def barplot(self, func=None, *args, **kwargs):
"""
Plots a bar chart comparing the phases for each period, as transformed
by the ``func`` function.
Parameters
----------
func : function, optional
Function to apply.
By default, use the :func:`numpy.ma.mean` function.
args : var
Mandatory arguments of function ``func``.
kwargs : var
Optional arguments of function ``func``.
"""
func = func or ma.mean
width = 0.2
colordict = ENSOcolors['fill']
barlist = []
pos = self.positions - 3 * width
for (i, s) in zip(['W', -1, 0, 1],
[self.series, self.cold, self.neutral, self.warm]):
pos += width
series = ma.apply_along_axis(func, 0, s, *funcopt)
b = self.bar(pos, series, width=width, bottom=0,
color=colordict[i], ecolor='k', capsize=3)
barlist.append(b[0])
self.barlist = barlist
self.figure.axes.append(self)
self.format_xaxis()
return barlist
def hdquantiles_sd(data, prob=list([.25, .5, .75]), axis=None):
"""Computes the standard error of the Harrell-Davis quantile estimates by jackknife.
Parameters
----------
data : ndarray
Data array.
prob : sequence
Sequence of quantiles to compute.
axis : int
Axis along which to compute the quantiles. If None, use a flattened array.
Notes
-----
The function is restricted to 2D arrays.
"""
def _hdsd_1D(data, prob):
"Computes the std error for 1D arrays."
xsorted = np.sort(data.compressed())
n = len(xsorted)
#.........
hdsd = np.empty(len(prob), float_)
if n < 2:
hdsd.flat = np.nan
#.........
vv = np.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_ = np.fromiter([
np.dot(
w, xsorted[np.r_[list(range(0, k)),
list(range(k + 1, n))].astype(int_)])
for k in range(n)
],
dtype=float_)
mx_var = np.array(mx_.var(), copy=False,
ndmin=1) * n / float(n - 1)
hdsd[i] = float(n - 1) * np.sqrt(
np.diag(mx_var).diagonal() / float(n))
return hdsd
# Initialization & checks ---------
data = ma.array(data, copy=False, dtype=float_)
p = np.array(prob, copy=False, ndmin=1)
# Computes quantiles along axis (or globally)
if (axis is None):
result = _hdsd_1D(data, p)
else:
if data.ndim > 2:
raise ValueError(
"Array 'data' must be at most two dimensional, but got data.ndim = %d"
% data.ndim)
result = ma.apply_along_axis(_hdsd_1D, axis, data, p)
#
return ma.fix_invalid(result, copy=False).ravel()
def hdquantiles_sd(data, prob=list([.25,.5,.75]), axis=None):
"""
The standard error of the Harrell-Davis quantile estimates by jackknife.
Parameters
----------
data : array_like
Data array.
prob : sequence, optional
Sequence of quantiles to compute.
axis : int, optional
Axis along which to compute the quantiles. If None, use a flattened
array.
Returns
-------
hdquantiles_sd : MaskedArray
Standard error of the Harrell-Davis quantile estimates.
See Also
--------
hdquantiles
"""
def _hdsd_1D(data, prob):
"Computes the std error for 1D arrays."
xsorted = np.sort(data.compressed())
n = len(xsorted)
hdsd = np.empty(len(prob), float_)
if n < 2:
hdsd.flat = np.nan
vv = np.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_ = np.fromiter([w[:k] @ xsorted[:k] + w[k:] @ xsorted[k+1:]
for k in range(n)], dtype=float_)
# mx_var = np.array(mx_.var(), copy=False, ndmin=1) * n / (n - 1)
# hdsd[i] = (n - 1) * np.sqrt(mx_var / n)
hdsd[i] = np.sqrt(mx_.var() * (n - 1))
return hdsd
# Initialization & checks
data = ma.array(data, copy=False, dtype=float_)
p = np.array(prob, copy=False, ndmin=1)
# Computes quantiles along axis (or globally)
if (axis is None):
result = _hdsd_1D(data, p)
else:
if data.ndim > 2:
raise ValueError("Array 'data' must be at most two dimensional, "
"but got data.ndim = %d" % data.ndim)
result = ma.apply_along_axis(_hdsd_1D, axis, data, p)
return ma.fix_invalid(result, copy=False).ravel()
def hdquantiles_sd(data, prob=list([.25,.5,.75]), axis=None):
"""
The standard error of the Harrell-Davis quantile estimates by jackknife.
Parameters
----------
data : array_like
Data array.
prob : sequence, optional
Sequence of quantiles to compute.
axis : int, optional
Axis along which to compute the quantiles. If None, use a flattened
array.
Returns
-------
hdquantiles_sd : MaskedArray
Standard error of the Harrell-Davis quantile estimates.
See Also
--------
hdquantiles
"""
def _hdsd_1D(data, prob):
"Computes the std error for 1D arrays."
xsorted = np.sort(data.compressed())
n = len(xsorted)
hdsd = np.empty(len(prob), float_)
if n < 2:
hdsd.flat = np.nan
vv = np.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_ = np.fromiter([np.dot(w,xsorted[np.r_[list(range(0,k)),
list(range(k+1,n))].astype(int_)])
for k in range(n)], dtype=float_)
mx_var = np.array(mx_.var(), copy=False, ndmin=1) * n / float(n-1)
hdsd[i] = float(n-1) * np.sqrt(np.diag(mx_var).diagonal() / float(n))
return hdsd
# Initialization & checks
data = ma.array(data, copy=False, dtype=float_)
p = np.array(prob, copy=False, ndmin=1)
# Computes quantiles along axis (or globally)
if (axis is None):
result = _hdsd_1D(data, p)
else:
if data.ndim > 2:
raise ValueError("Array 'data' must be at most two dimensional, "
"but got data.ndim = %d" % data.ndim)
result = ma.apply_along_axis(_hdsd_1D, axis, data, p)
return ma.fix_invalid(result, copy=False).ravel()
def hdquantiles_sd(data, prob=list([0.25, 0.5, 0.75]), axis=None):
"""Computes the standard error of the Harrell-Davis quantile estimates by jackknife.
Parameters
----------
data: ndarray
Data array.
prob: sequence
Sequence of quantiles to compute.
axis : int
Axis along which to compute the quantiles. If None, use a flattened array.
Notes
-----
The function is restricted to 2D arrays.
"""
def _hdsd_1D(data, prob):
"Computes the std error for 1D arrays."
xsorted = np.sort(data.compressed())
n = len(xsorted)
# .........
hdsd = np.empty(len(prob), float_)
if n < 2:
hdsd.flat = np.nan
# .........
vv = np.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_ = np.fromiter(
[np.dot(w, xsorted[np.r_[range(0, k), range(k + 1, n)].astype(int_)]) for k in range(n)], dtype=float_
)
mx_var = np.array(mx_.var(), copy=False, ndmin=1) * n / float(n - 1)
hdsd[i] = float(n - 1) * np.sqrt(np.diag(mx_var).diagonal() / float(n))
return hdsd
# Initialization & checks ---------
data = ma.array(data, copy=False, dtype=float_)
p = np.array(prob, copy=False, ndmin=1)
# Computes quantiles along axis (or globally)
if axis is None:
result = _hdsd_1D(data, p)
else:
assert data.ndim <= 2, "Array should be 2D at most !"
result = ma.apply_along_axis(_hdsd_1D, axis, data, p)
#
return ma.fix_invalid(result, copy=False).ravel()
def median_cihs(data, alpha=0.05, axis=None):
"""
Computes the alpha-level confidence interval for the median of the data.
Uses the Hettmasperger-Sheather method.
Parameters
----------
data : array_like
Input data. Masked values are discarded. The input should be 1D only,
or `axis` should be set to None.
alpha : float, optional
Confidence level of the intervals.
axis : int or None, optional
Axis along which to compute the quantiles. If None, use a flattened
array.
Returns
-------
median_cihs
Alpha level confidence interval.
