Python numpy broadcasting 3 dimensions (multiple weighted sums)

I have become kind of used to cast with 2-dimensional arrays, but I can't seem to get around this 3D thing I want to do.

I have two two dimensional arrays:

>>> a = np.array([[0.01,.2,.3,.4],[.2,.03,.4,.5],[.9,.8,.7,.06]])
>>> b= np.array([[1,2,3],[3.,4,5]])
>>> a
array([[ 0.01,  0.2 ,  0.3 ,  0.4 ],
       [ 0.2 ,  0.03,  0.4 ,  0.5 ],
       [ 0.9 ,  0.8 ,  0.7 ,  0.06]])
>>> b
array([[ 1.,  2.,  3.],
       [ 3.,  4.,  5.]])

      

        
        
        
      

    

Now, what I want is the sum of all rows in a, where each row is weighted by the values ​​of the column in b. So, I want 1. * a[0,:] + 2. * a[1,:] + 3. * a[2,:]

the same thing for the second line b.

So, I know how to do it step by step:

>>> (np.array([b[0]]).T * a).sum(0)
array([ 3.11,  2.66,  3.2 ,  1.58])

>>> (np.array([b[1]]).T * a).sum(0)
array([ 5.33,  4.72,  6.  ,  3.5 ]) 

      

        
        
        
      

    

But I have a feeling that if I knew how to properly cast the two as 3D arrays, I could get the result I want in one go. Result:

array([[ 3.11,  2.66,  3.2 ,  1.58],
       [ 5.33,  4.72,  6.  ,  3.5 ]]) 

      

        
        
        
      

    

I guess it shouldn't be too hard ..?!?