# Source code for astroML.stats._binned_statistic

```import numpy as np

[docs]def binned_statistic(x, values, statistic='mean',
bins=10, range=None):
"""
Compute a binned statistic for a set of data.

This is a generalization of a histogram function.  A histogram divides
the space into bins, and returns the count of the number of points in
each bin.  This function allows the computation of the sum, mean, median,
or other statistic of the values within each bin.

Parameters
----------
x : array_like
A sequence of values to be binned.
values : array_like
The values on which the statistic will be computed.  This must be
the same shape as x.
statistic : string or callable, optional
The statistic to compute (default is 'mean').
The following statistics are available:

* 'mean' : compute the mean of values for points within each bin.
Empty bins will be represented by NaN.
* 'median' : compute the median of values for points within each
bin. Empty bins will be represented by NaN.
* 'count' : compute the count of points within each bin.  This is
identical to an unweighted histogram.  `values` array is not
referenced.
* 'sum' : compute the sum of values for points within each bin.
This is identical to a weighted histogram.
* function : a user-defined function which takes a 1D array of
values, and outputs a single numerical statistic. This function
will be called on the values in each bin.  Empty bins will be
represented by function([]), or NaN if this returns an error.

bins : int or sequence of scalars, optional
If `bins` is an int, it defines the number of equal-width
bins in the given range (10, by default). If `bins` is a sequence,
it defines the bin edges, including the rightmost edge, allowing
for non-uniform bin widths.
range : (float, float), optional
The lower and upper range of the bins.  If not provided, range
is simply ``(x.min(), x.max())``.  Values outside the range are
ignored.

Returns
-------
statistic : array
The values of the selected statistic in each bin.
bin_edges : array of dtype float
Return the bin edges ``(length(statistic)+1)``.

Notes
-----
All but the last (righthand-most) bin is half-open.  In other words, if
`bins` is::

[1, 2, 3, 4]

then the first bin is ``[1, 2)`` (including 1, but excluding 2) and the
second ``[2, 3)``.  The last bin, however, is ``[3, 4]``, which *includes*
4.

Examples
--------
>>> binned_statistic([1, 2, 1], [2, 5, 3], bins=[0, 1, 2, 3], statistic='count')
(array([0., 2., 1.]), array([0., 1., 2., 3.]))

--------
np.histogram, binned_statistic_2d, binned_statistic_dd
"""
try:
N = len(bins)
except TypeError:
N = 1

if N != 1:
bins = [np.asarray(bins, float)]

medians, edges = binned_statistic_dd([x], values, statistic,
bins, range)

return medians, edges[0]

[docs]def binned_statistic_2d(x, y, values, statistic='mean',
bins=10, range=None):
"""
Compute a bidimensional binned statistic for a set of data.

This is a generalization of a histogram2d function.  A histogram divides
the space into bins, and returns the count of the number of points in
each bin.  This function allows the computation of the sum, mean, median,
or other statistic of the values within each bin.

Parameters
----------
x : array_like
A sequence of values to be binned along the first dimension.
y : array_like
A sequence of values to be binned along the second dimension.
values : array_like
The values on which the statistic will be computed.  This must be
the same shape as x.
statistic : string or callable, optional
The statistic to compute (default is 'mean').
The following statistics are available:

* 'mean' : compute the mean of values for points within each bin.
Empty bins will be represented by NaN.
* 'median' : compute the median of values for points within each
bin. Empty bins will be represented by NaN.
* 'count' : compute the count of points within each bin.  This is
identical to an unweighted histogram.  `values` array is not
referenced.
* 'sum' : compute the sum of values for points within each bin.
This is identical to a weighted histogram.
* function : a user-defined function which takes a 1D array of
values, and outputs a single numerical statistic. This function
will be called on the values in each bin.  Empty bins will be
represented by function([]), or NaN if this returns an error.

bins : int or [int, int] or array-like or [array, array], optional
The bin specification:

* the number of bins for the two dimensions (nx=ny=bins),
* the number of bins in each dimension (nx, ny = bins),
* the bin edges for the two dimensions (x_edges=y_edges=bins),
* the bin edges in each dimension (x_edges, y_edges = bins).

range : array_like, shape(2,2), optional
The leftmost and rightmost edges of the bins along each dimension
(if not specified explicitly in the `bins` parameters):
[[xmin, xmax], [ymin, ymax]]. All values outside of this range will be
considered outliers and not tallied in the histogram.

Returns
-------
statistic : ndarray, shape(nx, ny)
The values of the selected statistic in each two-dimensional bin
xedges : ndarray, shape(nx + 1,)
The bin edges along the first dimension.
yedges : ndarray, shape(ny + 1,)
The bin edges along the second dimension.

--------
np.histogram2d, binned_statistic, binned_statistic_dd
"""

# This code is based on np.histogram2d
try:
N = len(bins)
except TypeError:
N = 1

if N != 1 and N != 2:
xedges = yedges = np.asarray(bins, float)
bins = [xedges, yedges]

medians, edges = binned_statistic_dd([x, y], values, statistic,
bins, range)

return medians, edges[0], edges[1]

[docs]def binned_statistic_dd(sample, values, statistic='mean',
bins=10, range=None):
"""
Compute a multidimensional binned statistic for a set of data.

This is a generalization of a histogramdd function.  A histogram divides
the space into bins, and returns the count of the number of points in
each bin.  This function allows the computation of the sum, mean, median,
or other statistic of the values within each bin.

