788 lines
24 KiB
Python
788 lines
24 KiB
Python
"""
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Set operations for arrays based on sorting.
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:Contains:
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unique,
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isin,
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ediff1d,
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intersect1d,
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setxor1d,
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in1d,
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union1d,
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setdiff1d
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:Notes:
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For floating point arrays, inaccurate results may appear due to usual round-off
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and floating point comparison issues.
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Speed could be gained in some operations by an implementation of
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sort(), that can provide directly the permutation vectors, avoiding
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thus calls to argsort().
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To do: Optionally return indices analogously to unique for all functions.
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:Author: Robert Cimrman
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"""
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from __future__ import division, absolute_import, print_function
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import functools
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import numpy as np
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from numpy.core import overrides
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array_function_dispatch = functools.partial(
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overrides.array_function_dispatch, module='numpy')
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__all__ = [
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'ediff1d', 'intersect1d', 'setxor1d', 'union1d', 'setdiff1d', 'unique',
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'in1d', 'isin'
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]
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def _ediff1d_dispatcher(ary, to_end=None, to_begin=None):
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return (ary, to_end, to_begin)
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@array_function_dispatch(_ediff1d_dispatcher)
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def ediff1d(ary, to_end=None, to_begin=None):
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"""
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The differences between consecutive elements of an array.
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Parameters
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----------
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ary : array_like
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If necessary, will be flattened before the differences are taken.
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to_end : array_like, optional
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Number(s) to append at the end of the returned differences.
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to_begin : array_like, optional
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Number(s) to prepend at the beginning of the returned differences.
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Returns
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-------
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ediff1d : ndarray
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The differences. Loosely, this is ``ary.flat[1:] - ary.flat[:-1]``.
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See Also
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--------
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diff, gradient
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Notes
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-----
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When applied to masked arrays, this function drops the mask information
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if the `to_begin` and/or `to_end` parameters are used.
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Examples
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--------
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>>> x = np.array([1, 2, 4, 7, 0])
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>>> np.ediff1d(x)
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array([ 1, 2, 3, -7])
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>>> np.ediff1d(x, to_begin=-99, to_end=np.array([88, 99]))
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array([-99, 1, 2, ..., -7, 88, 99])
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The returned array is always 1D.
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>>> y = [[1, 2, 4], [1, 6, 24]]
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>>> np.ediff1d(y)
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array([ 1, 2, -3, 5, 18])
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"""
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# force a 1d array
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ary = np.asanyarray(ary).ravel()
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# enforce propagation of the dtype of input
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# ary to returned result
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dtype_req = ary.dtype
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# fast track default case
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if to_begin is None and to_end is None:
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return ary[1:] - ary[:-1]
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if to_begin is None:
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l_begin = 0
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else:
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_to_begin = np.asanyarray(to_begin, dtype=dtype_req)
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if not np.all(_to_begin == to_begin):
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raise ValueError("cannot convert 'to_begin' to array with dtype "
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"'%r' as required for input ary" % dtype_req)
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to_begin = _to_begin.ravel()
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l_begin = len(to_begin)
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if to_end is None:
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l_end = 0
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else:
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_to_end = np.asanyarray(to_end, dtype=dtype_req)
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# check that casting has not overflowed
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if not np.all(_to_end == to_end):
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raise ValueError("cannot convert 'to_end' to array with dtype "
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"'%r' as required for input ary" % dtype_req)
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to_end = _to_end.ravel()
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l_end = len(to_end)
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# do the calculation in place and copy to_begin and to_end
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l_diff = max(len(ary) - 1, 0)
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result = np.empty(l_diff + l_begin + l_end, dtype=ary.dtype)
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result = ary.__array_wrap__(result)
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if l_begin > 0:
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result[:l_begin] = to_begin
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if l_end > 0:
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result[l_begin + l_diff:] = to_end
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np.subtract(ary[1:], ary[:-1], result[l_begin:l_begin + l_diff])
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return result
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def _unpack_tuple(x):
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""" Unpacks one-element tuples for use as return values """
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if len(x) == 1:
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return x[0]
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else:
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return x
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def _unique_dispatcher(ar, return_index=None, return_inverse=None,
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return_counts=None, axis=None):
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return (ar,)
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@array_function_dispatch(_unique_dispatcher)
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def unique(ar, return_index=False, return_inverse=False,
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return_counts=False, axis=None):
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"""
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Find the unique elements of an array.
