# Copyright 2022-2023 XProbe Inc.
# derived from copyright 1999-2021 Alibaba Group Holding Ltd.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
import operator
import warnings
import numpy as np
from ... import opcodes as OperandDef
from ... import tensor as mt
from ...core import recursive_tile
from ...core.context import get_context
from ...serialization.serializables import AnyField, BoolField, KeyField, TupleField
from ...utils import has_unknown_shape
from ..arithmetic.utils import chunk_tree_add
from ..array_utils import as_same_device, device
from ..core import TENSOR_CHUNK_TYPE, TENSOR_TYPE, TensorOrder
from ..datasource import tensor as astensor
from ..operands import TensorOperand, TensorOperandMixin
from ..utils import is_asc_sorted
# note: some logic of this file were adopted from `numpy/lib/histograms`
def _ptp(range_):
"""Peak-to-peak value of x.
This implementation avoids the problem of signed integer arrays having a
peak-to-peak value that cannot be represented with the array's data type.
This function returns an unsigned value for signed integer arrays.
"""
return _unsigned_subtract(*range_[::-1])
class HistBinSelector:
def __init__(self, histogram_bin_edges_op, x, range, raw_range):
self._op = histogram_bin_edges_op
self._x = x
self._range = range
self._raw_range = raw_range
self._width = None
def check(self):
# not checked before
width = self()
if width is None:
return
self._width = width = yield from recursive_tile(width)
yield [c.data for c in width.chunks]
def __call__(self):
return
def get_result(self):
ctx = get_context()
width = ctx.get_chunks_result([self._width.chunks[0].key])[0]
return width
class HistBinSqrtSelector(HistBinSelector):
"""
Square root histogram bin estimator.
Bin width is inversely proportional to the data size. Used by many
programs for its simplicity.
"""
def get_result(self):
return _ptp(self._raw_range) / np.sqrt(self._x.size)
class HistBinSturgesSelector(HistBinSelector):
"""
Sturges histogram bin estimator.
A very simplistic estimator based on the assumption of normality of
the data. This estimator has poor performance for non-normal data,
which becomes especially obvious for large data sets. The estimate
depends only on size of the data.
"""
def get_result(self):
return _ptp(self._raw_range) / (np.log2(self._x.size) + 1.0)
class HistBinRiceSelector(HistBinSelector):
"""
Rice histogram bin estimator.
Another simple estimator with no normality assumption. It has better
performance for large data than Sturges, but tends to overestimate
the number of bins. The number of bins is proportional to the cube
root of data size (asymptotically optimal). The estimate depends
only on size of the data.
"""
def get_result(self):
return _ptp(self._raw_range) / (2.0 * self._x.size ** (1.0 / 3))
class HistBinScottSelector(HistBinSelector):
"""
Scott histogram bin estimator.
The binwidth is proportional to the standard deviation of the data
and inversely proportional to the cube root of data size
(asymptotically optimal).
"""
def __call__(self):
return (24.0 * np.pi**0.5 / self._x.size) ** (1.0 / 3.0) * mt.std(self._x)
class HistBinStoneSelector(HistBinSelector):
"""
Histogram bin estimator based on minimizing the estimated integrated squared error (ISE).
The number of bins is chosen by minimizing the estimated ISE against the unknown true distribution.
The ISE is estimated using cross-validation and can be regarded as a generalization of Scott's rule.
https://en.wikipedia.org/wiki/Histogram#Scott.27s_normal_reference_rule
This paper by Stone appears to be the origination of this rule.
http://digitalassets.lib.berkeley.edu/sdtr/ucb/text/34.pdf
"""
def __call__(self):
n = self._x.size
ptp_x = _ptp(self._raw_range)
if n <= 1 or ptp_x == 0:
return
nbins_upper_bound = max(100, int(np.sqrt(n)))
candidates = []
for nbins in range(1, nbins_upper_bound + 1):
hh = ptp_x / nbins
p_k = histogram(self._x, bins=nbins, range=self._range)[0] / n
candidate = (2 - (n + 1) * p_k.dot(p_k)) / hh
candidates.append(candidate)
nbins = mt.stack(candidates).argmin() + 1
return ptp_x / nbins
def get_result(self):
ptp_x = _ptp(self._raw_range)
if self._x.size <= 1 or ptp_x == 0:
return 0.0
else:
return super().get_result()
class HistBinDoaneSelector(HistBinSelector):
"""
Doane's histogram bin estimator.