"""
def _cihs_1D(data, alpha):
data = np.sort(data.compressed())
n = len(data)
alpha = min(alpha, 1 - alpha)
k = int(binom._ppf(alpha / 2., n, 0.5))
gk = binom.cdf(n - k, n, 0.5) - binom.cdf(k - 1, n, 0.5)
if gk < 1 - alpha:
k -= 1
gk = binom.cdf(n - k, n, 0.5) - binom.cdf(k - 1, n, 0.5)
gkk = binom.cdf(n - k - 1, n, 0.5) - binom.cdf(k, n, 0.5)
I = (gk - 1 + alpha) / (gk - gkk)
lambd = (n - k) * I / float(k + (n - 2 * k) * I)
lims = (lambd * data[k] + (1 - lambd) * data[k - 1],
lambd * data[n - k - 1] + (1 - lambd) * data[n - k])
return lims
data = ma.rray(data, copy=False)
# Computes quantiles along axis (or globally)
if (axis is None):
result = _cihs_1D(data.compressed(), alpha)
else:
if data.ndim > 2:
raise ValueError("Array 'data' must be at most two dimensional, "
"but got data.ndim = %d" % data.ndim)
result = ma.apply_along_axis(_cihs_1D, axis, data, alpha)
return result
def get_psi_bar(self, V=None, zpoint='F'):
"""Doc String"""
if V is None:
V = self.mnc('Tav.nc', 'VVEL', mask=self.HFacS[:])
vflux = V * self.dzf[:, np.newaxis, np.newaxis]
Vdx = vflux * self.HFacS
Vdx = ma.mean(Vdx, axis=2) * self.Lx
psi = ma.cumsum(Vdx, axis=0)
if zpoint == 'F':
return psi
elif zpoint == 'C':
psi = ma.apply_along_axis(np.vstack, 1,
[np.zeros(self.Ny + 1), psi])
return 0.5 * (psi[1:] + psi[:-1])
def median_cihs(data, alpha=0.05, axis=None):
"""
Computes the alpha-level confidence interval for the median of the data.
Uses the Hettmasperger-Sheather method.
Parameters
----------
data : array_like
Input data. Masked values are discarded. The input should be 1D only,
or `axis` should be set to None.
alpha : float, optional
Confidence level of the intervals.
axis : int or None, optional
Axis along which to compute the quantiles. If None, use a flattened
array.
Returns
-------
median_cihs
Alpha level confidence interval.
"""
def _cihs_1D(data, alpha):
data = np.sort(data.compressed())
n = len(data)
alpha = min(alpha, 1 - alpha)
k = int(binom._ppf(alpha / 2.0, n, 0.5))
gk = binom.cdf(n - k, n, 0.5) - binom.cdf(k - 1, n, 0.5)
if gk < 1 - alpha:
k -= 1
gk = binom.cdf(n - k, n, 0.5) - binom.cdf(k - 1, n, 0.5)
gkk = binom.cdf(n - k - 1, n, 0.5) - binom.cdf(k, n, 0.5)
I = (gk - 1 + alpha) / (gk - gkk)
lambd = (n - k) * I / float(k + (n - 2 * k) * I)
lims = (lambd * data[k] + (1 - lambd) * data[k - 1], lambd * data[n - k - 1] + (1 - lambd) * data[n - k])
return lims
data = ma.rray(data, copy=False)
# Computes quantiles along axis (or globally)
if axis is None:
result = _cihs_1D(data.compressed(), alpha)
else:
if data.ndim > 2:
raise ValueError("Array 'data' must be at most two dimensional, " "but got data.ndim = %d" % data.ndim)
result = ma.apply_along_axis(_cihs_1D, axis, data, alpha)
return result
def Mstep_part2(X,K,Mu,P,Var,post, minVariance=0.25):
n,d = np.shape(X) # n data points of dimension d
N = np.zeros(K)
mask = (X[:]==0)
post_T = np.transpose(post)
X_T = np.transpose(X)
X_Cu = ma.array(X,mask=mask)
# X_Cu = get_partial_X(X)
# print "---------------------STARTING M STEP---------------------"
N = np.sum(post,axis=0)
P = np.divide(N,n)
# update means
Mu_new = np.dot(post_T,X_Cu)
Mu_bot = np.dot(post_T,~mask)
mask_2 = (Mu_bot[:]<1)
Mu_bot = ma.array(Mu_bot,mask=mask_2) #masks out values <1
#print Mu_bot
Mu_new = np.divide(Mu_new, Mu_bot)
Mu = (Mu * mask_2) + Mu_new.filled(0) #keep original masked out values
# update variances
nonzeros = np.apply_along_axis(np.count_nonzero,1,~mask)
sig_denoms= np.sum(post * np.transpose([nonzeros]),axis=0)
#print post
for j in xrange(K):
norm = lambda x: LA.norm(x - Mu[j])**2
Var[j] = max(minVariance, np.sum(np.multiply(post_T[j],ma.apply_along_axis(norm,1,X_Cu)))/(sig_denoms[j]))
# for j in range(K):
# # Update parameters
# N[j] = math.fsum(post_T[j])
# P[j] = N[j]/n
# for l in range(d):
# Mu_bot = math.fsum([post[t][j] for t in range(n) if X[t][l] > 0])
# Mu_top = math.fsum([post[t][j] * X[t][l] for t in range(n) if X[t][l] > 0])
# if Mu_bot >= 1:
# Mu[j][l] = Mu_top / Mu_bot
# variances = np.array([variance(X_Cu[t], Mu[j]) for t in range(n)])
# var_top = np.dot(post_T[j], variances)
# var_bot = math.fsum( [post[t][j] * len(X_Cu[t]) for t in range(n)] )
# Var[j] = max(var_top / var_bot, minVariance)
return (Mu,P,Var)
def mjci(data, prob=[0.25, 0.5, 0.75], axis=None):
"""
Returns the Maritz-Jarrett estimators of the standard error of selected
experimental quantiles of the data.
Parameters
----------
data: ndarray
Data array.
prob: sequence
Sequence of quantiles to compute.
axis : int
Axis along which to compute the quantiles. If None, use a flattened
array.
"""
def _mjci_1D(data, p):
data = np.sort(data.compressed())
n = data.size
prob = (np.array(p) * n + 0.5).astype(int_)
betacdf = beta.cdf
#
mj = np.empty(len(prob), float_)
x = np.arange(1, n + 1, dtype=float_) / n
y = x - 1. / n
for (i, m) in enumerate(prob):
(m1, m2) = (m - 1, n - m)
W = betacdf(x, m - 1, n - m) - betacdf(y, m - 1, n - m)
C1 = np.dot(W, data)
C2 = np.dot(W, data**2)
mj[i] = np.sqrt(C2 - C1**2)
return mj
#
data = ma.array(data, copy=False)
if data.ndim > 2:
raise ValueError(
"Array 'data' must be at most two dimensional, but got data.ndim = %d"
% data.ndim)
p = np.array(prob, copy=False, ndmin=1)
# Computes quantiles along axis (or globally)
if (axis is None):
return _mjci_1D(data, p)
else:
return ma.apply_along_axis(_mjci_1D, axis, data, p)
def generate_histograms(self):
if self.state < 8:
raise InvalidContextBuilderState("Cannot generate histograms without indices")
self.logger.debug("10) Generating histograms")
if self.point_coords is self.environment_coords:
builder = lambda arr: np.bincount(arr[~arr.mask], minlength=self.num_bins)
self.histograms = ma.apply_along_axis(builder, -1, self.indices)
self.histograms = self.histograms.data.astype(np.uint16)
else:
builder = lambda arr: np.bincount(arr, minlength=self.num_bins)
self.histograms = np.apply_along_axis(builder, -1, self.indices)
self.histograms = self.histograms.astype(np.uint16)
self.state = 10
return self.histograms
def mjci(data, prob=[0.25,0.5,0.75], axis=None):
"""
Returns the Maritz-Jarrett estimators of the standard error of selected
experimental quantiles of the data.
Parameters
----------
data: ndarray
Data array.
prob: sequence
Sequence of quantiles to compute.
axis : int
Axis along which to compute the quantiles. If None, use a flattened
array.
