numpy multiply

numpy.multiply(x1, x2[, out]) : Multiply arguments element-wise, 广播法则。

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• numpy的multiply和*什么区别
  　　Numpy matrices必须是2维的,但是numpy arrays (ndarrays) 可以是多维的（1D，2D，3D····ND）. Matrix是Array的一个小的分支，包含于Array。所以matrix 拥有array的所有特性。

  　　在numpy中matrix的主要优势是：相对简单的乘法运算符号。例如，a和b是两个matrices，那么a*b，就是矩阵积。

  　　import numpy as np

  　　a=np.mat(‘4 3; 2 1’)
  　　b=np.mat(‘1 2; 3 4’)
  　　print(a)
  　　# [[4 3]
  　　# [2 1]]
  　　print(b)
  　　# [[1 2]
  　　# [3 4]]
  　　print(a*b)
  　　# [[13 20]
  　　# [ 5 8]]
  　　matrix 和 array 都可以通过在have.Tto return the transpose, but matrix objects also have.Hfor the conjugate transpose, and.Ifor the inverse.

  　　In contrast, numpy arrays consistently abide by the rule that operations are applied element-wise. Thus, if a and b are numpy arrays, then a*b is the array formed by multiplying the components element-wise:

  　　c=np.array([[4, 3], [2, 1]])
  　　d=np.array([[1, 2], [3, 4]])
  　　print(c*d)
  　　# [[4 6]
  　　# [6 4]]
  　　To obtain the result of matrix multiplication, you use np.dot :

  　　print(np.dot(c,d))
  　　# [[13 20]
  　　# [ 5 8]]
  　　The**operator also behaves differently:

  　　print(a**2)
  　　# [[22 15]
  　　# [10 7]]
  　　print(c**2)
  　　# [[16 9]
  　　# [ 4 1]]
  　　Sinceais a matrix,a**2returns the matrix producta*a. Sincecis an ndarray,c**2returns an ndarray with each component squared element-wise.

  　　There are other technical differences between matrix objects and ndarrays (having to do with np.ravel, item selection and sequence behavior).

  　　The main advantage of numpy arrays is that they are more general than 2-dimensional matrices. What happens when you want a 3-dimensional array? Then you have to use an ndarray, not a matrix object. Thus, learning to use matrix objects is more work – you have to learn matrix object operations, and ndarray operations.

  　　Writing a program that uses both matrices and arrays makes your life difficult because you have to keep track of what type of object your variables are, lest multiplication return something you don’t expect.

  　　In contrast, if you stick solely with ndarrays, then you can do everything matrix objects can do, and more, except with slightly different functions/notation.

  　　If you are willing to give up the visual appeal of numpy matrix product notation, then I think numpy arrays are definitely the way to go.

  　　PS. Of course, you really don’t have to choose one at the expense of the other, sincenp.asmatrixandnp.asarrayallow you to convert one to the other (as long as the array is 2-dimensional).

  　　One of the biggest practical differences for me of numpy ndarrays compared to numpy matrices or matrix languages like matlab, is that the dimension is not preserved in reduce operations. Matrices are always 2d, while the mean of an array, for example, has one dimension less.

  　　For example demean rows of a matrix or array:

  　　with matrix

  　　>>> m = np.mat([[1,2],[2,3]])
  　　>>> m
  　　matrix([[1, 2],
  　　[2, 3]])
  　　>>> mm = m.mean(1)
  　　>>> mm
  　　matrix([[ 1.5],
  　　[ 2.5]])
  　　>>> mm.shape
  　　(2, 1)
  　　>>> m - mm
  　　matrix([[-0.5, 0.5],
  　　[-0.5, 0.5]])
  　　with array

  　　>>> a = np.array([[1,2],[2,3]])
  　　>>> a
  　　array([[1, 2],
  　　[2, 3]])
  　　>>> am = a.mean(1)
  　　>>> am.shape
  　　(2,)
  　　>>> am
  　　array([ 1.5, 2.5])
  　　>>> a - am #wrong
  　　array([[-0.5, -0.5],
  　　[ 0.5, 0.5]])
  　　>>> a - am[:, np.newaxis] #right
  　　array([[-0.5, 0.5],
  　　[-0.5, 0.5]])
  　　I also think that mixing arrays and matrices gives rise to many “happy” debugging hours. However, scipy.sparse matrices are always matrices in terms of operators like multiplication.