NAG Library Routine Document

f08nff (dorghr)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:     $\mathbf{n}$ – IntegerInput

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

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

2:     $\mathbf{ilo}$ – IntegerInput

3:     $\mathbf{ihi}$ – IntegerInput

On entry: these must be the same arguments 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:     $\mathbf{a}\left(\mathbf{lda},*\right)$ – 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:     $\mathbf{lda}$ – 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:     $\mathbf{tau}\left(*\right)$ – 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:     $\mathbf{work}\left(\max \left(1,\mathbf{lwork}\right)\right)$ – 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:     $\mathbf{lwork}$ – 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:     $\mathbf{info}$ – 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)