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"""
Set operations for 1D numeric arrays based on sort() function.
Contains:
ediff1d,
unique1d,
intersect1d,
intersect1d_nu,
setxor1d,
setmember1d,
union1d,
setdiff1d
Concerning the speed, test_unique1d_speed() reveals that up to 10000000
elements unique1d() is about 10 times faster than the standard dictionary-based
numpy.unique().
Limitations: 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().
To do: Optionally return indices analogously to unique1d for all functions.
Author: Robert Cimrman
"""
# 02.11.2005, c
import time
import numpy
##
# 03.11.2005, c
def ediff1d( ar1, toEnd = None, toBegin = None ):
"""Array difference with prefixed and/or appended value."""
dar1 = ar1[1:] - ar1[:-1]
if toEnd and toBegin:
shape = (ar1.shape[0] + 1,) + ar1.shape[1:]
ed = numpy.empty( shape, dtype = ar1.dtype )
ed[0], ed[-1] = toBegin, toEnd
ed[1:-1] = dar1
elif toEnd:
ed = numpy.empty( ar1.shape, dtype = ar1.dtype )
ed[-1] = toEnd
ed[:-1] = dar1
elif toBegin:
ed = numpy.empty( ar1.shape, dtype = ar1.dtype )
ed[0] = toBegin
ed[1:] = dar1
else:
ed = dar1
return ed
##
# 01.11.2005, c
# 02.11.2005
def unique1d( ar1, retIndx = False ):
"""Unique elements of 1D array. When retIndx is True, return also the
indices indx such that ar1[indx] is the resulting array of unique
elements."""
ar = numpy.array( ar1 ).ravel()
if retIndx:
perm = numpy.argsort( ar )
aux = numpy.take( ar, perm, axis=0)
flag = ediff1d( aux, 1 ) != 0
return numpy.compress( flag, perm ,axis=-1), numpy.compress( flag, aux ,axis=-1)
else:
aux = numpy.sort( ar )
return numpy.compress( ediff1d( aux, 1 ) != 0, aux ,axis=-1)
##
# 01.11.2005, c
def intersect1d( ar1, ar2 ):
"""Intersection of 1D arrays with unique elements."""
aux = numpy.sort( numpy.concatenate( (ar1, ar2 ) ) )
return numpy.compress( (aux[1:] - aux[:-1]) == 0, aux ,axis=-1)
##
# 01.11.2005, c
def intersect1d_nu( ar1, ar2 ):
"""Intersection of 1D arrays with any elements."""
# Might be faster then unique1d( intersect1d( ar1, ar2 ) )?
aux = numpy.sort( numpy.concatenate( (unique1d( ar1 ),
unique1d( ar2 )) ) )
return numpy.compress( (aux[1:] - aux[:-1]) == 0, aux ,axis=-1)
##
# 01.11.2005, c
def setxor1d( ar1, ar2 ):
"""Set exclusive-or of 1D arrays with unique elements."""
aux = numpy.sort( numpy.concatenate( (ar1, ar2 ) ) )
flag = ediff1d( aux, toEnd = 1, toBegin = 1 ) == 0
flag2 = ediff1d( flag, 0 ) == 0
return numpy.compress( flag2, aux ,axis=-1)
##
# 03.11.2005, c
# 05.01.2006
def setmember1d( ar1, ar2 ):
"""Return an array of shape of ar1 containing 1 where the elements of
ar1 are in ar2 and 0 otherwise."""
ar = numpy.concatenate( (ar1, ar2 ) )
tt = numpy.concatenate( (numpy.zeros_like( ar1 ),
numpy.zeros_like( ar2 ) + 1) )
perm = numpy.argsort( ar )
aux = numpy.take( ar, perm, 0)
aux2 = numpy.take( tt, perm, 0 )
flag = ediff1d( aux, 1 ) == 0
ii = numpy.where( flag * aux2 )
aux = perm[ii+1]
perm[ii+1] = perm[ii]
perm[ii] = aux
indx = numpy.argsort( perm )[:len( ar1 )]
return numpy.take( flag, indx, 0 )
##
# 03.11.2005, c
def union1d( ar1, ar2 ):
"""Union of 1D arrays with unique elements."""
return unique1d( numpy.concatenate( (ar1, ar2) ) )
##
# 03.11.2005, c
def setdiff1d( ar1, ar2 ):
"""Set difference of 1D arrays with unique elements."""
