LSE_GQR {LSE}

LSE and GQR Factorization

Description

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

Usage

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 [e-mail]

References

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

Examples

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.