"""
def _mjci_1D(data, p):
data = np.sort(data.compressed())
n = data.size
prob = (np.array(p) * n + 0.5).astype(int_)
betacdf = beta.cdf
mj = np.empty(len(prob), float_)
x = np.arange(1,n+1, dtype=float_) / n
y = x - 1./n
for (i,m) in enumerate(prob):
(m1,m2) = (m-1, n-m)
W = betacdf(x,m-1,n-m) - betacdf(y,m-1,n-m)
C1 = np.dot(W,data)
C2 = np.dot(W,data**2)
mj[i] = np.sqrt(C2 - C1**2)
return mj
data = ma.array(data, copy=False)
if data.ndim > 2:
raise ValueError("Array 'data' must be at most two dimensional, "
"but got data.ndim = %d" % data.ndim)
p = np.array(prob, copy=False, ndmin=1)
# Computes quantiles along axis (or globally)
if (axis is None):
return _mjci_1D(data, p)
else:
return ma.apply_along_axis(_mjci_1D, axis, data, p)
def idealfourths(data, axis=None):
"""Returns an estimate of the lower and upper quartiles of the data along
the given axis, as computed with the ideal fourths.
"""
def _idf(data):
x = data.compressed()
n = len(x)
if n < 3:
return [np.nan,np.nan]
(j,h) = divmod(n/4. + 5/12.,1)
qlo = (1-h)*x[j-1] + h*x[j]
k = n - j
qup = (1-h)*x[k] + h*x[k-1]
return [qlo, qup]
data = ma.sort(data, axis=axis).view(MaskedArray)
if (axis is None):
return _idf(data)
else:
return ma.apply_along_axis(_idf, axis, data)
def idealfourths(data, axis=None):
"""Returns an estimate of the lower and upper quartiles of the data along
the given axis, as computed with the ideal fourths.
"""
def _idf(data):
x = data.compressed()
n = len(x)
if n < 3:
return [np.nan,np.nan]
(j,h) = divmod(n/4. + 5/12.,1)
qlo = (1-h)*x[j-1] + h*x[j]
k = n - j
qup = (1-h)*x[k] + h*x[k-1]
return [qlo, qup]
data = ma.sort(data, axis=axis).view(MaskedArray)
if (axis is None):
return _idf(data)
else:
return ma.apply_along_axis(_idf, axis, data)
def idealfourths(data, axis=None):
"""
Returns an estimate of the lower and upper quartiles.
Uses the ideal fourths algorithm.
Parameters
----------
data : array_like
Input array.
axis : int, optional
Axis along which the quartiles are estimated. If None, the arrays are
flattened.
Returns
-------
idealfourths : {list of floats, masked array}
Returns the two internal values that divide `data` into four parts
using the ideal fourths algorithm either along the flattened array
(if `axis` is None) or along `axis` of `data`.
"""
def _idf(data):
x = data.compressed()
n = len(x)
if n < 3:
return [np.nan, np.nan]
(j, h) = divmod(n / 4. + 5 / 12., 1)
j = int(j)
qlo = (1 - h) * x[j - 1] + h * x[j]
k = n - j
qup = (1 - h) * x[k] + h * x[k - 1]
return [qlo, qup]
data = ma.sort(data, axis=axis).view(MaskedArray)
if (axis is None):
return _idf(data)
else:
return ma.apply_along_axis(_idf, axis, data)
def idealfourths(data, axis=None):
"""
Returns an estimate of the lower and upper quartiles.
Uses the ideal fourths algorithm.
Parameters
----------
data : array_like
Input array.
axis : int, optional
Axis along which the quartiles are estimated. If None, the arrays are
flattened.
Returns
-------
idealfourths : {list of floats, masked array}
Returns the two internal values that divide `data` into four parts
using the ideal fourths algorithm either along the flattened array
(if `axis` is None) or along `axis` of `data`.
"""
def _idf(data):
x = data.compressed()
n = len(x)
if n < 3:
return [np.nan, np.nan]
(j, h) = divmod(n / 4.0 + 5 / 12.0, 1)
j = int(j)
qlo = (1 - h) * x[j - 1] + h * x[j]
k = n - j
qup = (1 - h) * x[k] + h * x[k - 1]
return [qlo, qup]
data = ma.sort(data, axis=axis).view(MaskedArray)
if axis is None:
return _idf(data)
else:
return ma.apply_along_axis(_idf, axis, data)
def median_cihs(data, alpha=0.05, axis=None):
"""Computes the alpha-level confidence interval for the median of the data,
following the Hettmasperger-Sheather method.
Parameters
----------
data : sequence
Input data. Masked values are discarded. The input should be 1D only, or
axis should be set to None.
alpha : float
Confidence level of the intervals.
axis : integer
Axis along which to compute the quantiles. If None, use a flattened array.
"""
def _cihs_1D(data, alpha):
data = np.sort(data.compressed())
n = len(data)
alpha = min(alpha, 1 - alpha)
k = int(binom._ppf(alpha / 2., n, 0.5))
gk = binom.cdf(n - k, n, 0.5) - binom.cdf(k - 1, n, 0.5)
if gk < 1 - alpha:
k -= 1
gk = binom.cdf(n - k, n, 0.5) - binom.cdf(k - 1, n, 0.5)
gkk = binom.cdf(n - k - 1, n, 0.5) - binom.cdf(k, n, 0.5)
I = (gk - 1 + alpha) / (gk - gkk)
lambd = (n - k) * I / float(k + (n - 2 * k) * I)
lims = (lambd * data[k] + (1 - lambd) * data[k - 1],
lambd * data[n - k - 1] + (1 - lambd) * data[n - k])
return lims
data = ma.rray(data, copy=False)
# Computes quantiles along axis (or globally)
if (axis is None):
result = _cihs_1D(data.compressed(), alpha)
else:
assert data.ndim <= 2, "Array should be 2D at most !"
result = ma.apply_along_axis(_cihs_1D, axis, data, alpha)
#
return result
def median_cihs(data, alpha=0.05, axis=None):
"""Computes the alpha-level confidence interval for the median of the data,
following the Hettmasperger-Sheather method.
Parameters
----------
data : sequence
Input data. Masked values are discarded. The input should be 1D only, or
axis should be set to None.
alpha : float
Confidence level of the intervals.
axis : integer
Axis along which to compute the quantiles. If None, use a flattened array.
"""
def _cihs_1D(data, alpha):
data = np.sort(data.compressed())
n = len(data)
alpha = min(alpha, 1 - alpha)
k = int(binom._ppf(alpha / 2.0, n, 0.5))
gk = binom.cdf(n - k, n, 0.5) - binom.cdf(k - 1, n, 0.5)
if gk < 1 - alpha:
k -= 1
gk = binom.cdf(n - k, n, 0.5) - binom.cdf(k - 1, n, 0.5)
gkk = binom.cdf(n - k - 1, n, 0.5) - binom.cdf(k, n, 0.5)
I = (gk - 1 + alpha) / (gk - gkk)
lambd = (n - k) * I / float(k + (n - 2 * k) * I)
lims = (lambd * data[k] + (1 - lambd) * data[k - 1], lambd * data[n - k - 1] + (1 - lambd) * data[n - k])
return lims
data = ma.rray(data, copy=False)
# Computes quantiles along axis (or globally)
if axis is None:
result = _cihs_1D(data.compressed(), alpha)
else:
assert data.ndim <= 2, "Array should be 2D at most !"
result = ma.apply_along_axis(_cihs_1D, axis, data, alpha)
#
return result
def barplot(self, func=None, *args, **kwargs):
"""
Plots a bar chart comparing the phases for each period, as transformed
by the ``func`` function.
Parameters
----------
func : function, optional
Function to apply.
By default, use the :func:`numpy.ma.mean` function.
args : var
Mandatory arguments of function ``func``.
kwargs : var
Optional arguments of function ``func``.
"""
func = func or ma.mean
width = 0.2
colordict = ENSOcolors['fill']
barlist = []
pos = self.positions - 3 * width
for (i, s) in zip(['W', -1, 0, 1],
[self.series, self.cold, self.neutral, self.warm]):
pos += width
series = ma.apply_along_axis(func, 0, s, *funcopt)
b = self.bar(pos,
series,
width=width,
bottom=0,
color=colordict[i],
ecolor='k',
capsize=3)
barlist.append(b[0])
self.barlist = barlist
self.figure.axes.append(self)
self.format_xaxis()
return barlist
def hdquantiles_sd(data, prob=list([.25, .5, .75]), axis=None):
"""
The standard error of the Harrell-Davis quantile estimates by jackknife.
Parameters
----------
data : array_like
Data array.
prob : sequence, optional
Sequence of quantiles to compute.
axis : int, optional
Axis along which to compute the quantiles. If None, use a flattened
array.
Returns
-------
hdquantiles_sd : MaskedArray
Standard error of the Harrell-Davis quantile estimates.
