 ### Python numpy program to find sum the diagonal elements of the matrix

Python numpy program to find sum the diagonal elements of the matrix

Description: we have to find the sum of diagonal elements in a matrix .
so first we create a matrix using numpy arange() function and then calculate the principal diagonal
elements sum using trace() function and diagonal element using diagonal() function.

1: trace(): trace of an n by n square matrix A is defined to be the sum of the elements on the main diagonal
(the diagonal from the upper left to the lower right) of matrix A.
Example:
import numpy as np
a=np.arange(9).reshape(3,3)
print("original matrix is :\n",a)
m=np.trace(a)
print("trace of matrix :", m)

output:
original matrix is :
[[ 0 1 2]
[ 3 4 5]
[ 6 7 8 ]]
trace of matrix : 12
2: diagonal(): diagonal function in numpy returns upper left o right diagonal elements.
If a is 2-D and not a matrix, a 1-D array of the same type as a containing the diagonal is
returned.
If a is a matrix, a 1-D array containing the diagonal is returned in order to maintain backward
compatibility.
If the dimension of a is greater than two, then an array of diagonals is returned, packed from
left-most dimension to right-most (e.g.,
if a is 3-D, then the diagonals are packed along rows).
Example: for 3-D matrix example code is here for 3-D matrix example code is here .

import numpy as np import numpy as np
a=np.arange(9).reshape(3,3) a=np.arange(9).reshape(2,3,3)
print("original matrix is :\n",a) print("original matrix is :\n",a)
m=a.diagonal() m=a.diagonal()
print("diagonal elements \n:", m) print("diagonal elements \n:", m)

output: output:
original matrix is : original matrix is :
[[[ 0 1 2] [[[ 0 1 2]
[ 3 4 5] [ 3 4 5]
[ 6 7 8]] [ 6 7 8]]
diagonal elements : [0,4,8]
[[
9 10 11]
[
12 13 14]
[
15 16 17]]]
diagonal elements
[[ 0 12]
[
1 13]
[
2 14]]

code:

#import numpy library
import numpy as np
# create a class
class diagnoal_sum:
# create function
def sum_diagonal( self,a, r,c):
# check whether a given a row and column is valid or not.
if c==0 and r==0:
return print("Enter valid matrix ,Matrix should be (n x n) format")

# we use diagonal() function used to return specified diagonal elements.
print(
"diagonal elements are :",a.diagonal())
# we use trace() function used to Sum along diagonals.
result = np.trace(a)
print(
"sum of diagonals Elements :",result)

# define main() function.
def main():
digsum=diagnoal_sum()
#taking input from console.
row,col=input(
"enter row and column :").split()
r=int(row)
c=int(col)
# create matrix using numpy function arange() in sequential order.
a=np.arange(r*c).reshape(r,c)
print(
"Original matrix :\n", a)
#call function to execute .
digsum.sum_diagonal(a,r,c)
if __name__ == "__main__":
main()

output:
case1: when row and column are equal .
enter row and column :3 3
Original matrix :
[[
0 1 2]
[
3 4 5]
[
6 7 8]]
diagonal elements are : [
0 4 8]
sum of diagonals Elements :
12

case2: when row and column are not equal
enter row and column :3 2
Original matrix :
[[
0 1]
[
2 3]
[
4 5]]
diagonal elements are : [
0 3]
sum of diagonals Elements :
3

case3: when row and column are both 0.
enter row and column :0 0
Original matrix :
[]
Enter valid matrix ,Matrix should be (n x n) format.

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