from collections.abc import Iterator from functools import wraps from numbers import Number import numpy as np from tlz import merge from ..base import tokenize from ..highlevelgraph import HighLevelGraph from .core import Array @wraps(np.percentile) def _percentile(a, q, interpolation="linear"): n = len(a) if not len(a): return None, n if isinstance(q, Iterator): q = list(q) if a.dtype.name == "category": result = np.percentile(a.codes, q, interpolation=interpolation) import pandas as pd return pd.Categorical.from_codes(result, a.categories, a.ordered), n if np.issubdtype(a.dtype, np.datetime64): a2 = a.astype("i8") result = np.percentile(a2, q, interpolation=interpolation).astype(a.dtype) if q[0] == 0: # https://github.com/dask/dask/issues/6864 result[0] = min(result[0], a.min()) return result, n if not np.issubdtype(a.dtype, np.number): interpolation = "nearest" return np.percentile(a, q, interpolation=interpolation), n def _tdigest_chunk(a): from crick import TDigest t = TDigest() t.update(a) return t def _percentiles_from_tdigest(qs, digests): from crick import TDigest t = TDigest() t.merge(*digests) return np.array(t.quantile(qs / 100.0)) def percentile(a, q, interpolation="linear", method="default"): """Approximate percentile of 1-D array Parameters ---------- a : Array q : array_like of float Percentile or sequence of percentiles to compute, which must be between 0 and 100 inclusive. interpolation : {'linear', 'lower', 'higher', 'midpoint', 'nearest'}, optional The interpolation method to use when the desired percentile lies between two data points ``i < j``. Only valid for ``method='dask'``. - 'linear': ``i + (j - i) * fraction``, where ``fraction`` is the fractional part of the index surrounded by ``i`` and ``j``. - 'lower': ``i``. - 'higher': ``j``. - 'nearest': ``i`` or ``j``, whichever is nearest. - 'midpoint': ``(i + j) / 2``. method : {'default', 'dask', 'tdigest'}, optional What method to use. By default will use dask's internal custom algorithm (``'dask'``). If set to ``'tdigest'`` will use tdigest for floats and ints and fallback to the ``'dask'`` otherwise. See Also -------- numpy.percentile : Numpy's equivalent Percentile function """ from .utils import array_safe, meta_from_array if not a.ndim == 1: raise NotImplementedError("Percentiles only implemented for 1-d arrays") if isinstance(q, Number): q = [q] q = array_safe(q, like=meta_from_array(a)) token = tokenize(a, q, interpolation) dtype = a.dtype if np.issubdtype(dtype, np.integer): dtype = (array_safe([], dtype=dtype, like=meta_from_array(a)) / 0.5).dtype meta = meta_from_array(a, dtype=dtype) allowed_methods = ["default", "dask", "tdigest"] if method not in allowed_methods: raise ValueError("method can only be 'default', 'dask' or 'tdigest'") if method == "default": internal_method = "dask" else: internal_method = method # Allow using t-digest if interpolation is allowed and dtype is of floating or integer type if ( internal_method == "tdigest" and interpolation == "linear" and (np.issubdtype(dtype, np.floating) or np.issubdtype(dtype, np.integer)) ): from dask.utils import import_required import_required( "crick", "crick is a required dependency for using the t-digest method." ) name = "percentile_tdigest_chunk-" + token dsk = dict( ((name, i), (_tdigest_chunk, key)) for i, key in enumerate(a.__dask_keys__()) ) name2 = "percentile_tdigest-" + token dsk2 = {(name2, 0): (_percentiles_from_tdigest, q, sorted(dsk))} # Otherwise use the custom percentile algorithm else: # Add 0 and 100 during calculation for more robust behavior (hopefully) calc_q = np.pad(q, 1, mode="constant") calc_q[-1] = 100 name = "percentile_chunk-" + token dsk = dict( ((name, i), (_percentile, key, calc_q, interpolation)) for i, key in enumerate(a.