See Also
--------
hdquantiles
"""
def _hdsd_1D(data, prob):
"Computes the std error for 1D arrays."
xsorted = np.sort(data.compressed())
n = len(xsorted)
hdsd = np.empty(len(prob), float_)
if n < 2:
hdsd.flat = np.nan
vv = np.arange(n) / float(n - 1)
betacdf = beta.cdf
for (i, p) in enumerate(prob):
_w = betacdf(vv, n * p, n * (1 - p))
w = _w[1:] - _w[:-1]
# cumulative sum of weights and data points if
# ith point is left out for jackknife
mx_ = np.zeros_like(xsorted)
mx_[1:] = np.cumsum(w * xsorted[:-1])
# similar but from the right
mx_[:-1] += np.cumsum(w[::-1] * xsorted[:0:-1])[::-1]
hdsd[i] = np.sqrt(mx_.var() * (n - 1))
return hdsd
# Initialization & checks
data = ma.array(data, copy=False, dtype=float_)
p = np.array(prob, copy=False, ndmin=1)
# Computes quantiles along axis (or globally)
if (axis is None):
result = _hdsd_1D(data, p)
else:
if data.ndim > 2:
raise ValueError("Array 'data' must be at most two dimensional, "
"but got data.ndim = %d" % data.ndim)
result = ma.apply_along_axis(_hdsd_1D, axis, data, p)
return ma.fix_invalid(result, copy=False).ravel()
def quantile(x,
probs=DEF_PROBS,
typ=DEF_TYPE,
method=DEF_METHOD,
limit=DEF_LIMIT,
na_rm=DEF_NARM,
is_sorted=False):
"""Compute the sample quantiles of any vector distribution.
>>> quantile(x, probs=DEF_PROBS, type = DEF_TYPE, method=DEF_METHOD, limit=DEF_LIMIT,
na_rm = DEF_NARM, is_sorted=False)
"""
## various parameter checkings
# check the data
if isinstance(x, (pd.DataFrame, pd.Series)):
try:
x = x.values
except:
raise TypeError("conversion type error for input dataset")
elif not isinstance(x, np.ndarray):
try:
x = np.asarray(x)
except:
raise TypeError("wrong type for input dataset")
ndim = x.ndim
if ndim > 2:
raise ValueError("array should be 2D at most !")
# check the probs
if isinstance(probs, (pd.DataFrame, pd.Series)):
try:
probs = probs.values
except:
raise TypeError("conversion type error for input probabilities")
elif isinstance(probs, (list, tuple)):
try:
probs = np.array(probs, copy=False, ndmin=1)
except:
raise TypeError("conversion type for error input probabilities")
elif not isinstance(probs, np.ndarray):
raise TypeError("wrong type for input probabilities")
# adjust the values: this is taken from R implementation, where alues up to
# 2e-14 outside that range are accepted and moved to the nearby endpoint
eps = 100 * np.finfo(np.double).eps
if (probs < -eps).any() or (probs > 1 + eps).any():
raise ValueError("probs values outside [0,1]")
probs = np.maximum(0, np.minimum(1, probs))
#weights = np.ones(x)
## check the weights
#if isinstance(weights, (pd.DataFrame,pd.Series)):
# try: weights = weights.values
# except: raise TypeError("conversion type error for input weights")
#elif not isinstance(weights, np.ndarray):
# try: weights = np.asarray(weights)
# except: raise TypeError("wrong type for input weights")
#if x.shape != weights.shape:
# raise ValueError("the length of data and weights must be the same")
# check parameter typ value
if typ not in TYPES:
raise ValueError(
"typ should be an integer in range [1,{}]!".format(TYPES))
# check parameter method value
if method not in METHODS:
raise ValueError("method should be in {}!".format(METHODS))
# check parameter method
if not isinstance(is_sorted, bool):
raise TypeError("wrong type for boolean flag is_sorted!")
# check parameter na_rm
if not isinstance(na_rm, bool):
raise TypeError("wrong type for boolean flag na_rm!")
# check parameter limit
if not isinstance(limit, (list, tuple, np.ndarray)):
raise TypeError("wrong type for boolean flag limit!")
if len(limit) != 2:
raise ValueError("the length of limit must be 2")
## algorithm implementation
def gamma_indice(g, j, typ):
gamma = np.zeros(len(j))
if typ == 1:
gamma[np.where(g > 0)] = 1
# gamma[np.where(g <= 0)] = 0
elif typ == 2:
gamma[np.where(g > 0)] = 1
gamma[np.where(g <= 0)] = 0.5
elif typ == 3:
gamma[np.where(np.logical_or(g != 0, j % 2 == 1))] = 1
elif typ >= 4:
gamma = g
return gamma
def _canonical_quantile1D(typ, sorted_x, probs):
"""Compute the quantile of a 1D numpy array using the canonical/direct
approach derived from the original algorithms from Hyndman & Fan, Cunane
and Filliben.
"""
# inspired by the _quantiles1D function of mquantiles
N = len(sorted_x) # sorted_x.count()
m_indice = lambda p, i: {1: 0, 2: 0, 3: -0.5, 4: 0, 5: 0.5, \
6: p, 7: 1-p, 8: (p+1)/3 , 9: (2*p+3)/8, \
10: .4 + .2 * p, 11: .3175 +.365*p}[i]
j_indice = lambda p, n, m: np.int_(np.floor(n * p + m))
g_indice = lambda p, n, m, j: p * n + m - j
m = m_indice(probs, typ)
j = j_indice(probs, N, m)
j_1 = j - 1
# adjust for the bounds
j_1[j_1 < 0] = 0
j[j > N - 1] = N - 1
x1 = sorted_x[j_1] # indexes start at 0...
x2 = sorted_x[j]
g = g_indice(probs, N, m, j)
gamma = gamma_indice(g, j, typ)
return (1 - gamma) * x1 + gamma * x2
def _mquantile1D(typ, sorted_x, probs):
"""Compute the quantiles of a 1D numpy array following the implementation
of the _quantiles1D function of mquantiles.
source: https://github.com/scipy/scipy/blob/master/scipy/stats/mstats_basic.py
"""
N = len(
sorted_x
) # sorted_x.count() # though ndarray's have no 'count' attribute
if N == 0:
return np_ma.array(np.empty(len(probs), dtype=float), mask=True)
elif N == 1:
return np_ma.array(np.resize(sorted_x, probs.shape),
mask=np_ma.nomask)
# note that, wrt to the original implementation (see source code mentioned
# above), we also added the definitions of (alphap,betap) for typ in [1,2,3]
abp_indice = lambda typ: {1: (0, 1), 2: (0, 1), 3: (-.5, -1.5), 4: (0, 1), \
5: (.5 , .5), 6: (0 , 0), 7:(1 , 1), 8: (1/3, 1/3), \
9: (3/8 , 3/8), 10: (.4,.4), 11: (.3175, .3175)}[typ]
alphap, betap = abp_indice(typ)
m = alphap + probs * (1. - alphap - betap)
aleph = (probs * N + m)
j = np.floor(aleph.clip(1, N - 1)).astype(int)
g = (aleph - j).clip(0, 1)
gamma = gamma_indice(g, j, typ)
return (1. - gamma) * sorted_x[
(j - 1).tolist()] + gamma * sorted_x[j.tolist()]
def _wquantile1D(typ, x, probs, weights): # not used
"""Compute the weighted quantile of a 1D numpy array.
"""
# Check the data
ind_sorted = np.argsort(x)
sorted_x = x[ind_sorted]
sorted_weights = weights[ind_sorted]
# Compute the auxiliary arrays
Sn = np.cumsum(sorted_weights)
#assert Sn != 0, "The sum of the weights must not be zero"
Pn = (Sn - 0.5 * sorted_weights) / np.sum(sorted_weights)
# Get the value of the weighted median
return np.interp(probs, Pn, sorted_x)
## actual calculation
# select method
if method == 'DIRECT':
_quantile1D = _canonical_quantile1D
elif method == 'INHERIT':
_quantile1D = _mquantile1D
# define input data
if na_rm is True:
data = np_ma.array(x, copy=True, mask=np.isnan(x))
# weights = np_ma.array(x, copy=True, mask = np.isnan(x))
elif np.isnan(x).any():
raise ValueError(
"missing values and NaN's not allowed if 'na_rm' is FALSE")
else:
data = np_ma.array(x, copy=False)
# filter the input data
if limit is True:
condition = (limit[0] < data) & (data < limit[1])
data[~condition.filled(True)] = np_ma.masked
# sort if not already the case
if is_sorted is False:
# ind_sorted = np.argsort(x)
# sorted_x = x[ind_sorted]
sorted_data = np_ma.sort(data.compressed())
# Computes quantiles along axis (or globally)
if ndim == 1:
return _quantile1D(typ, data if is_sorted else sorted_data, probs)
else:
return np_ma.apply_along_axis(_quantile1D, 1, typ, \
data if is_sorted else sorted_data, probs)
def hdquantiles(data, prob=list([.25, .5, .75]), axis=None, var=False, ):
"""
Computes quantile estimates with the Harrell-Davis method.
