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How can I use a calculated value of a function in another function in another Python file?

I have wrote the following code in derivation.py:
def Interpolation(ableitungWinkel,x_values):
z = medfilt(derivation,3)
diff = abs(derivation-z)
new_smootheddata = np.where(diff>3,z,derivation)
x=np.arange(0,len(x_values[:-2]))
f = interp1d(x,new_smootheddata,kind="linear")
xnew = np.arange(0, len(x_values[:-3]),0.01)
ynew = f(xnew)
s=plt.plot(x, z,"o",xnew, ynew, "-")
return s
In my project there is also integration.py. In this Python file I need the values which z calculates in the function def interpolation for this calculation:
def horizontalAcceleration(strideData):
resultsHorizontal = list()
for i in range (len(strideData)):
yAngle = z
xAcceleration = strideData.to_numpy()[i, 4]
yAcceleration = strideData.to_numpy()[i, 5]
a = ((m.cos(m.radians(yAngle)))*yAcceleration)-((m.sin(m.radians(yAngle)))*xAcceleration)
resultsHorizontal.append(a)
resultsHorizontal.insert(0, 0)
return resultsHorizontal
As you can see I have already added z to the function def horizontalAcceleration at the place where it should go.
To use z there, I tried the following: from derivation import z
But that doesn't work. Because then I get the error: ImportError: cannot import name 'z' from 'derivation'
Have anybody an idea how I can solve this problem? Thanks for helping me.

I think that your misunderstanding is because you think a function is like a script that has been run and modified a.global state. That's not what a function is. A function is a series of actions performed on its inputs (ignoring closures for a minute) which returns some results. You can call it many times, but without calling it, it never executes. Once it stops executing all its variables go out of scope.
You can import and call a function though. So you can change the return type of Interpolation to return everything you need somewhere else. E.g.
def Interpolation(...):
...
return {'z': z, 's': s}
Then somewhere you import that function, call it, get back all the data you need, then pass that to your other function.
import Interpolation from derivation
# get z and s in a dict result
result = Interpolation(...)
# pass s as well as the other argument to your other function
horizontalAcceleration(strideData, result['s'])

Getting mathematical function as user's input

I need to know how transfer string input into executable function.
For example - user write string 'x*Sin(x**2)' and then programm takes it as function, can calculate a value for given x, can plot derivation of this function etc. I've read that there is module called scitools.stringfunction, but as far as I know this module is not callable in python-3.
Any ideas how to make it?

For Python 2.X
f = lambda x: input() # the user inputs: x**2 + 1
y = f(3)
print y # outputs: 10
For Python 3.X
f = lambda x: eval(input())
y = f(5)
print y
Just make sure to import the required mathematical functions. And make sure the user inputs a valid Python arithmetic expression.

using sympy you could do something like this:
from sympy import var
from sympy import sympify
x = var('x') # the possible variable names must be known beforehand...
user_input = 'x * sin(x**2)'
expr = sympify(user_input)
res = expr.subs(x, 3.14)
print(res) # -1.322...
if you want to turn the user input into a function you can call you could to this:
from sympy.utilities.lambdify import lambdify
f = lambdify(x, expr)
# f(3.14) -> -1.322...
sympy can do sybolic calculations (including derivatives); if you want to make plots i strongly suggest matplotlib.
the advantage of using a math library opposed to eval is that you do not need to sanitize the user input (against malicious code).
(deleted this thanks to a comment from ejm).

Why does scipy.optimize.fmin_l_bfgs_b fail to print iteration details despite appropriate inputs?

