Как найти главную диагональ в матрице питон

Функция np.diag() определена в библиотеке numpy, которую можно импортировать как import numpy as np. Мы можем создавать многомерные массивы и получать другую математическую статистику с помощью numpy. Имя функции Python diag() происходит от diagonal.

Функция np.diag() извлекает и создает диагональный массив на Python. Она принимает массив и k в качестве параметров и возвращает диагональный массив из заданного массива.

Синтаксис

Параметры

Функция принимает два параметра, один из которых является необязательным.

• Первый параметр — это входной массив, представленный arr.
• Второй параметр — k, является необязательным и по умолчанию принимает значение 0. Если значение этого параметра больше 0, это означает, что диагональ находится выше главной диагонали, и наоборот, если нет.

Возвращаемое значение

Возвращает массив с диагональным массивом.

Примеры программ для метода diag() в Python

Напишем программу, показывающую работу функции diag() в Python.

Пример 1

Выход

В этом примере мы используем numpy diag() и можем видеть, что, передавая разные значения k, можем получить их диагональные элементы. Здесь мы увидели главную диагональ в матрице, затем диагональ выше главной диагонали при передаче значения k=1 и наоборот при передаче значения k=-1.

Пример 2

Напишем программу, которая берет матрицу 4×4 и применяет функцию diag().

См. следующий код.

Выход

В этом примере мы передали матрицу 4 × 4 и получили требуемый результат главной диагонали, выше главной диагонали (k = 1) и ниже главной диагонали (k = -1).

Создание массива и построение диагонали

См. следующий код.

Выход

В этом примере мы взяли k = 0. Это главная диагональ, которая состоит из

• 0
• 4
• 8

Если мы возьмем k = 1, он вернет [1, 5]. См. следующий код.

Выход

Если мы возьмем k = -1, это даст нам нижнюю диагональ главной диагонали.

См. следующий код.

Выход

Главная диагональ нашего массива — [0, 4, 8], а нижняя диагональ — [3, 7, 11]. Вот почему, когда мы устанавливаем k=-1, он вернет [3, 7, 11]. Если вы передадите k = -2, то он вернет [6, 10]

Построение диагонали из массива NumPy

Если вы хотите создать диагональ из массива, вы можете использовать метод np diag().

Выход

Если у вас есть вектор-строка, вы можете сделать следующее.

Выход

Заключение

Функция Python numpy.diagonal() используется для извлечения диагонали и записи в полученный массив; возвращает она копию или представление, зависит от того, какую версию numpy вы используете.

In python, we have seen many functions or methods of the numpy library. In this tutorial, we will be learning about the numpy diag() function. As we come in a situation where we need to calculate the diagonal, print the diagonal of an array of matrices. We will see all the ways through which we can print the values of the diagonal through the numpy diag() function.

What is Numpy Diag() function?

The diag() function is used to extract and construct a diagonal 2-d array with a numpy library. It contains two parameters: an input array and k, which decides the diagonal, i.e., main diagonal, lowe diagonal, or the upper diagonal. It is the numpy library function, which is used to perform the mathematical and statistics operation on the multidimensional array.

Syntax

numpy.diag(arr,k=0) 

Parameters

• arr: It is an input array. If it is a 2-D array, it returns a copy of its k-th diagonal. If it is a 1-D array, it returns a 2-D array with arr on the kth diagonal.
• k: It is an integer value and an optional input. If k>0, then the diagonal is above the main diagonal, and if k<0, then the diagonal is below the main diagonal. By default, it is 0.

Return value

It returns the extracted diagonal or a constructed diagonal.

Examples of numpy diag() function

Let us understand the numpy diag() function of the numpy module in details with the help of examples:

1. Finding diagonal without k parameter

In this example, we will create a multidimensional array(matrix) with the help of numpy and then apply the numpy diag() function without passing the k parameter. By default, it is set to 0 and also called as main diagonal. Let us look at the example for understanding the concept in detail.

#import numpy library
import numpy as np

a = np.matrix([[1, 2, 3], [4, 5, 6], [9, 8, 7]])

print("Main diagonal : ",np.diag(a))

Output:

Main diagonal :  [1 5 7]

Explanation:

• Firstly, we will be importing the numpy library with an alias name as np.
• Then, we will take the input for creating a multidimensional array.
• After that, we will apply the numpy diag() without the value of the k parameter. By default, it is set to 0.
• At last, we have printed the main diagonal of the multidimensional array.
• Hence, you can see the output.

2. Printing upper diagonal of main diagonal

In this example, we will be printing the upper diagonal of the main diagonal in the multidimensional array. In this, we will pass the k parameter with the positive value of k to give us the upper diagonal. By applying the numpy diag() function, we will print the upper diagonal. Let us look at the example for understanding the concept in detail.

#import numpy library
import numpy as np

a = np.matrix([[1, 2, 3], [4, 5, 6], [9, 8, 7]])

print(a)
print("Main diagonal : ",np.diag(a,1))

Output:

[[1 2 3]
 [4 5 6]
 [9 8 7]]
Main diagonal :  [2 6]

Explanation:

• Firstly, we will be importing the numpy library with an alias name as np.
• Then, we will take the input for creating a multidimensional array.
• After that, we will apply the numpy diag() with the k parameter value equal to 1.
• For the upper diagonal, we need to put the k value as positive and greater than 0.
• At last, we have printed the upper diagonal of the main diagonal of the multidimensional array.
• Hence, you can see the output.