The quantile estimates are calculated as a weighted linear combination
of order statistics.
Parameters
----------
data : array_like
Data array.
prob : sequence, optional
Sequence of quantiles to compute.
axis : int or None, optional
Axis along which to compute the quantiles. If None, use a flattened
array.
var : bool, optional
Whether to return the variance of the estimate.
Returns
-------
hdquantiles : MaskedArray
A (p,) array of quantiles (if `var` is False), or a (2,p) array of
quantiles and variances (if `var` is True), where ``p`` is the
number of quantiles.
"""
def _hd_1D(data, prob, var):
"Computes the HD quantiles for a 1D array. Returns nan for invalid data."
xsorted = np.squeeze(np.sort(data.compressed().view(ndarray)))
# Don't use length here, in case we have a numpy scalar
n = xsorted.size
hd = np.empty((2, len(prob)), float_)
if n < 2:
hd.flat = np.nan
if var:
return hd
return hd[0]
v = np.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 = np.dot(w, xsorted)
hd[0, i] = hd_mean
#
hd[1, i] = np.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] = np.nan
return hd
return hd[0]
# Initialization & checks
data = ma.array(data, copy=False, dtype=float_)
p = np.array(prob, copy=False, ndmin=1)
# Computes quantiles along axis (or globally)
if (axis is None) or (data.ndim == 1):
result = _hd_1D(data, p, var)
else:
if data.ndim > 2:
raise ValueError("Array 'data' must be at most two dimensional, "
"but got data.ndim = %d" % data.ndim)
result = ma.apply_along_axis(_hd_1D, axis, data, p, var)
return ma.fix_invalid(result, copy=False)
def hdquantiles(
data,
prob=list([.25, .5, .75]),
axis=None,
var=False,
):
"""Computes quantile estimates with the Harrell-Davis method, where the estimates
are calculated as a weighted linear combination of order statistics.
Parameters
----------
data: ndarray
Data array.
prob: sequence
Sequence of quantiles to compute.
axis : int
Axis along which to compute the quantiles. If None, use a flattened array.
var : boolean
Whether to return the variance of the estimate.
Returns
-------
A (p,) array of quantiles (if ``var`` is False), or a (2,p) array of quantiles
and variances (if ``var`` is True), where ``p`` is the number of quantiles.
Notes
-----
The function is restricted to 2D arrays.
"""
def _hd_1D(data, prob, var):
"Computes the HD quantiles for a 1D array. Returns nan for invalid data."
xsorted = np.squeeze(np.sort(data.compressed().view(ndarray)))
# Don't use length here, in case we have a numpy scalar
n = xsorted.size
#.........
hd = np.empty((2, len(prob)), float_)
if n < 2:
hd.flat = np.nan
if var:
return hd
return hd[0]
#.........
v = np.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 = np.dot(w, xsorted)
hd[0, i] = hd_mean
#
hd[1, i] = np.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] = np.nan
return hd
return hd[0]
# Initialization & checks ---------
data = ma.array(data, copy=False, dtype=float_)
p = np.array(prob, copy=False, ndmin=1)
# Computes quantiles along axis (or globally)
if (axis is None) or (data.ndim == 1):
result = _hd_1D(data, p, var)
else:
assert data.ndim <= 2, "Array should be 2D at most !"
result = ma.apply_along_axis(_hd_1D, axis, data, p, var)
#
return ma.fix_invalid(result, copy=False)
def hdquantiles(data, prob=list([0.25, 0.5, 0.75]), axis=None, var=False):
"""
Computes quantile estimates with the Harrell-Davis method.
The quantile estimates are calculated as a weighted linear combination
of order statistics.
Parameters
----------
data : array_like
Data array.
prob : sequence, optional
Sequence of quantiles to compute.
axis : int or None, optional
Axis along which to compute the quantiles. If None, use a flattened
array.
var : bool, optional
Whether to return the variance of the estimate.
Returns
-------
hdquantiles : MaskedArray
A (p,) array of quantiles (if `var` is False), or a (2,p) array of
quantiles and variances (if `var` is True), where ``p`` is the
number of quantiles.
"""
def _hd_1D(data, prob, var):
"Computes the HD quantiles for a 1D array. Returns nan for invalid data."
xsorted = np.squeeze(np.sort(data.compressed().view(ndarray)))
# Don't use length here, in case we have a numpy scalar
n = xsorted.size
hd = np.empty((2, len(prob)), float_)
if n < 2:
hd.flat = np.nan
if var:
return hd
return hd[0]
v = np.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 = np.dot(w, xsorted)
hd[0, i] = hd_mean
#
hd[1, i] = np.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] = np.nan
return hd
return hd[0]
# Initialization & checks
data = ma.array(data, copy=False, dtype=float_)
p = np.array(prob, copy=False, ndmin=1)
# Computes quantiles along axis (or globally)
if (axis is None) or (data.ndim == 1):
result = _hd_1D(data, p, var)
else:
if data.ndim > 2:
raise ValueError("Array 'data' must be at most two dimensional, " "but got data.ndim = %d" % data.ndim)
result = ma.apply_along_axis(_hd_1D, axis, data, p, var)
return ma.fix_invalid(result, copy=False)
def whiskerbox(series,
fsp=None,
positions=None,
mode='mquantiles',
width=0.8,
wisk=None,
plot_mean=False,
logscale=None,
color=None,
outliers=None):
"""
Draws a whisker plot.
The bottom and top of the boxes correspond to the lower and upper quartiles
respectively (25th and 75th percentiles).
Parameters
----------
series : Sequence
Input data.
If the sequence is 2D, each column is assumed to represent a different variable.
fsp : :class:`Subplot`
Subplot where to draw the data.
If None, uses the current axe.
positions : {None, sequence}, optional
Positions along the x-axis.
If None, use a scale from 1 to the number of columns.
mode : {'mquantiles', 'hdquantiles'}, optional
Type of algorithm used to compute the quantiles.
If 'mquantiles', use the classical form :func:`~scipy.stats.mstats.mquantiles`
If 'hdquantiles', use the Harrell-Davies estimators of the function
:func:`~scipy.stats.mmorestats.hdquantiles`.
wisk : {None, float}, optional
Whiskers size, as a multiplier of the inter-quartile range.
If None, the whiskers are drawn between the 5th and 95th percentiles.
plot_mean : {False, True}, optional
Whether to overlay the mean on the box.
color : {None, string}, optional
Color of the main box.
outliers : {dictionary}, optional
Options for plotting outliers.
