Linear system of equations with Casadi: A\b

[jtorde]

In the Python API of Casadi, is there any equivalent to the A\b command of Matlab? This is what I tried

from casadi import *
A = DM([[1.0,3.0,5.0],[2.0,4.0,1.0]]) #A is 2x3
b = DM([[1.0],[5.0]])                 #b is 2x1
solve(A,b)  #Fails with Assertion "a.size1() == a.size2()" failed: solve: A not square but 2x3
solve(A,b,"lapackqr") #Fails with Segmentation fault (core dumped)
solve(A,b,"lapacklu") #Return [-nan, inf]
solve(A,b,"lsqr") #Returns [0.636364, 1.07487] Why does it have only 2 elements instead of 3?
solve(A,b,"ma27") #Return [-0.338028, 1.69014] Why does it have only 2 elements instead of 3?

In Matlab this works as follows:

A = [1 3 5;
     2 4 1];
b = [1;5];
A\b  %It returns [0    1.4118    -0.6471]'

I read the examples at https://github.com/casadi/casadi/blob/main/test/python/linearsolver.py but couldn't find the solution

Thanks!

[jaeandersson]

The linear solvers might not handle non-square systems well. For overdetermined systems, you should be able to solve the normal equations. For underdetermined systems, maybe use QR:

import casadi as ca
A = ca.DM([[1.0,3.0,5.0],[2.0,4.0,1.0]]) #A is 2x3
b = ca.DM([[1.0],[5.0]])                 #b is 2x1
# Underdetermined system of equation, QR factorization of A transpose
Q, R = ca.qr(A.T)
# A*x = b <=> R.T*Q.T*x = b
x = ca.mtimes(Q, ca.solve(R.T, b))
x  # least-squares solution

Alternatively, consider reformulating your problem so that you don't get an underdetermined system of equations.