递归函数可将任何函数应用于任意长度的N个数组，以形成一个N个锯齿状的多维数组 [英] Recursive function to apply any function to N arrays of any length to form one jagged multidimensional array of N dimensions

问题描述

给出N个输入数组，所有 any 个长度，我希望能够将一个函数应用于每个组合的 all 个组合每个数组.

Given N input arrays, all of any length, I would like to be able to apply a function to all combinations of every combination of each arrays.

例如:

给出输入数组:

[1、2][3，4，5][6，7，8，9]

还有一个返回N个元素乘积的函数

And a function which returns the product of N elements

我希望能够将功能应用于这些元素的每种组合.在这种情况下，它会产生一个三维数组，长度分别为2、3和4.

I would like to be able to apply a function to every combination of these elements. In this case it results in a 3 dimensional array, of lengths 2, 3, and 4 respectively.

结果数组如下:

[
    [
        [18, 21, 24, 27], 
        [24, 28, 32, 36], 
        [30, 35, 40, 45]
    ], 
    [
        [36, 42, 48, 54], 
        [48, 56, 64, 72], 
        [60, 70, 80, 90]
    ]
]

推荐答案

使用np.frompyfunc创建所需函数的ufunc的另一种方法.这对n个参数使用ufuncs .outer方法n-1次.

An alternative approach using np.frompyfunc to create a ufunc of the required function. This is the applied with the ufuncs .outer method n-1 times for the n arguments.

import numpy as np

def testfunc( a, b):
    return a*(a+b) + b*b

def apply_func( func, *args, dtype = np.float ):
    """ Apply func sequentially to the args
    """
    u_func = np.frompyfunc( func, 2, 1) # Create a ufunc from func
    result = np.array(args[0])
    for vec in args[1:]:
        result = u_func.outer( result, vec )  # apply the outer method of the ufunc
        # This returns arrays of object type. 
    return np.array(result, dtype = dtype) # Convert to type and return the result

apply_func(lambda x,y: x*y, [1,2], [3,4,5],[6,7,8,9] )

# array([[[18., 21., 24., 27.],
#         [24., 28., 32., 36.],
#         [30., 35., 40., 45.]],

#        [[36., 42., 48., 54.],
#         [48., 56., 64., 72.],
#         [60., 70., 80., 90.]]])

apply_func( testfunc, [1,2], [3,4,5],[6,7,8,9])

# array([[[ 283.,  309.,  337.,  367.],
#         [ 603.,  637.,  673.,  711.],
#         [1183., 1227., 1273., 1321.]],

#        [[ 511.,  543.,  577.,  613.],
#         [ 988., 1029., 1072., 1117.],
#         [1791., 1843., 1897., 1953.]]])

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