问题
I need to solve a system of linear diophantine equations with either numpy or sympy.
Is there any way to constrain numpy's linalg.solve/linalg.lstsq method to return only integer solutions? (probably not but thought I should ask)
I looked into Sympy's diophantine solver and it does not seem to be applicable to solving whole systems
The problem I am working on is something along the lines of
P1(X) + P2(Y) = TargetPro
F1(X) + F2(Y) = TargetFat
C1(X) + C2(Y) = TargetCarb
In this case, X,Y,Z would represent the approximate serving sizes, and P1/F1/C1 would be the pro/fat/carb profile respectively.
based on this paper https://www.math.uwaterloo.ca/~wgilbert/Research/GilbertPathria.pdf
it seems as though I could conduct a row-reduction to find the ref of this system (row-echelon form) and then plug it into sympy's solver.
Is there an easier way to go about it?
Here's a trivial example:
pro = [4,5]
fat = [1,2]
carb = [3,6]
A = np.array((pro, fat, carb))
b = np.array([22,12,21])
print(np.linalg.lstsq(A, b))
I expected to get an integer solution [3,2] and instead got [ 2.16666667, 2.66666667]
Both solutions are correct, but I want to bound my solutions to only integer solutions
来源：https://stackoverflow.com/questions/37101110/finding-least-squares-integer-solutions-to-a-linear-system-with-numpy-sympy