To compute an orthogonal factorization of a sparse overdetermined matrix and optionally to solve the least squares problem . Given a sparse matrix of order , , of full column rank, this subroutine computes the factorization where is an orthogonal matrix and is an upper triangular matrix.
Given an -vector , this subroutine may also compute the minimum 2-norm solution of the linear system , by solving and performing the multiplication , or, if the factor is not stored, by solving and performing the multiplication .
The subroutine can also solve systems with the coeﬃcient matrix or , or will compute the product of or with a vector.
The method used is based on the multifrontal approach and makes use of Householder transformations. Because an ordering for the columns is chosen using the pattern of the matrix , this code is not designed for matrices with full rows.