Improved version of Sturges' formula which works better for
non-normal data. See
stats.stackexchange.com/questions/55134/doanes-formula-for-histogram-binning
"""
def __call__(self):
x = self._x
if x.size <= 2:
return
sg1 = np.sqrt(6.0 * (x.size - 2) / ((x.size + 1.0) * (x.size + 3)))
sigma = mt.std(x)
g1 = mt.mean(((x - mt.mean(x)) / sigma) ** 3)
ret = _ptp(self._raw_range) / (
1.0 + np.log2(x.size) + mt.log2(1.0 + mt.absolute(g1) / sg1)
)
return mt.where(sigma > 0.0, ret, 0.0)
def get_result(self):
if self._x.size <= 2:
return 0.0
else:
return super().get_result()
class HistBinFdSelector(HistBinSelector):
"""
The Freedman-Diaconis histogram bin estimator.
The Freedman-Diaconis rule uses interquartile range (IQR) to
estimate binwidth. It is considered a variation of the Scott rule
with more robustness as the IQR is less affected by outliers than
the standard deviation. However, the IQR depends on fewer points
than the standard deviation, so it is less accurate, especially for
long tailed distributions.
If the IQR is 0, this function returns 1 for the number of bins.
Binwidth is inversely proportional to the cube root of data size
(asymptotically optimal).
"""
def __call__(self):
iqr = mt.subtract(*mt.percentile(self._x, [75, 25]))
return 2.0 * iqr * self._x.size ** (-1.0 / 3.0)
class HistBinAutoSelector(HistBinSelector):
"""
Histogram bin estimator that uses the minimum width of the
Freedman-Diaconis and Sturges estimators if the FD bandwidth is non zero
and the Sturges estimator if the FD bandwidth is 0.
The FD estimator is usually the most robust method, but its width
estimate tends to be too large for small `x` and bad for data with limited
variance. The Sturges estimator is quite good for small (<1000) datasets
and is the default in the R language. This method gives good off the shelf
behaviour.
If there is limited variance the IQR can be 0, which results in the
FD bin width being 0 too. This is not a valid bin width, so
``np.histogram_bin_edges`` chooses 1 bin instead, which may not be optimal.
If the IQR is 0, it's unlikely any variance based estimators will be of
use, so we revert to the sturges estimator, which only uses the size of the
dataset in its calculation.
"""
def __init__(self, histogram_bin_edges_op, x, range, raw_range):
super().__init__(histogram_bin_edges_op, x, range, raw_range)
self._bin_fd = HistBinFdSelector(histogram_bin_edges_op, x, range, raw_range)
self._bin_sturges = HistBinSturgesSelector(
histogram_bin_edges_op, x, range, raw_range
)
def __call__(self):
return self._bin_fd()
def get_result(self):
fd_bw = super().get_result()
sturges_bw = self._bin_sturges.get_result()
if fd_bw:
return min(fd_bw, sturges_bw)
else:
# limited variance, so we return a len dependent bw estimator
return sturges_bw
# Private dict initialized at module load time
_hist_bin_selectors = {
"stone": HistBinStoneSelector,
"auto": HistBinAutoSelector,
"doane": HistBinDoaneSelector,
"fd": HistBinFdSelector,
"rice": HistBinRiceSelector,
"scott": HistBinScottSelector,
"sqrt": HistBinSqrtSelector,
"sturges": HistBinSturgesSelector,
}
def _ravel_and_check_weights(a, weights):
"""Check a and weights have matching shapes, and ravel both"""
a = astensor(a)
# Ensure that the array is a "subtractable" dtype
if a.dtype == np.bool_:
warnings.warn(
f"Converting input from {a.dtype} to {np.uint8} for compatibility.",
RuntimeWarning,
stacklevel=3,
)
a = a.astype(np.uint8)
if weights is not None:
weights = astensor(weights)
if weights.shape != a.shape:
raise ValueError("weights should have the same shape as a.")
weights = weights.ravel()
a = a.ravel()
return a, weights
def _check_range(range):
first_edge, last_edge = range
if first_edge > last_edge:
raise ValueError("max must be larger than min in range parameter.")