By default, the dictionary uses
``dict(marker='x', ms=4, mfc='#999999', ls='')``
"""
outliers = outliers or dict(
marker='x',
ms=4,
mfc='#999999',
mec='#999999',
ls='',
)
if fsp is None:
fsp = pyplot.gca()
if not fsp._hold:
fsp.cla()
# Make sure the series is a masked array
series = ma.array(series, copy=False, subok=False)
# Reshape the series ...................
if series.ndim == 1:
series = series.reshape(-1, 1)
elif series.ndim > 2:
series = np.swapaxes(series, 1, -1).reshape(-1, series.shape[1])
if positions is None:
positions = np.arange(1, series.shape[1] + 1)
# Get the quantiles ....................
plist = [0.05, 0.25, 0.5, 0.75, 0.95]
# Harrell-Davies ........
if mode == 'hdquantiles':
# 1D data ...........
if series.ndim == 0:
(qb, ql, qm, qh, qt) = mstats.hdquantiles(series.ravel(), plist)
# 2D data ...........
else:
(qb, ql, qm, qh, qt) = ma.apply_along_axis(mstats.hdquantiles, 0,
series, plist)
# Basic quantiles .......
else:
(qb, ql, qm, qh, qt) = mstats.mquantiles(series, plist, axis=0)
# Get the heights, bottoms, and whiskers positions
heights = qh - ql
bottoms = ql
if wisk is not None:
hival = qh + wisk * heights
loval = ql - wisk * heights
else:
(hival, loval) = (qt, qb)
# Plot the whiskers and outliers .......
for i, pos, xh, xl in np.broadcast(np.arange(len(positions)), positions,
hival, loval):
x = series[:, i]
# Get high extreme ..
wisk_h = x[(x <= xh).filled(False)]
if len(wisk_h) == 0:
wisk_h = qh[i]
else:
wisk_h = max(wisk_h)
# Low extremes ......
wisk_l = x[(x >= xl).filled(False)]
if len(wisk_l) == 0:
wisk_l = ql[i]
else:
wisk_l = min(wisk_l)
fsp.plot((pos, pos), (wisk_l, wisk_h), dashes=(1, 1), c='k', zorder=1)
fsp.plot((pos - 0.25 * width, pos + 0.25 * width), (wisk_l, wisk_l),
'-',
c='k')
fsp.plot((pos - 0.25 * width, pos + 0.25 * width), (wisk_h, wisk_h),
'-',
c='k')
# Outliers, if any...
if outliers is not None and len(outliers) > 0:
flh = x[(x > xh).filled(False)].view(ndarray)
fll = x[(x < xl).filled(False)].view(ndarray)
if len(flh) > 0 and len(fll) > 0:
fsp.plot([pos] * (len(flh) + len(fll)), np.r_[flh, fll],
**outliers)
# Plot the median....
fsp.plot((pos - 0.5 * width, pos + 0.5 * width), (qm[i], qm[i]),
ls='-',
c='k',
lw=1.2,
zorder=99)
# Plot the mean......
if plot_mean:
fsp.plot((pos - 0.5 * width, pos + 0.5 * width),
(x.mean(), x.mean()),
ls=':',
dashes=(1, 1),
c='#000000',
lw=1.1,
zorder=99)
# fsp.plot((pos,), (x.mean(),), marker='o', color=color, zorder=99)
# Plot the boxes .......................
bars = fsp.bar(positions - 0.5 * width,
heights,
width=width,
bottom=bottoms,
color=color,
yerr=None,
xerr=None,
ecolor='k',
capsize=3,
zorder=50)
if logscale:
fsp.set_yscale('log')
return bars
def hdquantiles(data, prob=list([0.25, 0.5, 0.75]), axis=None, var=False):
"""Computes quantile estimates with the Harrell-Davis method, where the estimates
are calculated as a weighted linear combination of order statistics.
Parameters
----------
data: ndarray
Data array.
prob: sequence
Sequence of quantiles to compute.
axis : int
Axis along which to compute the quantiles. If None, use a flattened array.
var : boolean
Whether to return the variance of the estimate.
Returns
-------
A (p,) array of quantiles (if ``var`` is False), or a (2,p) array of quantiles
and variances (if ``var`` is True), where ``p`` is the number of quantiles.
Notes
-----
The function is restricted to 2D arrays.
"""
def _hd_1D(data, prob, var):
"Computes the HD quantiles for a 1D array. Returns nan for invalid data."
xsorted = np.squeeze(np.sort(data.compressed().view(ndarray)))
# Don't use length here, in case we have a numpy scalar
n = xsorted.size
# .........
hd = np.empty((2, len(prob)), float_)
if n < 2:
hd.flat = np.nan
if var:
return hd
return hd[0]
# .........
v = np.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 = np.dot(w, xsorted)
hd[0, i] = hd_mean
#
hd[1, i] = np.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] = np.nan
return hd
return hd[0]
# Initialization & checks ---------
data = ma.array(data, copy=False, dtype=float_)
p = np.array(prob, copy=False, ndmin=1)
# Computes quantiles along axis (or globally)
if (axis is None) or (data.ndim == 1):
result = _hd_1D(data, p, var)
else:
assert data.ndim <= 2, "Array should be 2D at most !"
result = ma.apply_along_axis(_hd_1D, axis, data, p, var)
#
return ma.fix_invalid(result, copy=False)
def plotting_positions(data, alpha=0.4, beta=0.4, axis=0, masknan=False):
"""Returns the plotting positions (or empirical percentile points) for the
data.
Plotting positions are defined as (i-alpha)/(n+1-alpha-beta), where:
- i is the rank order statistics (starting at 1)
- n is the number of unmasked values along the given axis
- alpha and beta are two parameters.
Typical values for alpha and beta are:
- (0,1) : *p(k) = k/n* : linear interpolation of cdf (R, type 4)
- (.5,.5) : *p(k) = (k-1/2.)/n* : piecewise linear function (R, type 5)
(Bliss 1967: "Rankit")
- (0,0) : *p(k) = k/(n+1)* : Weibull (R type 6), (Van der Waerden 1952)
- (1,1) : *p(k) = (k-1)/(n-1)*. In this case, p(k) = mode[F(x[k])].
That's R default (R type 7)
- (1/3,1/3): *p(k) = (k-1/3)/(n+1/3)*. Then p(k) ~ median[F(x[k])].
The resulting quantile estimates are approximately median-unbiased
regardless of the distribution of x. (R type 8), (Tukey 1962)
- (3/8,3/8): *p(k) = (k-3/8)/(n+1/4)*.
The resulting quantile estimates are approximately unbiased
if x is normally distributed (R type 9) (Blom 1958)
- (.4,.4) : approximately quantile unbiased (Cunnane)
- (.35,.35): APL, used with PWM
Parameters
----------
x : sequence
Input data, as a sequence or array of dimension at most 2.
prob : sequence
List of quantiles to compute.
alpha : {0.4, float} optional
Plotting positions parameter.
beta : {0.4, float} optional
Plotting positions parameter.
Notes
-----
I think the adjustments assume that there are no ties in order to be a reasonable
approximation to a continuous density function. TODO: check this
References
----------
unknown,
dates to original papers from Beasley, Erickson, Allison 2009 Behav Genet
"""
if isinstance(data, np.ma.MaskedArray):
if axis is None or data.ndim == 1:
return stats.mstats.plotting_positions(data, alpha=alpha, beta=beta)
else:
return ma.apply_along_axis(stats.mstats.plotting_positions, axis, data, alpha=alpha, beta=beta)
if masknan:
nanmask = np.isnan(data)
if nanmask.any():
marr = ma.array(data, mask=nanmask)
#code duplication:
if axis is None or data.ndim == 1:
marr = stats.mstats.plotting_positions(marr, alpha=alpha, beta=beta)
else:
marr = ma.apply_along_axis(stats.mstats.plotting_positions, axis, marr, alpha=alpha, beta=beta)
return ma.filled(marr, fill_value=np.nan)
data = np.asarray(data)
if data.size == 1: # use helper function instead
data = np.atleast_1d(data)
axis = 0
if axis is None:
data = data.ravel()
axis = 0
n = data.shape[axis]
if data.ndim == 1:
plpos = np.empty(data.shape, dtype=float)
plpos[data.argsort()] = (np.arange(1,n+1) - alpha)/(n+1.-alpha-beta)
else:
#nd assignment instead of second argsort doesn't look easy
plpos = (data.argsort(axis).argsort(axis) + 1. - alpha)/(n+1.-alpha-beta)
return plpos
def mquantiles(a,
prob=list([.25, .5, .75]),
alphap=.4,
betap=.4,
axis=None,
limit=()):
"""
Computes empirical quantiles for a data array.
Samples quantile are defined by ``Q(p) = (1-gamma)*x[j] + gamma*x[j+1]``,
where ``x[j]`` is the j-th order statistic, and gamma is a function of
``j = floor(n*p + m)``, ``m = alphap + p*(1 - alphap - betap)`` and
``g = n*p + m - j``.
Reinterpreting the above equations to compare to **R** lead to the
equation: ``p(k) = (k - alphap)/(n + 1 - alphap - betap)``
Typical values of (alphap,betap) are:
- (0,1) : ``p(k) = k/n`` : linear interpolation of cdf
(**R** type 4)
- (.5,.5) : ``p(k) = (k - 1/2.)/n`` : piecewise linear function
(**R** type 5)
- (0,0) : ``p(k) = k/(n+1)`` :
(**R** type 6)
- (1,1) : ``p(k) = (k-1)/(n-1)``: p(k) = mode[F(x[k])].
