Python：binned_statistic_2d 均值计算忽略数据中的 NaN

Question

I am using scipy.stats.binned_statistic_2d to bin irregular data onto a uniform grid by finding the mean of points within every bin.

x,y = np.meshgrid(sort(np.random.uniform(0,1,100)),sort(np.random.uniform(0,1,100)))
z = np.sin(x*y)

statistic, xedges, yedges, binnumber = sp.stats.binned_statistic_2d(x.ravel(), y.ravel(), values=z.ravel(), statistic='mean',bins=[np.arange(0,1.1,.1), np.arange(0,1.1,.1)])

plt.figure(1)
plt.pcolormesh(x,y,z, vmin = 0, vmax = 1)
plt.figure(2)
plt.pcolormesh(xedges,yedges,statistic, vmin = 0, vmax = 1)

Produces these plots, as expected:

Scattered data:

Gridded data:

But the data I want to grid has NaNs in it. This is what the result is like when I add NaNs:

x,y = np.meshgrid(sort(np.random.uniform(0,1,100)),sort(np.random.uniform(0,1,100)))
z = np.sin(x*y)
z[50:55,50:55] = np.nan

statistic, xedges, yedges, binnumber = binned_statistic_2d(x.ravel(), y.ravel(), values=z.ravel(), statistic='mean',bins=[np.arange(0,1.1,.1), np.arange(0,1.1,.1)])

plt.figure(3)
plt.pcolormesh(x,y,z, vmin = 0, vmax = 1)
plt.figure(4)
plt.pcolormesh(xedges,yedges,statistic, vmin = 0, vmax = 1)

Scattered:

Gridded:

Obviously if a bin is entirely filled with NaNs, the the resulting mean of that bin should still be NaN. However, I would like bins that are not entirely filled with NaNs to just result in the mean of the non-NaN numbers.

I've tried replacing the "statistic" argument in sp.stats.binned_statistic_2d with np.nanmean . This works, but it goes very very slowly when I use it on large datasets. I've tried digging into the underlying code of `sp.stats.binned_statistic_2d', but I can't figure out exactly how it is calculating the mean, or how to make it ignore NaNs in it's calculation.

Any ideas?

Answer 1

I had the same problem and changed the definition of binned_statistic_dd in scipy.stats and saved a local copy so that it won't be changed if scipy is updated.

I added 'nanmean' to the list of known_stats and

elif statistic == 'nanmean':
    result.fill(np.nan)
    for i in np.unique(binnumbers):
        for vv in builtins.range(Vdim):
            result[vv, i] = np.nanmean(values[vv, binnumbers == i])

Full new definition:

def binned_statistic_dd(sample, values, statistic='mean',
                    bins=10, range=None, expand_binnumbers=False,
                    binned_statistic_result=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 N arrays of length D, or
    as an (N,D) array.
values : (N,) array_like or list of (N,) array_like
    The data on which the statistic will be computed.  This must be
    the same shape as `sample`, or a list of sequences - each with the
    same shape as `sample`.  If `values` is such a list, the statistic
    will be computed on each independently.
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.
      * 'std' : compute the standard deviation within each bin. This
        is implicitly calculated with ddof=0. If the number of values
        within a given bin is 0 or 1, the computed standard deviation value
        will be 0 for the bin.
      * 'min' : compute the minimum of values for points within each bin.
        Empty bins will be represented by NaN.
      * 'max' : compute the maximum of values for point within each bin.
        Empty bins will be represented by NaN.
      * 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 positive int, optional
    The bin specification must be in one of the following forms:

      * 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 explicitly in `bins`. Defaults to the minimum and maximum
    values along each dimension.
expand_binnumbers : bool, optional
    'False' (default): the returned `binnumber` is a shape (N,) array of
    linearized bin indices.
    'True': the returned `binnumber` is 'unraveled' into a shape (D,N)
    ndarray, where each row gives the bin numbers in the corresponding
    dimension.
    See the `binnumber` returned value, and the `Examples` section of
    `binned_statistic_2d`.
binned_statistic_result : binnedStatisticddResult
    Result of a previous call to the function in order to reuse bin edges
    and bin numbers with new values and/or a different statistic.
    To reuse bin numbers, `expand_binnumbers` must have been set to False
    (the default)

    .. versionadded:: 0.17.0

Returns
-------
statistic : ndarray, shape(nx1, nx2, nx3,...)
    The values of the selected statistic in each two-dimensional bin.
bin_edges : list of ndarrays
    A list of D arrays describing the (nxi + 1) bin edges for each
    dimension.
binnumber : (N,) array of ints or (D,N) ndarray of ints
    This assigns to each element of `sample` an integer that represents the
    bin in which this observation falls.  The representation depends on the
    `expand_binnumbers` argument.  See `Notes` for details.