__dask_keys__()) ) name2 = "percentile-" + token dsk2 = { (name2, 0): ( merge_percentiles, q, [calc_q] * len(a.chunks[0]), sorted(dsk), interpolation, ) } dsk = merge(dsk, dsk2) graph = HighLevelGraph.from_collections(name2, dsk, dependencies=[a]) return Array(graph, name2, chunks=((len(q),),), meta=meta) def merge_percentiles(finalq, qs, vals, interpolation="lower", Ns=None): """Combine several percentile calculations of different data. Parameters ---------- finalq : numpy.array Percentiles to compute (must use same scale as ``qs``). qs : sequence of :class:`numpy.array`s Percentiles calculated on different sets of data. vals : sequence of :class:`numpy.array`s Resulting values associated with percentiles ``qs``. Ns : sequence of integers The number of data elements associated with each data set. interpolation : {'linear', 'lower', 'higher', 'midpoint', 'nearest'} Specify the type of interpolation to use to calculate final percentiles. For more information, see :func:`numpy.percentile`. Examples -------- >>> finalq = [10, 20, 30, 40, 50, 60, 70, 80] >>> qs = [[20, 40, 60, 80], [20, 40, 60, 80]] >>> vals = [np.array([1, 2, 3, 4]), np.array([10, 11, 12, 13])] >>> Ns = [100, 100] # Both original arrays had 100 elements >>> merge_percentiles(finalq, qs, vals, Ns=Ns) array([ 1, 2, 3, 4, 10, 11, 12, 13]) """ from .utils import array_safe, empty_like_safe if isinstance(finalq, Iterator): finalq = list(finalq) finalq = array_safe(finalq, like=finalq) qs = list(map(list, qs)) vals = list(vals) if Ns is None: vals, Ns = zip(*vals) Ns = list(Ns) L = list(zip(*[(q, val, N) for q, val, N in zip(qs, vals, Ns) if N])) if not L: raise ValueError("No non-trivial arrays found") qs, vals, Ns = L # TODO: Perform this check above in percentile once dtype checking is easy # Here we silently change meaning if vals[0].dtype.name == "category": result = merge_percentiles( finalq, qs, [v.codes for v in vals], interpolation, Ns ) import pandas as pd return pd.Categorical.from_codes(result, vals[0].categories, vals[0].ordered) if not np.issubdtype(vals[0].dtype, np.number): interpolation = "nearest" if len(vals) != len(qs) or len(Ns) != len(qs): raise ValueError("qs, vals, and Ns parameters must be the same length") # transform qs and Ns into number of observations between percentiles counts = [] for q, N in zip(qs, Ns): count = empty_like_safe(finalq, shape=len(q)) count[1:] = np.diff(array_safe(q, like=q[0])) count[0] = q[0] count *= N counts.append(count) # Sort by calculated percentile values, then number of observations. combined_vals = np.concatenate(vals) combined_counts = array_safe(np.concatenate(counts), like=combined_vals) sort_order = np.argsort(combined_vals) combined_vals = np.take(combined_vals, sort_order) combined_counts = np.take(combined_counts, sort_order) # percentile-like, but scaled by total number of observations combined_q = np.cumsum(combined_counts) # rescale finalq percentiles to match combined_q finalq = array_safe(finalq, like=combined_vals) desired_q = finalq * sum(Ns) # the behavior of different interpolation methods should be # investigated further. if interpolation == "linear": rv = np.interp(desired_q, combined_q, combined_vals) else: left = np.searchsorted(combined_q, desired_q, side="left") right = np.searchsorted(combined_q, desired_q, side="right") - 1 np.minimum(left, len(combined_vals) - 1, left) # don't exceed max index lower = np.minimum(left, right) upper = np.maximum(left, right) if interpolation == "lower": rv = combined_vals[lower] elif interpolation == "higher": rv = combined_vals[upper] elif interpolation == "midpoint": rv = 0.5 * (combined_vals[lower] + combined_vals[upper]) elif interpolation == "nearest": lower_residual = np.abs(combined_q[lower] - desired_q) upper_residual = np.abs(combined_q[upper] - desired_q) mask = lower_residual > upper_residual index = lower # alias; we no longer need lower index[mask] = upper[mask] rv = combined_vals[index] else: raise ValueError( "interpolation can only be 'linear', 'lower', " "'higher', 'midpoint', or 'nearest'" ) return rv