Multivariable Cumulants and Moments in python -


in mathematica can convert multivariable moments in cumulants , using momentconvert: 

momentconvert[cumulant[{2, 2,1}], "moment"] // traditionalform

as 1 can try in wolframcloud.

i same in python. there library in python capable of this?

at least 1 direction programmed myself:

# http://code.activestate.com/recipes/577211-generate-the-partitions-of-a-set-by-index/  collections import defaultdict  class partition:      def __init__(self, s):                 self.data = list(s)                 self.m = len(s)         self.table = self.rgf_table()      def __getitem__(self, i):         #generates set partitions index         if > len(self) - 1:              raise indexerror         l =  self.unrank_rgf(i)         result = self.as_set_partition(l)         return result      def __len__(self):         return self.table[self.m,0]      def as_set_partition(self, l):         # transform restricted growth function partition         n = max(l[1:]+[1])         m = self.m         data = self.data         p = [[] _ in range(n)]         in range(m):             p[l[i+1]-1].append(data[i])         return p      def rgf_table(self):         # compute table values          m = self.m         d = defaultdict(lambda:1)         in range(1,m+1):             j in range(0,m-i+1):                 d[i,j] = j * d[i-1,j] + d[i-1,j+1]         return d      def unrank_rgf(self, r):         # unrank restricted growth function         m = self.m         l = [1 _ in range(m+1)]         j = 1         d = self.table         in range(2,m+1):             v = d[m-i,j]             cr = j*v             if cr <= r:                 l[i] = j + 1                 r -= cr                 j += 1             else:                 l[i] = r // v + 1                 r  %= v         return l    # s = set(range(4)) # p = partition(s) # x in p: #      print (x)   # using https://en.wikipedia.org/wiki/cumulant#joint_cumulants  import math  def cum2mom(arr, state):     def e(op):         return qu.expect(op, state)       def arr2str(arr,sep):         r = ''         i,x in enumerate(arr):             r += str(x)             if i<len(arr)-1:                 r += sep                         return r      if isinstance( arr[0],str):         myprod = lambda x: arr2str(x,'*')         mysum = lambda x: arr2str(x,'+')         e=lambda x: 'e('+str(x)+')'         myfloat = str     else:         myfloat = lambda x: x         myprod = np.prod         mysum = sum     s = set(range(len(arr)))     p = partition(s)        return mysum([           myprod([myfloat(math.factorial(len(pi)-1)   * (-1)**(len(pi)-1))         ,myprod([             e(myprod([                 arr[i]                 in b             ]))             b in pi])])         pi in p])  print(cum2mom(['a','b','c','d'],1)    ) import qutip qu print(cum2mom([qu.qeye(3) in range(3)],qu.qeye(3))    )

it's designed work qutip opjects , works strings verify correct separation , prefactors.

exponents of variables can represented repeating variable.


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