Data analysis - numpy quick start

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One 、numpy Installation

If you use the system directly python Environmental Science , Then use the following command to install

pip install numpy

If you use pipenv Virtual environment created by tools , Then use the following command ：

pipenv install numpy

Two 、Numpy Medium matrix array Basic properties of

• ndim： dimension
  such as 3x4 Matrix , its ndim by 2

• shape： A few lines and columns , Represented by tuples
  such as 3x4 matrix , its shape by (3,4)

• size: The total number of elements
  such as 3x4 Matrix , its size by 12

• dtype： Type of element
  You can use it directly python Type in ,numpy Some types such as numpy.int32, numpy.int16, numpy.float64 etc.

• itemsize： The size of the element
  Memory occupied by each element , Unit is byte , For example, when type int64, be itemsize by 8 Bytes , Equivalent to dtype.itemsize

Examples are as follows , among arr=np.arange(12).reshape((3,4)) Is used to create a 3x4 Matrix , The element is 0-11, How to create a matrix will be explained in detail later , This is to demonstrate the properties of a matrix

>>> import numpy as np
>>> arr=np.arange(12).reshape((3,4))
>>> arr
array([[ 0,  1,  2,  3],
       [ 4,  5,  6,  7],
       [ 8,  9, 10, 11]])
>>> arr.ndim
2
>>> arr.shape
(3, 4)
>>> arr.dtype
dtype('int32')
>>> arr.dtype.name
'int32'
>>> arr.size
12
>>> arr.itemsize
4
>>> type(arr)
<class 'numpy.ndarray'>
>>>

3、 ... and 、 Create a matrix

3.1 By using Python Of list perhaps tuple To create a matrix

as follows , Use one-dimensional lists respectively , One dimensional tuples , 2 d list , A two-dimensional tuple creates a matrix

>>> import numpy as np
>>> arr=np.array([1,2,3])
>>> arr
array([1, 2, 3])
>>> arr=np.array((1,2,3))
>>> arr
array([1, 2, 3])
>>> arr=np.array([[1,2,3],[4,5,6]])
>>> arr
array([[1, 2, 3],
       [4, 5, 6]])
>>> arr=np.array(((1,2,3),(4,5,6)))
>>> arr
array([[1, 2, 3],
       [4, 5, 6]])
>>>

There's a little bit of caution here ,np.array The argument to is a list or element , It is not possible to give several elements directly , Here is a common mistake for beginners

>>> import numpy as np
>>> arr=np.array(1,2,3,4)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: array() takes from 1 to 2 positional arguments but 4 were given

The correct should be as follows ：

>>> import numpy as np
>>> arr=np.array([1,2,3,4])
>>> arr
array([1, 2, 3, 4])

In addition, when creating a matrix , You can also specify the type of data , Let's take a look at the case when the data type is not specified , Default data type , Of course, this is related to the computer platform , as follows , By default 32 Bit int type

>>> import numpy as np
>>> arr=np.array([1,2,3])
>>> arr
array([1, 2, 3])
>>> arr.dtype
dtype('int32')
>>>

as follows , You can pass dtype Parameter specifies the type of matrix element

>>> import numpy as np
>>> arr=np.array([1,2,3],dtype=np.int64)
>>> arr
array([1, 2, 3], dtype=int64)
>>> arr.dtype
dtype('int64')
>>>

3.2 Create a matrix through common basic functions

The common functions are as follows

• zeros： Create all elements as 0 Matrix
• ones： Create all elements as 1 Matrix
• empty： Create a matrix with random elements , By default empty The element type created by the function is float64, Of course, you can also pass dtype Parameter specified type .
• arange： Be similar to python in range Function of , You can generate a sequence of equal differences by specifying the initial and end values and the step size , Yes, of course reshape Function to convert the generated one-dimensional arithmetic sequence into a multi-dimensional matrix .
• linspace： By specifying the start and end values and the number of generated numbers , And then it automatically performs equal difference segmentation , It can also be done by reshape Function to convert the generated one-dimensional list into a multi-dimensional matrix

