path: root/numpy/lib/arraysetops.py

"""
Set operations for 1D numeric arrays based on sorting.

:Contains:
  ediff1d,
  unique1d,
  intersect1d,
  intersect1d_nu,
  setxor1d,
  setmember1d,
  union1d,
  setdiff1d

:Notes:

All functions work best with integer numerical arrays on input (e.g. indices).
For floating point arrays, innacurate results may appear due to usual round-off
and floating point comparison issues.

Except unique1d, union1d and intersect1d_nu, all functions expect inputs with
unique elements. Speed could be gained in some operations by an implementaion of
sort(), that can provide directly the permutation vectors, avoiding thus calls
to argsort().

Run _test_unique1d_speed() to compare performance of numpy.unique1d() and
numpy.unique() - it should be the same.

To do: Optionally return indices analogously to unique1d for all functions.

created:       01.11.2005
last revision: 07.01.2007

:Author: Robert Cimrman
"""
__all__ = ['ediff1d', 'unique1d', 'intersect1d', 'intersect1d_nu', 'setxor1d',
           'setmember1d', 'union1d', 'setdiff1d']

import time
import numpy as nm

def ediff1d(ary, to_end = None, to_begin = None):
    """The differences between consecutive elements of an array, possibly with
    prefixed and/or appended values.

    :Parameters:
      - `ary` : array
        This array will be flattened before the difference is taken.
      - `to_end` : number, optional
        If provided, this number will be tacked onto the end of the returned
        differences.
      - `to_begin` : number, optional
        If provided, this number will be taked onto the beginning of the
        returned differences.

    :Returns:
      - `ed` : array
        The differences. Loosely, this will be (ary[1:] - ary[:-1]).
    """
    ary = nm.asarray(ary).flat
    ed = ary[1:] - ary[:-1]
    arrays = [ed]
    if to_begin is not None:
        arrays.insert(0, to_begin)
    if to_end is not None:
        arrays.append(to_end)

    if len(arrays) != 1:
        # We'll save ourselves a copy of a potentially large array in the common
        # case where neither to_begin or to_end was given.
        ed = nm.hstack(arrays)

    return ed

def unique1d(ar1, return_index=False):
    """Find the unique elements of 1D array.

    Most of the other array set operations operate on the unique arrays
    generated by this function.

    :Parameters:
      - `ar1` : array
        This array will be flattened if it is not already 1D.
      - `return_index` : bool, optional
        If True, also return the indices against ar1 that result in the unique
        array.

    :Returns:
      - `unique` : array
        The unique values.
      - `unique_indices` : int array, optional
        The indices of the unique values. Only provided if return_index is True.

    :See also:
      numpy.lib.arraysetops has a number of other functions for performing set
      operations on arrays.
    """
    ar = nm.asarray(ar1).flatten()
    if ar.size == 0:
        if return_index: return nm.empty(0, nm.bool), ar
        else: return ar

    if return_index:
        perm = ar.argsort()
        aux = ar[perm]
        flag = nm.concatenate( ([True], aux[1:] != aux[:-1]) )
        return perm[flag], aux[flag]

    else:
        ar.sort()
        flag = nm.concatenate( ([True], ar[1:] != ar[:-1]) )
        return ar[flag]

def intersect1d( ar1, ar2 ):
    """Intersection of 1D arrays with unique elements.

    Use unique1d() to generate arrays with only unique elements to use as inputs
    to this function. Alternatively, use intersect1d_nu() which will find the
    unique values for you.

    :Parameters:
      - `ar1` : array
      - `ar2` : array

    :Returns:
      - `intersection` : array

    :See also:
      numpy.lib.arraysetops has a number of other functions for performing set
      operations on arrays.
    """
    aux = nm.concatenate((ar1,ar2))
    aux.sort()
    return aux[aux[1:] == aux[:-1]]

def intersect1d_nu( ar1, ar2 ):
    """Intersection of 1D arrays with any elements.

    The input arrays do not have unique elements like intersect1d() requires.

    :Parameters:
      - `ar1` : array
      - `ar2` : array

    :Returns:
      - `intersection` : array

    :See also:
      numpy.lib.arraysetops has a number of other functions for performing set
      operations on arrays.
    """
    # Might be faster than unique1d( intersect1d( ar1, ar2 ) )?
    aux = nm.concatenate((unique1d(ar1), unique1d(ar2)))
    aux.sort()
    return aux[aux[1:] == aux[:-1]]

def setxor1d( ar1, ar2 ):
    """Set exclusive-or of 1D arrays with unique elements.

    Use unique1d() to generate arrays with only unique elements to use as inputs
    to this function.

    :Parameters:
      - `ar1` : array
      - `ar2` : array

    :Returns:
      - `xor` : array
        The values that are only in one, but not both, of the input arrays.

