percentile.py 8.77 KB
 Kruyff,D.L.W. (Dylan) committed Aug 26, 2020 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 ``````from collections.abc import Iterator from functools import wraps from numbers import Number import numpy as np from tlz import merge, merge_sorted from .core import Array from ..base import tokenize from ..highlevelgraph import HighLevelGraph @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) return result.astype(a.dtype), 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"): `````` Kruyff,D.L.W. (Dylan) committed Sep 01, 2020 55 `````` """Approximate percentile of 1-D array `````` Kruyff,D.L.W. (Dylan) committed Aug 26, 2020 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 `````` 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 """ if not a.ndim == 1: raise NotImplementedError("Percentiles only implemented for 1-d arrays") if isinstance(q, Number): q = [q] q = np.array(q) token = tokenize(a, q, interpolation) dtype = a.dtype if np.issubdtype(dtype, np.integer): dtype = (np.array([], dtype=dtype) / 0.5).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: name = "percentile_chunk-" + token dsk = dict( ((name, i), (_percentile, key, q, interpolation)) for i, key in enumerate(a.__dask_keys__()) ) name2 = "percentile-" + token dsk2 = { (name2, 0): ( merge_percentiles, q, [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),),), dtype=dtype) def merge_percentiles(finalq, qs, vals, interpolation="lower", Ns=None): `````` Kruyff,D.L.W. (Dylan) committed Sep 01, 2020 153 `````` """Combine several percentile calculations of different data. `````` Kruyff,D.L.W. (Dylan) committed Aug 26, 2020 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 `````` 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]) """ if isinstance(finalq, Iterator): finalq = list(finalq) finalq = np.array(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 = np.empty(len(q)) count[1:] = np.diff(q) count[0] = q[0] count *= N counts.append(count) # Sort by calculated percentile values, then number of observations. # >95% of the time in this function is spent in `merge_sorted` below. # An alternative that uses numpy sort is shown. It is sometimes # comparable to, but typically slower than, `merge_sorted`. # # >>> A = np.concatenate(map(np.array, map(zip, vals, counts))) # >>> A.sort(0, kind='mergesort') combined_vals_counts = merge_sorted(*map(zip, vals, counts)) combined_vals, combined_counts = zip(*combined_vals_counts) combined_vals = np.array(combined_vals) combined_counts = np.array(combined_counts) # percentile-like, but scaled by total number of observations combined_q = np.cumsum(combined_counts) # rescale finalq percentiles to match combined_q 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``````