## Linear Algebra Functions

The purpose of this project is to create a repository of functions for commonly used algorithms used in Linear Algebra. The following functions are given:

1. LU factorization.
2. LDM^T factorization.
3. Cholesky factorization by LDM^T factorization.
4. Cholesky factorization by outer product method.
5. QR factorization by Householder reflections.
6. QR factorization by Givens rotations.
7. Inverse of Upper traingular Matrix.
8. Least Square solution to Linear System of equations by QR factorization.

We use the algorithms mentioned in the following reference:

Reference : Golub, G.H., Van Loan, C.F. Matrix Computations

## Solving Rational Matrix Equation – CRAN R Package

Given a symmetrix positive definite matrix Q and a non-singular matrix L, Find symmetric positive definite solution X such that X = Q + L (X inv) L^T.

See project on CRAN – Solve-Rational-Matrix-Equation- R-Package

## R – Package – Bayesian Binary Probit

This R package implements the Bayesian Auxiliary variable Model for Binary Regression, It performs the Bayesian estimation of the coefficients of Binary Logistic Regression with Probit link.

It is a self-contained package with functions for Cholesky decomposition and generating samples from truncated Gaussian distribution, which are used in the Bayesian estimation algorithm. The codes for all major computations are written in C, which achieves a 40x improvement in speed.

CHECK IT on Bayesian binary probit

## Pothole Detection

The roads of Bengaluru are riddled with potholes. It would be beneficial to automate the process of detecting potholes, instead of manually looking for them. Drones can be used to collect images of roads. The purpose of this project is to build an algorithm for detecting whether there is a pothole on a road from the image of the road. We use a histogram based approach to detect potholes and image processing filters for building classification features.

## Gender Detection Algorithm

Gender detection using Dynamic Time Warping. The purpose of this project is to build an algorithm for detecting the gender of a person from the image of his/her face. It uses a novel Dynamic Time Warping distance metric to classify images.