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Returns the sorted unique elements of an array. There are three optional
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outputs in addition to the unique elements:
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* the indices of the input array that give the unique values
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* the indices of the unique array that reconstruct the input array
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* the number of times each unique value comes up in the input array
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Parameters
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----------
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ar : array_like
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Input array. Unless `axis` is specified, this will be flattened if it
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is not already 1-D.
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return_index : bool, optional
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If True, also return the indices of `ar` (along the specified axis,
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if provided, or in the flattened array) that result in the unique array.
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return_inverse : bool, optional
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If True, also return the indices of the unique array (for the specified
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axis, if provided) that can be used to reconstruct `ar`.
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return_counts : bool, optional
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If True, also return the number of times each unique item appears
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in `ar`.
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.. versionadded:: 1.9.0
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axis : int or None, optional
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The axis to operate on. If None, `ar` will be flattened. If an integer,
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the subarrays indexed by the given axis will be flattened and treated
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as the elements of a 1-D array with the dimension of the given axis,
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see the notes for more details. Object arrays or structured arrays
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that contain objects are not supported if the `axis` kwarg is used. The
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default is None.
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.. versionadded:: 1.13.0
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Returns
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-------
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unique : ndarray
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The sorted unique values.
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unique_indices : ndarray, optional
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The indices of the first occurrences of the unique values in the
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original array. Only provided if `return_index` is True.
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unique_inverse : ndarray, optional
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The indices to reconstruct the original array from the
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unique array. Only provided if `return_inverse` is True.
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unique_counts : ndarray, optional
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The number of times each of the unique values comes up in the
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original array. Only provided if `return_counts` is True.
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.. versionadded:: 1.9.0
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See Also
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--------
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numpy.lib.arraysetops : Module with a number of other functions for
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performing set operations on arrays.
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Notes
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-----
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When an axis is specified the subarrays indexed by the axis are sorted.
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This is done by making the specified axis the first dimension of the array
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and then flattening the subarrays in C order. The flattened subarrays are
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then viewed as a structured type with each element given a label, with the
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effect that we end up with a 1-D array of structured types that can be
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treated in the same way as any other 1-D array. The result is that the
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flattened subarrays are sorted in lexicographic order starting with the
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first element.
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Examples
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--------
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>>> np.unique([1, 1, 2, 2, 3, 3])
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array([1, 2, 3])
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>>> a = np.array([[1, 1], [2, 3]])
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>>> np.unique(a)
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array([1, 2, 3])
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Return the unique rows of a 2D array
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>>> a = np.array([[1, 0, 0], [1, 0, 0], [2, 3, 4]])
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>>> np.unique(a, axis=0)
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array([[1, 0, 0], [2, 3, 4]])
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Return the indices of the original array that give the unique values:
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>>> a = np.array(['a', 'b', 'b', 'c', 'a'])
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>>> u, indices = np.unique(a, return_index=True)
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>>> u
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array(['a', 'b', 'c'], dtype='<U1')
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>>> indices
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array([0, 1, 3])
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>>> a[indices]
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array(['a', 'b', 'c'], dtype='<U1')
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Reconstruct the input array from the unique values:
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>>> a = np.array([1, 2, 6, 4, 2, 3, 2])
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>>> u, indices = np.unique(a, return_inverse=True)
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>>> u
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array([1, 2, 3, 4, 6])
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>>> indices
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array([0, 1, 4, ..., 1, 2, 1])
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>>> u[indices]
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array([1, 2, 6, ..., 2, 3, 2])
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"""
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ar = np.asanyarray(ar)
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if axis is None:
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ret = _unique1d(ar, return_index, return_inverse, return_counts)
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return _unpack_tuple(ret)
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# axis was specified and not None
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try:
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ar = np.swapaxes(ar, axis, 0)
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except np.AxisError:
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# this removes the "axis1" or "axis2" prefix from the error message
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raise np.AxisError(axis, ar.ndim)
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# Must reshape to a contiguous 2D array for this to work...
