How to use least squares with weight matrix?
least-squares, matrix, numpy, python
Solution
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.
Problem
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.lstsq(A, B) print X[0] # [ 5.00000000e-01 5.00000000e-01 -1.66533454e-16 -1.11022302e-16] ``` But what about solving this same equation with a weight matrix not being Identity: ``` A.X = B (W) ``` 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] W=[1,2,3,4,5] ```