Integer, Intent (In)	::	n, incx, lda
Real (Kind=nag_wp), Intent (Out)	::	c(n)
Complex (Kind=nag_wp), Intent (In)	::	alpha
Complex (Kind=nag_wp), Intent (Inout)	::	x(), a(lda,)
Complex (Kind=nag_wp), Intent (Out)	::	s(n)

C Header Interface

#include <nag.h>

void	f06tqf_ (const Integer n, const Complex alpha, Complex x[], const Integer incx, Complex a[], const Integer lda, double c[], Complex s[])

The routine may be called by the names f06tqf or nagf_blas_zutupd.

3 Description

f06tqf performs the factorization

(\begin{matrix} U \\ α x^{T} \end{matrix}) = Q (\begin{array}{r} R \\ 0 \end{array})

where

U

and

R

are

n \times n

complex upper triangular matrices,

x

is an

n

-element complex vector,

α

is a complex scalar, and

Q

is a complex unitary matrix. If

U

has real diagonal elements, then so does

R

Q

is formed as a sequence of plane rotations

Q^{H} = Q_{n} \dots Q_{2} Q_{1}

where

Q_{k}

is a rotation in the

(k, n + 1)

plane, chosen to annihilate

x_{k}

The

2 \times 2

plane rotation part of

Q_{k}

has the form

(\begin{array}{r} c_{k} & {\bar{s}}_{k} \\ - s_{k} & c_{k} \end{array})

with

c_{k}

real.

4 References

None.

1: $n$ – Integer Input: On entry: $n$ , the order of the matrices $U$ and $R$ .

Constraint: $n \geq 0$ .
2: $alpha$ – Complex (Kind=nag_wp) Input: On entry: the scalar $α$ .
3: $x (*)$ – Complex (Kind=nag_wp) array Input/Output: Note: the dimension of the array x must be at least $\max (1, 1 + (n - 1) \times incx)$ .

On entry: the $n$ -element vector $x$ . $x_{i}$ must be stored in $x (1 + (i - 1) \times incx)$ , for $i = 1, 2, \dots, n$ .
Intermediate elements of x are not referenced.

On exit: the referenced elements are overwritten by details of the sequence of plane rotations.
4: $incx$ – Integer Input: On entry: the increment in the subscripts of x between successive elements of $x$ .

Constraint: $incx > 0$ .
5: $a (lda, *)$ – Complex (Kind=nag_wp) array Input/Output: Note: the second dimension of the array a must be at least $n$ .

On entry: the $n \times n$ upper triangular matrix $U$ .

On exit: the upper triangular matrix $R$ .
6: $lda$ – Integer Input: On entry: the first dimension of the array a as declared in the (sub)program from which f06tqf is called.

Constraint: $lda \geq \max (1, n)$ .
7: $c (n)$ – Real (Kind=nag_wp) array Output: On exit: the values $c_{k}$ , the cosines of the rotations $Q_{k}$ , for $k = 1, 2, \dots, n$ .
8: $s (n)$ – Complex (Kind=nag_wp) array Output: On exit: the values $s_{k}$ , the sines of the rotations $Q_{k}$ , for $k = 1, 2, \dots, n$ .