Skip to main content

calculate condition number and determinant in R and python


Introduction:


If you are working on machine learning, more than often, you will need to perform different types of matrix manipulations in r/python. I will mention some of such manipulations and regarding functions to use in r and python.

condition number finding:

condition number is generally used to find the stability as well non-singularity of a matrix. It is defined to be the ratio of absolute value of highest singular value and smallest singular value ( in terms of mod value). If a matrix has condition number more than 1000, then it is generally considered to be a unstable matrix.

For finding condition number of a matrix in r, we have to use the kappa() function. For normally using kappa, you need to use two parameters. First input to kappa has to be the matrix. The second one is exact parameter. This exact is set to be FALSE in general. In this setting, a cheap (computationally) approximation of condition number is obtained and provided. If you set kappa to be TRUE, then the method uses SVD and provides the exact value.

so the usecase is condition_number = kappa( matrix, exact = FALSE)

In case of python, you can import cond from numpy.linalg, i.e. the linear algebra library. cond takes the matrix as parameter and calculates the condition number.

determinant:

For determinant, it is amazing that both numpy.linalg and R has same function, called det(). det(), in both cases takes the matrix as parameter and provides the determinant value.
Labels:

Comments

Post a Comment

Popular posts from this blog

Tinder bio generation with OpenAI GPT-3 API

Introduction: Recently I got access to OpenAI API beta. After a few simple experiments, I set on creating a simple test project. In this project, I will try to create good tinder bio for a specific person.  The abc of openai API playground: In the OpenAI API playground, you get a prompt, and then you can write instructions or specific text to trigger a response from the gpt-3 models. There are also a number of preset templates which loads a specific kind of prompt and let's you generate pre-prepared results. What are the models available? There are 4 models which are stable. These are: (1) curie (2) babbage (3) ada (4) da-vinci da-vinci is the strongest of them all and can perform all downstream tasks which other models can do. There are 2 other new models which openai introduced this year (2021) named da-vinci-instruct-beta and curie-instruct-beta. These instruction models are specifically built for taking in instructions. As OpenAI blog explains and also you will see in our
Post a Comment
Read more

Can we write codes automatically with GPT-3?

 Introduction: OpenAI created and released the first versions of GPT-3 back in 2021 beginning. We wrote a few text generation articles that time and tested how to create tinder bio using GPT-3 . If you are interested to know more on what is GPT-3 or what is openai, how the server look, then read the tinder bio article. In this article, we will explore Code generation with OpenAI models.  It has been noted already in multiple blogs and exploration work, that GPT-3 can even solve leetcode problems. We will try to explore how good the OpenAI model can "code" and whether prompt tuning will improve or change those performances. Basic coding: We will try to see a few data structure coding performance by GPT-3. (a) Merge sort with python:  First with 200 words limit, it couldn't complete the Write sample code for merge sort in python.   def merge(arr, l, m, r):     n1 = m - l + 1     n2 = r- m       # create temp arrays     L = [0] * (n1)     R = [0] * (n
Post a Comment
Read more

What is Bort?

 Introduction: Bort, is the new and more optimized version of BERT; which came out this october from amazon science. I came to know about it today while parsing amazon science's news on facebook about bort. So Bort is the newest addition to the long list of great LM models with extra-ordinary achievements.  Why is Bort important? Bort, is a model of 5.5% effective and 16% total size of the original BERT model; and is 20x faster than BERT, while being able to surpass the BERT model in 20 out of 23 tasks; to quote the abstract of the paper,  ' it obtains performance improvements of between 0 . 3% and 31%, absolute, with respect to BERT-large, on multiple public natural language understanding (NLU) benchmarks. ' So what made this achievement possible? The main idea behind creation of Bort is to go beyond the shallow depth of weight pruning, connection deletion or merely factoring the NN into different matrix factorizations and thus distilling it. While methods like knowle
Post a Comment
Read more