class TDigest(object):
def __init__(self, delta=0.01, K=25):
self.C = RBTree()
self.n = 0
self.delta = delta
self.K = K
def __add__(self, other_digest):
C1 = list(self.C.values())
C2 = list(other_digest.C.values())
shuffle(C1)
shuffle(C2)
data = C1 + C2
new_digest = TDigest(self.delta, self.K)
for c in data:
new_digest.update(c.mean, c.count)
return new_digest
def __len__(self):
return len(self.C)
def __repr__(self):
return """<T-Digest: n=%d, centroids=%d>""" % (self.n, len(self))
def _add_centroid(self, centroid):
if centroid.mean not in self.C:
self.C.insert(centroid.mean, centroid)
else:
self.C[centroid.mean].update(centroid.mean, centroid.count)
def _compute_centroid_quantile(self, centroid):
denom = self.n
cumulative_sum = sum(
c_i.count for c_i in self.C.value_slice(-float('Inf'), centroid.mean))
return (centroid.count / 2. + cumulative_sum) / denom
def _update_centroid(self, centroid, x, w):
self.C.pop(centroid.mean)
centroid.update(x, w)
self._add_centroid(centroid)
def _find_closest_centroids(self, x):
try:
ceil_key = self.C.ceiling_key(x)
except KeyError:
floor_key = self.C.floor_key(x)
return [self.C[floor_key]]
try:
floor_key = self.C.floor_key(x)
except KeyError:
ceil_key = self.C.ceiling_key(x)
return [self.C[ceil_key]]
if abs(floor_key - x) < abs(ceil_key - x):
return [self.C[floor_key]]
elif abs(floor_key - x) == abs(ceil_key - x) and (ceil_key != floor_key):
return [self.C[ceil_key], self.C[floor_key]]
else:
return [self.C[ceil_key]]
def _theshold(self, q):
return 4 * self.n * self.delta * q * (1 - q)
def update(self, x, w=1):
"""
Update the t-digest with value x and weight w.
"""
self.n += w
if len(self) == 0:
self._add_centroid(Centroid(x, w))
return
S = self._find_closest_centroids(x)
while len(S) != 0 and w > 0:
j = choice(list(range(len(S))))
c_j = S[j]
q = self._compute_centroid_quantile(c_j)
# This filters the out centroids that do not satisfy the second part
# of the definition of S. See original paper by Dunning.
if c_j.count + w > self._theshold(q):
S.pop(j)
continue
delta_w = min(self._theshold(q) - c_j.count, w)
self._update_centroid(c_j, x, delta_w)
w -= delta_w
S.pop(j)
if w > 0:
self._add_centroid(Centroid(x, w))
if len(self) > self.K / self.delta:
self.compress()
return
def batch_update(self, values, w=1):
"""
Update the t-digest with an iterable of values. This assumes all points have the
same weight.
"""
for x in values:
self.update(x, w)
self.compress()
return
def compress(self):
T = TDigest(self.delta, self.K)
C = list(self.C.values())
shuffle(C)
for c_i in C:
T.update(c_i.mean, c_i.count)
self.C = T.C
def percentile(self, q):
"""
Computes the percentile of a specific value in [0,1], ie. computes F^{-1}(q) where F^{-1} denotes
the inverse CDF of the distribution.
"""
if not (0 <= q <= 1):
raise ValueError("q must be between 0 and 1, inclusive.")
t = 0
q *= self.n
for i, key in enumerate(self.C.keys()):
c_i = self.C[key]
k = c_i.count
if q < t + k:
if i == 0:
return c_i.mean
elif i == len(self) - 1:
return c_i.mean
else:
delta = (self.C.succ_item(key)[1].mean - self.C.prev_item(key)[1].mean) / 2.
return c_i.mean + ((q - t) / k - 0.5) * delta
t += k
return self.C.max_item()[1].mean
def quantile(self, q):
"""
Computes the quantile of a specific value, ie. computes F(q) where F denotes
the CDF of the distribution.
"""
t = 0
N = float(self.n)
for i, key in enumerate(self.C.keys()):
c_i = self.C[key]
if i == len(self) - 1:
delta = (c_i.mean - self.C.prev_item(key)[1].mean) / 2.
else:
delta = (self.C.succ_item(key)[1].mean - c_i.mean) / 2.
z = max(-1, (q - c_i.mean) / delta)
if z < 1:
return t / N + c_i.count / N * (z + 1) / 2
t += c_i.count
return 1
def trimmed_mean(self, q1, q2):
"""
Computes the mean of the distribution between the two percentiles q1 and q2.
This is a modified algorithm than the one presented in the original t-Digest paper.
