class Tdigest(object):
def __init__(self, delta=0.01, K=25, CX=1.1):
self.delta = delta
self.K = K
self.CX = CX
self.centroids = RBTree()
self.nreset = 0
self.reset()
def reset(self):
self.centroids.clear()
self.n = 0
self.nreset += 1
self.last_cumulate = 0
self.compressing = False
def push(self, x, n=1):
if not isinstance(x, list):
x = [x]
for item in x:
self._digest(item, n)
def percentile(self, p):
if self.size() == 0:
return None
self._cumulate(True)
cumn = self.n * p
lower = self.centroids.min_item()[1]
upper = self.centroids.max_item()[1]
for c in self.centroids.values():
if c.cumn <= cumn:
lower = c
else:
upper = c
break
if lower == upper:
return lower.mean
return lower.mean + (cumn - lower.cumn) * (upper.mean - lower.mean) / \
(upper.cumn - lower.cumn)
def serialize(self):
result = '%s~%s~%s~' % (self.delta, self.K, self.size())
if self.size() == 0:
return result
self._cumulate(True)
means = []
counts = []
for c in self.centroids.values():
means.append(str(c.mean))
counts.append(str(c.n))
return '%s%s~%s' % (result, '~'.join(means), '~'.join(counts))
@classmethod
def deserialize(cls, serialized_str):
if not isinstance(serialized_str, basestring):
raise Exception(u'serialized_str must be str')
data = serialized_str.split('~')
t = Tdigest(delta=float(data[0]), K=int(data[1]))
size = int(data[2])
for i in xrange(size):
t.push(float(data[i + 3]), int(data[size + i + 3]))
t._cumulate(True)
return t
def _digest(self, x, n):
if self.size() == 0:
self._new_centroid(x, n, 0)
else:
_min = self.centroids.min_item()[1]
_max = self.centroids.max_item()[1]
nearest = self.find_nearest(x)
if nearest and nearest.mean == x:
self._addweight(nearest, x, n)
elif nearest == _min:
self._new_centroid(x, n, 0)
elif nearest == _max:
self._new_centroid(x, n, self.n)
else:
p = (nearest.cumn + nearest.n / 2.0) / self.n
max_n = int(4 * self.n * self.delta * p * (1 - p))
if max_n >= nearest.n + n:
self._addweight(nearest, x, n)
else:
self._new_centroid(x, n, nearest.cumn)
self._cumulate(False)
if self.K and self.size() > self.K / self.delta:
self.compress()
def find_nearest(self, x):
if self.size() == 0:
return None
try:
lower = self.centroids.ceiling_item(x)[1]
except KeyError:
lower = None
if lower and lower.mean == x:
return lower
try:
prev = self.centroids.floor_item(x)[1]
except KeyError:
prev = None
if not lower:
return prev
if not prev:
return lower
if abs(prev.mean - x) < abs(lower.mean - x):
return prev
else:
return lower
def size(self):
return len(self.centroids)
def compress(self):
if self.compressing:
return
points = self.toList()
self.reset()
self.compressing = True
for point in sorted(points, key=lambda x: random()):
self.push(point['mean'], point['n'])
self._cumulate(True)
self.compressing = False
def _cumulate(self, exact):
if self.n == self.last_cumulate:
return
if not exact and self.CX and self.last_cumulate and \
self.CX > (self.n / self.last_cumulate):
return
cumn = 0
for c in self.centroids.values():
cumn = c.cumn = cumn + c.n
self.n = self.last_cumulate = cumn
def toList(self):
return [dict(mean=c.mean, n=c.n, cumn=c.cumn) for
c in self.centroids.values()]
def _addweight(self, nearest, x, n):
if x != nearest.mean:
nearest.mean += n * (x - nearest.mean) / (nearest.n + n)
nearest.cumn += n
nearest.n += n
self.n += n
def _new_centroid(self, x, n, cumn):
c = Centroid(x, n, cumn)
self.centroids.insert(x, c)
self.n += n
return c
class SparseArray(object):
def __init__(self):
self.tree = FastRBTree()
def __len__(self):
try:
k, v = self.tree.max_item()
except KeyError:
return 0
return k + len(v)
def __getitem__(self, ndx):
try:
base, chunk = self.tree.floor_item(ndx)
except KeyError:
return None
offset = ndx - base
if offset < len(chunk):
return chunk[offset]
else:
return None
def __setitem__(self, ndx, item):
try:
base, chunk = self.tree.floor_item(ndx)
except KeyError:
try:
base, chunk = self.tree.ceiling_item(ndx)
except KeyError:
self.tree[ndx] = [item]
return
if ndx + 1 == base:
chunk.insert(0, item)
del self.tree[base]
self.tree[ndx] = chunk
return
if base > ndx:
self.tree[ndx] = [item]
return
offset = ndx - base
if offset < len(chunk):
chunk[offset] = item
else:
nextbase, nextchunk = (None, None)
try:
nextbase, nextchunk = self.tree.succ_item(base)
except KeyError:
pass
if offset == len(chunk):
chunk.append(item)
if offset + 1 == nextbase:
chunk += nextchunk
del self.tree[nextbase]
elif offset + 1 == nextbase:
nextchunk.insert(0, item)
del self.tree[nextbase]
self.tree[ndx] = nextchunk
else:
self.tree[ndx] = [item]
def __delitem__(self, ndx):
base, chunk = self.tree.floor_item(ndx)
offset = ndx - base
if offset < len(chunk):
before = chunk[:offset]
after = chunk[offset + 1:]
if len(before):
self.tree[base] = before
else:
del self.tree[base]
if len(after):
self.tree[ndx + 1] = after
def items(self):
for k, vs in self.tree.items():
for n, v in enumerate(vs):
yield (k + n, v)
def runs(self):
return self.tree.items()
def run_count(self):
return len(self.tree)
def __repr__(self):
arep = []
for k, v in self.tree.items():
arep.append('[%r]=%s' % (k, ', '.join([repr(item) for item in v])))
return 'SparseArray(%s)' % ', '.join(arep)