Examples are as follows ：

>>> import numpy as np
>>> arr=np.zeros((3,4))
>>> arr
array([[0., 0., 0., 0.],
       [0., 0., 0., 0.],
       [0., 0., 0., 0.]])
>>> arr=np.ones((3,4))
>>> arr
array([[1., 1., 1., 1.],
       [1., 1., 1., 1.],
       [1., 1., 1., 1.]])
>>> arr=np.empty((3,4))
>>> arr
array([[1., 1., 1., 1.],
       [1., 1., 1., 1.],
       [1., 1., 1., 1.]])
>>> arr=np.empty((3,4),dtype=np.int32) >>> arr array([[ 0, 1, 2, 3], [ 4, 5, 6, 7], [ 8, 9, 10, 11]]) >>> arr=np.arange(0,12,1).reshape((3,4))
>>> arr
array([[ 0,  1,  2,  3],
       [ 4,  5,  6,  7],
       [ 8,  9, 10, 11]])
>>> arr=np.arange(0,24,2).reshape((3,4))
>>> arr
array([[ 0,  2,  4,  6],
       [ 8, 10, 12, 14],
       [16, 18, 20, 22]])
>>> arr=np.linspace(1,100,12).reshape((3,4))
>>> arr
array([[  1.,  10.,  19.,  28.],
       [ 37.,  46.,  55.,  64.],
       [ 73.,  82.,  91., 100.]])
>>>

Four 、 Print matrix

numpy When printing multidimensional matrix , The following layout will be followed

• The last dimension prints from left to right
• The penultimate dimension prints from top to bottom
• The rest are printed from top to bottom , And each dimension is separated by an empty line

The following is a table by table print 、 A two-dimensional 、 The three dimensional matrix

>>> import numpy as np
>>> arr=np.arange(6)
>>> print(arr)
[0 1 2 3 4 5]
>>> b=np.arange(12).reshape((3,4))
>>> print(b)
[[ 0  1  2  3]
 [ 4  5  6  7]
 [ 8  9 10 11]]
>>> c=np.arange(24).reshape((2,3,4))
>>> print(c)
[[[ 0  1  2  3]
  [ 4  5  6  7]
  [ 8  9 10 11]]

 [[12 13 14 15]
  [16 17 18 19]
  [20 21 22 23]]]
>>>

If there are too many matrix elements , be numpy There will be only a corner , The middle one uses … Instead of , as follows ：

>>> import numpy as np
>>> arr=np.arange(10000)
>>> print(arr)
[   0    1    2 ... 9997 9998 9999]
>>> arr=np.arange(10000).reshape((100,100))
>>> print(arr)
[[   0    1    2 ...   97   98   99]
 [ 100  101  102 ...  197  198  199]
 [ 200  201  202 ...  297  298  299]
 ...
 [9700 9701 9702 ... 9797 9798 9799]
 [9800 9801 9802 ... 9897 9898 9899]
 [9900 9901 9902 ... 9997 9998 9999]]
>>>

Of course, if you want to print all the elements, you can also set , By using set_printoptions To control

np.set_printoptions(threshold=sys.maxsize)

5、 ... and 、 Basic operation

The basic addition, subtraction, multiplication, division and power is the addition, subtraction, multiplication, division and power between the elements of a matrix , as follows

>>> import numpy as np
>>> a=np.array([1,2,3,4])
>>> b=np.arange(4)
>>> a
array([1, 2, 3, 4])
>>> b
array([0, 1, 2, 3])
>>> a+b
array([1, 3, 5, 7])
>>> a-b
array([1, 1, 1, 1])
>>> a*b
array([ 0,  2,  6, 12])
>>> b/a
array([0.        , 0.5       , 0.66666667, 0.75      ])
>>> a>0
array([ True,  True,  True,  True])
>>> a**2
array([ 1,  4,  9, 16])
>>> b>2
array([False, False, False,  True])
>>> np.sin(a)
array([ 0.84147098,  0.90929743,  0.14112001, -0.7568025 ])
>>> np.cos(a)
array([ 0.54030231, -0.41614684, -0.9899925 , -0.65364362])
>>> np.tan(a)
array([ 1.55740772, -2.18503986, -0.14254654,  1.15782128])