if not (np.isfinite(first_edge) and np.isfinite(last_edge)):
raise ValueError(f"supplied range of [{first_edge}, {last_edge}] is not finite")
return first_edge, last_edge
def _get_outer_edges(a, range):
"""
Determine the outer bin edges to use, from either the data or the range
argument
"""
if range is not None:
first_edge, last_edge = _check_range(range)
else:
assert a.size == 0
# handle empty arrays. Can't determine range, so use 0-1.
first_edge, last_edge = 0, 1
# expand empty range to avoid divide by zero
if first_edge == last_edge:
first_edge = first_edge - 0.5
last_edge = last_edge + 0.5
return first_edge, last_edge
def _unsigned_subtract(a, b):
"""
Subtract two values where a >= b, and produce an unsigned result
This is needed when finding the difference between the upper and lower
bound of an int16 histogram
"""
# coerce to a single type
signed_to_unsigned = {
np.byte: np.ubyte,
np.short: np.ushort,
np.intc: np.uintc,
np.int_: np.uint,
np.longlong: np.ulonglong,
}
dt = np.result_type(a, b)
try:
dt = signed_to_unsigned[dt.type]
except KeyError: # pragma: no cover
return np.subtract(a, b, dtype=dt)
else:
# we know the inputs are integers, and we are deliberately casting
# signed to unsigned
return np.subtract(a, b, casting="unsafe", dtype=dt)
def _get_bin_edges(op, a, bins, range, weights):
# parse the overloaded bins argument
n_equal_bins = None
bin_edges = None
first_edge = None
last_edge = None
if isinstance(bins, str):
# when `bins` is str, x.min() and x.max()
# will be calculated in advance
bin_name = bins
if a.size > 0:
assert range is not None
raw_range = range
first_edge, last_edge = _get_outer_edges(a, range)
if a.size == 0:
n_equal_bins = 1
else:
# Do not call selectors on empty arrays
selector = _hist_bin_selectors[bin_name](
op, a, (first_edge, last_edge), raw_range
)
yield from selector.check()
width = selector.get_result()
if width:
n_equal_bins = int(
np.ceil(_unsigned_subtract(last_edge, first_edge) / width)
)
else:
# Width can be zero for some estimators, e.g. FD when
# the IQR of the data is zero.
n_equal_bins = 1
elif mt.ndim(bins) == 0:
first_edge, last_edge = _get_outer_edges(a, range)
n_equal_bins = bins
else:
# cannot be Tensor, must be calculated first
assert mt.ndim(bins) == 1 and not isinstance(bins, TENSOR_TYPE)
bin_edges = np.asarray(bins)
if not is_asc_sorted(bin_edges):
raise ValueError("`bins` must increase monotonically, when an array")
if n_equal_bins is not None:
# numpy gh-10322 means that type resolution rules are dependent on array
# shapes. To avoid this causing problems, we pick a type now and stick
# with it throughout.
bin_type = np.result_type(first_edge, last_edge, a)
if np.issubdtype(bin_type, np.integer):
bin_type = np.result_type(bin_type, float)
# bin edges must be computed
bin_edges = mt.linspace(
first_edge,
last_edge,
n_equal_bins + 1,
endpoint=True,
dtype=bin_type,
gpu=op.gpu,
)
return bin_edges, (first_edge, last_edge, n_equal_bins)
else:
return mt.tensor(bin_edges), None
class TensorHistogramBinEdges(TensorOperand, TensorOperandMixin):
_op_type_ = OperandDef.HISTOGRAM_BIN_EDGES
_input = KeyField("input")
_bins = AnyField("bins")
_range = TupleField("range")
_weights = KeyField("weights")
_uniform_bins = TupleField("uniform_bins")
def __init__(
self,
input=None,
bins=None,
range=None,
weights=None,
**kw,
):
super().__init__(_input=input, _bins=bins, _range=range, _weights=weights, **kw)
@property
def input(self):
return self._input
@property
def bins(self):
return self._bins
@property
def range(self):
return self._range
@property
def weights(self):
return self._weights
def _set_inputs(self, inputs):
super()._set_inputs(inputs)
inputs_iter = iter(self._inputs)
self._input = next(inputs_iter)
if isinstance(self._bins, (TENSOR_TYPE, TENSOR_CHUNK_TYPE)):
self._bins = next(inputs_iter)
if self._weights is not None:
self._weights = next(inputs_iter)
def __call__(self, a, bins, range, weights):
if range is not None:
_check_range(range)
if isinstance(bins, str):
