Detailed introduction to common numpy usage

numpy Introduction

The existence of numpy makes python have powerful matrix computing capabilities, no less than matlab.
Official documentation (https://docs.scipy.org/doc/numpy-dev/user/quickstart.html)

Introduction to various usages

The first is # in numpy ##Data type, ndarray type, is different from array.array in the standard library.

Some

properties of ndarray

ndarray.ndimthe number of axes (dimensions) of the array. In the Python world, the number of dimensions is referred to as rank.

ndarray.shapethe dimensions of the array. This is a tuple of integers indicating the size of the array in
each dimension. For a matrix with n rows and m columns, shape will be (n,m). The length of the shape tuple is therefore the rank, or number of dimensions, ndim.
ndarray.sizethe total number of elements of the array. This is equal to the product of the elements of shape.

ndarray.dtypean object describing the type of the elements in the array. One can create or specify dtype's using standard Python types. Additionally NumPy provides types of its own. numpy.int32, numpy.int16, and numpy.
float64 are some examples.
ndarray.itemsizethe size in bytes of each element of the array. For example, an array of elements of type float64 has itemsize 8 (=64/8),
while one of type complex32 has itemsize 4 (=32/8). It is equivalent to ndarray.dtype.itemsize.
ndarray.datathe buffer containing the actual elements of the array. Normally, we won't need to use this attribute because we will access the elements in an array using indexing facilities.

Creation of ndarray

>>> import numpy as np>>> a = np.array([2,3,4])>>> a
array([2, 3, 4])>>> a.dtype
dtype('int64')>>> b = np.array([1.2, 3.5, 5.1])>>> b.dtype
dtype('float64')

two-dimensional

array

>>> b = np.array([(1.5,2,3), (4,5,6)])>>> b
array([[ 1.5,  2. ,  3. ],
       [ 4. ,  5. ,  6. ]])

Specify the type when creating

>>> c = np.array( [ [1,2], [3,4] ], dtype=complex )>>> c
array([[ 1.+0.j,  2.+0.j],
       [ 3.+0.j,  4.+0.j]])

Create some special matrices

>>> np.zeros( (3,4) )
array([[ 0.,  0.,  0.,  0.],
       [ 0.,  0.,  0.,  0.],
       [ 0.,  0.,  0.,  0.]])
>>> np.ones( (2,3,4), dtype=np.int16 )                # dtype can also be specified
array([[[ 1, 1, 1, 1],
        [ 1, 1, 1, 1],
        [ 1, 1, 1, 1]],
       [[ 1, 1, 1, 1],
        [ 1, 1, 1, 1],
        [ 1, 1, 1, 1]]], dtype=int16)
>>> np.empty( (2,3) )                                 # uninitialized, output may vary
array([[  3.73603959e-262,   6.02658058e-154,   6.55490914e-260],
       [  5.30498948e-313,   3.14673309e-307,   1.00000000e+000]])

Create some matrices with specific rules

>>> np.arange( 10, 30, 5 )
array([10, 15, 20, 25])
>>> np.arange( 0, 2, 0.3 )                 # it accepts float arguments
array([ 0. ,  0.3,  0.6,  0.9,  1.2,  1.5,  1.8])

>>> from numpy import pi
>>> np.linspace( 0, 2, 9 )                 # 9 numbers from 0 to 2
array([ 0.  ,  0.25,  0.5 ,  0.75,  1.  ,  1.25,  1.5 ,  1.75,  2.  ])
>>> x = np.linspace( 0, 2*pi, 100 )        # useful to evaluate function at lots of points
>>> f = np.sin(x)

Some basic operations

Addition, subtraction, multiplication and division triangle

FunctionLogical operation

>>> a = np.array( [20,30,40,50] )
>>> b = np.arange( 4 )
>>> b
array([0, 1, 2, 3])
>>> c = a-b
>>> c
array([20, 29, 38, 47])
>>> b**2
array([0, 1, 4, 9])
>>> 10*np.sin(a)
array([ 9.12945251, -9.88031624,  7.4511316 , -2.62374854])
>>> a<35
array([ True, True, False, False], dtype=bool)

Matrix operation

There are .*,./ etc. in matlab
But in numpy, if you use +, -, ×,/The priority is to perform addition, subtraction, multiplication and division between each point
If two matrices (square matrices) can both perform operations between elements and perform matrix operations, the operations between elements will be performed first