Dot multiplication of matrices uses dot Or use @ Symbol , as follows ：

>>> a=np.array([[1,1],[0,1]])
>>> b=np.array([[2,0],[3,4]])
>>> a
array([[1, 1],
       [0, 1]])
>>> b
array([[2, 0],
       [3, 4]])
>>> a*b
array([[2, 0],
       [0, 4]])
>>> [email protected]
array([[5, 4],
       [3, 4]])
>>> a.dot(b)
array([[5, 4],
       [3, 4]])
>>> np.dot(a,b)
array([[5, 4],
       [3, 4]])
>>>

Some operators, such as += or *=, It will directly process the existing matrix instead of creating a new matrix , as follows , among np.random.default_rng(1) Is the default random number generator

>>> import numpy as np
>>> rng=np.random.default_rng(1)
>>> a=np.ones((2,3),dtype=np.int32) >>> b=rng.random((2,3))
>>> a
array([[1, 1, 1],
       [1, 1, 1]])
>>> b
array([[0.51182162, 0.9504637 , 0.14415961],
       [0.94864945, 0.31183145, 0.42332645]])
>>> a*=3
>>> a
array([[3, 3, 3],
       [3, 3, 3]])
>>> b+=a
>>> b
array([[3.51182162, 3.9504637 , 3.14415961],
       [3.94864945, 3.31183145, 3.42332645]])
>>> a+=b
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
numpy.core._exceptions._UFuncOutputCastingError: Cannot cast ufunc 'add' output from dtype('float64') to dtype('int32') with casting rule 'same_kind'
>>>

When multiple types are involved in the operation , The result will follow the principle of upward conversion , as follows ：

>>> import numpy as np
>>> a=np.ones(3,dtype=np.int32)
>>> b=np.linspace(0,np.pi,3)
>>> a
array([1, 1, 1])
>>> b
array([0.        , 1.57079633, 3.14159265])
>>> c=a+b
>>> c
array([1.        , 2.57079633, 4.14159265])
>>> b.dtype
dtype('float64')
>>> c.dtype
dtype('float64')
>>> d=np.exp(c*1j)
>>> d
array([ 0.54030231+0.84147098j, -0.84147098+0.54030231j,
       -0.54030231-0.84147098j])
>>> d.dtype
dtype('complex128')
>>>

Calculate the sum of all the elements of the matrix 、 Maximum 、 Minimum function , namely sum、max and min, as follows ：

>>> import numpy as np
>>> a=np.arange(12).reshape((3,4))
>>> a
array([[ 0,  1,  2,  3],
       [ 4,  5,  6,  7],
       [ 8,  9, 10, 11]])
>>> a.sum()
66
>>> np.sum(a)
66
>>> a.max()
11
>>> np.max(a)
11
>>> a.min()
0
>>> np.min(a)
0
>>>

adopt axis Parameters can evaluate elements and by row or column 、 Maximum and minimum , When axis=0 when , Means by column , When axis=1 when , By line , as follows

>>> import numpy as np
>>> a=np.arange(12).reshape((3,4))
>>> a
array([[ 0,  1,  2,  3],
       [ 4,  5,  6,  7],
       [ 8,  9, 10, 11]])
>>> a.sum(axis=0)
array([12, 15, 18, 21])
>>> np.sum(a,axis=0)
array([12, 15, 18, 21])
>>> a.sum(axis=1)
array([ 6, 22, 38])
>>> np.sum(a,axis=1)
array([ 6, 22, 38])
>>> a.max(axis=0)
array([ 8,  9, 10, 11])
>>> np.max(a,axis=0)
array([ 8,  9, 10, 11])
>>> a.max(axis=1)
array([ 3,  7, 11])
>>> np.max(a,axis=1)
array([ 3,  7, 11])
>>> a.min(axis=0)
array([0, 1, 2, 3])
>>> np.min(a,axis=0)
array([0, 1, 2, 3])
>>> a.min(axis=1)
array([0, 4, 8])
>>> np.min(a,axis=1)
array([0, 4, 8])
>>>

