生成数组的组合 [英] generate combinations of arrays

问题描述

我要处理9个数组以查找所有可能的组合，因此结果数组的名称告诉我已组合了哪些数组.例如:

I have 9 arrays that I want to manipulate to find all possible combinations, so that the name of the resulting array tells me which arrays have been combined. For example:

a1_a2 = array1 - array2
a1_a3 = array1 - array3
a1_a4 = array1 - array4
.
.
.
a9_a6 = array9 - array6
a9_a7 = array9 - array7
a9_a8 = array9 - array8

很明显，我可以对其进行硬编码，但是如何循环进行呢?

Obviously I could hardcode it, but how could I do it in a loop?

我想为此编写一个函数，例如:

I thought of writing a function for it, something like:

def combineArrays(array1, array2):
    result_name = name_of_array1 + '_' + name_of_array2 # How would I do this bit?
    result = array1 - array2
    return result

for firstArray in arrays:
    for secondArray in reversed(arrays): # to go backwards through the list of arrays
        combineArrays(firstArray, secondArray)

例如，以下数组:

array1 = [1,2,nan,4,5]
array2 = [5,4,3,2,1]
array3 = [2,4,6,8,10]

应产生输出

a1_a2 = [-4,-2,nan,2,4]
a1_a3 = [-2,-4,nan,-8,-10]
a2_a1 = [4,2,nan,-2,-4]
a2_a3 = [2,-2,-6,-10,-14]
a3_a2 = [-2,2,6,10,14]
a3_a1 = [2,4,nan,8,10]

因此，对每种可能的数组组合进行逐元素减法.

so, element-wise subtraction for each possible combination of arrays.

由于我使用的是 numpy ，是否甚至还有线性代数类型的方法?以及如何让程序为我命名数组?

Since I'm using numpy, is there even a linear algebra-type way to do this? And how can I get the program to name the arrays for me?

这个问题似乎在问类似的问题，但我不明白答案

This question seems to be asking something similar, but I don't understand the answer.

推荐答案

这是可与任何功能一起使用的通用代码:您可以通过它来理解，但它确实可以满足您的要求:

This is a generalized code that works with any function: You might go through it to understand but it does what you exactly want:

def factorial(n):
    if n==0:
        return 1
    else:
        return n*factorial(n-1)



def choose(n,m):
    if n < m:
        raise ValueError("n is less than m!")
    if m < 0:
        raise ValueError("m cannot be negative!!")
    else:
        return int(factorial(n)/factorial(m)/factorial(n-m))


def combn(x, m, FUN = None):
    import numpy as np
    if not isinstance(m,int):
        raise ValueError("m must be a single integer")

    if isinstance(x, int)  and x > 0:
      x = np.arange(1, x+1)

    n, x, e, h, a, nofun = len(x), np.array(x), 0, m, np.arange(1,m+1), FUN==None

    if not nofun and not callable(FUN):
        raise TypeError("'FUN' must be a function or None")

    if (nofun):r = x[a-1] 
    else: r = FUN(x[a-1])   
    out = [None] * choose(n, m)
    out[0] = r

    if m > 0:  
        i = 2
        nmmp1 = n - m + 1
        while a[0] != nmmp1:
          if e < n - h:
            h, e, j = 1, a[m-1], 1
          else:
            e = a[m - h-1]
            h += 1
            j = np.arange(1,h+1)

          a[m - h + j-1] = e + j
          if (nofun): r = x[a-1]
          else: r = FUN(x[a-1])
          out[i-1] = r
          i += 1
    return out

您可以将其保存以供将来使用:.现在，在此之后，您可以进行所需的任何组合:

You can save this for future use:. Now after this you can do any combinations that you want:

 combn(4,3)
Out[854]: [array([1, 2, 3]), array([1, 2, 4]), array([1, 3, 4]), array([2, 3, 4])]

combn([1,2,3,4],3)
Out[855]: [array([1, 2, 3]), array([1, 2, 4]), array([1, 3, 4]), array([2, 3, 4])]

 combn([1,2,3,4],3,sum)
Out[856]: [6, 7, 8, 9]

您可以这样做:

array1 = [1,2,np.nan,4,5]
array2 = [5,4,3,2,1]
array3 = [2,4,6,8,10]

combn([array1,array2,array3],2,lambda x: x[0]-x[1])
Out[859]: 
[array([-4., -2., nan,  2.,  4.]),
 array([-1., -2., nan, -4., -5.]),
 array([ 3.,  0., -3., -6., -9.])]

现在使用 lambda x:x [1] -x [0] 运行相同的代码，从而为您提供所需的所有组合

Now run the same code with lambda x:x[1]-x[0] thus giving you all the combinations that you want

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