test.py

from numpy import zeros, dot, diag, tensordot
from numpy.random import random
n = 6
m = 4
b = random((n, m))
d = random((m, m))

bdb = zeros(n, 'd')
for i in xrange(n):
    bdb[i] = dot(b[i,:], dot(d, b[i, :]))

print bdb
bd = dot(b, d)
bdb = diag(dot(bd, b.T))
print bdb