NAG Library Routine Document

F08NFF (DORGHR)

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     $\mathrm{N}$ – INTEGERInput

On entry: $n$, the order of the matrix $Q$.

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

2:     $\mathrm{ILO}$ – INTEGERInput

3:     $\mathrm{IHI}$ – INTEGERInput

On entry: these must be the same parameters ILO and IHI, respectively, as supplied to F08NEF (DGEHRD).

Constraints:

• if $\mathbf{N}>0$, $1\le \mathbf{ILO}\le \mathbf{IHI}\le \mathbf{N}$;
• if $\mathbf{N}=0$, $\mathbf{ILO}=1$ and $\mathbf{IHI}=0$.

4:     $\mathrm{A}\left(\mathbf{LDA},*\right)$ – REAL (KIND=nag_wp) arrayInput/Output

Note: the second dimension of the array A must be at least $\max \left(1,\mathbf{N}\right)$.

On entry: details of the vectors which define the elementary reflectors, as returned by F08NEF (DGEHRD).

On exit: the $n$ by $n$ orthogonal matrix $Q$.

5:     $\mathrm{LDA}$ – INTEGERInput

On entry: the first dimension of the array A as declared in the (sub)program from which F08NFF (DORGHR) is called.

Constraint: $\mathbf{LDA}\ge \max \left(1,\mathbf{N}\right)$.

6:     $\mathrm{TAU}\left(*\right)$ – REAL (KIND=nag_wp) arrayInput

Note: the dimension of the array TAU must be at least $\max \left(1,\mathbf{N}-1\right)$.

On entry: further details of the elementary reflectors, as returned by F08NEF (DGEHRD).

7:     $\mathrm{WORK}\left(\max \left(1,\mathbf{LWORK}\right)\right)$ – REAL (KIND=nag_wp) arrayWorkspace

On exit: if $\mathbf{INFO}=\mathbf{0}$, $\mathbf{WORK}\left(1\right)$ contains the minimum value of LWORK required for optimal performance.

8:     $\mathrm{LWORK}$ – INTEGERInput

On entry: the dimension of the array WORK as declared in the (sub)program from which F08NFF (DORGHR) is called, unless $\mathbf{LWORK}=-1$, in which case a workspace query is assumed and the routine only calculates the optimal dimension of WORK (using the formula given below).

Suggested value: for optimal performance LWORK should be at least $\left(\mathbf{IHI}-\mathbf{ILO}\right)\times nb$, where $nb$ is the block size.

Constraint: $\mathbf{LWORK}\ge \max \left(1,\mathbf{IHI}-\mathbf{ILO}\right)$ or $\mathbf{LWORK}=-1$.

9:     $\mathrm{INFO}$ – INTEGEROutput

On exit: $\mathbf{INFO}=0$ unless the routine detects an error (see Section 6).

6  Error Indicators and Warnings

$\mathbf{INFO}<0$

If $\mathbf{INFO}=-i$, argument $i$ had an illegal value. An explanatory message is output, and execution of the program is terminated.

7  Accuracy

8  Parallelism and Performance

9  Further Comments

10  Example

10.1  Program Text

Program Text (f08nffe.f90)

10.2  Program Data

Program Data (f08nffe.d)

10.3  Program Results

Program Results (f08nffe.r)