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orig_shape, orig_dtype = ar.shape, ar.dtype
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ar = ar.reshape(orig_shape[0], -1)
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ar = np.ascontiguousarray(ar)
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dtype = [('f{i}'.format(i=i), ar.dtype) for i in range(ar.shape[1])]
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try:
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consolidated = ar.view(dtype)
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except TypeError:
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# There's no good way to do this for object arrays, etc...
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msg = 'The axis argument to unique is not supported for dtype {dt}'
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raise TypeError(msg.format(dt=ar.dtype))
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def reshape_uniq(uniq):
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uniq = uniq.view(orig_dtype)
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uniq = uniq.reshape(-1, *orig_shape[1:])
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uniq = np.swapaxes(uniq, 0, axis)
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return uniq
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output = _unique1d(consolidated, return_index,
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return_inverse, return_counts)
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output = (reshape_uniq(output[0]),) + output[1:]
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return _unpack_tuple(output)
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def _unique1d(ar, return_index=False, return_inverse=False,
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return_counts=False):
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"""
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Find the unique elements of an array, ignoring shape.
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"""
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ar = np.asanyarray(ar).flatten()
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optional_indices = return_index or return_inverse
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if optional_indices:
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perm = ar.argsort(kind='mergesort' if return_index else 'quicksort')
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aux = ar[perm]
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else:
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ar.sort()
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aux = ar
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mask = np.empty(aux.shape, dtype=np.bool_)
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mask[:1] = True
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mask[1:] = aux[1:] != aux[:-1]
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ret = (aux[mask],)
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if return_index:
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ret += (perm[mask],)
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if return_inverse:
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imask = np.cumsum(mask) - 1
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inv_idx = np.empty(mask.shape, dtype=np.intp)
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inv_idx[perm] = imask
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ret += (inv_idx,)
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if return_counts:
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idx = np.concatenate(np.nonzero(mask) + ([mask.size],))
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ret += (np.diff(idx),)
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return ret
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def _intersect1d_dispatcher(
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ar1, ar2, assume_unique=None, return_indices=None):
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return (ar1, ar2)
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@array_function_dispatch(_intersect1d_dispatcher)
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def intersect1d(ar1, ar2, assume_unique=False, return_indices=False):
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"""
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Find the intersection of two arrays.
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Return the sorted, unique values that are in both of the input arrays.
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Parameters
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----------
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ar1, ar2 : array_like
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Input arrays. Will be flattened if not already 1D.
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assume_unique : bool
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If True, the input arrays are both assumed to be unique, which
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can speed up the calculation. Default is False.
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return_indices : bool
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If True, the indices which correspond to the intersection of the two
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arrays are returned. The first instance of a value is used if there are
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multiple. Default is False.
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.. versionadded:: 1.15.0
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Returns
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-------
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intersect1d : ndarray
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Sorted 1D array of common and unique elements.
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comm1 : ndarray
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The indices of the first occurrences of the common values in `ar1`.
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Only provided if `return_indices` is True.
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comm2 : ndarray
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The indices of the first occurrences of the common values in `ar2`.
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Only provided if `return_indices` is True.
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See Also
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--------
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numpy.lib.arraysetops : Module with a number of other functions for
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performing set operations on arrays.