6、 ... and 、 The generic function

The common functions are as follows ：

• sin
• cos
• exp
• sqrt
• add
• all
• any
• apply_along_axis
• argmax
• argmin
• argsort
• average
• bincount
• ceil
• clip
• conj
• corrcoef
• cov
• cross
• cumprod
• cumsum
• diff
• dot
• floor
• inner
• invert
• lexsort
• max
• maximum
• mean
• median
• min
• minimum
• nonzero
• outer
• prod
• re
• round
• sort
• std
• sum
• trace
• transpose
• var
• vdot
• vectorize
• where

Examples are as follows ：

>>> import numpy as np
>>> a=np.arange(3)
>>> a
array([0, 1, 2])
>>> np.exp(a)
array([1.        , 2.71828183, 7.3890561 ])
>>> np.sqrt(a)
array([0.        , 1.        , 1.41421356])
>>> b=np.array([4,5,6])
>>> b
array([4, 5, 6])
>>> np.add(a,b)
array([4, 6, 8])
>>>

7、 ... and 、 Indexes 、 Slicing and iteration

7.1 Index of one-dimensional matrix 、 Slicing and iteration are used

Index of one-dimensional matrix 、 Slicing and iteration use methods like python Index of the list in 、 section 、 Same as iteration , as follows ：

>>> import numpy as np
>>> a=np.arange(10)
>>> a
array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
>>> a[2]
2
>>> a[2:5]
array([2, 3, 4])
>>> a[:6:2]
array([0, 2, 4])
>>> a[::-1]
array([9, 8, 7, 6, 5, 4, 3, 2, 1, 0])
>>> for i in a:
...    print(i)
...
0
1
2
3
4
5
6
7
8
9
>>>

7.2 Index of multidimensional matrix 、 Slicing and iteration

Index of multidimensional matrix 、 Slicing and iteration , The main difference is that each dimension uses an index , The middle is separated by commas , as follows ：

>>> import numpy as np
>>> a=np.arange(20).reshape((5,4))
>>> a
array([[ 0,  1,  2,  3],
       [ 4,  5,  6,  7],
       [ 8,  9, 10, 11],
       [12, 13, 14, 15],
       [16, 17, 18, 19]])
>>> a[2,3]
11
>>> a[0:4,1]
array([ 1,  5,  9, 13])
>>> a[:,1]
array([ 1,  5,  9, 13, 17])
>>> a[1:3:,:]
array([[ 4,  5,  6,  7],
       [ 8,  9, 10, 11]])
>>> for elem in a[:,1]:
...     print(elem)
...
1
5
9
13
17
>>> for elem in a[:,:]:
...     print(elem)
...
[0 1 2 3]
[4 5 6 7]
[ 8  9 10 11]
[12 13 14 15]
[16 17 18 19]
>>>

When the number of indexes provided is less than the dimension of the matrix , The following defaults to ：, as follows a[2], It's the equivalent of a[2,:]

>>> import numpy as np
>>> a=np.arange(20).reshape((4,5))
>>> a
array([[ 0,  1,  2,  3,  4],
       [ 5,  6,  7,  8,  9],
       [10, 11, 12, 13, 14],
       [15, 16, 17, 18, 19]])
>>> a[2]
array([10, 11, 12, 13, 14])
>>>

When multidimensional matrix , You can replace other dimensions by using three points , For example, the following assumptions a Is a five dimensional matrix , be ：

• a[1,2,…] Equivalent to a[1,2,:,:,:]
• a[…,3] Equivalent to a[:,:,:,:,3]
• a[4,…,5,:] Equivalent to a[4,:,:,5,:]

as follows

>>> import numpy as np
>>> a=np.arange(24).reshape((2,3,4))
>>> a
array([[[ 0,  1,  2,  3],
        [ 4,  5,  6,  7],
        [ 8,  9, 10, 11]],

