text: """
  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)]
  