overridden by subclasses. One of the important functions is to
         delete points no longer needed by the history.
          
         :params population: The previous population with its fitness scores. 
         :type population: list of (point, score) tuples
         
        """
        pass

    def score(self, point, fitness, space):
        """Get the fitness score, caching where possible.
      
         :param point: A valid point in the space
         :type point: Must match ``space.type``
         :param fitness: The fitness function
         :type fitness: Any callable
         :param space: The space to which the point belongs
         :type space: :class:`Space`
         :returns: The fitness value, cached if possible
         
        """
        if fitness is None:
            return None

        #self.config.stats.start("history.score")

        if self.useCache:
            try:
                hashed = space.hash(point)
                if self.cache.has_key(hashed):
                    ret = self.cache[hashed]
                    #self.config.stats.stop("history.score")
                    return ret
            except Exception:
                pass

        if not space.in_bounds(point):
            # use NaN so that the result is less than nor greater than
            # any other score, and therefore NEVER optimal
            s = np.inf - np.inf
        else:
            try:
                s = fitness(space.convert(point))
            except ValueError:
                s = np.inf - np.inf

        if self.useCache:
            try:
                hashed = space.hash(point)
                self.cache[hashed] = s
            except Exception:
                pass
        #self.config.stats.stop("history.score")
        return s

    def setCache(self, cache):
        self.cache = cache
Example #9
0
class History(object):
    """A History used to track the progress of an optimization algorithm.
    
    Different algorithms should extend this class in order to define
    the minimal amount of history that needs to be stored in order for the
    algorthm to operate.
    
    """
    useCache = True
    attrs = set()
    sorted = False
    root = True # whether the current history is the top level root for
                # all histories of this algorithm
    
    def __init__(self, config):
        super(History, self).__init__()
        self.config = config
        self.evals = 0
        self.minSolution = None
        self.minScore = np.inf
        self.maxSolution = None
        self.maxScore = -np.inf 
        self._empty = True
        if not hasattr(self, 'cache'):
            self.cache = LRUCache() # 10,000 items by default
        self.updates = 0
        #how often to print generation report
        self.printEvery = config.printEvery or 1000000000000L 
        self.attrs = set(["evals","minSolution","minScore","maxScore","attrs",
                          "minSolution", "maxSolution","_empty","cache",
                          "updates","printEvery", "useCache"])
    
    def __getstate__(self):
        """Used by :class:`CheckpointedHistory`
        and :class:`CheckpointedMultipleHistory` to checkpoint a history
        so it can be rolled back after updates.
        
        Should return all objects in the history in a dictionary, sensitive
        to the fact that object references may need to be copied.
        
        :returns: A dictionary with the state of the history
        
        """
        state = {}
      
        for attr in self.attrs:
            val = getattr(self, attr)
            if isinstance(val, list):
                val = [x for x in val]
            state[attr] = val
         
        state['cfg'] = self.config.__properties__
        return state

    def __setstate__(self, state):
        for attr in self.attrs:
            val = state[attr]
            setattr(self, attr, val)
         
        import pyec.config
        self.config = pyec.config.Config(**state['cfg'])  
    
    def empty(self):
        """Whether the history has been used or not."""
        return self._empty
    
    def better(self, score1, score2):
        """Return whether one score is better than another.
        
        Uses ``config.minimize`` to decide whether lesser or greater
        numbers are better.
        
        :param score1: the score in question (floating point number)
        :type score1: ``float``
        :param score2: the score being compared
        :type score2: ``float``
        :returns: whether ``score1`` is better than ``score2``
        """
        if self.config.minimize:
            return score1 < score2
        else:
            return score1 > score2
    
    def best(self):
        """Get the best solution, whether minimizing or maximizing.
        
        Same as ``optimal``
        
        """
        if self.config.minimize:
            return self.minimal()
        else:
            return self.maximal()
    
    optimal = best
    
    def minimal(self):
        """Get the minimal solution and its score.
        
        :returns: A tuple of two item with the solution object first
                  and the score of that item second 
                  
        """
        return self.minSolution, self.minScore
        
    def maximal(self):
        """Get the maximal solution and its score.
        
