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편집 파일: arraysetops.py

""" Set operations for arrays based on sorting. :Contains: unique, isin, ediff1d, intersect1d, setxor1d, in1d, union1d, setdiff1d :Notes: For floating point arrays, inaccurate results may appear due to usual round-off and floating point comparison issues. Speed could be gained in some operations by an implementation of sort(), that can provide directly the permutation vectors, avoiding thus calls to argsort(). To do: Optionally return indices analogously to unique for all functions. :Author: Robert Cimrman """ from __future__ import division, absolute_import, print_function import numpy as np __all__ = [ 'ediff1d', 'intersect1d', 'setxor1d', 'union1d', 'setdiff1d', 'unique', 'in1d', 'isin' ] def ediff1d(ary, to_end=None, to_begin=None): """ The differences between consecutive elements of an array. Parameters ---------- ary : array_like If necessary, will be flattened before the differences are taken. to_end : array_like, optional Number(s) to append at the end of the returned differences. to_begin : array_like, optional Number(s) to prepend at the beginning of the returned differences. Returns ------- ediff1d : ndarray The differences. Loosely, this is ``ary.flat[1:] - ary.flat[:-1]``. See Also -------- diff, gradient Notes ----- When applied to masked arrays, this function drops the mask information if the `to_begin` and/or `to_end` parameters are used. Examples -------- >>> x = np.array([1, 2, 4, 7, 0]) >>> np.ediff1d(x) array([ 1, 2, 3, -7]) >>> np.ediff1d(x, to_begin=-99, to_end=np.array([88, 99])) array([-99, 1, 2, 3, -7, 88, 99]) The returned array is always 1D. >>> y = [[1, 2, 4], [1, 6, 24]] >>> np.ediff1d(y) array([ 1, 2, -3, 5, 18]) """ # force a 1d array ary = np.asanyarray(ary).ravel() # fast track default case if to_begin is None and to_end is None: return ary[1:] - ary[:-1] if to_begin is None: l_begin = 0 else: to_begin = np.asanyarray(to_begin).ravel() l_begin = len(to_begin) if to_end is None: l_end = 0 else: to_end = np.asanyarray(to_end).ravel() l_end = len(to_end) # do the calculation in place and copy to_begin and to_end l_diff = max(len(ary) - 1, 0) result = np.empty(l_diff + l_begin + l_end, dtype=ary.dtype) result = ary.__array_wrap__(result) if l_begin > 0: result[:l_begin] = to_begin if l_end > 0: result[l_begin + l_diff:] = to_end np.subtract(ary[1:], ary[:-1], result[l_begin:l_begin + l_diff]) return result def unique(ar, return_index=False, return_inverse=False, return_counts=False, axis=None): """ Find the unique elements of an array. Returns the sorted unique elements of an array. There are three optional outputs in addition to the unique elements: the indices of the input array that give the unique values, the indices of the unique array that reconstruct the input array, and the number of times each unique value comes up in the input array. Parameters ---------- ar : array_like Input array. Unless `axis` is specified, this will be flattened if it is not already 1-D. return_index : bool, optional If True, also return the indices of `ar` (along the specified axis, if provided, or in the flattened array) that result in the unique array. return_inverse : bool, optional If True, also return the indices of the unique array (for the specified axis, if provided) that can be used to reconstruct `ar`. return_counts : bool, optional If True, also return the number of times each unique item appears in `ar`. .. versionadded:: 1.9.0 axis : int or None, optional The axis to operate on. If None, `ar` will be flattened beforehand. Otherwise, duplicate items will be removed along the provided axis, with all the other axes belonging to the each of the unique elements. Object arrays or structured arrays that contain objects are not supported if the `axis` kwarg is used. .. versionadded:: 1.13.0 Returns ------- unique : ndarray The sorted unique values. unique_indices : ndarray, optional The indices of the first occurrences of the unique values in the original array. Only provided if `return_index` is True. unique_inverse : ndarray, optional The indices to reconstruct the original array from the unique array. Only provided if `return_inverse` is True. unique_counts : ndarray, optional The number of times each