numpy函数fromfunction分析

    从函数规则创建数组是非常方便的方法。在numpy中我们常用fromfunction函数来实现这个功能。

    在numpy的官网有这么一个例子。

>>> def f(x,y):
...         return 10*x+y
...
>>> b = fromfunction(f,(5,4),dtype=int)
>>> b
array([[ 0,  1,  2,  3],
       [10, 11, 12, 13],
       [20, 21, 22, 23],
       [30, 31, 32, 33],
       [40, 41, 42, 43]])

      查找help()解释如下：

  numpy.fromfunction(function, shape, **kwargs)[source]

Construct an array by executing a function over each coordinate.

The resulting array therefore has a value fn(x, y, z) at coordinate (x, y, z).

Parameters:

function : callable The function is called with N parameters, where N is the rank of shape. Each parameter represents the coordinates of the array varying along a specific axis. For example, if shape were (2, 2), then the parameters in turn be (0, 0), (0, 1), (1, 0), (1, 1). shape : (N,) tuple of ints Shape of the output array, which also determines the shape of the coordinate arrays passed to function. dtype : data-type, optional Data-type of the coordinate arrays passed to function. By default, dtype is float.

Returns:

fromfunction : any The result of the call to function is passed back directly. Therefore the shape of fromfunction is completely determined by function. If function returns a scalar value, the shape of fromfunction would match the shape parameter.

    主要是第二个参数shape，(N,)定义了fromfunction的输出数据形式。

    说起来比较绕口，下面用几个例子说明。

     

# -*- coding: utf-8 -*-
from numpy import *

def f1(x,y):
    return x

def f2(x,y):
    return y   

def f3(x,y):
    return 2*x+y

  运行测试：

>>> b=fromfunction(f1, (5,5), dtype = int)
>>> b
array([[0, 0, 0, 0, 0],
[1, 1, 1, 1, 1],
[2, 2, 2, 2, 2],
[3, 3, 3, 3, 3],
[4, 4, 4, 4, 4]])

>>> b=fromfunction(f1, (5,4), dtype = int)
>>> b
array([[0, 0, 0, 0],
[1, 1, 1, 1],
[2, 2, 2, 2],
[3, 3, 3, 3],
[4, 4, 4, 4]])

>>> b=fromfunction(f2, (5,5), dtype = int)
>>> b
array([[0, 1, 2, 3, 4],
[0, 1, 2, 3, 4],
[0, 1, 2, 3, 4],
[0, 1, 2, 3, 4],
[0, 1, 2, 3, 4]])
>>> b=fromfunction(f3, (5,5), dtype = int)
>>> b
array([[ 0, 1, 2, 3, 4],
[ 2, 3, 4, 5, 6],
[ 4, 5, 6, 7, 8],
[ 6, 7, 8, 9, 10],
[ 8, 9, 10, 11, 12]])
>>>

　　从上面的测试可以看出，shape()定义了输出矩阵的大小。如shape(5,4)，则x参数是5行1列行列式[0,1,2,3,4]. y参数1行4列行列式[0,1,2,3]. 

      将x,y带人func函数计算，最后结果的每个元素是根据func 函数来计算得出。