def _hd_1D(data,prob,var):
"Computes the HD quantiles for a 1D array."
xsorted = numpy.squeeze(numpy.sort(data.compressed().view(ndarray)))
n = len(xsorted)
#.........
hd = empty((2,len(prob)), float_)
if n < 2:
hd.flat = numpy.nan
if var:
return hd
return hd[0]
#.........
v = arange(n+1) / float(n)
betacdf = beta.cdf
for (i,p) in enumerate(prob):
_w = betacdf(v, (n+1)*p, (n+1)*(1-p))
w = _w[1:] - _w[:-1]
hd_mean = dot(w, xsorted)
hd[0,i] = hd_mean
#
hd[1,i] = dot(w, (xsorted-hd_mean)**2)
#
hd[0, prob == 0] = xsorted[0]
hd[0, prob == 1] = xsorted[-1]
if var:
hd[1, prob == 0] = hd[1, prob == 1] = numpy.nan
return hd
return hd[0]
def cov(x, y=None, rowvar=True, bias=False, strict=False):
"""
Estimate the covariance matrix.
If x is a vector, return the variance. For matrices, returns the covariance
matrix.
If y is given, it is treated as an additional (set of) variable(s).
Normalization is by (N-1) where N is the number of observations (unbiased
estimate). If bias is True then normalization is by N.
If rowvar is non-zero (default), then each row is a variable with observations
in the columns, otherwise each column is a variable and the observations are
in the rows.
If strict is True, masked values are propagated: if a masked value appears in
a row or column, the whole row or column is considered masked.
"""
X = narray(x, ndmin=2, subok=True, dtype=float)
if X.shape[0] == 1:
rowvar = True
if rowvar:
axis = 0
tup = (slice(None),None)
else:
axis = 1
tup = (None, slice(None))
#
if y is not None:
y = narray(y, copy=False, ndmin=2, subok=True, dtype=float)
X = concatenate((X,y),axis)
#
X -= X.mean(axis=1-axis)[tup]
n = X.count(1-axis)
#
if bias:
fact = n*1.0
else:
fact = n-1.0
#
if not rowvar:
return (dot(X.T, X.conj(), strict=False) / fact).squeeze()
else:
return (dot(X, X.T.conj(), strict=False) / fact).squeeze()
def _hdsd_1D(data,prob):
"Computes the std error for 1D arrays."
xsorted = numpy.sort(data.compressed())
n = len(xsorted)
#.........
hdsd = empty(len(prob), float_)
if n < 2:
hdsd.flat = numpy.nan
#.........
vv = arange(n) / float(n-1)
betacdf = beta.cdf
#
for (i,p) in enumerate(prob):
_w = betacdf(vv, (n+1)*p, (n+1)*(1-p))
w = _w[1:] - _w[:-1]
mx_ = numpy.fromiter([dot(w,xsorted[r_[range(0,k),
range(k+1,n)].astype(int_)])
for k in range(n)], dtype=float_)
mx_var = numpy.array(mx_.var(), copy=False, ndmin=1) * n / float(n-1)
hdsd[i] = float(n-1) * sqrt(numpy.diag(mx_var).diagonal() / float(n))
return hdsd
