How to use least squares with weight matrix?

Question

I know how to solve A.X = B by least squares using Python:

Example:

A=[[1,1,1,1],[1,1,1,1],[1,1,1,1],[1,1,1,1],[1,1,0,0]]
B=[1,1,1,1,1]
X=numpy.linalg.ls         


        

Answer 1

I found another approach (using W as a diagonal matrix, and matricial products) :

A=[[1,1,1,1],[1,1,1,1],[1,1,1,1],[1,1,1,1],[1,1,0,0]]
B = [1,1,1,1,1]
W = [1,2,3,4,5]
W = np.sqrt(np.diag(W))
Aw = np.dot(W,A)
Bw = np.dot(B,W)
X = np.linalg.lstsq(Aw, Bw)

Same values and same results.