Parameters
----------
sample : array_like
Data to histogram passed as a sequence of D arrays of length N, or
as an (N,D) array.
values : array_like
The values on which the statistic will be computed.  This must be
the same shape as x.
statistic : string or callable, optional
The statistic to compute (default is 'mean').
The following statistics are available:

* 'mean' : compute the mean of values for points within each bin.
Empty bins will be represented by NaN.
* 'median' : compute the median of values for points within each
bin. Empty bins will be represented by NaN.
* 'count' : compute the count of points within each bin.  This is
identical to an unweighted histogram.  `values` array is not
referenced.
* 'sum' : compute the sum of values for points within each bin.
This is identical to a weighted histogram.
* function : a user-defined function which takes a 1D array of
values, and outputs a single numerical statistic. This function
will be called on the values in each bin.  Empty bins will be
represented by function([]), or NaN if this returns an error.

bins : sequence or int, optional
The bin specification:

* A sequence of arrays describing the bin edges along each dimension.
* The number of bins for each dimension (nx, ny, ... =bins)
* The number of bins for all dimensions (nx=ny=...=bins).

range : sequence, optional
A sequence of lower and upper bin edges to be used if the edges are
not given explicitely in `bins`. Defaults to the minimum and maximum
values along each dimension.

Returns
-------
statistic : ndarray, shape(nx1, nx2, nx3,...)
The values of the selected statistic in each two-dimensional bin
edges : list of ndarrays
A list of D arrays describing the (nxi + 1) bin edges for each
dimension

--------
np.histogramdd, binned_statistic, binned_statistic_2d
"""
if type(statistic) == str:
if statistic not in ['mean', 'median', 'count', 'sum']:
raise ValueError('unrecognized statistic "%s"' % statistic)
elif callable(statistic):
pass
else:
raise ValueError("statistic not understood")

# This code is based on np.histogramdd
try:
# Sample is an ND-array.
N, D = sample.shape
except (AttributeError, ValueError):
# Sample is a sequence of 1D arrays.
sample = np.atleast_2d(sample).T
N, D = sample.shape

nbin = np.empty(D, int)
edges = D * [None]
dedges = D * [None]

try:
M = len(bins)
if M != D:
raise AttributeError('The dimension of bins must be equal '
'to the dimension of the sample x.')
except TypeError:
bins = D * [bins]

# Select range for each dimension
# Used only if number of bins is given.
if range is None:
smin = np.atleast_1d(np.array(sample.min(0), float))
smax = np.atleast_1d(np.array(sample.max(0), float))
else:
smin = np.zeros(D)
smax = np.zeros(D)
for i in np.arange(D):
smin[i], smax[i] = range[i]

# Make sure the bins have a finite width.
for i in np.arange(len(smin)):
if smin[i] == smax[i]:
smin[i] = smin[i] - .5
smax[i] = smax[i] + .5

# Create edge arrays
for i in np.arange(D):
if np.isscalar(bins[i]):
nbin[i] = bins[i] + 2  # +2 for outlier bins
edges[i] = np.linspace(smin[i], smax[i], nbin[i] - 1)
else:
edges[i] = np.asarray(bins[i], float)
nbin[i] = len(edges[i]) + 1  # +1 for outlier bins
dedges[i] = np.diff(edges[i])

nbin = np.asarray(nbin)

# Compute the bin number each sample falls into.
Ncount = {}
for i in np.arange(D):
Ncount[i] = np.digitize(sample[:, i], edges[i])

# Using digitize, values that fall on an edge are put in the right bin.
# For the rightmost bin, we want values equal to the right
# edge to be counted in the last bin, and not as an outlier.
for i in np.arange(D):
# Rounding precision
decimal = int(-np.log10(dedges[i].min())) + 6
# Find which points are on the rightmost edge.
on_edge = np.where(np.around(sample[:, i], decimal)
== np.around(edges[i][-1], decimal))[0]
# Shift these points one bin to the left.
Ncount[i][on_edge] -= 1

# Compute the sample indices in the flattened statistic matrix.
ni = nbin.argsort()
xy = np.zeros(N, int)
for i in np.arange(0, D - 1):
xy += Ncount[ni[i]] * nbin[ni[i + 1:]].prod()
xy += Ncount[ni[-1]]

result = np.empty(nbin.prod(), float)

if statistic == 'mean':
result.fill(np.nan)
flatcount = np.bincount(xy, None)
flatsum = np.bincount(xy, values)
a = np.arange(len(flatcount))
result[a] = flatsum
result[a] /= flatcount
elif statistic == 'count':
result.fill(0)
flatcount = np.bincount(xy, None)
a = np.arange(len(flatcount))
result[a] = flatcount
elif statistic == 'sum':
result.fill(0)
flatsum = np.bincount(xy, values)
a = np.arange(len(flatsum))
result[a] = flatsum
elif statistic == 'median':
result.fill(np.nan)
for i in np.unique(xy):
result[i] = np.median(values[xy == i])
elif callable(statistic):
try:
null = statistic([])
except Exception:
null = np.nan
result.fill(null)
for i in np.unique(xy):
result[i] = statistic(values[xy == i])

# Shape into a proper matrix
result = result.reshape(np.sort(nbin))
for i in np.arange(nbin.size):
j = ni.argsort()[i]
result = result.swapaxes(i, j)
ni[i], ni[j] = ni[j], ni[i]

# Remove outliers (indices 0 and -1 for each dimension).
core = D * [slice(1, -1)]
result = result[tuple(core)]

if (result.shape != nbin - 2).any():
raise RuntimeError('Internal Shape Error')
return result, edges
```