       [[12, 13, 14, 15],
        [16, 17, 18, 19],
        [20, 21, 22, 23]]])
>>> a[1,...]
array([[12, 13, 14, 15],
       [16, 17, 18, 19],
       [20, 21, 22, 23]])
>>> a[1,:,:]
array([[12, 13, 14, 15],
       [16, 17, 18, 19],
       [20, 21, 22, 23]])
>>> a[...,2]
array([[ 2,  6, 10],
       [14, 18, 22]])
>>> a[:,:,2]
array([[ 2,  6, 10],
       [14, 18, 22]])
>>>

When a multidimensional matrix is traversed, it is usually traversed according to the first dimension , When you want to traverse each element , have access to flat attribute , as follows

>>> import numpy as np
>>> a=np.arange(12).reshape((3,4))
>>> a
array([[ 0,  1,  2,  3],
       [ 4,  5,  6,  7],
       [ 8,  9, 10, 11]])
>>> for elem in a:
...     print(elem)
...
[0 1 2 3]
[4 5 6 7]
[ 8  9 10 11]
>>> for elem in a.flat:
...     print(elem)
...
0
1
2
3
4
5
6
7
8
9
10
11
>>>

8、 ... and 、 The matrix shape The operation of

For a matrix, the following three methods do not change the matrix shape Original value

• ravel： Expand the matrix into a one-dimensional matrix
• T： Matrix rank transformation
• reshape： To readjust shape, But it will not modify the original shape

as follows

>>> import numpy as np
>>> a=np.arange(12).reshape((3,4))
>>> a
array([[ 0,  1,  2,  3],
       [ 4,  5,  6,  7],
       [ 8,  9, 10, 11]])
>>> b=a.ravel()
>>> a
array([[ 0,  1,  2,  3],
       [ 4,  5,  6,  7],
       [ 8,  9, 10, 11]])
>>> b
array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11])
>>> c=a.reshape(6,2)
>>> a
array([[ 0,  1,  2,  3],
       [ 4,  5,  6,  7],
       [ 8,  9, 10, 11]])
>>> c
array([[ 0,  1],
       [ 2,  3],
       [ 4,  5],
       [ 6,  7],
       [ 8,  9],
       [10, 11]])
>>> d=a.T
>>> a
array([[ 0,  1,  2,  3],
       [ 4,  5,  6,  7],
       [ 8,  9, 10, 11]])
>>> d
array([[ 0,  4,  8],
       [ 1,  5,  9],
       [ 2,  6, 10],
       [ 3,  7, 11]])
>>> a.shape
(3, 4)
>>> a.T.shape
(4, 3)
>>> e=a.reshape((6,2))
>>> a
array([[ 0,  1,  2,  3],
       [ 4,  5,  6,  7],
       [ 8,  9, 10, 11]])
>>> e
array([[ 0,  1],
       [ 2,  3],
       [ 4,  5],
       [ 6,  7],
       [ 8,  9],
       [10, 11]])
>>>

If you want to change the shape Adjustment , have access to resize function , as follows , You can find resize Function is to adjust the original matrix directly , And there's no return value , That is, in the following example b It's empty

>>> import numpy as np
>>> a=np.arange(12).reshape((3,4))
>>> a
array([[ 0,  1,  2,  3],
       [ 4,  5,  6,  7],
       [ 8,  9, 10, 11]])
>>> b=a.resize(6,2)
>>> a
array([[ 0,  1],
       [ 2,  3],
       [ 4,  5],
       [ 6,  7],
       [ 8,  9],
       [10, 11]])
>>> b
>>>

Reuse reshape Function , If a dimension is set to -1, Indicates that this dimension is automatically calculated , as follows

>>> import numpy as np
>>> a=np.arange(12).reshape((3,4))
>>> a
array([[ 0,  1,  2,  3],
       [ 4,  5,  6,  7],
       [ 8,  9, 10, 11]])
>>> b=a.reshape(6,-1)
>>> a
array([[ 0,  1,  2,  3],
       [ 4,  5,  6,  7],
       [ 8,  9, 10, 11]])
>>> b
array([[ 0,  1],
       [ 2,  3],
       [ 4,  5],
       [ 6,  7],
       [ 8,  9],
       [10, 11]])
>>>