"""
if not (q1 < q2):
raise ValueError("q must be between 0 and 1, inclusive.")
s = k = t = 0
q1 *= self.n
q2 *= self.n
for i, key in enumerate(self.C.keys()):
c_i = self.C[key]
k_i = c_i.count
if q1 < t + k_i:
if i == 0:
delta = self.C.succ_item(key)[1].mean - c_i.mean
elif i == len(self) - 1:
delta = c_i.mean - self.C.prev_item(key)[1].mean
else:
delta = (self.C.succ_item(key)[1].mean - self.C.prev_item(key)[1].mean) / 2.
nu = ((q1 - t) / k_i - 0.5) * delta
s += nu * k_i * c_i.mean
k += nu * k_i
if q2 < t + k_i:
return s/k
t += k_i
return s/k
class TDigest(object):
def __init__(self, delta=0.01, K=25):
self.C = RBTree()
self.n = 0
self.delta = delta
self.K = K
def __add__(self, other_digest):
data = list(chain(self.C.values(), other_digest.C.values()))
new_digest = TDigest(self.delta, self.K)
if len(data) > 0:
for c in pyudorandom.items(data):
new_digest.update(c.mean, c.count)
return new_digest
def __len__(self):
return len(self.C)
def __repr__(self):
return """<T-Digest: n=%d, centroids=%d>""" % (self.n, len(self))
def _add_centroid(self, centroid):
if centroid.mean not in self.C:
self.C.insert(centroid.mean, centroid)
else:
self.C[centroid.mean].update(centroid.mean, centroid.count)
def _compute_centroid_quantile(self, centroid):
denom = self.n
cumulative_sum = sum(
c_i.count
for c_i in self.C.value_slice(-float('Inf'), centroid.mean))
return (centroid.count / 2. + cumulative_sum) / denom
def _update_centroid(self, centroid, x, w):
self.C.pop(centroid.mean)
centroid.update(x, w)
self._add_centroid(centroid)
def _find_closest_centroids(self, x):
try:
ceil_key = self.C.ceiling_key(x)
except KeyError:
floor_key = self.C.floor_key(x)
return [self.C[floor_key]]
try:
floor_key = self.C.floor_key(x)
except KeyError:
ceil_key = self.C.ceiling_key(x)
return [self.C[ceil_key]]
if abs(floor_key - x) < abs(ceil_key - x):
return [self.C[floor_key]]
elif abs(floor_key - x) == abs(ceil_key -
x) and (ceil_key != floor_key):
return [self.C[ceil_key], self.C[floor_key]]
else:
return [self.C[ceil_key]]
def _theshold(self, q):
return 4 * self.n * self.delta * q * (1 - q)
def update(self, x, w=1):
"""
Update the t-digest with value x and weight w.
"""
self.n += w
if len(self) == 0:
self._add_centroid(Centroid(x, w))
return
S = self._find_closest_centroids(x)
while len(S) != 0 and w > 0:
j = choice(list(range(len(S))))
c_j = S[j]
q = self._compute_centroid_quantile(c_j)
# This filters the out centroids that do not satisfy the second part
# of the definition of S. See original paper by Dunning.
if c_j.count + w > self._theshold(q):
S.pop(j)
continue
delta_w = min(self._theshold(q) - c_j.count, w)
self._update_centroid(c_j, x, delta_w)
w -= delta_w
S.pop(j)
if w > 0:
self._add_centroid(Centroid(x, w))
if len(self) > self.K / self.delta:
self.compress()
return
def batch_update(self, values, w=1):
"""
Update the t-digest with an iterable of values. This assumes all points have the
same weight.
"""
for x in values:
self.update(x, w)
self.compress()
return
def compress(self):
T = TDigest(self.delta, self.K)
C = list(self.C.values())
for c_i in pyudorandom.items(C):
T.update(c_i.mean, c_i.count)
self.C = T.C
def percentile(self, p):
"""
Computes the percentile of a specific value in [0,100].
"""
if not (0 <= p <= 100):
raise ValueError("p must be between 0 and 100, inclusive.")
t = 0
p = float(p) / 100.
p *= self.n
for i, key in enumerate(self.C.keys()):
c_i = self.C[key]
k = c_i.count
if p < t + k:
if i == 0:
return c_i.mean
elif i == len(self) - 1:
return c_i.mean
else:
delta = (self.C.succ_item(key)[1].mean -
self.C.prev_item(key)[1].mean) / 2.
return c_i.mean + ((p - t) / k - 0.5) * delta
t += k
return self.C.max_item()[1].mean
def quantile(self, q):
"""
Computes the quantile of a specific value, ie. computes F(q) where F denotes
the CDF of the distribution.
"""
t = 0
N = float(self.n)
for i, key in enumerate(self.C.keys()):
c_i = self.C[key]
if i == len(self) - 1:
delta = (c_i.mean - self.C.prev_item(key)[1].mean) / 2.
else:
delta = (self.C.succ_item(key)[1].mean - c_i.mean) / 2.
z = max(-1, (q - c_i.mean) / delta)
if z < 1:
return t / N + c_i.count / N * (z + 1) / 2
t += c_i.count
return 1
def trimmed_mean(self, p1, p2):
"""
Computes the mean of the distribution between the two percentiles p1 and p2.
This is a modified algorithm than the one presented in the original t-Digest paper.
"""
if not (p1 < p2):
raise ValueError("p1 must be between 0 and 100 and less than p2.")
s = k = t = 0
p1 /= 100.
p2 /= 100.
p1 *= self.n
p2 *= self.n
for i, key in enumerate(self.C.keys()):
c_i = self.C[key]
k_i = c_i.count
if p1 < t + k_i:
if i == 0:
delta = self.C.succ_item(key)[1].mean - c_i.mean
elif i == len(self) - 1:
delta = c_i.mean - self.C.prev_item(key)[1].mean
else:
delta = (self.C.succ_item(key)[1].mean -
self.C.prev_item(key)[1].mean) / 2.
nu = ((p1 - t) / k_i - 0.5) * delta
s += nu * k_i * c_i.mean
k += nu * k_i
if p2 < t + k_i:
return s / k
t += k_i
return s / k