of the unique values comes up in the original array. Only provided if `return_counts` is True. .. versionadded:: 1.9.0 See Also -------- numpy.lib.arraysetops : Module with a number of other functions for performing set operations on arrays. Examples -------- >>> np.unique([1, 1, 2, 2, 3, 3]) array([1, 2, 3]) >>> a = np.array([[1, 1], [2, 3]]) >>> np.unique(a) array([1, 2, 3]) Return the unique rows of a 2D array >>> a = np.array([[1, 0, 0], [1, 0, 0], [2, 3, 4]]) >>> np.unique(a, axis=0) array([[1, 0, 0], [2, 3, 4]]) Return the indices of the original array that give the unique values: >>> a = np.array(['a', 'b', 'b', 'c', 'a']) >>> u, indices = np.unique(a, return_index=True) >>> u array(['a', 'b', 'c'], dtype='|S1') >>> indices array([0, 1, 3]) >>> a[indices] array(['a', 'b', 'c'], dtype='|S1') Reconstruct the input array from the unique values: >>> a = np.array([1, 2, 6, 4, 2, 3, 2]) >>> u, indices = np.unique(a, return_inverse=True) >>> u array([1, 2, 3, 4, 6]) >>> indices array([0, 1, 4, 3, 1, 2, 1]) >>> u[indices] array([1, 2, 6, 4, 2, 3, 2]) """ ar = np.asanyarray(ar) if axis is None: return _unique1d(ar, return_index, return_inverse, return_counts) if not (-ar.ndim <= axis < ar.ndim): raise ValueError('Invalid axis kwarg specified for unique') ar = np.swapaxes(ar, axis, 0) orig_shape, orig_dtype = ar.shape, ar.dtype # Must reshape to a contiguous 2D array for this to work... ar = ar.reshape(orig_shape[0], -1) ar = np.ascontiguousarray(ar) if ar.dtype.char in (np.typecodes['AllInteger'] + np.typecodes['Datetime'] + 'S'): # Optimization: Creating a view of your data with a np.void data type of # size the number of bytes in a full row. Handles any type where items # have a unique binary representation, i.e. 0 is only 0, not +0 and -0. dtype = np.dtype((np.void, ar.dtype.itemsize * ar.shape[1])) else: dtype = [('f{i}'.format(i=i), ar.dtype) for i in range(ar.shape[1])] try: consolidated = ar.view(dtype) except TypeError: # There's no good way to do this for object arrays, etc... msg = 'The axis argument to unique is not supported for dtype {dt}' raise TypeError(msg.format(dt=ar.dtype)) def reshape_uniq(uniq): uniq = uniq.view(orig_dtype) uniq = uniq.reshape(-1, *orig_shape[1:]) uniq = np.swapaxes(uniq, 0, axis) return uniq output = _unique1d(consolidated, return_index, return_inverse, return_counts) if not (return_index or return_inverse or return_counts): return reshape_uniq(output) else: uniq = reshape_uniq(output[0]) return (uniq,) + output[1:] def _unique1d(ar, return_index=False, return_inverse=False, return_counts=False): """ Find the unique elements of an array, ignoring shape. """ ar = np.asanyarray(ar).flatten() optional_indices = return_index or return_inverse optional_returns = optional_indices or return_counts if ar.size == 0: if not optional_returns: ret = ar else: ret = (ar,) if return_index: ret += (np.empty(0, np.bool),) if return_inverse: ret += (np.empty(0, np.bool),) if return_counts: ret += (np.empty(0, np.intp),) return ret if optional_indices: perm = ar.argsort(kind='mergesort' if return_index else 'quicksort') aux = ar[perm] else: ar.sort() aux = ar flag = np.concatenate(([True], aux[1:] != aux[:-1])) if not optional_returns: ret = aux[flag] else: ret = (aux[flag],) if return_index: ret += (perm[flag],) if return_inverse: iflag = np.cumsum(flag) - 1 inv_idx = np.empty(ar.shape, dtype=np.intp) inv_idx[perm] = iflag ret += (inv_idx,) if return_counts: idx = np.concatenate(np.nonzero(flag) + ([ar.size],)) ret += (np.diff(idx),) return ret def intersect1d(ar1, ar2, assume_unique=False): """ Find the intersection of two arrays. Return the sorted, unique values that are in both of the input arrays. Parameters ---------- ar1, ar2 : array_like Input arrays. assume_unique : bool If True, the input arrays are both assumed to be unique, which can speed up the calculation. Default is False. Returns ------- intersect1d : ndarray Sorted 1D array of common and unique elements. See Also -------- numpy.lib.arraysetops : Module with a number of other functions for performing set operations on arrays. Examples -------- >>> np.intersect1d([1, 3, 4, 3], [3, 1, 2, 1]) array([1, 3]) To intersect more than two arrays, use functools.reduce: >>> from functools import reduce >>> reduce(np.intersect1d, ([1, 3, 4, 3], [3, 1, 2, 1], [6, 3, 4, 2])) array([3]) """ if not assume_unique: # Might be faster than unique( intersect1d( ar1, ar2 ) )? ar1 = unique(ar1) ar2 = unique(ar2) aux = np.concatenate((ar1, ar2)) aux.sort() return aux[:-1][aux[1:] == aux[:-1]] def setxor1d(ar1, ar2, assume_unique=False): """ Find the set exclusive-or of two arrays. Return the sorted, unique values that are in only one (not both) of the input arrays. Parameters ---------- ar1, ar2 : array_like Input arrays. assume_unique : bool If True, the input arrays are both assumed to be unique, which can speed up the calculation. Default is False. Returns ------- setxor1d : ndarray Sorted 1D array of unique values that are in only one of the input arrays. Examples -------- >>> a = np.array([1, 2, 3, 2, 4]) >>> b = np.array([2, 3, 5, 7, 5]) >>> np.setxor1d(a,b) array([1, 4, 5, 7]) """ if not assume_unique: ar1 = unique(ar1) ar2 = unique(ar2) aux = np.concatenate((ar1, ar2)) if aux.size == 0: return aux aux.sort() # flag = ediff1d( aux, to_end = 1, to_begin = 1 ) == 0 flag = np.concatenate(([True], aux[1:] != aux[:-1], [True])) # flag2 = ediff1d( flag ) == 0 flag2 = flag[1:] == flag[:-1] return aux[flag2] def in1d(ar1, ar2, assume_unique=False, invert=False): """ Test whether each element of a 1-D array is also present in a second array. Returns a boolean array the same length as `ar1` that is True where an element of `ar1` is in `ar2` and False otherwise. We recommend using :func:`isin` instead of `in1d` for new code. Parameters ---------- ar1 : (M,) array_like Input array. ar2 : array_like The values against which to test each value of `ar1`. assume_unique : bool, optional If True, the input arrays are both assumed to be unique, which can speed up the calculation. Default is False. invert : bool, optional If True, the values in the returned array are inverted (that is, False where an element of `ar1` is in `ar2` and True otherwise). Default is False. ``np.in1d(a, b, invert=True)`` is equivalent to (but is faster than) ``np.invert(in1d(a, b))``. .. versionadded:: 1.8.0 Returns ------- in1d : (M,) ndarray, bool The values `ar1[in1d]` are in `ar2`. See Also -------- isin : Version of this function that preserves the shape of ar1. numpy.lib.arraysetops : Module with a number of other functions for performing set operations on arrays. Notes ----- `in1d` can be considered as an element-wise function version of the python keyword `in`, for 1-D sequences. ``in1d(a, b)`` is roughly equivalent to ``np.array([item in b for item in a])``. However, this idea fails if `ar2` is a set, or similar (non-sequence) container: As ``ar2`` is converted to an array, in those cases ``asarray(ar2)`` is an object array rather than the expected array of contained values. .. versionadded:: 1.4.0 Examples -------- >>> test = np.array([0, 1, 2, 5, 0]) >>> states = [0, 2] >>> mask = np.in1d(test, states) >>> mask array([ True, False, True, False, True], dtype=bool) >>> test[mask] array([0, 2, 0]) >>> mask = np.in1d(test, states, invert=True) >>> mask array([False, True, False, True, False], dtype=bool) >>> test[mask] array([1, 5]) """ # Ravel both arrays, behavior for the first array could be different ar1 = np.asarray(ar1).ravel() ar2 = np.asarray(ar2).ravel() # This code is significantly faster when the condition is satisfied. if len(ar2) < 10 * len(ar1) ** 0.145: if invert: mask = np.ones(len(ar1), dtype=np.bool) for a in ar2: mask &= (ar1 != a) else: mask = np.zeros(len(ar1), dtype=np.bool) for a in ar2: mask |= (ar1 == a) return mask # Otherwise use sorting if not assume_unique: ar1, rev_idx = np.unique(ar1, return_inverse=True) ar2 = np.unique(ar2) ar = np.concatenate((ar1, ar2)) # We need this to be a stable sort, so always use 'mergesort' # here. The values from the first array should always come before # the values from the second array. order = ar.argsort(kind='mergesort') sar = ar[order] if invert: bool_ar = (sar[1:] != sar[:-1]) else: bool_ar = (sar[1:] == sar[:-1]) flag = np.concatenate((bool_ar, [invert])) ret = np.empty(ar.shape, dtype=bool) ret[order] = flag if assume_unique: return ret[:len(ar1)] else: return ret[rev_idx] def isin(element, test_elements, assume_unique=False, invert=False): """ Calculates `element in