See Also
--------
numpy.digitize, numpy.histogramdd, binned_statistic, binned_statistic_2d

Notes
-----
Binedges:
All but the last (righthand-most) bin is half-open in each dimension.  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.

`binnumber`:
This returned argument assigns to each element of `sample` an integer that
represents the bin in which it belongs.  The representation depends on the
`expand_binnumbers` argument. If 'False' (default): The returned
`binnumber` is a shape (N,) array of linearized indices mapping each
element of `sample` to its corresponding bin (using row-major ordering).
If 'True': The returned `binnumber` is a shape (D,N) ndarray where
each row indicates bin placements for each dimension respectively.  In each
dimension, a binnumber of `i` means the corresponding value is between
(bin_edges[D][i-1], bin_edges[D][i]), for each dimension 'D'.

.. versionadded:: 0.11.0

Examples
--------
>>> from scipy import stats
>>> import matplotlib.pyplot as plt
>>> from mpl_toolkits.mplot3d import Axes3D

Take an array of 600 (x, y) coordinates as an example.
`binned_statistic_dd` can handle arrays of higher dimension `D`. But a plot
of dimension `D+1` is required.

>>> mu = np.array([0., 1.])
>>> sigma = np.array([[1., -0.5],[-0.5, 1.5]])
>>> multinormal = stats.multivariate_normal(mu, sigma)
>>> data = multinormal.rvs(size=600, random_state=235412)
>>> data.shape
(600, 2)

Create bins and count how many arrays fall in each bin:

>>> N = 60
>>> x = np.linspace(-3, 3, N)
>>> y = np.linspace(-3, 4, N)
>>> ret = stats.binned_statistic_dd(data, np.arange(600), bins=[x, y],
...                                 statistic='count')
>>> bincounts = ret.statistic

Set the volume and the location of bars:

>>> dx = x[1] - x[0]
>>> dy = y[1] - y[0]
>>> x, y = np.meshgrid(x[:-1]+dx/2, y[:-1]+dy/2)
>>> z = 0

>>> bincounts = bincounts.ravel()
>>> x = x.ravel()
>>> y = y.ravel()

>>> fig = plt.figure()
>>> ax = fig.add_subplot(111, projection='3d')
>>> with np.errstate(divide='ignore'):   # silence random axes3d warning
...     ax.bar3d(x, y, z, dx, dy, bincounts)

Reuse bin numbers and bin edges with new values:

>>> ret2 = stats.binned_statistic_dd(data, -np.arange(600),
...                                  binned_statistic_result=ret,
...                                  statistic='mean')
"""
known_stats = ['mean', 'median', 'count', 'sum', 'std', 'min', 'max',
               'nanmean']
if not callable(statistic) and statistic not in known_stats:
    raise ValueError('invalid statistic %r' % (statistic,))

try:
    bins = index(bins)
except TypeError:
    # bins is not an integer
    pass
# If bins was an integer-like object, now it is an actual Python int.

# NOTE: for _bin_edges(), see e.g. gh-11365
if isinstance(bins, int) and not np.isfinite(sample).all():
    raise ValueError('%r contains non-finite values.' % (sample,))

# `Ndim` is the number of dimensions (e.g. `2` for `binned_statistic_2d`)
# `Dlen` is the length of elements along each dimension.
# This code is based on np.histogramdd
try:
    # `sample` is an ND-array.
    Dlen, Ndim = sample.shape
except (AttributeError, ValueError):
    # `sample` is a sequence of 1D arrays.
    sample = np.atleast_2d(sample).T
    Dlen, Ndim = sample.shape

# Store initial shape of `values` to preserve it in the output
values = np.asarray(values)
input_shape = list(values.shape)
# Make sure that `values` is 2D to iterate over rows
values = np.atleast_2d(values)
Vdim, Vlen = values.shape

# Make sure `values` match `sample`
if(statistic != 'count' and Vlen != Dlen):
    raise AttributeError('The number of `values` elements must match the '
                         'length of each `sample` dimension.')

