""" 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 : Module with 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 : Module with 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 : Module with 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 : Module with 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 : Module with a number of other functions for performing set operations on arrays. """ ar1 = nm.asarray( ar1 ) ar2 = nm.asarray( ar2 ) ar = nm.concatenate( (ar1, ar2 ) ) b1 = nm.zeros( ar1.shape, dtype = nm.int8 ) b2 = nm.ones( ar2.shape, dtype = nm.int8 ) tt = nm.concatenate( (b1, b2) ) # 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 : Module with 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 : Module with 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 )