def checkMatrix(m, fV, AS=4, reversible=True):
#print m
for i in xrange(0, AS):
j = sum(m[i])
#print "AAAAA", j
assert j <= 1.0001
assert j >= 0.9999
if reversible:
for k in xrange(0, AS):
#print "comp2", (fV[i] * m[i][k]), (fV[k] * m[k][i] )
assert misc.close(fV[i] * m[i][k], fV[k] * m[k][i], 0.00001)
wV = fV
wV2 = fV
wV3 = transformByDistance(wV, m, AS)
wV4 = transformByDistance(wV2, m, AS)
i = sum(multiplyWV(wV2, wV3, AS))
j = sum(multiplyWV(wV, wV4, AS))
#print i, j
assert misc.close(i, j, 0.00001)
def subMatrix_HalpernBruno(d, freqColumn, subMatrix, AS=4):
#return subMatrix_HKY(d, freqColumn[0], freqColumn[1], freqColumn[2], freqColumn[3], 2.0)
#return subMatrix
matrix = [[0.0] * AS for i in xrange(0, AS)]
for i in xrange(0, AS):
for j in xrange(0, AS):
a = freqColumn[i] * subMatrix[i][j]
b = freqColumn[j] * subMatrix[j][i]
if not misc.close(a, b, 0.0001):
matrix[i][j] = subMatrix[i][j] * (math.log(b / a) / (1 -
(a / b)))
else:
matrix[i][j] = subMatrix[i][j]
#for i in xrange(0, AS):
# #print matrix[i][i], sum(matrix[i])
# matrix[i][i] -= sum(matrix[i]) - 1.0
# assert matrix[i][i] >= 0
#checkMatrix(matrix, freqColumn)
return matrix