使用 lmfit 进行曲线拟合，通过参数总和限制结果

Question

I have created a curve fitting algorithm that works, up to a point.
I have six parameters: a, b, c, d, e, f.
Each parameter can be between 0 and 100, but with the constraint (a+b+c+d+e+f) <= 100
Is there anyway to do this?

params.add('a', value=1, min=0, max = 100, vary=True)
params.add('b', value=1, min=0, max = 100, vary=True)
params.add('c', value=1, min=0, max = 100, vary=True)
params.add('d', value=1, min=0, max = 100, vary=True)
params.add('e', value=1, min=0, max = 100, vary=True)
params.add('f', value=1, min=0, max = 100, vary=True)

I did manage to find a, probably not very elegant, solution.
In the function I'm trying to solve I check if the the sum of a+b...+f is greater than 100. If it is I reset the coefficients with random numbers, forcing the algorithm to find another solution.

def myfunc(a, b, c, d, e, f):
    sum = a+b+c+d+e+f
    if sum>100:
        a = np.random.randint(low=0, high=10)
        b = np.random.randint(low=0, high=10)
        c = np.random.randint(low=0, high=10)
        d = np.random.randint(low=0, high=10)
        e = np.random.randint(low=0, high=10)
        f = np.random.randint(low=0, high=10)
Rest of function

Answer 1

Consider that (a+b+c+d+e+f) <= 100 can be written as

f = 100 - (a+b+c+d+e) - epsilon

with epsilon >= 0 . Now, use that with epsilon as the variable and f derived from that:

params.add('a', value=1, min=0, max = 100, vary=True)
params.add('b', value=1, min=0, max = 100, vary=True)
params.add('c', value=1, min=0, max = 100, vary=True)
params.add('d', value=1, min=0, max = 100, vary=True)
params.add('e', value=1, min=0, max = 100, vary=True)
params.add('epsilon', value=1, min=0, vary=True)
params.add('f', expr='100-a-b-c-d-e-epsilon')

You still have 6 variables, but now f is not independent of epsilon .