在python中使用递归函数进行动态编程

Question

I'm new to python, and I'm struggling to write a recursive function. I have these lines of code for a dynamic programming function in Matlab which were given as an example from a professor:

function [policy,fstar] =StochasticInventoryControl(N,K,c,h,M,g,Dmax,p)
   fstar=zeros(M+1,N+1);
   for n=N:-1:1
      for s=0:M
         for x=0:M-s
            temp=0;
            for d=0:Dmax
               temp=temp+p(d+1)*(g*min(s+x,d)+fstar(1+max(s+x-d,0),n+1));
            end
            f(1+s,1+x)=-K*(x>0)-c*x-h*(s+x)+temp;
         end
      [fstar(1+s,n),policy(1+s,n)]=max(f(1+s,1:M-s+1));
      end
   end
   policy=policy-1; 
end

I'm trying to re-write the same function in python, and I came up with this code:

def StochasticInventoryControl(N, K, c, h, M, g, Dmax, p):
    fstar = zeros(M + 1, N + 1)
    for n in range (N, 1, -1):
        for s in range (0, M):
            for x in range (0, M - s):
                temp = 0
            for d in range (0, Dmax):
                temp = temp + p(d + 1)*(g*min(s + x, d) + fstar(1 + max(s + x - d,0), n + 1))
        f(1 + s, 1 + x).lvalue = -K * (x > 0) - c * x - h * (s + x) + temp
    [fstar(1 + s, n), policy(1 + s, n)] = max(f(1 + s, n in range (1, M - s + 1))

The last line is incorrect, I know I can't define the function's recursive relation this way in python. How should I write the last line in python?

Answer 1

First, your indexing and ranges are off. Like most programming languages, python indexes and ranges start with 0, and ranges are half-open (they exclude the last value), so you need to take that into account in your ranges.

Second, numpy uses square brackets for indexing, so it would be f[s,x] not f(s,x) .

Third, you can do slicing in numpy arrays just like in MATLAB, but you need to take into account the indexing differences and the fact that for x:y:z indexing the last element is the step size in Python while in MATLAB the middle element is.

Fourth, indentation is significant in Python, so your inner loop needs to be indented one more level to work the same as in MATLAB.

As for your question about the last line last line, there is no single function in numpy that handles both the max value and max index. You need to use np.max for the value and np.argmax for the index, like so:

fstar[s, n-1] = np.max(f[s, :M-s+1])
policy[s, n-1] = np.argmax(f[s, :M-s+1])+1

Or better yet use the numpy method approach:

fstar[s, n-1] = f[s, :M-s+1].max()
policy[s, n-1] = f[s, :M-s+1].argmax()+1