I am trying to solve a underdetermined system of nonlinear equations in python. At the moment my plan is to proceed as follows but unfortunately it does not work out. I'll give a small example.
I have this input data.
Lins = np.array([[[1, 2, 3], [4, 5, 6], [1, 5, 2], [5, 2, 6]],
[[7, 2, 3], [4, 5, 6], [5, 8, 7], [2, 1, 4]]], np.int32)
Each of the lines representing polynoms. Meaning [1, 2, 3] represents 1x^2+2x+3, and [5, 8, 7] 5x^2+8x+7 and so on.
To "create" the equations for my system I do the following:
def f(x):
X = np.array([x**2, x, np.ones_like(x)]).T
return np.sum(Lins * X[:,None], axis=(1, 2))
So my plan is to get this two equations with the four unknowns x1-x4:
1x1^2+2x1+3 + 4x2^2+5x2+6 + 1x3^2+5x3+6 + 5x4^2+2x4+6
7x1^2+2x1+3 + 4x2^2+5x2+6 + 5x3^2+8x3+7 + 2x4^2+1x4+4
After that I import my solver, and define the solution vector b.
from scipy.optimize import least_squares
b = np.array([52, 62])
Finally, I try to solve the system:
x = least_squares(lambda x: f(x) - b, np.asarray((1,1,1,1,1)), bounds=(0, 1)).x
I am expecting four values representing the solutions for the 4 unknowns x1-x4. Unfortunately I get this error:
ValueError: operands could not be broadcast together with shapes (2,4,3) (4,1,3)
For me it seems as if there is a mistake in the way I put my data into the least_squares solver. But I can`t figure out the problem. Or is least_squares not appropriate to solve underdetermined systems?
Thank you in advance for all of your help :)