from random import uniform, sample
def order(x, NoneIsLast = True, decreasing = False):
"""
Returns the ordering of the elements of x. The list
[ x[j] for j in order(x) ] is a sorted version of x.
Missing values in x are indicated by None. If NoneIsLast is true,
then missing values are ordered to be at the end.
Otherwise, they are ordered at the beginning.
"""
omitNone = False
if NoneIsLast == None:
NoneIsLast = True
omitNone = True
n = len(x)
ix = range(n)
if None not in x:
ix.sort(reverse = decreasing, key = lambda j : x[j])
else:
# Handle None values properly.
def key(i, x = x):
elem = x[i]
# Valid values are True or False only.
if decreasing == NoneIsLast:
return not(elem is None), elem
else:
return elem is None, elem
ix = range(n)
ix.sort(key=key, reverse=decreasing)
if omitNone:
n = len(x)
for i in range(n-1, -1, -1):
if x[ix[i]] == None:
n -= 1
return ix[:n]
return ix
def rank(x, NoneIsLast=True, decreasing = False, ties = "first"):
"""
Returns the ranking of the elements of x. The position of the first
element in the original vector is rank[0] in the sorted vector.
Missing values are indicated by None. Calls the order() function.
Ties are NOT averaged by default. Choices are:
"first" "average" "min" "max" "random" "average"
"""
omitNone = False
if NoneIsLast == None:
NoneIsLast = True
omitNone = True
O = order(x, NoneIsLast = NoneIsLast, decreasing = decreasing)
R = O[:]
n = len(O)
for i in range(n):
R[O[i]] = i
if ties == "first" or ties not in ["first", "average", "min", "max", "random"]:
return R
blocks = []
isnewblock = True
newblock = []
for i in range(1,n) :
if x[O[i]] == x[O[i-1]]:
if i-1 not in newblock:
newblock.append(i-1)
newblock.append(i)
else:
if len(newblock) > 0:
blocks.append(newblock)
newblock = []
if len(newblock) > 0:
blocks.append(newblock)
for i, block in enumerate(blocks):
# Don't process blocks of None values.
if x[O[block[0]]] == None:
continue
if ties == "average":
s = 0.0
for j in block:
s += j
s /= float(len(block))
for j in block:
R[O[j]] = s
elif ties == "min":
s = min(block)
for j in block:
R[O[j]] = s
elif ties == "max":
s =max(block)
for j in block:
R[O[j]] = s
elif ties == "random":
s = sample([O[i] for i in block], len(block))
for i,j in enumerate(block):
R[O[j]] = s[i]
else:
for i,j in enumerate(block):
R[O[j]] = j
if omitNone:
R = [ R[j] for j in range(n) if x[j] != None]
return R
if __name__ == "__main__":
"""
Output when run from the command line:
vector [5, None, None, 6, 2, 3, 2, 0, 5, 5, 1, None]
order(NoneIsLast= True ,decreasing= True ) [3, 0, 8, 9, 5, 4, 6, 10, 7, 1, 2, 11]
rank(x, NoneIsLast= True ,decreasing= True ,ties= first ) [1, 9, 10, 0, 5, 4, 6, 8, 2, 3, 7, 11]
rank(x, NoneIsLast= True ,decreasing= True ,ties= average ) [2.0, 9, 10, 0, 5.5, 4, 5.5, 8, 2.0, 2.0, 7, 11]
rank(x, NoneIsLast= True ,decreasing= True ,ties= min ) [1, 9, 10, 0, 5, 4, 5, 8, 1, 1, 7, 11]
rank(x, NoneIsLast= True ,decreasing= True ,ties= max ) [3, 9, 10, 0, 6, 4, 6, 8, 3, 3, 7, 11]
rank(x, NoneIsLast= True ,decreasing= True ,ties= random ) [0, 9, 10, 0, 6, 4, 4, 8, 9, 8, 7, 11]
order(NoneIsLast= True ,decreasing= False ) [7, 10, 4, 6, 5, 0, 8, 9, 3, 1, 2, 11]
