Search code examples
pythonscipynumerical-integration

Python: integrate across 100 functions and integration variables

I want to compute an integral of the form: large integral.

I am struggling to implement this in python. Is there a programic way to accomplish this? I tried doing this with several for loops but I'm stuck on the error SystemError: too many statically nested blocks.

fs = {}
for i in range(100):
   fs[i] = lamda x: x*i

for x1 in np.arange(0,1,.01):
   for x2 in np.arange(0,1,.01):
      ....
          for x100 in np.arange(0,1,.01):
             for i in range(100):
                exec("summ+= fs[i](x%i"%i)
Solution

  • Of course it is slow: The "for i in range(100)" (1) part is reached 100 * 100 * 100 * ... * 100 (100 '*100's) = 100 ^ 100; and people say n^2 is bad... Anyways I would do it like this: 

    - Put 100 values initialized with 0 into a list.
 - for i = 0 to 100 ^ 100:
   - go through the list and use the k-th value as the parameter for the k-th function. do the summing thing
   - Add 0.1 to the n-th value in the list; 
     if this value is now == 1; set it to 0 and go to the (n+1)-th value and repeat this procedure until you reach the end of the list or one value is < 1. 
     Start with the first value in the list.
now you have your sum.