NAG Library Routine Document

Integer, Intent (In)	::	n, incx
Real (Kind=nag_wp), Intent (Inout)	::	alpha, x(*)
Real (Kind=nag_wp), Intent (Out)	::	c(n), s(n)
Character (1), Intent (In)	::	pivot, direct

C Header Interface

#include <nagmk26.h>

void	f06fqf_ (const char pivot, const char direct, const Integer n, double alpha, double x[], const Integer *incx, double c[], double s[], const Charlen length_pivot, const Charlen length_direct)

3

Description

f06fqf generates the parameters of a real orthogonal matrix

P

, of order

n + 1

, chosen so as to set to zero the elements of a supplied

n

-element real vector

x

pivot ='F'

and

direct ='F'

, or if

pivot ='V'

and

direct ='B'

P (\begin{array}{r} α \\ x \end{array}) = (\begin{array}{r} β \\ 0 \end{array});

pivot ='F'

and

direct ='B'

, or if

pivot ='V'

and

direct ='F'

P (\begin{array}{r} x \\ α \end{array}) = (\begin{array}{r} 0 \\ β \end{array}) .

Here

α

and

β

are real scalars.

P

is represented as a sequence of

n

plane rotations

P_{k}

, as specified by pivot and direct;

P_{k}

is chosen to annihilate

x_{k}

, and its

2

2

plane rotation part has the form

(\begin{array}{r} c_{k} & s_{k} \\ - s_{k} & c_{k} \end{array}) .

The tangent of the rotation,

t_{k}

, is overwritten on

x_{k}

4

References

None.

5

Arguments

1: $pivot$ – Character(1)Input

On entry: specifies the plane rotated by

P_{k}

$pivot ='V'$ (variable pivot): $P_{k}$ rotates the $(k, k + 1)$ plane.
$pivot ='F'$ (fixed pivot): $P_{k}$ rotates the $(1, k + 1)$ plane if $direct ='F'$ , or the $(k, n + 1)$ plane if $direct ='B'$ .

Constraint:

pivot ='V'

'F'

2: $direct$ – Character(1)Input

On entry: specifies the sequence direction.

$direct ='F'$ (forward sequence): $P = P_{n} \dots P_{2} P_{1}$ .
$direct ='B'$ (backward sequence): $P = P_{1} P_{2} \dots P_{n}$ .

Constraint:

direct ='F'

'B'

3: $n$ – IntegerInput

On entry:

n

, the number of elements in

x

4: $alpha$ – Real (Kind=nag_wp)Input/Output

On entry: the scalar

α

On exit: the scalar

β

5: $x (*)$ – Real (Kind=nag_wp) arrayInput/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.

6: $incx$ – IntegerInput

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

x

Constraint:

incx > 0

7: $c (n)$ – Real (Kind=nag_wp) arrayOutput

On exit: the values

c_{k}

, the cosines of the rotations.

8: $s (n)$ – Real (Kind=nag_wp) arrayOutput

On exit: the values

s_{k}

, the sines of the rotations.

6

Error Indicators and Warnings

None.

7

Accuracy

Not applicable.

8

Parallelism and Performance

f06fqf is not threaded in any implementation.

9

Further Comments

None.

10

Example

None.

NAG Library Manual, Mark 26

NAG AD Library Manual, Mark 26

NAG C Library Manual, Mark 26

F06 (blas) Chapter Contents

F06 (blas) Chapter Introduction

NAG Library Routine Document

f06fqf (dsrotg)

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

6

Error Indicators and Warnings

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example