python scipy-fsolve doesn`t work. why fsolve return 'None'?

Question

first, sorry about my poor English skill.

I make BDT-model, but something problem here.

this function is change code for column 4

def f(x):
    a=1 / (1 + f_tree.loc[1, 4] + x)
    b=1 / (1 + f_tree.loc[2, 4] + x)
    c=1 / (1 + f_tree.loc[3, 4] + x)
    d=1 / (1 + f_tree.loc[4, 4] + x)
    e=0.5*(a+b)/ (1 + f_tree.loc[1, 3])
    f=0.5*(b+c)/ (1 + f_tree.loc[2, 3])    
    g=0.5*(c+d)/ (1 + f_tree.loc[3, 3]) 
    h=0.5*(e+f)/ (1 + f_tree.loc[1, 2])
    i=0.5*(f+g)/ (1 + f_tree.loc[2, 2])  
    return -Market_data['PV'][3] + (0.5 * (h+i) / (1+f_tree.loc[1,1]))
x=fsolve(f,0)
x
f_tree.loc[1,4]+=x
f_tree.loc[2,4]+=x
f_tree.loc[3,4]+=x
f_tree.loc[4,4]+=x
f_tree

table before

	1	2	3	4	5
1	0.05	0.065334	0.081673	0.067493	0.074591
2	0.00	0.055317	0.070603	0.055259	0.061070
3	0.00	0.000000	0.061539	0.045242	0.050000
4	0.00	0.000000	0.000000	0.037041	0.040937
5	0.00	0.000000	0.000000	0.000000	0.033516

Answer 1

Here's how to read the error: focus on not iterable. Something in the line is attempting to iterate. The only part that makes sense for is sum(map(float, final)). So we know that final is None.

final is the return value of calculate. Looking at the code, calculate does indeed return nothing, rather than the expected iterable.

At one point, calculate states

if set_row == 3:
    return cal_temp

However, the corresponding else recursively calls calculate(loop_temp, set_row) and discards the return value. You probably want to keep the recursive return value and return it:

return calculate(loop_temp, set_row)

As usual with these types of problems, the error is entirely in your code, and not in the thoroughly tested and generally well thought-out libraries you are using.