Driver routines are provided for two types of generalized linear least squares problems.

The first is

where `A` is an `m`-by-`m` matrix and `B` is a `p`-by-`n` matrix,
`c` is a given `m`-vector, and `d` is a given `p`-vector,
with `p` < = `n` < = `m` + `p`.
This is
called a **linear equality-constrained least squares problem (LSE)**.
The routine xGGLSE
solves this problem using the generalized `RQ`
(GRQ) factorization, on the
assumptions that `B` has full row rank `p` and
the matrix has full column rank `n`.
Under these assumptions, the problem LSE has a unique solution.

The second generalized linear least squares problem is

where `A` is an `n`-by-`m` matrix, `B` is an `n`-by-`p` matrix,
and `d` is a given `n`-vector,
with `m` < = `n` < = `m` + `p`.
This is sometimes called a **general** (Gauss-Markov) **linear model problem (GLM)**.
When `B` = `I`, the problem reduces to an ordinary linear least squares problem.
When `B` is square and nonsingular, the GLM problem is equivalent to the
**weighted linear least squares problem**:

The routine xGGGLM
solves this problem using the generalized `QR` (GQR)
factorization, on the
assumptions that `A` has full column rank `m`, and the
matrix (`A` , `B`) has full row rank `n`. Under these assumptions, the
problem is always consistent, and there are unique solutions `x` and `y`.
The driver routines for generalized linear least squares problems are listed
in Table 2.4.

------------------------------------------------------------------ Single precision Double precision Operation real complex real complex ------------------------------------------------------------------ solve LSE problem using GQR SGGLSE CGGLSE DGGLSE ZGGLSE solve GLM problem using GQR SGGGLM CGGGLM DGGGLM ZGGGLM ------------------------------------------------------------------

Tue Nov 29 14:03:33 EST 1994