# string, 'auto', 'stone', ...
# shape is unknown
bin_name = bins
# if `bins` is a string for an automatic method,
# this will replace it with the number of bins calculated
if bin_name not in _hist_bin_selectors:
raise ValueError(f"{bin_name!r} is not a valid estimator for `bins`")
if weights is not None:
raise TypeError(
"Automated estimation of the number of "
"bins is not supported for weighted data"
)
if isinstance(range, tuple) and len(range) == 2:
# if `bins` is a string, e.g. 'auto', 'stone'...,
# and `range` provided as well,
# `a` should be trimmed first
first_edge, last_edge = _get_outer_edges(a, range)
a = a[(a >= first_edge) & (a <= last_edge)]
shape = (np.nan,)
elif mt.ndim(bins) == 0:
try:
n_equal_bins = operator.index(bins)
except TypeError: # pragma: no cover
raise TypeError("`bins` must be an integer, a string, or an array")
if n_equal_bins < 1:
raise ValueError("`bins` must be positive, when an integer")
shape = (bins + 1,)
elif mt.ndim(bins) == 1:
if not isinstance(bins, TENSOR_TYPE):
bins = np.asarray(bins)
if not is_asc_sorted(bins):
raise ValueError(
"`bins` must increase monotonically, when an array"
)
shape = astensor(bins).shape
else:
raise ValueError("`bins` must be 1d, when an array")
inputs = [a]
if isinstance(bins, TENSOR_TYPE):
inputs.append(bins)
if weights is not None:
inputs.append(weights)
return self.new_tensor(inputs, shape=shape, order=TensorOrder.C_ORDER)
@classmethod
def tile(cls, op):
ctx = get_context()
a = op.input
range_ = op.range
bins = op.bins
if isinstance(bins, str):
if has_unknown_shape(a):
yield
if (
(a.size > 0 or np.isnan(a.size))
and (isinstance(bins, str) or mt.ndim(bins) == 0)
and not range_
):
input_min = a.min(keepdims=True)
input_max = a.max(keepdims=True)
input_min, input_max = yield from recursive_tile(input_min, input_max)
chunks = [input_min.chunks[0], input_max.chunks[0]]
yield chunks + a.chunks
range_results = ctx.get_chunks_result([c.key for c in chunks])
# make sure returned bounds are valid
if all(x.size > 0 for x in range_results):
range_ = tuple(x[0] for x in range_results)
if isinstance(bins, TENSOR_TYPE):
# `bins` is a Tensor, needs to be calculated first
yield
bin_datas = ctx.get_chunks_result([c.key for c in bins.chunks])
bins = np.concatenate(bin_datas)
else:
bins = op.bins
bin_edges, _ = yield from _get_bin_edges(op, op.input, bins, range_, op.weights)
bin_edges = yield from recursive_tile(bin_edges)
return [bin_edges]
[docs]def histogram_bin_edges(a, bins=10, range=None, weights=None):
r"""
Function to calculate only the edges of the bins used by the `histogram`
function.
Parameters
----------
a : array_like
Input data. The histogram is computed over the flattened tensor.
bins : int or sequence of scalars or str, 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.
If `bins` is a string from the list below, `histogram_bin_edges` will use
the method chosen to calculate the optimal bin width and
consequently the number of bins (see `Notes` for more detail on
the estimators) from the data that falls within the requested
range. While the bin width will be optimal for the actual data
in the range, the number of bins will be computed to fill the
entire range, including the empty portions. For visualisation,
using the 'auto' option is suggested. Weighted data is not
supported for automated bin size selection.
'auto'
Maximum of the 'sturges' and 'fd' estimators. Provides good
all around performance.
'fd' (Freedman Diaconis Estimator)
Robust (resilient to outliers) estimator that takes into
account data variability and data size.
'doane'
An improved version of Sturges' estimator that works better
with non-normal datasets.
'scott'
Less robust estimator that that takes into account data
variability and data size.
'stone'
Estimator based on leave-one-out cross-validation estimate of
the integrated squared error. Can be regarded as a generalization
of Scott's rule.
'rice'
Estimator does not take variability into account, only data
size. Commonly overestimates number of bins required.
'sturges'
R's default method, only accounts for data size. Only
optimal for gaussian data and underestimates number of bins
for large non-gaussian datasets.
