https://blog.csdn.net/taxueguilai1992/article/details/46581861
The library provides a python numpy matrix calculation function, so when we need matrix operations, need to import numpy package.
The introduction and use 1.numpy
from numpy import *; # import numpy library functions import numpy as np; # this mode when using numpy function, you need to start with np..
2. Create a matrix
Create a matrix of one-dimensional or two-dimensional data
>>> from numpy import *
>>> a1=array([1,2,3])
>>> a1
array([1, 2, 3])
>>> a1=mat(a1)
>>> a1
matrix([[1, 2, 3]])
>>> shape(a1)
(1, 3)
>>> b=matrix([1,2,3])
>>> shape(b)
(1, 3)
Create a common matrix
>>> data1 = mat (zeros (( 3,3))) # 3 * 3 to create a zero matrix, where the matrix parameter is a function zeros tuple type (3,3)
>>> DATAl
Matrix ([[0 ., 0., 0.],
[0., 0., 0.],
[0., 0., 0.]])
>>> data2 = MAT (ones ((2, 4))) # create 1 a 2 * 4 matrix, the default floating-point data, if the int type when needed, may be used int = DTYPE
>>> DATA2
matrix ([[1., 1., 1., 1.],
[1 ., 1., 1., 1.]])
>>> DATA3 = MAT (random.rand (2,2 &)) where # is a random module numpy the random module, random.rand (2,2 ) is a two-dimensional array is created, it is necessary to convert it into #matrix
>>> DATA3
Matrix ([[.57341802, 0.51016034],
[.56438599, 0.70515605]])
>>> DATA4, MAT = (the random.randint (10, size = (3,3))) * 3 # 3 generates a random integer between 0 and 10 of the matrix, if necessary to specify a lower bound can be more parameters
>>> DATA4,
matrix ([[. 9,. 5,. 6],
[3, 0, 4],
[. 6, 0,. 7]])
>>> DATA5 = MAT (the random.randint (2,8, size = (2,5))) # generates a random integer matrix between 2-8
>>> DATA5
Matrix ([[. 5,. 4,. 6,. 3,. 7],
[. 5,. 3,. 3,. 4,. 6]])
>>> Data6 = MAT (Eye (2,2 &, DTYPE = int)) to generate a # 2 * diagonal matrix 2
>>> Data6
matrix ([[. 1, 0],
[0,. 1]])
A1 = [l, 2,3]
A2 = MAT (diag (A1)) to generate a diagonal # 1,2,3 diagonal matrix
>>> A2
matrix ([[. 1, 0, 0],
[0, 2, 0],
[0, 0,. 3]])
3. Common matrix operations
1. Matrix Multiplication
A1 = MAT >>> ([1,2]); >>> A2 = MAT ([[1], [2]]); >>> A3 = A1 * A2 * # 2 is multiplied by a matrix of 2 * 1 matrix to obtain a matrix of 1 * 1
>>> A3
matrix ([[. 5]])
2. dot matrix
Corresponding elements of the matrix multiplication
>>>a1=mat([1,1]); >>>a2=mat([2,2]); >>>a3=multiply(a1,a2) >>> a3 matrix([[2, 2]])
Dot matrix
>>>a1=mat([2,2]); >>>a2=a1*2>>>a2 matrix([[4, 4]])
3. The matrix inversion, transpose
matrix inversion
A1 = MAT >>> (Eye (2,2 &) * 0.5)
>>> A1
matrix ([[0.5, of 0. The],
[of 0. The, 0.5]])
>>> A2 = # of Matrix matrix A1.i ([[0.5,0], [0, 0.5]]) is the inverse matrix
>>> A2
matrix ([[2., of 0. the],
[of 0. the, 2.]])
Matrix transpose
>>> a1=mat([[1,1],[0,0]])
>>> a1
matrix([[1, 1],
[0, 0]])
>>> a2=a1.T
>>> a2
matrix([[1, 0],
[1, 0]])