Goal:
To view the value of the objective function at each iteration for scipy.optimize.fmin_l_bfgs_b.
Problem:
Giving the optional argument iprint=1 should cause output to be printed. However, doing so does not result in any output.
Other info:
I am using the Anaconda 4.3 distribution of Python 2.7 on a Windows 7 machine, Spyder IDE with IPython console.
Example Code:
import numpy as np
import scipy.optimize as opt
A = np.random.rand(20,40)
b = np.random.rand(20,)
x0 = np.ones((40,))
def objective_func(x,A,b):
objective = np.sum((A.dot(x)-b)**2) + np.sum(np.abs(x))
return objective
def gradient_func(x,A,b):
gradient = 2*A.T.dot(A.dot(x)-b) + 2*x/np.sqrt(x**2 + 10**(-8))
return gradient
x_bar = opt.fmin_l_bfgs_b(func=objective_func,
x0=x0,
fprime = gradient_func,
args=(A,b),
iprint=1)

One solution is to use a lambda function as the callback function. This allows one to pass A, b to the callback function in addition to x.

multiple functions as arguments in python

I have the following problem: I have two sets of data (set T and set F). And the following functions:
x(T) = arctan(T-c0), A(x(T)) = arctan(x(T) -c1),
B(x(T)) = arctan(x(T) -c2)
and Y(x(t),F) = ((A(x(t)) - B(x(t)))/2 - A(x(t))arctan(F-c3) + B(x(t))arctan(F-c4))
# where c0,c1,c2,c3,c4 are constants
Now I want to create a surface plot of Y. And for that I would like to implement Y as a python (numpy) function what turns out to be quite complicated, because Y takes other functions as input.
Another idea of mine was to evaluate x, B and A on the data separately and store the results in numpy arrays. With those I also could get the output of the function Y , but I don't know which way is better in order to plot the data and I really would like to know how to write Y as a python function.
Thank you very much for your help

It is absolutely possible to use functions as input parameters to other functions. A use case could look like:
def plus_one(standard_input_parameter_like_int):
return standard_input_parameter_like_int + 1
def apply_function(function_as_input, standard_input_parameter):
return function_as_input(standard_input_parameter)
if(__name__ == '__main__'):
print(apply_function(plus_one, 1))
I hope that helps to solve your specific problem.

[...] somethin like def s(x,y,z,*args,*args2): will yield an
error.
This is perfectly normal as (at least as far as I know) there is only one variable length non-keyword argument list allowed per function (that has to be exactly labeled as *args). So if you remove the asterisks (*) you should actually be able to run s properly.
Regarding your initial question you could do something like:
c = [0.2,-0.2,0,0,0,0]
def x(T):
return np.arctan(T-c[0])
def A(xfunc,T):
return np.arctan(xfunc(T) - c[1])
def B(xfunc,T):
return np.arctan(xfunc(T) - c[2])
def Y(xfunc,Afunc,Bfunc,t,f):
return (Afunc(xfunc,t) - Bfunc(xfunc,t))/2.0 - Afunc(xfunc,t) * np.arctan(f - c[3]) + Bfunc(xfunc,t)*np.arctan(f-c[4])
_tSet = np.linspace(-1,1,20)
_fSet = np.arange(-1,1,20)
print Y(x,A,B,_tSet,_fSet)
As you can see (and probably already tested by yourself judging from your comment) you can use functions as arguments. And as long as you don't use any 'if' conditions or other non-vectorized functions in your 'sub'-functions the top-level function should already be vectorized.

How can i use a function with "variable" constants in scipy.optimize?

how can i use "variable" constants in scipy.optimize functions? I am trying to create an iterative optimisation algorithm, which updates certain parameters in the objective function after each optimisation run.
to use a very simple example of what i want to do:
from scipy import optimize as opt
def f(x, R):
return R * (x[0]**2 + x[1]**3)
R = 0.1 # initial R value
y = []
y.append([2,2]) # initial point
for i in range(0,10):
y.append(opt.fmin(f, y[i])) # how can i include 'R' in this line??
R = some_function_to_update_R(R)
any help would be appreciated
EDIT:
would it help to re-declare the objective function each time i optimise? so make the loop look like this instead?
for i in range(0,10):
def f_temp(x_temp):
return f(x_temp,R)
y.append(opt.fmin(f_temp, y[i]))
R = some_function_to_update_R(R)
or is there some better way?

fmin supports an optional args argument, representing a tuple of additional arguments to be passed to the function you're trying to optimize:
y.append(opt.fmin(f, y[i], args=(R,)))
This is explained in the documentation for fmin; you should get into the habit of checking the documentation when you want to figure out how to do something.