I have a problem analogous to this one, i.e. the optimization of four parameters:
a+b+c+1750=T
12=a/T*100
15=b/T*100
37=c/T*100
It can be solved via conversion to matrix formalism then using linear algebra methods:
a + b + c - T = -1750
100 * a - 12 * T = 0
100 * b - 15 * T = 0
100 * c - 37 * T = 0
import numpy as np
a = np.array([[1., 1., 1., -1.],
[100., 0, 0, -12.],
[0, 100., 0, -15.],
[0, 0, 100., -37.]])
b = np.array([-1750., 0, 0, 0])
res, err, _, __ = np.linalg.lstsq(a, b)
# res: [ 583.33333333 729.16666667 1798.61111111 4861.11111111]
My real problem needs integer-restricted solutions, i.e. the solutions can only be integers. Is there a restriction that I can place on the np.linalg.lstsq method, or perhaps a different method to solve which will return positive integer-only values for a,b, and c?
I want to be very deliberate in my questioning: This is NOT the same problem as
Solving linear system over integers with numpy
Since that problem was based all on integers, ie the equations and solutions contain only integers. The present question is different. From some experimental data, I get decimal values, since the measurement is imperfect. So my equations have decimals. Since the system in reality is quantized (coming from number of molecules) the solutions can only be integers. So there is some integer solution which best fits the data. Even though the problem can be solved analytically, the solution in reality has integer- only solutions so must be fitted via some optimization procedure.
So I reiterate the question: does someone know of a method to find the best solution to a system of equations where the solutions can only be zero or postive integers?