'sqrt'
Square root (of data size) estimator, used by Excel and
other programs for its speed and simplicity.
range : (float, float), optional
The lower and upper range of the bins. If not provided, range
is simply ``(a.min(), a.max())``. Values outside the range are
ignored. The first element of the range must be less than or
equal to the second. `range` affects the automatic bin
computation as well. While bin width is computed to be optimal
based on the actual data within `range`, the bin count will fill
the entire range including portions containing no data.
weights : array_like, optional
A tensor of weights, of the same shape as `a`. Each value in
`a` only contributes its associated weight towards the bin count
(instead of 1). This is currently not used by any of the bin estimators,
but may be in the future.
Returns
-------
bin_edges : tensor of dtype float
The edges to pass into `histogram`
See Also
--------
histogram
Notes
-----
The methods to estimate the optimal number of bins are well founded
in literature, and are inspired by the choices R provides for
histogram visualisation. Note that having the number of bins
proportional to :math:`n^{1/3}` is asymptotically optimal, which is
why it appears in most estimators. These are simply plug-in methods
that give good starting points for number of bins. In the equations
below, :math:`h` is the binwidth and :math:`n_h` is the number of
bins. All estimators that compute bin counts are recast to bin width
using the `ptp` of the data. The final bin count is obtained from
``np.round(np.ceil(range / h))``.
'auto' (maximum of the 'sturges' and 'fd' estimators)
A compromise to get a good value. For small datasets the Sturges
value will usually be chosen, while larger datasets will usually
default to FD. Avoids the overly conservative behaviour of FD
and Sturges for small and large datasets respectively.
Switchover point is usually :math:`a.size \approx 1000`.
'fd' (Freedman Diaconis Estimator)
.. math:: h = 2 \frac{IQR}{n^{1/3}}
The binwidth is proportional to the interquartile range (IQR)
and inversely proportional to cube root of a.size. Can be too
conservative for small datasets, but is quite good for large
datasets. The IQR is very robust to outliers.
'scott'
.. math:: h = \sigma \sqrt[3]{\frac{24 * \sqrt{\pi}}{n}}
The binwidth is proportional to the standard deviation of the
data and inversely proportional to cube root of ``x.size``. Can
be too conservative for small datasets, but is quite good for
large datasets. The standard deviation is not very robust to
outliers. Values are very similar to the Freedman-Diaconis
estimator in the absence of outliers.
'rice'
.. math:: n_h = 2n^{1/3}
The number of bins is only proportional to cube root of
``a.size``. It tends to overestimate the number of bins and it
does not take into account data variability.
'sturges'
.. math:: n_h = \log _{2}n+1
The number of bins is the base 2 log of ``a.size``. This
estimator assumes normality of data and is too conservative for
larger, non-normal datasets. This is the default method in R's
``hist`` method.
'doane'
.. math:: n_h = 1 + \log_{2}(n) +
\log_{2}(1 + \frac{|g_1|}{\sigma_{g_1}})
g_1 = mean[(\frac{x - \mu}{\sigma})^3]
\sigma_{g_1} = \sqrt{\frac{6(n - 2)}{(n + 1)(n + 3)}}
An improved version of Sturges' formula that produces better
estimates for non-normal datasets. This estimator attempts to
account for the skew of the data.
'sqrt'
.. math:: n_h = \sqrt n
The simplest and fastest estimator. Only takes into account the
data size.
Examples
--------
>>> import mars.tensor as mt
>>> arr = mt.array([0, 0, 0, 1, 2, 3, 3, 4, 5])
>>> mt.histogram_bin_edges(arr, bins='auto', range=(0, 1)).execute()
array([0. , 0.25, 0.5 , 0.75, 1. ])
>>> mt.histogram_bin_edges(arr, bins=2).execute()
array([0. , 2.5, 5. ])
For consistency with histogram, a tensor of pre-computed bins is
passed through unmodified:
>>> mt.histogram_bin_edges(arr, [1, 2]).execute()
array([1, 2])
This function allows one set of bins to be computed, and reused across
multiple histograms:
>>> shared_bins = mt.histogram_bin_edges(arr, bins='auto')
>>> shared_bins.execute()
array([0., 1., 2., 3., 4., 5.])
