```import numpy as np

# http://www.johndcook.com/blog/standard_deviation/
class RunningStat(object):
def __init__(self, shape):
self._n = 0
self._M = np.zeros(shape)
self._S = np.zeros(shape)
def push(self, x):
x = np.asarray(x)
assert x.shape == self._M.shape
self._n += 1
if self._n == 1:
self._M[...] = x
else:
oldM = self._M.copy()
self._M[...] = oldM + (x - oldM)/self._n
self._S[...] = self._S + (x - oldM)*(x - self._M)
@property
def n(self):
return self._n
@property
def mean(self):
return self._M
@property
def var(self):
return self._S/(self._n - 1) if self._n > 1 else np.square(self._M)
@property
def std(self):
return np.sqrt(self.var)
@property
def shape(self):
return self._M.shape

def test_running_stat():
for shp in ((), (3,), (3,4)):
li = []
rs = RunningStat(shp)
for _ in range(5):
val = np.random.randn(*shp)
rs.push(val)
li.append(val)
m = np.mean(li, axis=0)
assert np.allclose(rs.mean, m)
v = np.square(m) if (len(li) == 1) else np.var(li, ddof=1, axis=0)
assert np.allclose(rs.var, v)
```