Htykuut

I have to solve a non linear problem with three equations. The variables of the equation are Bx, By, Bz (which I imported from an excel file), mx, my, mz (which are float numbers inputed from the user) and x,y,z (which I want to calculate).
I first imported the excel file (180,6), with headed values, using pandas.

import pandas as pd

from scipy.optimize import fsolve



# Import Data

data = pd.read_excel('Cylinder.xlsx')

dfObj = pd.DataFrame(data, columns = ['y', 'x', 'Bx', 'By', 'Bz', 'B'])



Bx = dfObj['Bx']

By = dfObj['By']

Bz = dfObj['Bz']



mx = float(input("mx=  "))

my = float(input("my=  "))

mz = float(input("mz=  "))

After many attempts and searching / reading I end up trying two ways according to solve the non-linear equation system. In both I used fsolve from scipy.optimize.
In the first one I defined the equations and then with an initial guess I used fsolve, like the codex below, and had an error:
'''ValueError: setting an array element with a sequence.'''
'''error: Result from function call is not a proper array of floats.'''

# fsolve functions

def magnetic_field(w): 

    x = w[0]

    y = w[1]

    z = w[2]



    F = [3] 

    F.append(0) 

    F[0] = Bx - (10**-7)*(mx*3*x**2/(x**2+y**2+z**2)**2.5 + 

           my*3*x*y/(x**2+y**2+z**2)**2.5 + mz*3*x*z/(x**2+y**2+z**2)**2.5 - 

           mx/(x**2+y**2+z**2)**1.5)

    F.append(1)

    F[1] = By - (10**-7)*(mx*3*x*y/(x**2+y**2+z**2)**2.5 + 

           my*3*y**2/(x**2+y**2+z**2)**2.5 + mz*3*y*z/(x**2+y**2+z**2)**2.5 - 

           my/(x**2+y**2+z**2)**1.5)

    F.append(2)

    F[2] = Bz - (10**-7)*(mx*3*x*z/(x**2+y**2+z**2)**2.5 + 

           my*3*y*z/(x**2+y**2+z**2)**2.5 + mz*3*z**2/(x**2+y**2+z**2)**2.5 - 

           mz/(x**2+y**2+z**2)**1.5)

    return F



wGuess = [1,1,1,1] 

w = fsolve(magnetic_field,wGuess)

print(w)

print(magnetic_field)

The second attempt was with lambda functions, in which the error is:
'''TypeError: fsolve: there is a mismatch between the input and output shape of the 'func' argument ''.Shape should be (3,) but it is (3, 180).'''

def magnetic_field(f1,f2,f3,x0,y0,z0):

    func = lambda x: [f1(x[0], x[1], x[2]), f2(x[0], x[1], x[2]), f3(x[0], 

           x[1], x[2])]

    return fsolve(func,[x0,y0,z0])



f1 = lambda x, y, z : Bx - (10**-7)*(mx*3*x**2/(x**2+y**2+z**2)**2.5 + 

my*3*x*y/(x**2+y**2+z**2)**2.5 + mz*3*x*z/(x**2+y**2+z**2)**2.5 - 

mx/(x**2+y**2+z**2)**1.5)

f2 = lambda x, y, z : By - (10**-7)*(mx*3*x*y/(x**2+y**2+z**2)**2.5 + 

my*3*y**2/(x**2+y**2+z**2)**2.5 + mz*3*y*z/(x**2+y**2+z**2)**2.5 - 

my/(x**2+y**2+z**2)**1.5)

f3 = lambda x, y, z : Bz - (10**-7)*(mx*3*x*z/(x**2+y**2+z**2)**2.5 + 

my*3*y*z/(x**2+y**2+z**2)**2.5 + mz*3*z**2/(x**2+y**2+z**2)**2.5 - 

mz/(x**2+y**2+z**2)**1.5)



res = magnetic_field(f1,f2,f3,1,1,1)

print(res)

I am new in python and I don’t understand the errors. Where am i mistaken?
Thanks in advance.