Both scipy and numpy has least square estimation but I got slightly confused after reading the documentation.
So, my problem is classical regression where I am trying to find the best matrix transformation between two pairs of values. So something of the form:
Ax = b
Here, I know x and b. A has 9 unique components and x and b are 3D vectors. So, I need at least 3 points. So, 3 non-collinear x and b and I have them and I can create a 3x3 concatenated x and b vectors.
However, from the documentation, I see that it is designed for solving systems when A and b are known. So we solve for x. Assuming A is invertible, this would mean something like:
x = A(-1)b (-1) indicating the inverse or pseudo inverse.
In my case, the solution becomes
A = b x(-1)
I was wondering if I can still somehow use the built in numpy machinery for my setup.
Look at this:
Ax = b
x^TA^T = b^T
where A^T indicates the transpose of A. Now define the symbols Ap=x^T and Xp = A^T and bp=b^T and your problem becomes:
Ap Xp = bp
that is exactly in the form that you can treat with least squares