I have a function which is multivariate (code below), depending on x1 and x2 and I have a target output value in mind for this function, named target. I fix x1 and provide my target in the outer function: find_x2. The objective is to minimize the inner function error, which is just the squared distance between my output target and the resulting value est, with respect to x2.

But having run it:

find_x2(target = .12, x1 = 100) yields x2 = 0.99899, but it should be roughly .80.

It appears the function is minimizing with respect to est instead of x2, but I can't see why. Any help would be appreciated.

Code:

import numpy as np
from scipy.optimize import minimize_scalar, minimize 

def find_x2(x1, target): 
    def error(x2, x1 = x1, target = target):
        k = np.zeros(x1) 
        V = np.zeros(x1) 
        for i in range(x1): 
            try:
                k[i-1] = (i/x1)**(-1/x2)
            except: 
                k[x1-1]=1
        for i in range(x1): 
            V[i] = k[i]/sum(k)
        est = sum(V**2) 
        return (target - est)**2
    return minimize_scalar(error, bounds = (.001,.999), method = 'bounded') 

CodePudding user response：

Try this version:

def find_x2(x1, target): 
    def error(x2, x1 = x1, target = target):
        k = np.zeros(x1) 
        V = np.zeros(x1) 
        for i in range(x1): 
            try:
                k[i-1] = (x1/i)**(1/x2)
            except:
                k[x1-1]=1
        for i in range(x1):
            V[i] = k[i]/sum(k)
        est = sum(V**2)
        return (target - est)**2
    return minimize_scalar(error, bounds = (.001,.999), method = 'bounded')

find_x2(100, 0.12)

prints

    fun: 9.668753433849857e-14
 message: 'Solution found.'
    nfev: 14
  status: 0
 success: True
       x: 0.801701074855243