Consider the following idea: I want to generate a sequence of functions f_k,
for k = 1,...,50 and store them in a Python dictionary.
To give a concrete example, lets say
f_k(x) = f_{k-1}(x) * sqrt(x)
This is just an example, the problem I have is more complicated, but this does not matter for my question.
Because in my real problem f_{k-1} is very noisy and contains rounding errors, I do not want to build f_k directly from f_{k-1}, but instead
I first approximate f_{k-1} through a spline approximation, and then determine f_k from that spline approximation. Strangely, this results in an error message saying that maximum recursion depth is exceeded. Here is an example of the code:
import numpy as np
from scipy.interpolate import interp1d
n = 50 # number of functions I want to create
args = np.linspace(1,4,20) # where to evaluate for spline approximation
fdict = dict() # dictionary that stores all the functions
fdict[0] = lambda x: x**2 # the first function
# generate function f_k as follows: First, take function f_{k-1} and
# approximate it through a spline. Multiply that spline approximation
# by sqrt(x) and store this as function f_k.
for k in range(1,n+1):
spline_approx = lambda x: interp1d( args,fdict[k-1](args) )(x)
fdict[k] = lambda x: spline_approx(x) * np.sqrt(x)
print('test evalutation: ', fdict[n](3))
This results in the error
RecursionError: maximum recursion depth exceeded
My problem must be very Python specific. It must have something to do with the interpolation through interp1d. For instance. If I replace the line
spline_approx = lambda x: interp1d( args,fdict[k-1](args) )(x)
by a polyfit
coefs = np.polyfit(args,fdict[k-1](args),10) # polyfit coefficients
spline_approx = lambda x: np.polyval(coefs,x) # approximation of f_{k-1}
the code runs fine. I suspect that the problem arises because fdict[k-1] is not directly evaluated but only passed on as a reference. But how can I solve this issue?
