Calculate The Trace Of A Matrix

h1ros

Goal¶

This post aims to show how to calculate the trace of a matrix using numpy i.e., $tr(A)$

$tr(A)$ is defined as

$tr(A) = \sum_{i=1}^{n} a_{ii} = a_{11} + a_{22} + \cdots + a_{nn}$

Reference:

In [1]:

import numpy as np

In [2]:

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

Out[2]:

array([[1, 2, 3],
       [4, 5, 6],
       [7, 8, 9]])

In [4]:

arr.trace()

Out[4]:

In [7]:

sum([arr[i, i] for i in range(len(arr))])

Out[7]:

h1ros

This post aims to create a sparse matrix in python using following modules:

Reference:

Scipy Document
Chris Albon's blog (I look at his post's title and wrote my own contents to deepen my understanding about the topic.)

In [8]:

import numpy as np
import scipy.sparse

CSR stands for "Compressed Sparse Row" matrix

In [9]:

nrow = 10000
ncol = 10000

# CSR stands for "Compressed Sparse Row" matrix
arr_sparse = scipy.sparse.csr_matrix((nrow, ncol))
arr_sparse

Out[9]:

<10000x10000 sparse matrix of type '<class 'numpy.float64'>'
	with 0 stored elements in Compressed Sparse Row format>