4. Calculate the matrix corresponding to the ranks of the maximum, minimum, and.
3>>>a1=mat([[1,1],[2,3],[4,2]])
>>> a1
matrix([[1, 1],
[2, 3],
[4, 2]])
Calculated for each column, row, and
>>> a2 = a1.sum (axis = 0 ) # and columns, the matrix here is that 1 * 2
>>> A2
Matrix ([[. 7,. 6]])
>>> A3 = a1.sum (Axis = 1) and # line, obtained here is the matrix of 3 * 1
>>> A3
matrix ([[2],
[. 5],
[. 6]])
>>> A4 = SUM (A1 [1 ,:]) # calculating a first row and all the columns, is a value obtained here
>>> A4
. 5 line # 0: 1 + 1; line 2: 3 + 2; lane 3: 4 + 2
Calculate the maximum, minimum and index
>>> a1.max () # a1 calculated maximum value of all elements in the matrix, the result is a value obtained here . 4 >>> A2 = max (a1 [:,. 1]) calculated maximum of the second column #, a matrix obtained here is 1 * 1 >>> A2 matrix ([[. 3]]) >>> A1 [1,:] max () calculates the maximum value of the second row #, obtained here is a one. value . 3 >>> np.max (A1,0) # calculates the maximum value of all the columns, the max function used here is the numpy
Matrix ([[. 4,. 3]]) >>> np.max (a1,1 ) # calculates the maximum of all the rows, there is obtained a matrix matrix ([[. 1],
[. 3],
[. 4]]) >>> np.argmax (A1,0) # calculated maximum value corresponding to all columns in the column index
Matrix ([[2, 1]]) >>> np.argmax (A1 [1 ,:]) # calculating a second line corresponding to the maximum index of the row
1
The separated and combined matrix
separated matrix consistent with the partition arrays and lists.
MAT = A >>> (ones ((3,3)))
>>> A
Matrix ([[1., 1., 1.],
[1., 1., 1.],
[1.,. 1 ., 1.]])
>>> B = a [. 1:,. 1:] # divided row after row of the second column and second row all elements subsequent
>>> B
Matrix ([[1., 1],
[1, 1]])
The combined matrix
MAT = A >>> (ones ((2,2 &)))
>>> A
Matrix ([[1., 1.],
[1., 1.]])
>>> B = MAT (Eye (2 ))
>>> B
Matrix ([[1., of 0. The],
[of 0. The, 1.]])
>>> vStack C = ((A, B)) # columns were combined, i.e., increasing the number of rows
>> > C
Matrix ([[1., 1.],
[1., 1.],
[1., of 0. The],
[of 0. The, 1.]])
>>> hstack D = ((A, B) ) # rows were combined, i.e. the same number of rows, columns extend
>>> D
Matrix ([[1., 1., 1., of 0. The],
[1., 1., of 0. The, 1.]])
4. The conversion matrix, a list, an array of
The list can be modified, and the elements in the list can make different types of data, as follows:
l1=[[1],'hello',3];
numpy in an array, with all the elements of an array must be the same type, there are several common attributes:
>>>a=array([[2],[1]])
>>> a
array([[2],
[1]])
>>>dimension=a.ndim
>>> dimension
2
>>>m,n=a.shape
>>> m
2
>>> n
1
>>>number=a.size #元素总个数
>>> number
2
>>>str=a.dtype #元素的类型
>>> str
dtype('int64')
numpy matrix in there with an array of several common attributes.
Conversion between them:
>>> a1 = [[1,2], [3,2], [5,2]] # listing
>>> A1
[[. 1, 2], [. 3, 2], [. 5, 2]]
> >> a2 = array (a1) # the list into a two-dimensional array
>>> A2
array ([[. 1, 2],
[. 3, 2],
[. 5, 2]])
>>> A3 = MAT (A1 ) is converted into a matrix list #
>>> A3
matrix ([[. 1, 2],
[. 3, 2],
[. 5, 2]])
>>> array A4 = (A3) to the transformation matrix array #
>> > A4
array ([[. 1, 2],
[. 3, 2],
[. 5, 2]])
>>> A41 = a3.getA () # convert into an array matrix
>>> A41
array ([[. 1, 2]
[3,2-]
[5,2]])
>>> A5 = a3.tolist () into the transformation matrix list #
>>> A5
[[. 1, 2], [. 3, 2], [. 5, 2]]
>>> a6 = a2.tolist () # the array into the list
>>> a6>> a6 = a2.tolist () # converting the array into a list
[[1, 2], [3, 2], [5, 2]]
Here can be found between the three conversion is very simple to note here is that, when the lists are one-dimensional, and converts it into an array matrix, and then by ToList () is converted into a list is not the same, We need to make some minor modifications. as follows:
>>>a1=[1,2,3] #列表 >>>a2=array(a1) >>> a2 array([1, 2, 3]) >>>a3=mat(a1) >>> a3 matrix([[1, 2, 3]]) >>> a4=a2.tolist() >>> a4 [1, 2, 3] >>> a5=a3.tolist() >>> a5 [[1, 2, 3]] >>> a6=(a4==a5) >>> a6 False >>> a7=(a4 is a5[0]) >>> a7 True
Converted into a numerical matrix, the presence of the following conditions:
MAT = Datamat >>> ([. 1]) >>> Datamat Val = [0,0] # is the matrix element values acquired at this time, rather than the type of matrix >>> Val . 1