NAG Toolbox: nag_matop_real_gen_rq_formq (f01qk)

Purpose

Syntax

Description

References

Parameters

Compulsory Input Parameters

1:     $\mathrm{wheret}$ – string (length ≥ 1)

Indicates where the elements of $\zeta$ are to be found.

$\mathbf{wheret}=\text{'I'}$ (In a)

The elements of $\zeta$ are in a.

$\mathbf{wheret}=\text{'S'}$ (Separate)

The elements of $\zeta$ are separate from a, in zeta.

Constraint: $\mathbf{wheret}=\text{'I'}$ or $\text{'S'}$.

2:     $\mathrm{m}$ – int64int32nag_int scalar

$m$, the number of rows of the matrix $A$.

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

3:     $\mathrm{nrowp}$ – int64int32nag_int scalar

$\ell$, the required number of rows of $P$.

If $\mathbf{nrowp}=0$, an immediate return is effected.

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

4:     $\mathrm{a}\left(\mathit{lda},:\right)$ – double array

The first dimension of the array a must be at least $\max \left(1,\mathbf{m},\mathbf{nrowp}\right)$.

The second dimension of the array a must be at least $\max \left(1,\mathbf{n}\right)$.

The leading $m$ by $m$ strictly lower triangular part of the array a, and the $m$ by $\left(n-m\right)$ rectangular part of a with top left-hand corner at element $\mathbf{a}\left(1,\mathbf{m}+1\right)$ must contain details of the matrix $P$. In addition, if $\mathbf{wheret}=\text{'I'}$, the diagonal elements of a must contain the elements of $\zeta$.

5:     $\mathrm{zeta}\left(:\right)$ – double array

The dimension of the array zeta must be at least $\max \left(1,\mathbf{m}\right)$ if $\mathbf{wheret}=\text{'S'}$, and at least $1$ otherwise

With $\mathbf{wheret}=\text{'S'}$, the array zeta must contain the elements of $\zeta$. If $\mathbf{zeta}\left(k\right)=0.0$ then $P_k$ is assumed to be $I$, otherwise $\mathbf{zeta}\left(k\right)$ is assumed to contain ${\zeta }_k$.

When $\mathbf{wheret}=\text{'I'}$, the array zeta is not referenced.

Optional Input Parameters

1:     $\mathrm{n}$ – int64int32nag_int scalar

Default: the second dimension of the array a.

$n$, the number of columns of the matrix $A$.

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

Output Parameters

1:     $\mathrm{a}\left(\mathit{lda},:\right)$ – double array

The first dimension of the array a will be $\max \left(1,\mathbf{m},\mathbf{nrowp}\right)$.

The second dimension of the array a will be $\max \left(1,\mathbf{n}\right)$.

The first nrowp rows of the array a store the first nrowp rows of the $n$ by $n$ orthogonal matrix $P^{\mathrm{T}}$.

2:     $\mathrm{ifail}$ – int64int32nag_int scalar

$\mathbf{ifail}=\mathbf{0}$ unless the function detects an error (see Error Indicators and Warnings).

Error Indicators and Warnings

   $\mathbf{ifail}=-1$

On entry,	$\mathbf{wheret}\ne \text{'I'}$ or $\text{'S'}$,
or	$\mathbf{m}<0$,
or	$\mathbf{n}<\mathbf{m}$,
or	$\mathbf{nrowp}<0$ or $\mathbf{nrowp}>\mathbf{n}$,
or	$\mathit{lda}<\max \left(\mathbf{m},\mathbf{nrowp}\right)$.

   $\mathbf{ifail}=-99$

An unexpected error has been triggered by this routine. Please contact NAG.

   $\mathbf{ifail}=-399$

Your licence key may have expired or may not have been installed correctly.

   $\mathbf{ifail}=-999$

Dynamic memory allocation failed.

Accuracy

Further Comments

Example

Open in the MATLAB editor: f01qk_example

function f01qk_example


fprintf('f01qk example results\n\n');

a = [2,   2,    1.6,  2,    1.2;
     2.5, 2.5, -0.4, -0.5, -0.3;
     2.5, 2.5,  2.8,  0.5, -2.9];

[RQ, zeta, ifail] = f01qj(a);

wheret = 'Separate';
m     = int64(size(a,1));
nrowp = int64(size(a,2));
RQ(m+1:nrowp,1:nrowp) = 0;

[PT, ifail] = f01qk( ...
                    wheret, m, nrowp, RQ, zeta);

P = PT';
disp('Matrix P');
disp(P);

f01qk example results

Matrix P
   -0.1310   -0.5170   -0.4642   -0.5054   -0.4946
   -0.1310   -0.5170   -0.4642    0.5054    0.4946
   -0.3276    0.5499   -0.5199   -0.3957    0.4043
   -0.6551    0.2494   -0.0928    0.4946   -0.5054
   -0.6551   -0.3175    0.5385   -0.2967    0.3032