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Examples
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--------
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>>> np.intersect1d([1, 3, 4, 3], [3, 1, 2, 1])
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array([1, 3])
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To intersect more than two arrays, use functools.reduce:
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>>> from functools import reduce
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>>> reduce(np.intersect1d, ([1, 3, 4, 3], [3, 1, 2, 1], [6, 3, 4, 2]))
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array([3])
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To return the indices of the values common to the input arrays
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along with the intersected values:
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>>> x = np.array([1, 1, 2, 3, 4])
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>>> y = np.array([2, 1, 4, 6])
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>>> xy, x_ind, y_ind = np.intersect1d(x, y, return_indices=True)
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>>> x_ind, y_ind
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(array([0, 2, 4]), array([1, 0, 2]))
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>>> xy, x[x_ind], y[y_ind]
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(array([1, 2, 4]), array([1, 2, 4]), array([1, 2, 4]))
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"""
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ar1 = np.asanyarray(ar1)
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ar2 = np.asanyarray(ar2)
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if not assume_unique:
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if return_indices:
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ar1, ind1 = unique(ar1, return_index=True)
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ar2, ind2 = unique(ar2, return_index=True)
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else:
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ar1 = unique(ar1)
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ar2 = unique(ar2)
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else:
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ar1 = ar1.ravel()
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ar2 = ar2.ravel()
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aux = np.concatenate((ar1, ar2))
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if return_indices:
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aux_sort_indices = np.argsort(aux, kind='mergesort')
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aux = aux[aux_sort_indices]
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else:
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aux.sort()
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mask = aux[1:] == aux[:-1]
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int1d = aux[:-1][mask]
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if return_indices:
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ar1_indices = aux_sort_indices[:-1][mask]
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ar2_indices = aux_sort_indices[1:][mask] - ar1.size
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if not assume_unique:
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ar1_indices = ind1[ar1_indices]
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ar2_indices = ind2[ar2_indices]
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return int1d, ar1_indices, ar2_indices
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else:
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return int1d
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def _setxor1d_dispatcher(ar1, ar2, assume_unique=None):
|
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return (ar1, ar2)
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@array_function_dispatch(_setxor1d_dispatcher)
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def setxor1d(ar1, ar2, assume_unique=False):
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"""
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Find the set exclusive-or of two arrays.
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Return the sorted, unique values that are in only one (not both) of the
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input arrays.
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Parameters
|
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----------
|
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ar1, ar2 : array_like
|
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Input arrays.
|
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assume_unique : bool
|
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If True, the input arrays are both assumed to be unique, which
|
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can speed up the calculation. Default is False.
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|
|
Returns
|
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-------
|
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setxor1d : ndarray
|
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Sorted 1D array of unique values that are in only one of the input
|
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arrays.
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|
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Examples
|
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--------
|
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>>> a = np.array([1, 2, 3, 2, 4])
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>>> b = np.array([2, 3, 5, 7, 5])
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>>> np.setxor1d(a,b)
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array([1, 4, 5, 7])
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"""
|
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if not assume_unique:
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ar1 = unique(ar1)
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ar2 = unique(ar2)
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aux = np.concatenate((ar1, ar2))
|
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if aux.size == 0:
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return aux
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aux.sort()
|
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flag = np.concatenate(([True], aux[1:] != aux[:-1], [True]))
|
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return aux[flag[1:] & flag[:-1]]
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|
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|
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def _in1d_dispatcher(ar1, ar2, assume_unique=None, invert=None):
|
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return (ar1, ar2)
|
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|
|
|
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@array_function_dispatch(_in1d_dispatcher)
|
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def in1d(ar1, ar2, assume_unique=False, invert=False):
|
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"""
|
|
Test whether each element of a 1-D array is also present in a second array.
|
|
|
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Returns a boolean array the same length as `ar1` that is True
|
|
where an element of `ar1` is in `ar2` and False otherwise.
|
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|
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We recommend using :func:`isin` instead of `in1d` for new code.
|
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|
|
Parameters
|
|
----------
|
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ar1 : (M,) array_like
|
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Input array.
|
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ar2 : array_like
|
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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))``.
|
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|
|
.. versionadded:: 1.8.0
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|
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Returns
|
|
-------
|
|
in1d : (M,) ndarray, bool
|
|
The values `ar1[in1d]` are in `ar2`.
|
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|
|
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
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python keyword `in`, for 1-D sequences. ``in1d(a, b)`` is roughly
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equivalent to ``np.array([item in b for item in a])``.
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However, this idea fails if `ar2` is a set, or similar (non-sequence)
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container: As ``ar2`` is converted to an array, in those cases
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``asarray(ar2)`` is an object array rather than the expected array of
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contained values.