rank(x, NoneIsLast= True ,decreasing= False ,ties= first ) [5, 9, 10, 8, 2, 4, 3, 0, 6, 7, 1, 11]
rank(x, NoneIsLast= True ,decreasing= False ,ties= average ) [6.0, 9, 10, 8, 2.5, 4, 2.5, 0, 6.0, 6.0, 1, 11]
rank(x, NoneIsLast= True ,decreasing= False ,ties= min ) [5, 9, 10, 8, 2, 4, 2, 0, 5, 5, 1, 11]
rank(x, NoneIsLast= True ,decreasing= False ,ties= max ) [7, 9, 10, 8, 3, 4, 3, 0, 7, 7, 1, 11]
rank(x, NoneIsLast= True ,decreasing= False ,ties= random ) [0, 9, 10, 8, 6, 4, 4, 0, 8, 9, 1, 11]
order(NoneIsLast= False ,decreasing= True ) [1, 2, 11, 3, 0, 8, 9, 5, 4, 6, 10, 7]
rank(x, NoneIsLast= False ,decreasing= True ,ties= first ) [4, 0, 1, 3, 8, 7, 9, 11, 5, 6, 10, 2]
rank(x, NoneIsLast= False ,decreasing= True ,ties= average ) [5.0, 0, 1, 3, 8.5, 7, 8.5, 11, 5.0, 5.0, 10, 2]
rank(x, NoneIsLast= False ,decreasing= True ,ties= min ) [4, 0, 1, 3, 8, 7, 8, 11, 4, 4, 10, 2]
rank(x, NoneIsLast= False ,decreasing= True ,ties= max ) [6, 0, 1, 3, 9, 7, 9, 11, 6, 6, 10, 2]
rank(x, NoneIsLast= False ,decreasing= True ,ties= random ) [9, 0, 1, 3, 6, 7, 4, 11, 0, 8, 10, 2]
order(NoneIsLast= False ,decreasing= False ) [1, 2, 11, 7, 10, 4, 6, 5, 0, 8, 9, 3]
rank(x, NoneIsLast= False ,decreasing= False ,ties= first ) [8, 0, 1, 11, 5, 7, 6, 3, 9, 10, 4, 2]
rank(x, NoneIsLast= False ,decreasing= False ,ties= average ) [9.0, 0, 1, 11, 5.5, 7, 5.5, 3, 9.0, 9.0, 4, 2]
rank(x, NoneIsLast= False ,decreasing= False ,ties= min ) [8, 0, 1, 11, 5, 7, 5, 3, 8, 8, 4, 2]
rank(x, NoneIsLast= False ,decreasing= False ,ties= max ) [10, 0, 1, 11, 6, 7, 6, 3, 10, 10, 4, 2]
rank(x, NoneIsLast= False ,decreasing= False ,ties= random ) [9, 0, 1, 11, 4, 7, 6, 3, 0, 8, 4, 2]
order(NoneIsLast= None ,decreasing= True ) [3, 0, 8, 9, 5, 4, 6, 10, 7]
rank(x, NoneIsLast= None ,decreasing= True ,ties= first ) [1, 9, 10, 0, 5, 4, 6, 8, 2, 3, 7, 11]
rank(x, NoneIsLast= None ,decreasing= True ,ties= average ) [2.0, 0, 5.5, 4, 5.5, 8, 2.0, 2.0, 7]
rank(x, NoneIsLast= None ,decreasing= True ,ties= min ) [1, 0, 5, 4, 5, 8, 1, 1, 7]
rank(x, NoneIsLast= None ,decreasing= True ,ties= max ) [3, 0, 6, 4, 6, 8, 3, 3, 7]
rank(x, NoneIsLast= None ,decreasing= True ,ties= random ) [9, 0, 6, 4, 4, 8, 8, 0, 7]
order(NoneIsLast= None ,decreasing= False ) [7, 10, 4, 6, 5, 0, 8, 9, 3]
rank(x, NoneIsLast= None ,decreasing= False ,ties= first ) [5, 9, 10, 8, 2, 4, 3, 0, 6, 7, 1, 11]
rank(x, NoneIsLast= None ,decreasing= False ,ties= average ) [6.0, 8, 2.5, 4, 2.5, 0, 6.0, 6.0, 1]
rank(x, NoneIsLast= None ,decreasing= False ,ties= min ) [5, 8, 2, 4, 2, 0, 5, 5, 1]
rank(x, NoneIsLast= None ,decreasing= False ,ties= max ) [7, 8, 3, 4, 3, 0, 7, 7, 1]
rank(x, NoneIsLast= None ,decreasing= False ,ties= random ) [9, 8, 4, 4, 6, 0, 0, 8, 1]
"""
x = [5, None, None, 6, 2, 3, 2, 0, 5, 5, 1, None]
print "vector ", x
for NoneIsLast in [True, False, None]:
for decreasing in [True, False]:
O = order(x, NoneIsLast=NoneIsLast, decreasing=decreasing)
print "order(NoneIsLast=", NoneIsLast, ",decreasing=", decreasing, ")", O
for ties in ["first", "average", "min", "max", "random"]:
R = rank(x, NoneIsLast=NoneIsLast, decreasing=decreasing, ties=ties)
print "rank(x, NoneIsLast=", NoneIsLast, ",decreasing=", decreasing, ",ties=", ties, ")", R
print
print