>>> import numpy as np>>> A = np.arange(10,20)>>> B = np.arange(20,30)>>> A + B
array([30, 32, 34, 36, 38, 40, 42, 44, 46, 48])>>> A * B
array([200, 231, 264, 299, 336, 375, 416, 459, 504, 551])>>> A / B
array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0])>>> B / A
array([2, 1, 1, 1, 1, 1, 1, 1, 1, 1])

If you need to perform a matrix operation, it is usually a matrix multiplication operation

>>> A = np.array([1,1,1,1])
>>> B = np.array([2,2,2,2])
>>> A.reshape(2,2)
array([[1, 1],
       [1, 1]])
>>> B.reshape(2,2)
array([[2, 2],
       [2, 2]])
>>> A * B
array([2, 2, 2, 2])
>>> np.dot(A,B)
8
>>> A.dot(B)
8

Some commonly used

global functions

>>> B = np.arange(3)
>>> B
array([0, 1, 2])
>>> np.exp(B)
array([ 1.        ,  2.71828183,  7.3890561 ])
>>> np.sqrt(B)
array([ 0.        ,  1.        ,  1.41421356])
>>> C = np.array([2., -1., 4.])
>>> np.add(B, C)
array([ 2.,  0.,  6.])

Matrix index slice traversal

>>> a = np.arange(10)**3
>>> a
array([  0,   1,   8,  27,  64, 125, 216, 343, 512, 729])
>>> a[2]
8
>>> a[2:5]
array([ 8, 27, 64])
>>> a[:6:2] = -1000    # equivalent to a[0:6:2] = -1000; from start to position 6, exclusive, set every 2nd element to -1000
>>> a
array([-1000,     1, -1000,    27, -1000,   125,   216,   343,   512,   729])
>>> a[ : :-1]                                 # reversed a
array([  729,   512,   343,   216,   125, -1000,    27, -1000,     1, -1000])
>>> for i in a:
...     print(i**(1/3.))
...
nan
1.0
nan
3.0
nan
5.0
6.0
7.0
8.0
9.0

Traversal of matrices

>>> import numpy as np
>>> b = np.arange(16).reshape(4, 4)
>>> for row in b:
...  print(row)
... 
[0 1 2 3]
[4 5 6 7]
[ 8  9 10 11]
[12 13 14 15]
>>> for node in b.flat:
...  print(node)
... 
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15

Special operations of matrices

Change the shape of the matrix--reshape

>>> a = np.floor(10 * np.random.random((3,4)))
>>> a
array([[ 6.,  5.,  1.,  5.],
       [ 5.,  5.,  8.,  9.],
       [ 5.,  5.,  9.,  7.]])
>>> a.ravel()
array([ 6.,  5.,  1.,  5.,  5.,  5.,  8.,  9.,  5.,  5.,  9.,  7.])
>>> a
array([[ 6.,  5.,  1.,  5.],
       [ 5.,  5.,  8.,  9.],
       [ 5.,  5.,  9.,  7.]])

The difference between resize and reshape

resize will change the original matrix, reshape will not

>>> a
array([[ 6.,  5.,  1.,  5.],
       [ 5.,  5.,  8.,  9.],
       [ 5.,  5.,  9.,  7.]])
>>> a.reshape(2,-1)
array([[ 6.,  5.,  1.,  5.,  5.,  5.],
       [ 8.,  9.,  5.,  5.,  9.,  7.]])
>>> a
array([[ 6.,  5.,  1.,  5.],
       [ 5.,  5.,  8.,  9.],
       [ 5.,  5.,  9.,  7.]])
>>> a.resize(2,6)
>>> a
array([[ 6.,  5.,  1.,  5.,  5.,  5.],
       [ 8.,  9.,  5.,  5.,  9.,  7.]])

Merger of matrices

>>> a = np.floor(10*np.random.random((2,2)))>>> a
array([[ 8.,  8.],
       [ 0.,  0.]])>>> b = np.floor(10*np.random.random((2,2)))>>> b
array([[ 1.,  8.],
       [ 0.,  4.]])>>> np.vstack((a,b))
array([[ 8.,  8.],
       [ 0.,  0.],
       [ 1.,  8.],
       [ 0.,  4.]])>>> np.hstack((a,b))
array([[ 8.,  8.,  1.,  8.],
       [ 0.,  0.,  0.,  4.]])

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