def kappa(X, Y, mode=None):
'''
Kappa statistic
@param X Raster array.
@param Y Raster array.
@param mode Kappa sttistic to compute:
mode = None: classic kappa
mode = loc: kappa location
mode = histo kappa histogram
'''
table = CrossTable(X, Y)
rows, cols = table.shape
if rows != cols:
raise CoeffError('Kappa is applicable for NxN crosstable only!')
t_expect = table.getProbtable()
pa = 0
for i in range(rows):
pa = pa + t_expect[i,i]
prows = table.getProbRows()
pcols = table.getProbCols()
pexpect = sum(prows * pcols)
pmax = sum(np.min([prows, pcols], axis=0))
if mode == None:
result = (pa - pexpect)/(1-pexpect)
elif mode == "loc":
result = (pa - pexpect)/(pmax - pexpect)
elif mode == "histo":
result = (pmax - pexpect)/(1 - pexpect)
else:
raise CoeffError('Unknown mode of kappa statistics!')
return result
def jiu(X, Y):
'''
Define Joint Information Uncertainty coef., based on entropy., for discrete values
Coefficient change between [0, 1]
0 - no connection
1 - full connection
@param X First raster's array
@param Y Second raster's array
'''
#T, sum_r, sum_s, total, r, s = compute_table(X, Y)
table = CrossTable(X, Y)
T = table.getProbtable() #Pij = Tij / total
sum_rows = table.getProbRows() #Pi. = Ti. / total i=[0,(r-1)]
sum_cols = table.getProbCols() #P.j = T.j / total j=[0,(s-1)]
#to calculate the entropy we take the logarithm,
#logarithm of zero does not exist, so we must mask zero values
sum_rows = np.compress(sum_rows != 0, sum_rows)
sum_cols = np.compress(sum_cols != 0, sum_cols)
#Compute the entropy coeff. of two raster
H_x = -np.sum(sum_rows * np.log(sum_rows))
H_y = -np.sum(sum_cols * np.log(sum_cols))
#Compute the joint entropy coeff.
T = np.ma.array(T, mask=(T == 0))
T = np.ma.compressed(T)
H_xy = -np.sum(T * np.log(T))
# Compute the Joint Information Uncertainty
U = 2.0 * ((H_x + H_y - H_xy)/(H_x + H_y))
return U
