# 论numpy中matrix 和 array的区别

2014-03-07 18:10 本站整理 浏览(8325)

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。

``````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`.T`to

return the transpose, but matrix objects also have`.H`for the conjugate transpose, and`.I`for

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]]``````
Since`a`is

a matrix,`a**2`returns the matrix product`a*a`.

Since`c`is an ndarray,`c**2`returns

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, since`np.asmatrix`and`np.asarray`allow 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.