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

if binned_statistic_result is None:
    nbin, edges, dedges = _bin_edges(sample, bins, range)
    binnumbers = _bin_numbers(sample, nbin, edges, dedges)
else:
    edges = binned_statistic_result.bin_edges
    nbin = np.array([len(edges[i]) + 1 for i in builtins.range(Ndim)])
    # +1 for outlier bins
    dedges = [np.diff(edges[i]) for i in builtins.range(Ndim)]
    binnumbers = binned_statistic_result.binnumber

result = np.empty([Vdim, nbin.prod()], float)

if statistic == 'mean':
    result.fill(np.nan)
    flatcount = np.bincount(binnumbers, None)
    a = flatcount.nonzero()
    for vv in builtins.range(Vdim):
        flatsum = np.bincount(binnumbers, values[vv])
        result[vv, a] = flatsum[a] / flatcount[a]
elif statistic == 'std':
    result.fill(0)
    flatcount = np.bincount(binnumbers, None)
    a = flatcount.nonzero()
    for vv in builtins.range(Vdim):
        for i in np.unique(binnumbers):
            # NOTE: take std dev by bin, np.std() is 2-pass and stable
            binned_data = values[vv, binnumbers == i]
            # calc std only when binned data is 2 or more for speed up.
            if len(binned_data) >= 2:
                result[vv, i] = np.std(binned_data)
elif statistic == 'count':
    result.fill(0)
    flatcount = np.bincount(binnumbers, None)
    a = np.arange(len(flatcount))
    result[:, a] = flatcount[np.newaxis, :]
elif statistic == 'sum':
    result.fill(0)
    for vv in builtins.range(Vdim):
        flatsum = np.bincount(binnumbers, values[vv])
        a = np.arange(len(flatsum))
        result[vv, a] = flatsum
elif statistic == 'median':
    result.fill(np.nan)
    for i in np.unique(binnumbers):
        for vv in builtins.range(Vdim):
            result[vv, i] = np.median(values[vv, binnumbers == i])
elif statistic == 'min':
    result.fill(np.nan)
    for i in np.unique(binnumbers):
        for vv in builtins.range(Vdim):
            result[vv, i] = np.min(values[vv, binnumbers == i])
elif statistic == 'max':
    result.fill(np.nan)
    for i in np.unique(binnumbers):
        for vv in builtins.range(Vdim):
            result[vv, i] = np.max(values[vv, binnumbers == i])
elif statistic == 'nanmean':
    result.fill(np.nan)
    for i in np.unique(binnumbers):
        for vv in builtins.range(Vdim):
            result[vv, i] = np.nanmean(values[vv, binnumbers == i])
elif callable(statistic):
    with np.errstate(invalid='ignore'), suppress_warnings() as sup:
        sup.filter(RuntimeWarning)
        try:
            null = statistic([])
        except Exception:
            null = np.nan
    result.fill(null)
    for i in np.unique(binnumbers):
        for vv in builtins.range(Vdim):
            result[vv, i] = statistic(values[vv, binnumbers == i])

# Shape into a proper matrix
result = result.reshape(np.append(Vdim, nbin))

# Remove outliers (indices 0 and -1 for each bin-dimension).
core = tuple([slice(None)] + Ndim * [slice(1, -1)])
result = result[core]

# Unravel binnumbers into an ndarray, each row the bins for each dimension
if(expand_binnumbers and Ndim > 1):
    binnumbers = np.asarray(np.unravel_index(binnumbers, nbin))

if np.any(result.shape[1:] != nbin - 2):
    raise RuntimeError('Internal Shape Error')

# Reshape to have output (`result`) match input (`values`) shape
result = result.reshape(input_shape[:-1] + list(nbin-2))

return BinnedStatisticddResult(result, edges, binnumbers)