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.. versionadded:: 1.4.0
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Examples
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--------
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>>> test = np.array([0, 1, 2, 5, 0])
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>>> states = [0, 2]
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>>> mask = np.in1d(test, states)
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>>> mask
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array([ True, False, True, False, True])
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>>> test[mask]
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array([0, 2, 0])
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>>> mask = np.in1d(test, states, invert=True)
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>>> mask
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array([False, True, False, True, False])
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>>> test[mask]
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array([1, 5])
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"""
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# Ravel both arrays, behavior for the first array could be different
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ar1 = np.asarray(ar1).ravel()
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ar2 = np.asarray(ar2).ravel()
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# Check if one of the arrays may contain arbitrary objects
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contains_object = ar1.dtype.hasobject or ar2.dtype.hasobject
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# This code is run when
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# a) the first condition is true, making the code significantly faster
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# b) the second condition is true (i.e. `ar1` or `ar2` may contain
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# arbitrary objects), since then sorting is not guaranteed to work
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if len(ar2) < 10 * len(ar1) ** 0.145 or contains_object:
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if invert:
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mask = np.ones(len(ar1), dtype=bool)
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for a in ar2:
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mask &= (ar1 != a)
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else:
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mask = np.zeros(len(ar1), dtype=bool)
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for a in ar2:
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mask |= (ar1 == a)
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return mask
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|
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# Otherwise use sorting
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if not assume_unique:
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ar1, rev_idx = np.unique(ar1, return_inverse=True)
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ar2 = np.unique(ar2)
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|
|
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ar = np.concatenate((ar1, ar2))
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# We need this to be a stable sort, so always use 'mergesort'
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# here. The values from the first array should always come before
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# the values from the second array.
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order = ar.argsort(kind='mergesort')
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sar = ar[order]
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if invert:
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bool_ar = (sar[1:] != sar[:-1])
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else:
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bool_ar = (sar[1:] == sar[:-1])
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flag = np.concatenate((bool_ar, [invert]))
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ret = np.empty(ar.shape, dtype=bool)
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ret[order] = flag
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if assume_unique:
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return ret[:len(ar1)]
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else:
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return ret[rev_idx]
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|
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def _isin_dispatcher(element, test_elements, assume_unique=None, invert=None):
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return (element, test_elements)
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|
|
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@array_function_dispatch(_isin_dispatcher)
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def isin(element, test_elements, assume_unique=False, invert=False):
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"""
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|
Calculates `element in test_elements`, broadcasting over `element` only.
|
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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
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Input array.
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|
test_elements : array_like
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|
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]])
|
|
>>> element[mask]
|
|
array([2, 4])
|
|
|
|
The indices of the matched values can be obtained with `nonzero`:
|
|
|
|
>>> np.nonzero(mask)
|
|
(array([0, 1]), array([1, 0]))
|
|
|
|
The test can also be inverted:
|
|
|
|
>>> mask = np.isin(element, test_elements, invert=True)
|
|
>>> mask
|
|
array([[ True, False],
|
|
[False, True]])
|
|
>>> 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]])
|
|
|
|
Casting the set to a list gives the expected result:
|
|
|
|
>>> np.isin(element, list(test_set))
|
|
array([[False, True],
|
|
[ True, False]])
|
|
"""
|
|
element = np.asarray(element)
|
|
return in1d(element, test_elements, assume_unique=assume_unique,
|
|
invert=invert).reshape(element.shape)
|
|
|
|
|
|
def _union1d_dispatcher(ar1, ar2):
|
|
return (ar1, ar2)
|
|
|
|
|
|
@array_function_dispatch(_union1d_dispatcher)
|
|
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), axis=None))
|
|
|
|
|
|
def _setdiff1d_dispatcher(ar1, ar2, assume_unique=None):
|
|
return (ar1, ar2)
|
|
|
|
|
|
@array_function_dispatch(_setdiff1d_dispatcher)
|
|
def setdiff1d(ar1, ar2, assume_unique=False):
|
|
"""
|
|
Find the set difference of two arrays.
|
|
|
|
Return the 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
|
|
1D array of values in `ar1` that are not in `ar2`. The result
|
|
is sorted when `assume_unique=False`, but otherwise only sorted
|
|
if the input is sorted.
|
|
|
|
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)]
|
|
|