(**R** type 7, **R** default)
- (1/3,1/3): ``p(k) = (k-1/3)/(n+1/3)``: Then p(k) ~ median[F(x[k])].
The resulting quantile estimates are approximately median-unbiased
regardless of the distribution of x.
(**R** type 8)
- (3/8,3/8): ``p(k) = (k-3/8)/(n+1/4)``: Blom.
The resulting quantile estimates are approximately unbiased
if x is normally distributed
(**R** type 9)
- (.4,.4) : approximately quantile unbiased (Cunnane)
- (.35,.35): APL, used with PWM
Parameters
----------
a : array_like
Input data, as a sequence or array of dimension at most 2.
prob : array_like, optional
List of quantiles to compute.
alphap : float, optional
Plotting positions parameter, default is 0.4.
betap : float, optional
Plotting positions parameter, default is 0.4.
axis : int, optional
Axis along which to perform the trimming.
If None (default), the input array is first flattened.
limit : tuple
Tuple of (lower, upper) values.
Values of `a` outside this open interval are ignored.
Returns
-------
mquantiles : MaskedArray
An array containing the calculated quantiles.
Notes
-----
This formulation is very similar to **R** except the calculation of
``m`` from ``alphap`` and ``betap``, where in **R** ``m`` is defined
with each type.
References
----------
.. [1] *R* statistical software at http://www.r-project.org/
Examples
--------
>>> from scipy.stats.mstats import mquantiles
>>> a = np.array([6., 47., 49., 15., 42., 41., 7., 39., 43., 40., 36.])
>>> mquantiles(a)
array([ 19.2, 40. , 42.8])
Using a 2D array, specifying axis and limit.
>>> data = np.array([[ 6., 7., 1.],
[ 47., 15., 2.],
[ 49., 36., 3.],
[ 15., 39., 4.],
[ 42., 40., -999.],
[ 41., 41., -999.],
[ 7., -999., -999.],
[ 39., -999., -999.],
[ 43., -999., -999.],
[ 40., -999., -999.],
[ 36., -999., -999.]])
>>> mquantiles(data, axis=0, limit=(0, 50))
array([[ 19.2 , 14.6 , 1.45],
[ 40. , 37.5 , 2.5 ],
[ 42.8 , 40.05, 3.55]])
>>> data[:, 2] = -999.
>>> mquantiles(data, axis=0, limit=(0, 50))
masked_array(data =
[[19.2 14.6 --]
[40.0 37.5 --]
[42.8 40.05 --]],
mask =
[[False False True]
[False False True]
[False False True]],
fill_value = 1e+20)
"""
def _quantiles1D(data, m, p):
x = np.sort(data.compressed())
n = len(x)
if n == 0:
return ma.array(np.empty(len(p), dtype=float), mask=True)
elif n == 1:
return ma.array(np.resize(x, p.shape), mask=nomask)
aleph = (n * p + m)
k = np.floor(aleph.clip(1, n - 1)).astype(int)
gamma = (aleph - k).clip(0, 1)
return (1. - gamma) * x[(k - 1).tolist()] + gamma * x[k.tolist()]
# Initialization & checks ---------
data = ma.array(a, copy=False)
if data.ndim > 2:
raise TypeError("Array should be 2D at most !")
#
if limit:
condition = (limit[0] < data) & (data < limit[1])
data[~condition.filled(True)] = masked
#
p = np.array(prob, copy=False, ndmin=1)
m = alphap + p * (1. - alphap - betap)
# Computes quantiles along axis (or globally)
if (axis is None):
return _quantiles1D(data, m, p)
return ma.apply_along_axis(_quantiles1D, axis, data, m, p)
def whiskerbox(
series,
fsp=None,
positions=None,
mode="mquantiles",
width=0.8,
wisk=None,
plot_mean=False,
logscale=None,
color=None,
outliers=None,
):
"""
Draws a whisker plot.
The bottom and top of the boxes correspond to the lower and upper quartiles
respectively (25th and 75th percentiles).
Parameters
----------
series : Sequence
Input data.
If the sequence is 2D, each column is assumed to represent a different variable.
fsp : :class:`Subplot`
Subplot where to draw the data.
If None, uses the current axe.
positions : {None, sequence}, optional
Positions along the x-axis.
If None, use a scale from 1 to the number of columns.
mode : {'mquantiles', 'hdquantiles'}, optional
Type of algorithm used to compute the quantiles.
If 'mquantiles', use the classical form :func:`~scipy.stats.mstats.mquantiles`
If 'hdquantiles', use the Harrell-Davies estimators of the function
:func:`~scipy.stats.mmorestats.hdquantiles`.
wisk : {None, float}, optional
Whiskers size, as a multiplier of the inter-quartile range.
If None, the whiskers are drawn between the 5th and 95th percentiles.
plot_mean : {False, True}, optional
Whether to overlay the mean on the box.
color : {None, string}, optional
Color of the main box.
outliers : {dictionary}, optional
Options for plotting outliers.
By default, the dictionary uses
``dict(marker='x', ms=4, mfc='#999999', ls='')``
"""
outliers = outliers or dict(marker="x", ms=4, mfc="#999999", mec="#999999", ls="")
if fsp is None:
fsp = pyplot.gca()
if not fsp._hold:
fsp.cla()
# Make sure the series is a masked array
series = ma.array(series, copy=False, subok=False)
# Reshape the series ...................
if series.ndim == 1:
series = series.reshape(-1, 1)
elif series.ndim > 2:
series = np.swapaxes(series, 1, -1).reshape(-1, series.shape[1])
if positions is None:
positions = np.arange(1, series.shape[1] + 1)
# Get the quantiles ....................
plist = [0.05, 0.25, 0.5, 0.75, 0.95]
# Harrell-Davies ........
if mode == "hdquantiles":
# 1D data ...........
if series.ndim == 0:
(qb, ql, qm, qh, qt) = mstats.hdquantiles(series.ravel(), plist)
# 2D data ...........
else:
(qb, ql, qm, qh, qt) = ma.apply_along_axis(mstats.hdquantiles, 0, series, plist)
# Basic quantiles .......
else:
(qb, ql, qm, qh, qt) = mstats.mquantiles(series, plist, axis=0)
# Get the heights, bottoms, and whiskers positions
heights = qh - ql
bottoms = ql
if wisk is not None:
hival = qh + wisk * heights
loval = ql - wisk * heights
else:
(hival, loval) = (qt, qb)
# Plot the whiskers and outliers .......
for i, pos, xh, xl in np.broadcast(np.arange(len(positions)), positions, hival, loval):
x = series[:, i]
# Get high extreme ..
wisk_h = x[(x <= xh).filled(False)]
if len(wisk_h) == 0:
wisk_h = qh[i]
else:
wisk_h = max(wisk_h)
# Low extremes ......
wisk_l = x[(x >= xl).filled(False)]
if len(wisk_l) == 0:
wisk_l = ql[i]
else:
wisk_l = min(wisk_l)
fsp.plot((pos, pos), (wisk_l, wisk_h), dashes=(1, 1), c="k", zorder=1)
fsp.plot((pos - 0.25 * width, pos + 0.25 * width), (wisk_l, wisk_l), "-", c="k")
fsp.plot((pos - 0.25 * width, pos + 0.25 * width), (wisk_h, wisk_h), "-", c="k")
# Outliers, if any...
if outliers is not None and len(outliers) > 0:
flh = x[(x > xh).filled(False)].view(ndarray)
fll = x[(x < xl).filled(False)].view(ndarray)
if len(flh) > 0 and len(fll) > 0:
fsp.plot([pos] * (len(flh) + len(fll)), np.r_[flh, fll], **outliers)
# Plot the median....
fsp.plot((pos - 0.5 * width, pos + 0.5 * width), (qm[i], qm[i]), ls="-", c="k", lw=1.2, zorder=99)
# Plot the mean......
if plot_mean:
fsp.plot(
(pos - 0.5 * width, pos + 0.5 * width),
(x.mean(), x.mean()),
ls=":",
dashes=(1, 1),
c="#000000",
lw=1.1,
zorder=99,
)
# fsp.plot((pos,), (x.mean(),), marker='o', color=color, zorder=99)
# Plot the boxes .......................
bars = fsp.bar(
positions - 0.5 * width,
heights,
width=width,
bottom=bottoms,
color=color,
yerr=None,
xerr=None,
ecolor="k",
capsize=3,
zorder=50,
)
if logscale:
fsp.set_yscale("log")
return bars
def plotting_positions(data, alpha=0.4, beta=0.4, axis=0, masknan=False):
"""Returns the plotting positions (or empirical percentile points) for the
data.