>>> group_id = mt.array([0, 1, 1, 0, 1, 1, 0, 1, 1])
>>> a = arr[group_id == 0]
>>> a.execute()
array([0, 1, 3])
>>> hist_0, _ = mt.histogram(a, bins=shared_bins).execute()
>>> b = arr[group_id == 1]
>>> b.execute()
array([0, 0, 2, 3, 4, 5])
>>> hist_1, _ = mt.histogram(b, bins=shared_bins).execute()
>>> hist_0; hist_1
array([1, 1, 0, 1, 0])
array([2, 0, 1, 1, 2])
Which gives more easily comparable results than using separate bins for
each histogram:
>>> hist_0, bins_0 = mt.histogram(a, bins='auto').execute()
>>> hist_1, bins_1 = mt.histogram(b, bins='auto').execute()
>>> hist_0; hist_1
array([1, 1, 1])
array([2, 1, 1, 2])
>>> bins_0; bins_1
array([0., 1., 2., 3.])
array([0. , 1.25, 2.5 , 3.75, 5. ])
"""
a, weights = _ravel_and_check_weights(a, weights)
op = TensorHistogramBinEdges(
input=a, bins=bins, range=range, weights=weights, dtype=a.dtype
)
return op(a, bins, range, weights)
class TensorHistogram(TensorOperand, TensorOperandMixin):
_op_type_ = OperandDef.HISTOGRAM
_input = KeyField("input")
_bins = AnyField("bins")
_range = TupleField("range")
_weights = KeyField("weights")
_density = BoolField("density")
_ret_bins = BoolField("ret_bins")
def __init__(
self,
input=None,
bins=None,
range=None,
weights=None,
density=None,
ret_bins=None,
**kw,
):
super().__init__(
_input=input,
_bins=bins,
_range=range,
_weights=weights,
_density=density,
_ret_bins=ret_bins,
**kw,
)
@property
def input(self):
return self._input
@property
def bins(self):
return self._bins
@property
def range(self):
return self._range
@property
def weights(self):
return self._weights
@property
def density(self):
return self._density
@property
def ret_bins(self):
return self._ret_bins
@property
def output_limit(self):
return 1 if not self._ret_bins else 2
def _set_inputs(self, inputs):
super()._set_inputs(inputs)
inputs_iter = iter(self._inputs)
self._input = next(inputs_iter)
if isinstance(self._bins, (TENSOR_TYPE, TENSOR_CHUNK_TYPE)):
self._bins = next(inputs_iter)
if self._weights is not None:
self._weights = next(inputs_iter)
def __call__(self, a, bins, range, weights):
a, weights = _ravel_and_check_weights(a, weights)
histogram_bin_edges_op = TensorHistogramBinEdges(
input=a, bins=bins, range=range, weights=weights, dtype=np.dtype(np.float64)
)
bins = self._bins = histogram_bin_edges_op(a, bins, range, weights)
inputs = [histogram_bin_edges_op.input]
if isinstance(bins, TENSOR_TYPE):
inputs.append(bins)
# Histogram is an integer or a float array depending on the weights.
if weights is None:
dtype = np.dtype(np.intp)
else:
inputs.append(weights)
dtype = weights.dtype
self.dtype = dtype
hist = self.new_tensor(
inputs, shape=(bins.size - 1,), order=TensorOrder.C_ORDER
)
return mt.ExecutableTuple([hist, bins])
@classmethod
def tile(cls, op):
bins = op.bins.rechunk(op.bins.shape)
shape = (bins.size - 1,)
out = op.outputs[0]
weights = None
if op.weights is not None:
# make input and weights have the same nsplits
weights = yield from recursive_tile(op.weights.rechunk(op.input.nsplits))
out_chunks = []
for chunk in op.input.chunks:
chunk_op = op.copy().reset_key()
chunk_op._range = None
chunk_op._ret_bins = False
chunk_op._density = False
chunk_inputs = [chunk, bins.chunks[0]]
if weights is not None:
weights_chunk = weights.cix[chunk.index]
chunk_inputs.append(weights_chunk)
out_chunk = chunk_op.new_chunk(
chunk_inputs, shape=shape, index=chunk.index, order=out.order
)
out_chunks.append(out_chunk)
# merge chunks together
chunk = chunk_tree_add(out.dtype, out_chunks, (0,), shape)
new_op = op.copy()
n = new_op.new_tensor(
op.inputs,
shape=shape,
order=out.order,
chunks=[chunk],
nsplits=((shape[0],),),
)
if op.density:
db = mt.array(mt.diff(bins), float)
hist = n / db / n.sum()
hist = yield from recursive_tile(hist)
return [hist]
else:
return [n]
@classmethod
def execute(cls, ctx, op):
inputs, device_id, xp = as_same_device(
[ctx[inp.key] for inp in op.inputs], device=op.device, ret_extra=True
)
a = inputs[0]
bins = inputs[1] if isinstance(op.bins, TENSOR_CHUNK_TYPE) else op.bins
weights = None
if op.weights is not None:
weights = inputs[-1]
with device(device_id):
hist, bin_edges = xp.histogram(
a, bins=bins, range=op.range, weights=weights, density=op.density
)
ctx[op.outputs[0].key] = hist
if op.ret_bins:
ctx[op.outputs[1].key] = bin_edges
[docs]def histogram(a, bins=10, range=None, weights=None, density=None):
r"""
Compute the histogram of a set of data.
