def Bray_Curtis(original, test):
"""
Complement Bray and Curtis coefficient for interval or ratio data.
Lower boundary of Bray and Curtis coefficient represents complete
similarity (no difference).
Coefficient:
M{1 - S{sum}(abs((A + B)(i) - (A + C)(i))) /
(S{sum}((A + B)(i)) + S{sum}((A + C)(i)))}
@see: Bray JR and Curtis JT. 1957. An ordination of the upland
forest communities of S. Winconsin. Ecological Monographs 27:
325-349.
@param original: list of original data
@param test: list of data to test against original
@status: Tested function
@since: version 0.4
"""
if len(original) != len(test):
raise DistanceInputSizeError("Size (length) of inputs must be \
equal for Bray-Curtis distance")
return 1 - (Manhattan(original, test) / \
float(sum(original) + sum(test)))
def Manhattan(original, test):
"""
Manhattan coefficient for interval or ratio data.
Coefficient: M{S{sum}(abs((A + B)(i) - (A + C)(i)))}
Manhattan Distance is also known as City Block Distance. It is
essentially summation of the absolute difference between each
element.
@see: Krause, Eugene F. 1987. Taxicab Geometry. Dover. ISBN 0-486-
25202-7.
@param original: list of original data
@param test: list of data to test against original
@status: Tested function
@since: version 0.4
"""
if len(original) != len(test):
raise DistanceInputSizeError("Size (length) of inputs must be \
equal for Manhattan distance")
sum = 0
for i in range(len(original)):
sum = sum + abs(original[i] - test[i])
return float(sum)
def Euclidean(original, test):
"""
Euclidean coefficient for interval or ratio data.
Coefficient: M{sqrt(S{sum}(((A + B)(i) - (A + C)(i)) ^ 2))}
euclidean(original, test) -> euclidean distance between original
and test. Adapted from BioPython
@param original: list of original data
@param test: list of data to test against original
@status: Tested function
@since: version 0.1
"""
# lightly modified from implementation by Thomas Sicheritz-Ponten.
# This works faster than the Numeric implementation on shorter
# vectors.
if len(original) != len(test):
raise DistanceInputSizeError("Size (length) of inputs must be \
equal for Euclidean distance")
sum = 0
for i in range(len(original)):
sum = sum + (original[i] - test[i]) ** 2
return math.sqrt(sum)
def Cosine(original, test):
"""
Cosine coefficient for interval or ratio data.
Coefficient:
M{S{sum}(abs((A + B)(i) * (A + C)(i))) /
(S{sum}((A + B) ^ 2) * S{sum}((A + C) ^ 2))}
@param original: list of original data
@param test: list of data to test against original"""
if len(original) != len(test):
raise DistanceInputSizeError("Size (length) of inputs must be \
equal for Cosine distance")
original = [float(x) for x in original]
test = [float(x) for x in test]
numerator = sum([original[x] * test[x] for x in range(len(original))])
denominator = sum([x * x for x in original]) ** 0.5
denominator = denominator * (sum([x * x for x in test]) ** 0.5)
return numerator / denominator
def Hamming(original, test):
"""
Hamming coefficient for ordinal data - only for positional data.
Coefficient: number of mismatches with respect to position
@param original: list of original data
@param test: list of data to test against original
@see: Ling, MHT. 2010. COPADS, I: Distances Measures between Two
Lists or Sets. The Python Papers Source Codes 2:2.
"""
if len(original) <> len(test):
raise DistanceInputSizeError("Size (length) of inputs must be \
equal for Hamming's distance")
mismatch = 0
for index in range(len(original)):
if original[index] <> test[index]: mismatch = mismatch + 1
return mismatch
def Canberra(original, test):
"""
Canberra coefficient for interval or ratio data.
Coefficient:
M{S{sum}(abs((A + B)(i) - (A + C)(i)) / abs((A + B)(i) + (A + C)(i)))}
@see: Lance GN and Williams WT. 1966. Computer programs for
hierarchical polythetic classification. Computer Journal 9: 60-64.
@param original: list of original data
@param test: list of data to test against original"""
if len(original) != len(test):
raise DistanceInputSizeError("Size (length) of inputs must be \
equal for Canberra distance")
sum = 0
for i in range(len(original)):
sum = sum + (abs(original[i] - test[i]) / abs(original[i] + \
test[i]))
return sum
def Minkowski(original, test, power=3):
"""
Minkowski coefficient for interval or ratio data.
Coefficient: M{power-th root(S{sum}(((A + B)(i) - (A + C)(i)) ^ power))}
Minkowski Distance is a generalized absolute form of Euclidean
Distance. Minkowski Distance = Euclidean Distance when power = 2
@param original: list of original data
@param test: list of data to test against original
@param power: expontential variable
@type power: integer"""
if len(original) != len(test):
raise DistanceInputSizeError("Size (length) of inputs must be \
equal for Minkowski distance")
sum = 0
for i in range(len(original)):
sum = sum + abs(original[i] - test[i]) ** power
return sum ** (1 / float(power))
def Sokal_Michener(original, test, absent=0, type='Set'):
"""
Sokal and Michener coefficient for nominal or ordinal data.
Coefficient: M{(A + D) / (A + B + C + D)}
@param original: list of original data
@param test: list of data to test against original
@param absent: user-defined identifier for absent of region,
default = 0
@param type: {Set | List}, define whether use Set comparison
(non-positional) or list comparison (positional), default = Set
@see: Ling, MHT. 2010. COPADS, I: Distances Measures between Two
Lists or Sets. The Python Papers Source Codes 2:2.
"""
if len(original) <> len(test):
raise DistanceInputSizeError("Size (length) of inputs must be \
equal for Sokal & Michener's distance")
(original, test, both, none) = compare(original, test, absent, type)
return (both + none) / (original + test + both + none)
def Tanimoto(original, test):
"""
Tanimoto coefficient for interval or ratio data.
Coefficient:
M{S{sum}(abs((A + B)(i) * (A + C)(i))) /
(S{sum}((A + B) ^ 2) + S{sum}((A + C) ^ 2) -
S{sum}(abs((A + B)(i) * (A + C)(i))))}
@param original: list of original data
@param test: list of data to test against original
@status: Tested function
@since: version 0.4
"""
if len(original) != len(test):
raise DistanceInputSizeError("Size (length) of inputs must be \
equal for Cosine distance")
original = [float(x) for x in original]
test = [float(x) for x in test]
numerator = sum([original[x] * test[x] for x in range(len(original))])
denominator = sum([x * x for x in original])
denominator = denominator + (sum([x * x for x in test])) - numerator
return numerator / denominator