To learn the basics of Python, see One day introduction Python serieshttps://blog.csdn.net/day_and_night_2017/category_8729957.html

numpy Foundation

numpy is a set of mathematical calculation library based on python. It has rich APIs related to matrix operation and provides convenient calculation tools for in-depth learning.

numpy import

import numpy as np 

Use import to import numpy and specify the alias np

Generate array (one-dimensional vector)

x = np.array([1, 2, 3])

numpy uses ndarray to represent arrays.

>>> x = np.array([1.0, 2.0, 3.0])
>>> print(x)
[ 1. 2. 3.]
>>> type(x)
<class 'numpy.ndarray'>

tips: we generally call one-dimensional arrays vectors; A two-dimensional array is called a matrix; Arrays above three dimensions are called tensors.  

Vector and basic operation of vector

Basic operations of corresponding position elements can be performed between vectors:

>>> x = np.array([1.0, 2.0, 3.0])
>>> y = np.array([2.0, 4.0, 6.0])

>>> x + y # Addition of corresponding elements
array([ 3., 6., 9.])

>>> x - y
array([ -1., -2., -3.])

>>> x * y # element-wise product
array([ 2., 8., 18.])

>>> x / y
array([ 0.5, 0.5, 0.5])

When the lengths of two vectors are the same, this operation can be performed. In case of inconsistency, an error will be reported.

Vector and scalar operations

When calculating vector and scalar, it is equivalent to calculating between each element of vector and scalar:

>>> x = np.array([1.0, 2.0, 3.0])
>>> x / 2.0
array([ 0.5, 1. , 1.5])

Generate multidimensional array

numpy can generate multidimensional arrays, for example:

>>> A = np.array([[1, 2], [3, 4]])
>>> print(A)
[[1 2]
[3 4]]

>>> A.shape
(2, 2)

>>> A.dtype
dtype('int64')

As long as multiple one-dimensional vectors are stacked together, a two-dimensional matrix is formed.

ndarray has two common attributes:

shape: get the dimension of the tensor.

dtype: get the type of data element

Operations between matrices

The operation between matrices also conforms to the principle of corresponding position calculation:

>>> B = np.array([[3, 0],[0, 6]])
>>> A + B
array([[ 4, 2],
[ 3, 10]])

>>> A * B
array([[ 3, 0],
[ 0, 24]])

 

Matrix and scalar computation

Matrix and constant calculations are still the result of each element and scalar calculation:

>>> print(A)
[[1 2]
[3 4]]

>>> A * 10
array([[ 10, 20],
[ 30, 40]])

Here, when calculating between one-dimensional vector or two-dimensional array and scalar, the method of "broadcast" is used.

radio broadcast

Broadcast is used in scalar and vector computing. What is broadcast?

When calculating the two-dimensional matrix and scalar 10, it is equivalent to expanding the scalar into a matrix with the same dimension and scalar element values at the corresponding position of the matrix, and then calculating the corresponding position, which is called broadcast.

In fact, matrices and vectors are broadcast directly:

>>> A = np.array([[1, 2], [3, 4]])
>>> B = np.array([10, 20])

>>> A * B
array([[ 10, 40],
[ 30, 80]])

Here, it is equivalent to expanding the B vector into A corresponding matrix according to the format of A matrix, and then calculating the corresponding position.

Random reading and writing of vectors

The bottom layer of a vector is an array, so its reading and writing method is similar to that of an array:

>>> X = np.array([[51, 55], [14, 19], [0, 4]])
>>> print(X)
[[51 55]
[14 19]
[ 0 4]]

>>> X[0] # Line 0
array([51, 55])

>>> X[0][1] # Elements of (0,1)
55

The first index starts from 0. X[0] represents a one-dimensional array (vector) composed of the first row elements of the matrix

We can also get each row in turn through the for loop:

>>> for row in X:
... print(row)
...
[51 55]
[14 19]
[0 4]

Merge matrices into one-dimensional arrays

>>> X = X.flatten() # Convert X to a one-dimensional array
>>> print(X)
[51 55 14 19 0 4]

Using flatten, the matrices can be merged into one-dimensional matrices from top to bottom and from left to right.

We can specify the index to get elements in batch:

>>> X[np.array([0, 2, 4])] # Get element with index 0, 2, 4
array([51, 14, 0])

Matrix element judgment and filtering

The operation on the matrix is equivalent to the operation on each element:

>>> X > 15
array([ True, True, False, True, False, False], dtype=bool)

According to the judgment result, filter the elements at the corresponding position when the result is True

>>> X[X>15]
array([51, 55, 19])