Nine 、 Stacking between different matrices

Horizontal and vertical stacking between different matrices , as follows

>>> import numpy as np
>>> a=np.arange(4).reshape((2,2))
>>> b=np.arange(4,8).reshape((2,2))
>>> a
array([[0, 1],
       [2, 3]])
>>> b
array([[4, 5],
       [6, 7]])
>>> np.vstack((a,b))
array([[0, 1],
       [2, 3],
       [4, 5],
       [6, 7]])
>>> np.hstack((a,b))
array([[0, 1, 4, 5],
       [2, 3, 6, 7]])
>>>

column_stack Only in two-dimensional matrix is it equivalent to hstack, and row_stack Namely vstack Another name for , as follows

>>> import numpy as np
>>> a=np.arange(3)
>>> b=np.arange(3,6)
>>> a
array([0, 1, 2])
>>> b
array([3, 4, 5])
>>> np.column_stack((a,b))
array([[0, 3],
       [1, 4],
       [2, 5]])
>>> np.hstack((a,b))
array([0, 1, 2, 3, 4, 5])
>>> np.row_stack((a,b))
array([[0, 1, 2],
       [3, 4, 5]])
>>> np.vstack((a,b))
array([[0, 1, 2],
       [3, 4, 5]])
>>> a=np.arange(4).reshape((2,2))
>>> b=np.arange(4,8).reshape((2,2))
>>> a
array([[0, 1],
       [2, 3]])
>>> b
array([[4, 5],
       [6, 7]])
>>> np.column_stack((a,b))
array([[0, 1, 4, 5],
       [2, 3, 6, 7]])
>>> np.hstack((a,b))
array([[0, 1, 4, 5],
       [2, 3, 6, 7]])
>>> np.row_stack((a,b))
array([[0, 1],
       [2, 3],
       [4, 5],
       [6, 7]])
>>> np.vstack((a,b))
array([[0, 1],
       [2, 3],
       [4, 5],
       [6, 7]])
>>> np.column_stack is np.hstack
False
>>> np.row_stack is np.vstack
True
>>>

Ten 、 adopt newaxis Add a dimension to the existing matrix

To put it simply, I will newaxis Where is the parameter placed , The dimension corresponding to the location is set to 1, Examples are as follows

>>> import numpy as np
>>> a=np.array([1,2,3,4])
>>> a
array([1, 2, 3, 4])
>>> a.shape
(4,)
>>> b=a[:,np.newaxis]
>>> b
array([[1],
       [2],
       [3],
       [4]])
>>> b.shape
(4, 1)
>>> c=a[np.newaxis,:]
>>> c
array([[1, 2, 3, 4]])
>>> c.shape
(1, 4)
>>>

11、 ... and 、 Cut the matrix into many smaller matrices

The partition matrix can use hsplit and vsplit, The parameter can be a number , Indicates that the matrix is divided into columns or rows n A small matrix , It can also be an element , It means to split after the column or row corresponding to each number in the tuple , as follows

>>> import numpy as np
>>> a=np.arange(24).reshape((4,6))
>>> a
array([[ 0,  1,  2,  3,  4,  5],
       [ 6,  7,  8,  9, 10, 11],
       [12, 13, 14, 15, 16, 17],
       [18, 19, 20, 21, 22, 23]])
>>> np.hsplit(a,3)  #  It means that you will a Divided into... By column 3 A small matrix 
[array([[ 0,  1],
       [ 6,  7],
       [12, 13],
       [18, 19]]), array([[ 2,  3],
       [ 8,  9],
       [14, 15],
       [20, 21]]), array([[ 4,  5],
       [10, 11],
       [16, 17],
       [22, 23]])]
>>> np.vsplit(a,2) #  It means that you will a Divided into... By line 2 A small matrix 
[array([[ 0,  1,  2,  3,  4,  5],
       [ 6,  7,  8,  9, 10, 11]]), array([[12, 13, 14, 15, 16, 17],
       [18, 19, 20, 21, 22, 23]])]
>>> np.hsplit(a,(2,4)) #  It means that you will a As listed in 2 Column and the first 4 Split after column 
[array([[ 0,  1],
       [ 6,  7],
       [12, 13],
       [18, 19]]), array([[ 2,  3],
       [ 8,  9],
       [14, 15],
       [20, 21]]), array([[ 4,  5],
       [10, 11],
       [16, 17],
       [22, 23]])]
>>> np.vsplit(a,(1,3)) #  It means that you will a Divide by line after the first and third lines 
[array([[0, 1, 2, 3, 4, 5]]), array([[ 6,  7,  8,  9, 10, 11],
       [12, 13, 14, 15, 16, 17]]), array([[18, 19, 20, 21, 22, 23]])]
>>>