    :See also:
      numpy.lib.arraysetops has a number of other functions for performing set
      operations on arrays.
    """
    aux = nm.concatenate((ar1, ar2))
    if aux.size == 0:
        return aux

    aux.sort()
#    flag = ediff1d( aux, to_end = 1, to_begin = 1 ) == 0
    flag = nm.concatenate( ([True], aux[1:] != aux[:-1], [True] ) )
#    flag2 = ediff1d( flag ) == 0
    flag2 = flag[1:] == flag[:-1]
    return aux[flag2]

def setmember1d( ar1, ar2 ):
    """Return a boolean array of shape of ar1 containing True where the elements
    of ar1 are in ar2 and False otherwise.

    Use unique1d() to generate arrays with only unique elements to use as inputs
    to this function.

    :Parameters:
      - `ar1` : array
      - `ar2` : array

    :Returns:
      - `mask` : bool array
        The values ar1[mask] are in ar2.

    :See also:
      numpy.lib.arraysetops has a number of other functions for performing set
      operations on arrays.
    """
    zlike = nm.zeros_like
    ar = nm.concatenate( (ar1, ar2 ) )
    tt = nm.concatenate( (zlike( ar1 ), zlike( ar2 ) + 1) )
    # 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.
    perm = ar.argsort(kind='mergesort')
    aux = ar[perm]
    aux2 = tt[perm]
#    flag = ediff1d( aux, 1 ) == 0
    flag = nm.concatenate( (aux[1:] == aux[:-1], [False] ) )

    ii = nm.where( flag * aux2 )[0]
    aux = perm[ii+1]
    perm[ii+1] = perm[ii]
    perm[ii] = aux

    indx = perm.argsort(kind='mergesort')[:len( ar1 )]

    return flag[indx]

def union1d( ar1, ar2 ):
    """Union of 1D arrays with unique elements.

    Use unique1d() to generate arrays with only unique elements to use as inputs
    to this function.

    :Parameters:
      - `ar1` : array
      - `ar2` : array

    :Returns:
      - `union` : array

    :See also:
      numpy.lib.arraysetops has a number of other functions for performing set
      operations on arrays.
    """
    return unique1d( nm.concatenate( (ar1, ar2) ) )

def setdiff1d( ar1, ar2 ):
    """Set difference of 1D arrays with unique elements.

    Use unique1d() to generate arrays with only unique elements to use as inputs
    to this function.

    :Parameters:
      - `ar1` : array
      - `ar2` : array

    :Returns:
      - `difference` : array
        The values in ar1 that are not in ar2.

    :See also:
      numpy.lib.arraysetops has a number of other functions for performing set
      operations on arrays.
    """
    aux = setmember1d(ar1,ar2)
    if aux.size == 0:
        return aux
    else:
        return nm.asarray(ar1)[aux == 0]

def _test_unique1d_speed( plot_results = False ):
#    exponents = nm.linspace( 2, 7, 9 )
    exponents = nm.linspace( 2, 7, 9 )
    ratios = []
    nItems = []
    dt1s = []
    dt2s = []
    for ii in exponents:

        nItem = 10 ** ii
        print 'using %d items:' % nItem
        a = nm.fix( nItem / 10 * nm.random.random( nItem ) )

        print 'unique:'
        tt = time.clock()
        b = nm.unique( a )
        dt1 = time.clock() - tt
        print dt1

        print 'unique1d:'
        tt = time.clock()
        c = unique1d( a )
        dt2 = time.clock() - tt
        print dt2


        if dt1 < 1e-8:
            ratio = 'ND'
        else:
            ratio = dt2 / dt1
        print 'ratio:', ratio
        print 'nUnique: %d == %d\n' % (len( b ), len( c ))

        nItems.append( nItem )
        ratios.append( ratio )
        dt1s.append( dt1 )
        dt2s.append( dt2 )

        assert nm.alltrue( b == c )

    print nItems
    print dt1s
    print dt2s
    print ratios

    if plot_results:
        import pylab

        def plotMe( fig, fun, nItems, dt1s, dt2s ):
            pylab.figure( fig )
            fun( nItems, dt1s, 'g-o', linewidth = 2, markersize = 8 )
            fun( nItems, dt2s, 'b-x', linewidth = 2, markersize = 8 )
            pylab.legend( ('unique', 'unique1d' ) )
            pylab.xlabel( 'nItem' )
            pylab.ylabel( 'time [s]' )

        plotMe( 1, pylab.loglog, nItems, dt1s, dt2s )
        plotMe( 2, pylab.plot, nItems, dt1s, dt2s )
        pylab.show()

if (__name__ == '__main__'):
    _test_unique1d_speed( plot_results = True )