NAG Library Function Document

nag_zggglm (f08zpc)

1  Purpose

2  Specification

3  Description

4  References

5  Arguments

1:     order – Nag_OrderTypeInput

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 3.2.1.3 in the Essential Introduction for a more detailed explanation of the use of this argument.

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

2:     m – IntegerInput

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

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

3:     n – IntegerInput

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

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

4:     p – IntegerInput

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

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

5:     a[$\mathit{dim}$] – ComplexInput/Output

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

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

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

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

On entry: the $m$ by $n$ matrix $A$.

On exit: a is overwritten.

6:     pda – IntegerInput

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

Constraints:

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

7:     b[$\mathit{dim}$] – ComplexInput/Output

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

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

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

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

On entry: the $m$ by $p$ matrix $B$.

On exit: b is overwritten.

8:     pdb – IntegerInput

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

Constraints:

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

9:     d[m] – ComplexInput/Output

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

On exit: d is overwritten.

10:   x[n] – ComplexOutput

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

11:   y[p] – ComplexOutput

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

12:   fail – NagError *Input/Output

The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.

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: $\mathbf{pda}\ge \max \left(1,\mathbf{m}\right)$.

On entry, $\mathbf{pda}=〈\mathit{\text{value}}〉$ and $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{pda}\ge \max \left(1,\mathbf{n}\right)$.

On entry, $\mathbf{pdb}=〈\mathit{\text{value}}〉$ and $\mathbf{m}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{pdb}\ge \max \left(1,\mathbf{m}\right)$.

On entry, $\mathbf{pdb}=〈\mathit{\text{value}}〉$ and $\mathbf{p}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{pdb}\ge \max \left(1,\mathbf{p}\right)$.

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.

NE_SINGULAR

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

7  Accuracy

8  Further Comments

9  Example

9.1  Program Text

Program Text (f08zpce.c)

9.2  Program Data

Program Data (f08zpce.d)

9.3  Program Results

Program Results (f08zpce.r)