如何在二维numpy数组/矩阵中应用每个元素的函数/映射值? [英] How to apply a function / map values of each element in a 2d numpy array/matrix?

问题描述

给出以下numpy矩阵:

Given the following numpy matrix:

import numpy as np
mymatrix = mymatrix = np.matrix('-1 0 1; -2 0 2; -4 0 4')


matrix([[-1,  0,  1],
        [-2,  0,  2],
        [-4,  0,  4]])

和以下功能(S形/物流):

and the following function (sigmoid/logistic):

import math
def myfunc(z):
    return 1/(1+math.exp(-z))

我想获得一个新的numpy数组/矩阵，其中每个元素都是将myfunc函数应用于原始矩阵中相应元素的结果.

I want to get a new numpy array/matrix where each element is the result of applying the myfunc function to the corresponding element in the original matrix.

map(myfunc, mymatrix)失败，因为它尝试将myfunc应用于行，而不是应用于每个元素.我尝试使用numpy.apply_along_axis和numpy.apply_over_axis，但是它们也意在将函数应用于行或列，而不是逐个元素地应用.

the map(myfunc, mymatrix) fails because it tries to apply myfunc to the rows not to each element. I tried to use numpy.apply_along_axis and numpy.apply_over_axis but they are meant also to apply the function to rows or columns and not on a element by element basis.

那么如何将myfunc(z)应用于myarray的每个元素以获得:

So how can apply myfunc(z) to each element of myarray to get:

matrix([[ 0.26894142,  0.5       ,  0.73105858],
        [ 0.11920292,  0.5       ,  0.88079708],
        [ 0.01798621,  0.5       ,  0.98201379]])

推荐答案

显然，将函数应用于元素的方法是将函数转换为向量化版本，该向量化版本将数组作为输入，并将数组作为输出.

Apparently the way to apply a function to elements is to convert your function into a vectorized version that takes arrays as input and return arrays as output.

您可以使用numpy.vectorize轻松地将函数转换为矢量化形式，如下所示:

You can easily convert your function to vectorized form using numpy.vectorize as follows:

myfunc_vec = np.vectorize(myfunc)
result = myfunc_vec(mymatrix)

或一次性使用:

np.vectorize(myfunc)(mymatrix)

如@Divakar所指出的那样，如果可以从头开始编写一个已经矢量化的函数(使用numpy构建的

As pointed out by @Divakar, it's better (performance-wise) if you can write an already vectorized function from scratch (using numpy built ufuncs without using numpy.vectorize) like so:

def my_vectorized_func(m):
    return 1/(1+np.exp(-m))  # np.exp() is a built-in ufunc

myvectorized_func(mymatrix)

由于 numpy.exp 已经向量化(不是math.exp)，整个表达式1/(1+np.exp(-m))将被向量化(并且更快地将我的原始函数应用于每个元素).

Since numpy.exp is already vectorized (and math.exp wasn't) the whole expression 1/(1+np.exp(-m)) will be vectorized (and faster that applying my original function to each element).

以下完整示例产生了所需的输出:

The following complete example produced the required output:

import numpy as np
mymatrix = mymatrix = np.matrix('-1 0 1; -2 0 2; -4 0 4')
import math
def myfunc(z):
    return 1/(1+math.exp(-z))

np.vectorize(myfunc)(mymatrix) # ok, but slow

def my_vectorized_func(m):
    return 1/(1+np.exp(-m))

my_vectorized_func(mymatrix) # faster using numpy built-in ufuncs

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