Twelve 、 Copy and view

12.1 No copy occurs

When directly assigning values or passing objects in functions , There will be no copying , The function passes arguments because in python What is passed in is a reference to an object , So there will be no copying , as follows

>>> import numpy as mp
>>> a=np.array([1,2,3,4])
>>> b=a
>>> a
array([1, 2, 3, 4])
>>> b
array([1, 2, 3, 4])
>>> b is a
True
>>> def f(x):
...     print(id(x))
...
>>> id(a)
2211569938384
>>> f(a)
2211569938384
>>>

12.2 View or light copy

adopt view The view created by the function is essentially a shallow copy , The copied objects are resize Does not affect the source object , However, the operation of modifying the value will cause the corresponding value of the source matrix to be modified synchronously , In addition, slicing essentially produces a new view , as follows

>>> import numpy as np
>>> a=np.arange(12).reshape((3,4))
>>> a
array([[ 0,  1,  2,  3],
       [ 4,  5,  6,  7],
       [ 8,  9, 10, 11]])
>>> b=a.view()
>>> b
array([[ 0,  1,  2,  3],
       [ 4,  5,  6,  7],
       [ 8,  9, 10, 11]])
>>> id(a)
2211558280336
>>> id(b)
2211569938192
>>> b is a
False
>>> b.base is a
False
>>> b.flags.owndata
False
>>> b.resize((2,6))
>>> b
array([[ 0,  1,  2,  3,  4,  5],
       [ 6,  7,  8,  9, 10, 11]])
>>> a
array([[ 0,  1,  2,  3],
       [ 4,  5,  6,  7],
       [ 8,  9, 10, 11]])
>>> b[0,0]=100
>>> b
array([[100,   1,   2,   3,   4,   5],
       [  6,   7,   8,   9,  10,  11]])
>>> a
array([[100,   1,   2,   3],
       [  4,   5,   6,   7],
       [  8,   9,  10,  11]])
>>> c=a[:,0:2]
>>> c
array([[100,   1],
       [  4,   5],
       [  8,   9]])
>>> c.flags.owndata
False
>>> c[0,0]=10000
>>> c
array([[10000,     1],
       [    4,     5],
       [    8,     9]])
>>> a
array([[10000,     1,     2,     3],
       [    4,     5,     6,     7],
       [    8,     9,    10,    11]])
>>> b
array([[10000,     1,     2,     3,     4,     5],
       [    6,     7,     8,     9,    10,    11]])
>>>

12.3 Deep copy

adopt copy The object created by the function is a deep copy , That is, modifying the value of the newly generated object will not affect the source matrix , as follows

>>> import numpy as np
>>> a=np.arange(12).reshape((3,4))
>>> a
array([[ 0,  1,  2,  3],
       [ 4,  5,  6,  7],
       [ 8,  9, 10, 11]])
>>> b=a.copy()
>>> b
array([[ 0,  1,  2,  3],
       [ 4,  5,  6,  7],
       [ 8,  9, 10, 11]])
>>> b.base is a
False
>>> b[0,0]=100
>>> a
array([[ 0,  1,  2,  3],
       [ 4,  5,  6,  7],
       [ 8,  9, 10, 11]])
>>> b
array([[100,   1,   2,   3],
       [  4,   5,   6,   7],
       [  8,   9,  10,  11]])
>>>

13、 ... and 、 Advanced use of indexes

An index can also be a list , In this way, multiple data can be fetched at one time , as follows

