# Copyright 1999-2020 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 warnings import operator import numpy as np from ... import opcodes as OperandDef from ... import tensor as mt from ...serialize import AnyField, TupleField, KeyField, BoolField from ...tiles import TilesError from ...context import get_context from ...utils import check_chunks_unknown_shape, recursive_tile from ..core import TENSOR_TYPE, TENSOR_CHUNK_TYPE, TensorOrder from ..operands import TensorOperand, TensorOperandMixin from ..datasource import tensor as astensor from ..arithmetic.utils import tree_add from ..utils import is_asc_sorted from ..array_utils import as_same_device, device # 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 def check(self): if len(self._op._calc_bin_edges_dependencies) == 0: # not checked before width = self() if width is None: return err = TilesError('bin edges calculation requires ' 'some dependencies executed first') self._op._calc_bin_edges_dependencies = [width] recursive_tile(width) err.partial_tiled_chunks = [c.data for c in width.chunks] raise err def __call__(self): return def get_result(self): ctx = get_context() width = ctx.get_chunk_results( [self._op._calc_bin_edges_dependencies[0].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) 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): __slots__ = '_calc_bin_edges_dependencies', _op_type_ = OperandDef.HISTOGRAM_BIN_EDGES _input = KeyField('input') _bins = AnyField('bins') _range = TupleField('range') _weights = KeyField('weights') _input_min = KeyField('input_min') _input_max = KeyField('input_max') _uniform_bins = TupleField('uniform_bins') def __init__(self, input=None, bins=None, range=None, weights=None, input_min=None, input_max=None, dtype=None, **kw): super().__init__(_input=input, _bins=bins, _range=range, _weights=weights, _input_min=input_min, _input_max=input_max, _dtype=dtype, **kw) if getattr(self, '_calc_bin_edges_dependencies', None) is None: self._calc_bin_edges_dependencies = [] @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 input_min(self): return self._input_min @property def input_max(self): return self._input_max 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): self._bins = next(inputs_iter) if self._weights is not None: self._weights = next(inputs_iter) if self._input_min is not None: self._input_min = next(inputs_iter) if self._input_max is not None: self._input_max = 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) if a.size > 0 and \ (isinstance(bins, str) or mt.ndim(bins) == 0) and not range: # for bins that is str or integer, # requires min max calculated first input_min = self._input_min = a.min() inputs.append(input_min) input_max = self._input_max = a.max() inputs.append(input_max) return self.new_tensor(inputs, shape=shape, order=TensorOrder.C_ORDER) @classmethod def tile(cls, op): ctx = get_context() range_ = op.range if isinstance(op.bins, str): check_chunks_unknown_shape([op.input], TilesError) if op.input_min is not None: # check if input min and max are calculated min_max_chunk_keys = \ [inp.chunks[0].key for inp in (op.input_min, op.input_max)] metas = ctx.get_chunk_metas(min_max_chunk_keys) if any(meta is None for meta in metas): raise TilesError('`input_min` or `input_max` need be executed first') range_ = tuple(ctx.get_chunk_results(min_max_chunk_keys)) if isinstance(op.bins, TENSOR_TYPE): # `bins` is a Tensor, needs to be calculated first bins_chunk_keys = [c.key for c in op.bins.chunks] metas = ctx.get_chunk_metas(bins_chunk_keys) if any(meta is None for meta in metas): raise TilesError('`bins` should be executed first if it\'s a tensor') bin_datas = ctx.get_chunk_results(bins_chunk_keys) bins = np.concatenate(bin_datas) else: bins = op.bins bin_edges, _ = _get_bin_edges(op, op.input, bins, range_, op.weights) bin_edges = bin_edges._inplace_tile() 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): 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 = op.weights.rechunk(op.input.nsplits)._inplace_tile() 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 = 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() 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() """ op = TensorHistogram(input=a, bins=bins, range=range, weights=weights, density=density) return op(a, bins, range, weights)