Numpy is a numerical calculation library for Python, which provides many convenient and easy-to-use matrix operation methods. Let's see how to use it.
You need to install this module before using Numpy. It's very simple. The command line executes:
pip install numpy
Import is required before use, generally as follows:
import numpy as np
1. Definition of Matrix
A = np.mat([
[1, 2, 3],
[4, 5, 6],
[7, 8, 9]
], dtype=int)
Define the matrix using mat, we define a 3 X 3 matrix here; dtype indicates the data type in the matrix, here is int, the default is floating point number. Here's how some special matrices are defined, taking the creation of a 3 X 3 square matrix as an example:
A matrix with all zero elements:
A = np.mat(np.zeros((3, 3), dtype=int))
A matrix with all 1s:
A = np.mat(np.ones((3, 3), dtype=int))
Unit array:
A = np.mat(np.eye(3, 3, dtype=int))
Diagonal matrix, the diagonal elements are passed as a list:
A = np.diag ([1, 2, 3])
Initialize all elements with a value:
A=np.mat(np.full((3, 3), 12, dtype=int))
2. Matrix operations
Define two matrices A and B as follows:
A = np.mat([
[1, 2, 3],
[4, 5, 6],
[7, 8, 9]
], dtype=int)
B = np.mat([
[9, 8, 7],
[6, 5, 4],
[3, 2, 1]
], dtype=int)
Addition, Subtraction, Multiplication and Transpose:
print(A + B)
print(A - B)
print(A * B)
print(A .T)
The following method is to multiply the elements in sequence, pay attention to distinguish it from matrix multiplication
print (np.multiply (A, B))
Inverse:
C = np.mat([
[0, 1, 2],
[1, 0, 3],
[4, -3, 8]
])
print(C .I)
The example is a non-singular matrix. If the matrix is a singular matrix, a CI exception will be thrown.
3. The determinant of a square matrix
To find the determinant of a square matrix, you can use det
A = np.mat([
[1, 2, 3],
[0, 2, 3],
[1, 2, 0]
])
print (np.linalg.det (A))
4. Rank, eigenvalues and eigenvectors of a matrix
value, vectors = np.linalg.eig(A)
print(value)
print(vectors)
Eigenvalues and eigenvectors can be calculated using eig under numpy's linalg. In the above example, values are eigenvalues and vectors are eigenvectors.
The above are some methods of matrix operations in Numpy, which are very simple and easy to use. I do not give the running results here. With Numpy, we have a powerful numerical calculator.