3. Printing lower diagonal of main diagonal

In this example, we will be printing the lower diagonal of the main diagonal in the multidimensional array. In this, we will pass the k parameter with the negative value of k to give us the lower diagonal. By applying the numpy diag() function, we will print the lower diagonal. Let us look at the example for understanding the concept in detail.

#import numpy library
import numpy as np

a = np.matrix([[1, 2, 3], [4, 5, 6], [9, 8, 7]])

print(a)
print("Main diagonal : ",np.diag(a,-1))

Output:

[[1 2 3]
 [4 5 6]
 [9 8 7]]
Main diagonal :  [4 8]

Explanation:

• Firstly, we will be importing the numpy library with an alias name as np.
• Then, we will take the input for creating a multidimensional array.
• After that, we will apply the numpy diag() with the k parameter value equal to 1.
• For the lower diagonal, we need to put the k value as negative and lesser than 0.
• At last, we have printed the lower diagonal of the main diagonal of the multidimensional array.
• Hence, you can see the output.

4. Using arange function to create an array and then construct the diagonal

In this example, we will be importing the numpy library. Then, we will use arange() from numpy to create the multidimensional array. After that, we will print the main diagonal of the array created. Let us look at the example for understanding the concept in detail.

#import numpy library
import numpy as np

x = np.arange(9).reshape((3,3))

print(x)
print("Main diagonal : ",np.diag(x))

Output:

[[0 1 2]
 [3 4 5]
 [6 7 8]]
Main diagonal :  [0 4 8]

Explanation:

• Firstly, we will be importing the numpy library with an alias name as np.
• Then, we will apply the np.arange() function from the numpy library to create a multidimensional array.
• After that, we have printed the matrix formed.
• At last, we have applied the diag() function and printed the diagonal of the array.
• Hence, you can see the output.

5. Constructing diagonal from array

In this example, we will be importing the numpy library. Then, we will be passing the array values in the numpy array() function. Finally, we will apply the numpy diag function to create the diagonal of the values passed inside the array. This will construct a diagonal array. Let us look at the example for understanding the concept in detail.

#importing numpy library
import numpy as np

a = np.array([5, 6, 7, 8])

print(a)
print("Diagonal : ",np.diag(a))

Output:

[5 6 7 8]
Diagonal : 
  [[5 0 0 0]
 [0 6 0 0]
 [0 0 7 0]
 [0 0 0 8]]

Explanation:

• Firstly, we will be importing the numpy library with an alias name as np.
• Then, we have created an array with the help of the numpy library.
• After that, we have printed the array, which we have taken as an input.
• Finally, we have applied the numpy diag() function for constructing the diagonal for the array values and print the output.
• Hence, you can see the output.

What is numpy diagonal() of a 3-D array?

The numpy diagonal() function is used to extract and construct a diagonal of a 2-d and 3-d array with a numpy library.

Let us take an example and understand the concept in detail.

#import numpy library
import numpy as np

a = np.arange(8).reshape(2,2,2);
print(a)
print("n")
print(" diagonal output : ",a.diagonal(0,0,1))

Output:

[[[0 1]
  [2 3]]

 [[4 5]
  [6 7]]]


diagonal output :  [[0 6]
 [1 7]]

Explanation:

• Firstly, we will be importing the numpy library with an alias name as np.
• Then, we will apply the np.arange() function from the numpy library to create a 3-d multidimensional array.
• Then, we will print the 3-d array.
• After that, we will apply the diagonal() function with all the parameters and print the output.
• Hence, you can see the output.

Difference between numpy diag() and numpy diagonal() ?

Numpy diag()

The diag() function is used to extract and construct a diagonal 2-d array with a numpy library.

Numpy diagonal()

The diagonal() function is used to extract and construct a diagonal of a 2-d and 3-d array with a numpy library.

Example of numpy diag() and numpy diagonal()

In this example, we will explain the examples of the numpy diag() function operating on the 2-d array and numpy diagonal() function operating on the 2-d and 3-d array both. We will understand the difference between in a more efficient way through this example.

#import numpy library
import numpy as np

x = np.arange(9).reshape((3,3))

print(x)
print("n")
print("2-d Main diagonal : ",np.diag(x))
print("n")

#numpy diagonal() example
import numpy as np

#2-d array
x = np.arange(9).reshape((3,3))
print("2-d Main diagonal : ",np.diagonal(x))

#3-d array
a = np.arange(8).reshape(2,2,2);
print(a)
print("n")
print(" 3-d diagonal output : ",a.diagonal(0,0,1))

Output:

[[0 1 2]
 [3 4 5]
 [6 7 8]]


2-d Main diagonal :  [0 4 8]


2-d Main diagonal :  [0 4 8]
[[[0 1]
  [2 3]]

 [[4 5]
  [6 7]]]


 3-d diagonal output :  [[0 6]
 [1 7]]

Explanation:

• Firstly, we will be importing the numpy library with an alias name as np.
• Then, we will apply the np.arange() function from the numpy library to create a 2-d multidimensional array.
• After that, we have printed the matrix formed.
• At last, we have applied the diag() function and printed the diagonal of the array.
• Hence, you can see the output.

Conclusion

In this tutorial, we have learned about the concept of the numpy diagonal() function. We have seen how to print the diagonal of the multidimensional array and also construct a multidimensional diagonal. We have all the ways through which we can do so and all the examples are explained in detail for a better understanding of the concept. You can use any of the methods according to your need in the program.

However, if you have any doubts or questions, do let me know in the comment section below. I will try to help you as soon as possible.