aux = setmember1d( ar1, ar2 )
return numpy.compress( aux == 0, ar1 ,axis=-1)
##
# 03.11.2005, c
def test_unique1d():
a = numpy.array( [5, 7, 1, 2, 1, 5, 7] )
ec = numpy.array( [1, 2, 5, 7] )
c = unique1d( a )
assert numpy.alltrue( c == ec ,axis=0)
##
# 03.11.2005, c
def test_intersect1d():
a = numpy.array( [5, 7, 1, 2] )
b = numpy.array( [2, 4, 3, 1, 5] )
ec = numpy.array( [1, 2, 5] )
c = intersect1d( a, b )
assert numpy.alltrue( c == ec ,axis=0)
##
# 03.11.2005, c
def test_intersect1d_nu():
a = numpy.array( [5, 5, 7, 1, 2] )
b = numpy.array( [2, 1, 4, 3, 3, 1, 5] )
ec = numpy.array( [1, 2, 5] )
c = intersect1d_nu( a, b )
assert numpy.alltrue( c == ec ,axis=0)
##
# 03.11.2005, c
def test_setxor1d():
a = numpy.array( [5, 7, 1, 2] )
b = numpy.array( [2, 4, 3, 1, 5] )
ec = numpy.array( [3, 4, 7] )
c = setxor1d( a, b )
assert numpy.alltrue( c == ec ,axis=0)
a = numpy.array( [1, 2, 3] )
b = numpy.array( [6, 5, 4] )
ec = numpy.array( [1, 2, 3, 4, 5, 6] )
c = setxor1d( a, b )
assert numpy.alltrue( c == ec ,axis=0)
a = numpy.array( [1, 8, 2, 3] )
b = numpy.array( [6, 5, 4, 8] )
ec = numpy.array( [1, 2, 3, 4, 5, 6] )
c = setxor1d( a, b )
assert numpy.alltrue( c == ec ,axis=0)
##
# 03.11.2005, c
def test_setmember1d():
a = numpy.array( [5, 7, 1, 2] )
b = numpy.array( [2, 4, 3, 1, 5] )
ec = numpy.array( [True, False, True, True] )
c = setmember1d( a, b )
assert numpy.alltrue( c == ec ,axis=0)
a[0] = 8
ec = numpy.array( [False, False, True, True] )
c = setmember1d( a, b )
assert numpy.alltrue( c == ec ,axis=0)
a[0], a[3] = 4, 8
ec = numpy.array( [True, False, True, False] )
c = setmember1d( a, b )
assert numpy.alltrue( c == ec ,axis=0)
##
# 03.11.2005, c
def test_union1d():
a = numpy.array( [5, 4, 7, 1, 2] )
b = numpy.array( [2, 4, 3, 3, 2, 1, 5] )
ec = numpy.array( [1, 2, 3, 4, 5, 7] )
c = union1d( a, b )
assert numpy.alltrue( c == ec ,axis=0)
##
# 03.11.2005, c
def test_setdiff1d():
a = numpy.array( [6, 5, 4, 7, 1, 2] )
b = numpy.array( [2, 4, 3, 3, 2, 1, 5] )
ec = numpy.array( [6, 7] )
c = setdiff1d( a, b )
assert numpy.alltrue( c == ec ,axis=0)
##
# 03.11.2005, c
def test_manyways():
nItem = 100
a = numpy.fix( nItem / 10 * numpy.random.random( nItem ) )
b = numpy.fix( nItem / 10 * numpy.random.random( nItem ) )
c1 = intersect1d_nu( a, b )
c2 = unique1d( intersect1d( a, b ) )
assert numpy.alltrue( c1 == c2 ,axis=0)
a = numpy.array( [5, 7, 1, 2, 8] )
b = numpy.array( [9, 8, 2, 4, 3, 1, 5] )
c1 = setxor1d( a, b )
aux1 = intersect1d( a, b )
aux2 = union1d( a, b )
c2 = setdiff1d( aux2, aux1 )
assert numpy.alltrue( c1 == c2 ,axis=0)
##
# 02.11.2005, c
def test_unique1d_speed( plotResults = False ):
# exponents = numpy.linspace( 2, 7, 9 )
exponents = numpy.linspace( 2, 6, 9 )
ratios = []
nItems = []
dt1s = []
dt2s = []
for ii in exponents:
nItem = 10 ** ii
print 'using %d items:' % nItem
a = numpy.fix( nItem / 10 * numpy.random.random( nItem ) )
print 'dictionary:'
tt = time.clock()
b = numpy.unique( a )
dt1 = time.clock() - tt
print dt1
print 'array:'
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 numpy.alltrue( b == c ,axis=0)
print nItems
print dt1s
print dt2s
print ratios
if plotResults:
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( ('dictionary', 'array' ) )
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()
test_intersect1d()
test_intersect1d_nu()
test_setxor1d()
test_setmember1d()
test_union1d()
test_setdiff1d()
test_manyways()
test_unique1d_speed( plotResults = True )
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