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[ What is the best vectorization method here? ]
I am wondering what would be the best way to vectorize the following formula:
c= Sum(u(i)*<u(i),y>/v(i) )
<.,.>
means dot product of two matrix.
let say we have a matrix K= U*Diag(w)*U^-1
(w
and u
are eigenvalues and eigenvectors of matrix k
of size nxn
) . and y
is a vector of size n
.
so if :
k=np.array([[1,2,3],[2,3,4],[2,7,8]])
y=np.array([1,4,5])
w,u=np.linalg.eigh(k)
then :
w=array([ -2.02599523, 0.47346124, 13.552534 ])
u=array([[-0.18897996, 0.95770742, 0.21698634],
[ 0.82245177, 0.03363605, 0.5678395 ],
[-0.53652554, -0.28577109, 0.79402471]])
This is how I implemented it:
uDoty=np.dot(u,y)
div=np.divide(y,w)
div=np.divide(uDoty,w)
r=np.tile(div,(len(u),1))
a=u*r.T
c=sum(a)
But it actually It doesn't look nice to me.So is there any suggestion?
Answer 1
You can avoid using np.tile
with some broadcasting:
U = np.dot(u, y)
d = U/w
a = u*d[:,None]
c = a.sum()