NAG CL Interface
f08zbc (dggglm)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

1: $\mathbf{order}$ – Nag_OrderType Input

On entry: the order argument specifies the two-dimensional storage scheme being used, i.e., row-major ordering or column-major ordering. C language defined storage is specified by $\mathbf{order}=\mathrm{Nag\_RowMajor}$. See Section 3.1.3 in the Introduction to the NAG Library CL Interface for a more detailed explanation of the use of this argument.

Constraint: $\mathbf{order}=\mathrm{Nag\_RowMajor}$ or $\mathrm{Nag\_ColMajor}$.

2: $\mathbf{m}$ – Integer Input

On entry: $m$, the number of rows of the matrices $A$ and $B$.

Constraint: $\mathbf{m}\ge 0$.

3: $\mathbf{n}$ – Integer Input

On entry: $n$, the number of columns of the matrix $A$.

Constraint: $0\le \mathbf{n}\le \mathbf{m}$.

4: $\mathbf{p}$ – Integer Input

On entry: $p$, the number of columns of the matrix $B$.

Constraint: $\mathbf{p}\ge \mathbf{m}-\mathbf{n}$.

5: $\mathbf{a}\left[\mathit{dim}\right]$ – double Input/Output

Note: the dimension, dim, of the array a must be at least

• $\max (1,\mathbf{pda}\times \mathbf{n})$ when $\mathbf{order}=\mathrm{Nag\_ColMajor}$;
• $\max (1,\mathbf{m}\times \mathbf{pda})$ when $\mathbf{order}=\mathrm{Nag\_RowMajor}$.

The $(i,j)$th element of the matrix $A$ is stored in

• $\mathbf{a}\left[(j-1)\times \mathbf{pda}+i-1\right]$ when $\mathbf{order}=\mathrm{Nag\_ColMajor}$;
• $\mathbf{a}\left[(i-1)\times \mathbf{pda}+j-1\right]$ when $\mathbf{order}=\mathrm{Nag\_RowMajor}$.

On entry: the $m\times n$ matrix $A$.

On exit: a is overwritten.

6: $\mathbf{pda}$ – Integer Input

On entry: the stride separating row or column elements (depending on the value of order) in the array a.

Constraints:

• if $\mathbf{order}=\mathrm{Nag\_ColMajor}$, $\mathbf{pda}\ge \max (1,\mathbf{m})$;
• if $\mathbf{order}=\mathrm{Nag\_RowMajor}$, $\mathbf{pda}\ge \max (1,\mathbf{n})$.

7: $\mathbf{b}\left[\mathit{dim}\right]$ – double Input/Output

Note: the dimension, dim, of the array b must be at least

• $\max (1,\mathbf{pdb}\times \mathbf{p})$ when $\mathbf{order}=\mathrm{Nag\_ColMajor}$;
• $\max (1,\mathbf{m}\times \mathbf{pdb})$ when $\mathbf{order}=\mathrm{Nag\_RowMajor}$.

The $(i,j)$th element of the matrix $B$ is stored in

• $\mathbf{b}\left[(j-1)\times \mathbf{pdb}+i-1\right]$ when $\mathbf{order}=\mathrm{Nag\_ColMajor}$;
• $\mathbf{b}\left[(i-1)\times \mathbf{pdb}+j-1\right]$ when $\mathbf{order}=\mathrm{Nag\_RowMajor}$.

On entry: the $m\times p$ matrix $B$.

On exit: b is overwritten.

8: $\mathbf{pdb}$ – Integer Input

On entry: the stride separating row or column elements (depending on the value of order) in the array b.

Constraints:

• if $\mathbf{order}=\mathrm{Nag\_ColMajor}$, $\mathbf{pdb}\ge \max (1,\mathbf{m})$;
• if $\mathbf{order}=\mathrm{Nag\_RowMajor}$, $\mathbf{pdb}\ge \max (1,\mathbf{p})$.

9: $\mathbf{d}\left[\mathbf{m}\right]$ – double Input/Output

On entry: the left-hand side vector $d$ of the GLM equation.

On exit: d is overwritten.

10: $\mathbf{x}\left[\mathbf{n}\right]$ – double Output

On exit: the solution vector $x$ of the GLM problem.

11: $\mathbf{y}\left[\mathbf{p}\right]$ – double Output

On exit: the solution vector $y$ of the GLM problem.

12: $\mathbf{fail}$ – NagError * Input/Output

The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.

NE_BAD_PARAM

On entry, argument $⟨\mathit{\text{value}}⟩$ had an illegal value.

NE_INT

On entry, $\mathbf{m}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{m}\ge 0$.

On entry, $\mathbf{pda}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{pda}>0$.

On entry, $\mathbf{pdb}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{pdb}>0$.

NE_INT_2

On entry, $\mathbf{m}=⟨\mathit{\text{value}}⟩$ and $\mathbf{n}=⟨\mathit{\text{value}}⟩$.
Constraint: $0\le \mathbf{n}\le \mathbf{m}$.

On entry, $\mathbf{pda}=⟨\mathit{\text{value}}⟩$ and $\mathbf{m}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{pda}\ge \max (1,\mathbf{m})$.

On entry, $\mathbf{pda}=⟨\mathit{\text{value}}⟩$ and $\mathbf{n}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{pda}\ge \max (1,\mathbf{n})$.

On entry, $\mathbf{pdb}=⟨\mathit{\text{value}}⟩$ and $\mathbf{m}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{pdb}\ge \max (1,\mathbf{m})$.

On entry, $\mathbf{pdb}=⟨\mathit{\text{value}}⟩$ and $\mathbf{p}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{pdb}\ge \max (1,\mathbf{p})$.

NE_INT_3

On entry, $\mathbf{p}=⟨\mathit{\text{value}}⟩$, $\mathbf{m}=⟨\mathit{\text{value}}⟩$ and $\mathbf{n}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{p}\ge \mathbf{m}-\mathbf{n}$.

NE_INTERNAL_ERROR

An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 7.5 in the Introduction to the NAG Library CL Interface for further information.

NE_NO_LICENCE

Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.

NE_SINGULAR

The bottom $(m-n)\times (m-n)$ part of the upper trapezoidal factor $T$ associated with $B$ in the generalized $QR$ factorization of the pair $(A,B)$ is singular, so that $\mathrm{rank}\left(\begin{array}{cc}A& B\end{array}\right)<n$; the least squares solutions could not be computed.

The upper triangular factor $R$ associated with $A$ in the generalized $RQ$ factorization of the pair $(A,B)$ is singular, so that $\mathrm{rank}\left(A\right)<n$; the least squares solution could not be computed.

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results