>>> import numpy as np
>>> arr=np.arange(10,20)
>>> arr
array([10, 11, 12, 13, 14, 15, 16, 17, 18, 19])
>>> index=np.array([1,1,3,7,4])
>>> index
array([1, 1, 3, 7, 4])
>>> arr[index]
array([11, 11, 13, 17, 14])
>>> index=np.array([[1,2,3],[4,5,6],[3,4,7]])
>>> index
array([[1, 2, 3],
       [4, 5, 6],
       [3, 4, 7]])
>>> arr[index]
array([[11, 12, 13],
       [14, 15, 16],
       [13, 14, 17]])
>>>

When the matrix is two-dimensional data , The elements in the indexed matrix represent each row , Such as the following

>>> import numpy as np
>>> arr=np.arange(10,22).reshape((3,4))
>>> arr
array([[10, 11, 12, 13],
       [14, 15, 16, 17],
       [18, 19, 20, 21]])
>>> index=np.array([0,1,0,2])
>>> arr[index]
array([[10, 11, 12, 13],
       [14, 15, 16, 17],
       [10, 11, 12, 13],
       [18, 19, 20, 21]])
>>> index=np.array([[0,1,1,0],[1,2,2,1]])
>>> index
array([[0, 1, 1, 0],
       [1, 2, 2, 1]])
>>> arr[index]
array([[[10, 11, 12, 13],
        [14, 15, 16, 17],
        [14, 15, 16, 17],
        [10, 11, 12, 13]],

       [[14, 15, 16, 17],
        [18, 19, 20, 21],
        [18, 19, 20, 21],
        [14, 15, 16, 17]]])
>>>

Besides , When the source matrix is multidimensional , You can get a number at a specified position by using two index matrices when indexing , At this point, the two index matrices need to have the same shape, as follows

>>> import numpy as np
>>> arr=np.arange(10,22).reshape((3,4))
>>> arr
array([[10, 11, 12, 13],
       [14, 15, 16, 17],
       [18, 19, 20, 21]])
>>> i=np.array([[0,1],[1,2]])
>>> j=np.array([[2,1],[3,3]])
>>> i
array([[0, 1],
       [1, 2]])
>>> j
array([[2, 1],
       [3, 3]])
>>> arr[i,j]
array([[12, 15],
       [17, 21]])
>>> arr[i,2]
array([[12, 16],
       [16, 20]])
>>> arr[:,j]
array([[[12, 11],
        [13, 13]],

       [[16, 15],
        [17, 17]],

       [[20, 19],
        [21, 21]]])
>>>

A Boolean matrix can be used to assign values to a matrix , as follows

>>> import numpy as np
>>> a=np.arange(12).reshape((3,4))
>>> a
array([[ 0,  1,  2,  3],
       [ 4,  5,  6,  7],
       [ 8,  9, 10, 11]])
>>> b=a>4
>>> b
array([[False, False, False, False],
       [False,  True,  True,  True],
       [ True,  True,  True,  True]])
>>> a[b]
array([ 5,  6,  7,  8,  9, 10, 11])
>>> a[b]=0
>>> a
array([[0, 1, 2, 3],
       [4, 0, 0, 0],
       [0, 0, 0, 0]])
>>>

fourteen 、 Generate a Cartesian product from two arrays

Use np.ix_() The mapping relationship of Cartesian product can be generated according to the input two arrays , as follows , among np.ix_([0,1,2,3],[0,1,2]) Will produce (0,0),(0,1),(0,2),(1,0,(1,1,(1,2),(2,0),(2,1),(2,2), Then index the matrix , Therefore, the expected results are as follows

>>> import numpy as np
>>> index=np.ix_([0,1,2,3],[0,1,2])
>>> index
(array([[0],
       [1],
       [2],
       [3]]), array([[0, 1, 2]]))
>>> arr=np.arange(24).reshape((4,6))
>>> arr[index]
array([[ 0,  1,  2],
       [ 6,  7,  8],
       [12, 13, 14],
       [18, 19, 20]])
>>> arr
array([[ 0,  1,  2,  3,  4,  5],
       [ 6,  7,  8,  9, 10, 11],
       [12, 13, 14, 15, 16, 17],
       [18, 19, 20, 21, 22, 23]])
>>>