        :returns: A tuple of two item with the solution object first
                  and the score of that item second 
                  
        """
        return self.maxSolution, self.maxScore
        
    def num_evaluations(self):
        """Get the number of function evaluations performed in this 
        history object.
        
        :returns: An integer representing the number of times the fitness
                  function or objective has been evaluated
                  
        """
        return self.evals
        
    def update(self, population, fitness, space, opt):
        """
         Update the state of the :class:`History` with the latest population 
         and its fitness scores. Subclasses should probably override
         ``internalUpdate`` rather than ``update``, unless they want to
         change how the min/max are tracked.
         
         Returns the history for use in continuations.
         
         If ``population`` is ``None``, then this method does nothing; this
         is so that you can set up a loop like to run an optimizer like::
         
         p = None
         f = lambda x: 
         t = History()
         o = some_optimizer
         s = o.config.space
         for i in xrange(generations):
             p = some_optimizer[t.update(p,f,s,0), f]()
         t.update(p,f,s,o)
          
         :params population: The previous population.
         :type population: list of points in the search domain
         :params fitness: The fitness / cost / objective function
         :type fitness: Any callable object
         :params space: The search domain
         :type space: :class:`Space`
         :params opt: The optimizer reporting this population
         :type opt: :class:`PopulationDistribution`
         :returns: The history (``self``), for continuations
         
        """
        if population is None:
            return
        
        #self.config.stats.start(repr(self) + "history.update.all")
        self._empty = False
        self.evals += len(population)
        self.updates += 1
        
        #self.config.stats.start(repr(self) + "history.update.scoreall")
        # score the sample
        pop  = population
        scored = [(x, self.score(x, fitness, space)) for x in pop]
        #self.config.stats.stop(repr(self) + "history.update.scoreall")
        #self.config.stats.start(repr(self) + "history.update.findbest")
        
        if self.root and self.config.observer is not None:
            self.config.observer.report(opt, scored)
        
        for x,s in scored:
            if s > self.maxScore:
                 self.maxScore = s
                 self.maxSolution = x
               
            if s < self.minScore:
                 self.minScore = s
                 self.minSolution = x
        #self.config.stats.stop(repr(self) + "history.update.findbest")
        
        if not (self.updates % self.printEvery):
            genmin = min([s for x,s in scored])
            genmax = max([s for x,s in scored])
            genavg = np.average([s for x,s in scored])
            print self.updates, ": min", self.minScore, " max", self.maxScore,
            print " this generation (min, avg, max): ", genmin, genavg, genmax
        
        #self.config.stats.start(repr(self) + "history.update.internal")       
        self.internalUpdate(scored)
        #self.config.stats.stop(repr(self) + "history.update.internal")
        #self.config.stats.stop(repr(self) + "history.update.all")
        return self
        
    def internalUpdate(self, population):
        """
         Update the state of the :class:`History` with the latest population 
         and its fitness scores. This is an internal call intended for
         overridden by subclasses. One of the important functions is to
         delete points no longer needed by the history.
          
         :params population: The previous population with its fitness scores. 
         :type population: list of (point, score) tuples
         
        """    
        pass

    def score(self, point, fitness, space):
        """Get the fitness score, caching where possible.
      
         :param point: A valid point in the space
         :type point: Must match ``space.type``
         :param fitness: The fitness function
         :type fitness: Any callable
         :param space: The space to which the point belongs
         :type space: :class:`Space`
         :returns: The fitness value, cached if possible
         
        """
        if fitness is None: 
            return None
        
        #self.config.stats.start("history.score")
            
        if self.useCache: 
            try:
                hashed = space.hash(point)
                if self.cache.has_key(hashed):
                    ret = self.cache[hashed]
                    #self.config.stats.stop("history.score")
                    return ret
            except Exception:
                pass
        
        if not space.in_bounds(point):
            # use NaN so that the result is less than nor greater than
            # any other score, and therefore NEVER optimal
            s = np.inf - np.inf
        else:
            try:
                s = fitness(space.convert(point))
            except ValueError:
                s = np.inf - np.inf
        
        if self.useCache:
            try:
                hashed = space.hash(point)
                self.cache[hashed] = s
            except Exception:
                pass
        #self.config.stats.stop("history.score")
        return s
    
    def setCache(self, cache):
        self.cache = cache