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"""
Set operations for 1D numeric arrays based on sort() function.
Contains:
ediff1d,
unique1d,
intersect1d,
intersect1d_nu,
setxor1d,
setmember1d,
union1d,
setdiff1d
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.
Author: Robert Cimrman
created: 01.11.2005
last revision: 12.10.2006
"""
__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):
"""Array difference with prefixed and/or appended value.
See also: unique1d, intersect1d, intersect1d_nu, setxor1d,
setmember1d, union1d, setdiff1d
"""
ary = nm.asarray(ary).flat
ed = ary[1:] - ary[:-1]
if to_begin is not None:
if to_end is not None:
ed = nm.r_[to_begin, ed, to_end]
else:
ed = nm.insert(ed, 0, to_begin)
elif to_end is not None:
ed = nm.append(ed, to_end)
return ed
def unique1d(ar1, return_index=False):
"""Unique elements of 1D array. When return_index is True, return
also the indices indx such that ar1.flat[indx] is the resulting
array of unique elements.
See also: ediff1d, intersect1d, intersect1d_nu, setxor1d,
setmember1d, union1d, setdiff1d
"""
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.
See also: ediff1d, unique1d, intersect1d_nu, setxor1d,
setmember1d, union1d, setdiff1d
"""
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.
See also: ediff1d, unique1d, intersect1d, setxor1d,
setmember1d, union1d, setdiff1d
"""
# Might be faster then 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.
See also: ediff1d, unique1d, intersect1d, intersect1d_nu,
setmember1d, union1d, setdiff1d
"""
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 an array of shape of ar1 containing 1 where the elements of
ar1 are in ar2 and 0 otherwise.
See also: ediff1d, unique1d, intersect1d, intersect1d_nu, setxor1d,
union1d, setdiff1d
"""
zlike = nm.zeros_like
ar = nm.concatenate( (ar1, ar2 ) )
tt = nm.concatenate( (zlike( ar1 ), zlike( ar2 ) + 1) )
perm = ar.argsort()
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()[:len( ar1 )]
return flag[indx]
def union1d( ar1, ar2 ):
"""Union of 1D arrays with unique elements.
See also: ediff1d, unique1d, intersect1d, intersect1d_nu, setxor1d,
setmember1d, setdiff1d
"""
return unique1d( nm.concatenate( (ar1, ar2) ) )
def setdiff1d( ar1, ar2 ):
"""Set difference of 1D arrays with unique elements.
See also: ediff1d, unique1d, intersect1d, intersect1d_nu, setxor1d,
setmember1d, union1d
"""
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 )
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