Parameters
----------
a : array_like
Input data. The histogram is computed over the flattened tensor.
bins : int or sequence of scalars or str, 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 a monotonically increasing tensor of bin edges,
including the rightmost edge, allowing for non-uniform bin widths.
If `bins` is a string, it defines the method used to calculate the
optimal bin width, as defined by `histogram_bin_edges`.
range : (float, float), optional
The lower and upper range of the bins. If not provided, range
is simply ``(a.min(), a.max())``. Values outside the range are
ignored. The first element of the range must be less than or
equal to the second. `range` affects the automatic bin
computation as well. While bin width is computed to be optimal
based on the actual data within `range`, the bin count will fill
the entire range including portions containing no data.
weights : array_like, optional
A tensor of weights, of the same shape as `a`. Each value in
`a` only contributes its associated weight towards the bin count
(instead of 1). If `density` is True, the weights are
normalized, so that the integral of the density over the range
remains 1.
density : bool, optional
If ``False``, the result will contain the number of samples in
each bin. If ``True``, the result is the value of the
probability *density* function at the bin, normalized such that
the *integral* over the range is 1. Note that the sum of the
histogram values will not be equal to 1 unless bins of unity
width are chosen; it is not a probability *mass* function.
Overrides the ``normed`` keyword if given.
Returns
-------
hist : tensor
The values of the histogram. See `density` and `weights` for a
description of the possible semantics.
bin_edges : tensor of dtype float
Return the bin edges ``(length(hist)+1)``.
See Also
--------
histogramdd, bincount, searchsorted, digitize, histogram_bin_edges
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
--------
>>> import mars.tensor as mt
>>> mt.histogram([1, 2, 1], bins=[0, 1, 2, 3]).execute()
(array([0, 2, 1]), array([0, 1, 2, 3]))
>>> mt.histogram(mt.arange(4), bins=mt.arange(5), density=True).execute()
(array([0.25, 0.25, 0.25, 0.25]), array([0, 1, 2, 3, 4]))
>>> mt.histogram([[1, 2, 1], [1, 0, 1]], bins=[0,1,2,3]).execute()
(array([1, 4, 1]), array([0, 1, 2, 3]))
>>> a = mt.arange(5)
>>> hist, bin_edges = mt.histogram(a, density=True)
>>> hist.execute()
array([0.5, 0. , 0.5, 0. , 0. , 0.5, 0. , 0.5, 0. , 0.5])
>>> hist.sum().execute()
2.4999999999999996
>>> mt.sum(hist * mt.diff(bin_edges)).execute()
1.0
Automated Bin Selection Methods example, using 2 peak random data
with 2000 points:
>>> import matplotlib.pyplot as plt
>>> rng = mt.random.RandomState(10) # deterministic random data
>>> a = mt.hstack((rng.normal(size=1000),
... rng.normal(loc=5, scale=2, size=1000)))
>>> _ = plt.hist(np.asarray(a), bins='auto') # arguments are passed to np.histogram
>>> plt.title("Histogram with 'auto' bins")
Text(0.5, 1.0, "Histogram with 'auto' bins")
>>> plt.show()
"""
a, weights = _ravel_and_check_weights(a, weights)
op = TensorHistogram(
input=a, bins=bins, range=range, weights=weights, density=density
)
return op(a, bins, range, weights)