# LSE_GQR: LSE and GQR Factorization In LSE: Constrained Least Squares and Generalized QR Factorization

## Description

This code provides the solution of equality constrained least squares problem through Generalized QR Factorization. Require MASS package.

## Usage

 `1` ```LSE_GQR(A,C,b,d) ```

## Arguments

 `A` Design matrix, m rows and n columns. `C` Constraint matrix, p rows and n columns. `b` Response vector for A, Ax=b, m rows and 1 column. `d` Response vector for C, Cx=d, p rows and 1 column.

## Details

This algorithm provides the solution of the equality constrained least squares problem through Generalized QR factorization. This algorithm requires the same number of columns for matrices A and C.

## Value

Numerical vector for a LSE problem.

## Author(s)

Sergio Andrés Cabrera Miranda Statician sergio05acm@gmail.com

## References

Anderson, E., Bai, Z., & Dongarra, J. (1992). Generalized QR factorization and its applications. Linear Algebra and its Applications, 162, 243-271.

## Examples

 ```1 2 3 4 5 6``` ```A = matrix(c(1,2,3,4,5,6),3,2,byrow = TRUE) C = matrix(c(1,1),1,2,byrow=TRUE) b = matrix(c(7,1,3),3,1,byrow=TRUE) d = matrix(c(1),1,1,byrow=TRUE) LSE_GQR(A,C,b,d) #You can verify that x+y=1 satisfies the constraint. ```

LSE documentation built on Feb. 2, 2022, 5:07 p.m.