NAG Library Routine Document

F06TQF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     $\mathrm{N}$ – INTEGERInput

On entry: $n$, the order of the matrices $U$ and $R$.

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

2:     $\mathrm{ALPHA}$ – COMPLEX (KIND=nag_wp)Input

On entry: the scalar $\alpha$.

3:     $\mathrm{X}\left(*\right)$ – COMPLEX (KIND=nag_wp) arrayInput/Output

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

On entry: the $n$-element vector $x$. $x_{\mathit{i}}$ must be stored in $\mathbf{X}\left(1+\left(\mathit{i}-1\right)\times \mathbf{INCX}\right)$, for $\mathit{i}=1,2,\dots ,\mathbf{N}$.

Intermediate elements of X are not referenced.

On exit: the referenced elements are overwritten by details of the sequence of plane rotations.

4:     $\mathrm{INCX}$ – INTEGERInput

On entry: the increment in the subscripts of X between successive elements of $x$.

Constraint: $\mathbf{INCX}>0$.

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

Note: the second dimension of the array A must be at least $\mathbf{N}$.

On entry: the $n$ by $n$ upper triangular matrix $U$.

On exit: the upper triangular matrix $R$.

6:     $\mathrm{LDA}$ – INTEGERInput

On entry: the first dimension of the array A as declared in the (sub)program from which F06TQF is called.

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

7:     $\mathrm{C}\left(\mathbf{N}\right)$ – REAL (KIND=nag_wp) arrayOutput

On exit: the values $c_{\mathit{k}}$, the cosines of the rotations $Q_{\mathit{k}}$, for $\mathit{k}=1,2,\dots ,n$.

8:     $\mathrm{S}\left(\mathbf{N}\right)$ – COMPLEX (KIND=nag_wp) arrayOutput

On exit: the values $s_{\mathit{k}}$, the sines of the rotations $Q_{\mathit{k}}$, for $\mathit{k}=1,2,\dots ,n$.

6  Error Indicators and Warnings

7  Accuracy

8  Parallelism and Performance

9  Further Comments

10  Example