Plotting positions are defined as (i-alpha)/(n+1-alpha-beta), where:
- i is the rank order statistics (starting at 1)
- n is the number of unmasked values along the given axis
- alpha and beta are two parameters.
Typical values for alpha and beta are:
- (0,1) : *p(k) = k/n* : linear interpolation of cdf (R, type 4)
- (.5,.5) : *p(k) = (k-1/2.)/n* : piecewise linear function (R, type 5)
(Bliss 1967: "Rankit")
- (0,0) : *p(k) = k/(n+1)* : Weibull (R type 6), (Van der Waerden 1952)
- (1,1) : *p(k) = (k-1)/(n-1)*. In this case, p(k) = mode[F(x[k])].
That's R default (R type 7)
- (1/3,1/3): *p(k) = (k-1/3)/(n+1/3)*. Then p(k) ~ median[F(x[k])].
The resulting quantile estimates are approximately median-unbiased
regardless of the distribution of x. (R type 8), (Tukey 1962)
- (3/8,3/8): *p(k) = (k-3/8)/(n+1/4)*.
The resulting quantile estimates are approximately unbiased
if x is normally distributed (R type 9) (Blom 1958)
- (.4,.4) : approximately quantile unbiased (Cunnane)
- (.35,.35): APL, used with PWM
Parameters
----------
x : sequence
Input data, as a sequence or array of dimension at most 2.
prob : sequence
List of quantiles to compute.
alpha : {0.4, float} optional
Plotting positions parameter.
beta : {0.4, float} optional
Plotting positions parameter.
Notes
-----
I think the adjustments assume that there are no ties in order to be a reasonable
approximation to a continuous density function. TODO: check this
References
----------
unknown,
dates to original papers from Beasley, Erickson, Allison 2009 Behav Genet
"""
if isinstance(data, np.ma.MaskedArray):
if axis is None or data.ndim == 1:
return stats.mstats.plotting_positions(data,
alpha=alpha,
beta=beta)
else:
return ma.apply_along_axis(stats.mstats.plotting_positions,
axis,
data,
alpha=alpha,
beta=beta)
if masknan:
nanmask = np.isnan(data)
if nanmask.any():
marr = ma.array(data, mask=nanmask)
#code duplication:
if axis is None or data.ndim == 1:
marr = stats.mstats.plotting_positions(marr,
alpha=alpha,
beta=beta)
else:
marr = ma.apply_along_axis(stats.mstats.plotting_positions,
axis,
marr,
alpha=alpha,
beta=beta)
return ma.filled(marr, fill_value=np.nan)
data = np.asarray(data)
if data.size == 1: # use helper function instead
data = np.atleast_1d(data)
axis = 0
if axis is None:
data = data.ravel()
axis = 0
n = data.shape[axis]
if data.ndim == 1:
plpos = np.empty(data.shape, dtype=float)
plpos[data.argsort()] = (np.arange(1, n + 1) - alpha) / (n + 1. -
alpha - beta)
else:
#nd assignment instead of second argsort does not look easy
plpos = (data.argsort(axis).argsort(axis) + 1. -
alpha) / (n + 1. - alpha - beta)
return plpos
def mquantiles(a, prob=list([.25,.5,.75]), alphap=.4, betap=.4, axis=None,
limit=()):
"""
Computes empirical quantiles for a data array.
Samples quantile are defined by ``Q(p) = (1-gamma)*x[j] + gamma*x[j+1]``,
where ``x[j]`` is the j-th order statistic, and gamma is a function of
``j = floor(n*p + m)``, ``m = alphap + p*(1 - alphap - betap)`` and
``g = n*p + m - j``.
Reinterpreting the above equations to compare to **R** lead to the
equation: ``p(k) = (k - alphap)/(n + 1 - alphap - betap)``
Typical values of (alphap,betap) are:
- (0,1) : ``p(k) = k/n`` : linear interpolation of cdf
(**R** type 4)
- (.5,.5) : ``p(k) = (k - 1/2.)/n`` : piecewise linear function
(**R** type 5)
- (0,0) : ``p(k) = k/(n+1)`` :
(**R** type 6)
- (1,1) : ``p(k) = (k-1)/(n-1)``: p(k) = mode[F(x[k])].
(**R** type 7, **R** default)
- (1/3,1/3): ``p(k) = (k-1/3)/(n+1/3)``: Then p(k) ~ median[F(x[k])].
The resulting quantile estimates are approximately median-unbiased
regardless of the distribution of x.
(**R** type 8)
- (3/8,3/8): ``p(k) = (k-3/8)/(n+1/4)``: Blom.
The resulting quantile estimates are approximately unbiased
if x is normally distributed
(**R** type 9)
- (.4,.4) : approximately quantile unbiased (Cunnane)
- (.35,.35): APL, used with PWM
Parameters
----------
a : array_like
Input data, as a sequence or array of dimension at most 2.
prob : array_like, optional
List of quantiles to compute.
alphap : float, optional
Plotting positions parameter, default is 0.4.
betap : float, optional
Plotting positions parameter, default is 0.4.
axis : int, optional
Axis along which to perform the trimming.
If None (default), the input array is first flattened.
limit : tuple
Tuple of (lower, upper) values.
Values of `a` outside this open interval are ignored.
Returns
-------
mquantiles : MaskedArray
An array containing the calculated quantiles.
Notes
-----
This formulation is very similar to **R** except the calculation of
``m`` from ``alphap`` and ``betap``, where in **R** ``m`` is defined
with each type.
References
----------
.. [1] *R* statistical software at http://www.r-project.org/
Examples
--------
>>> from scipy.stats.mstats import mquantiles
>>> a = np.array([6., 47., 49., 15., 42., 41., 7., 39., 43., 40., 36.])
>>> mquantiles(a)
array([ 19.2, 40. , 42.8])
Using a 2D array, specifying axis and limit.
>>> data = np.array([[ 6., 7., 1.],
[ 47., 15., 2.],
[ 49., 36., 3.],
[ 15., 39., 4.],
[ 42., 40., -999.],
[ 41., 41., -999.],
[ 7., -999., -999.],
[ 39., -999., -999.],
[ 43., -999., -999.],
[ 40., -999., -999.],
[ 36., -999., -999.]])
>>> mquantiles(data, axis=0, limit=(0, 50))
array([[ 19.2 , 14.6 , 1.45],
[ 40. , 37.5 , 2.5 ],
[ 42.8 , 40.05, 3.55]])
>>> data[:, 2] = -999.
>>> mquantiles(data, axis=0, limit=(0, 50))
masked_array(data =
[[19.2 14.6 --]
[40.0 37.5 --]
[42.8 40.05 --]],
mask =
[[False False True]
[False False True]
[False False True]],
fill_value = 1e+20)
"""
def _quantiles1D(data,m,p):
x = np.sort(data.compressed())
n = len(x)
if n == 0:
return ma.array(np.empty(len(p), dtype=float), mask=True)
elif n == 1:
return ma.array(np.resize(x, p.shape), mask=nomask)
aleph = (n*p + m)
k = np.floor(aleph.clip(1, n-1)).astype(int)
gamma = (aleph-k).clip(0,1)
return (1.-gamma)*x[(k-1).tolist()] + gamma*x[k.tolist()]
# Initialization & checks ---------
data = ma.array(a, copy=False)
if data.ndim > 2:
raise TypeError("Array should be 2D at most !")
#
if limit:
condition = (limit[0] < data) & (data < limit[1])
data[~condition.filled(True)] = masked
#
p = np.array(prob, copy=False, ndmin=1)
m = alphap + p*(1.-alphap-betap)
# Computes quantiles along axis (or globally)
if (axis is None):
return _quantiles1D(data, m, p)
return ma.apply_along_axis(_quantiles1D, axis, data, m, p)