test_elements`, broadcasting over `element` only. Returns a boolean array of the same shape as `element` that is True where an element of `element` is in `test_elements` and False otherwise. Parameters ---------- element : array_like Input array. test_elements : array_like The values against which to test each value of `element`. This argument is flattened if it is an array or array_like. See notes for behavior with non-array-like parameters. assume_unique : bool, optional If True, the input arrays are both assumed to be unique, which can speed up the calculation. Default is False. invert : bool, optional If True, the values in the returned array are inverted, as if calculating `element not in test_elements`. Default is False. ``np.isin(a, b, invert=True)`` is equivalent to (but faster than) ``np.invert(np.isin(a, b))``. Returns ------- isin : ndarray, bool Has the same shape as `element`. The values `element[isin]` are in `test_elements`. See Also -------- in1d : Flattened version of this function. numpy.lib.arraysetops : Module with a number of other functions for performing set operations on arrays. Notes ----- `isin` is an element-wise function version of the python keyword `in`. ``isin(a, b)`` is roughly equivalent to ``np.array([item in b for item in a])`` if `a` and `b` are 1-D sequences. `element` and `test_elements` are converted to arrays if they are not already. If `test_elements` is a set (or other non-sequence collection) it will be converted to an object array with one element, rather than an array of the values contained in `test_elements`. This is a consequence of the `array` constructor's way of handling non-sequence collections. Converting the set to a list usually gives the desired behavior. .. versionadded:: 1.13.0 Examples -------- >>> element = 2*np.arange(4).reshape((2, 2)) >>> element array([[0, 2], [4, 6]]) >>> test_elements = [1, 2, 4, 8] >>> mask = np.isin(element, test_elements) >>> mask array([[ False, True], [ True, False]], dtype=bool) >>> element[mask] array([2, 4]) >>> mask = np.isin(element, test_elements, invert=True) >>> mask array([[ True, False], [ False, True]], dtype=bool) >>> element[mask] array([0, 6]) Because of how `array` handles sets, the following does not work as expected: >>> test_set = {1, 2, 4, 8} >>> np.isin(element, test_set) array([[ False, False], [ False, False]], dtype=bool) Casting the set to a list gives the expected result: >>> np.isin(element, list(test_set)) array([[ False, True], [ True, False]], dtype=bool) """ element = np.asarray(element) return in1d(element, test_elements, assume_unique=assume_unique, invert=invert).reshape(element.shape) def union1d(ar1, ar2): """ Find the union of two arrays. Return the unique, sorted array of values that are in either of the two input arrays. Parameters ---------- ar1, ar2 : array_like Input arrays. They are flattened if they are not already 1D. Returns ------- union1d : ndarray Unique, sorted union of the input arrays. See Also -------- numpy.lib.arraysetops : Module with a number of other functions for performing set operations on arrays. Examples -------- >>> np.union1d([-1, 0, 1], [-2, 0, 2]) array([-2, -1, 0, 1, 2]) To find the union of more than two arrays, use functools.reduce: >>> from functools import reduce >>> reduce(np.union1d, ([1, 3, 4, 3], [3, 1, 2, 1], [6, 3, 4, 2])) array([1, 2, 3, 4, 6]) """ return unique(np.concatenate((ar1, ar2))) def setdiff1d(ar1, ar2, assume_unique=False): """ Find the set difference of two arrays. Return the sorted, unique values in `ar1` that are not in `ar2`. Parameters ---------- ar1 : array_like Input array. ar2 : array_like Input comparison array. assume_unique : bool If True, the input arrays are both assumed to be unique, which can speed up the calculation. Default is False. Returns ------- setdiff1d : ndarray Sorted 1D array of values in `ar1` that are not in `ar2`. See Also -------- numpy.lib.arraysetops : Module with a number of other functions for performing set operations on arrays. Examples -------- >>> a = np.array([1, 2, 3, 2, 4, 1]) >>> b = np.array([3, 4, 5, 6]) >>> np.setdiff1d(a, b) array([1, 2]) """ if assume_unique: ar1 = np.asarray(ar1).ravel() else: ar1 = unique(ar1) ar2 = unique(ar2) return ar1[in1d(ar1, ar2, assume_unique=True, invert=True)]