f06hqf (zsrotg) : NAG Library, Mark 27

Keyword Search:

f06hq: FL CL CPP AD

▸▿ 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

Fortran Interface

Subroutine f06hqf (

pivot, direct, n, alpha, x, incx, c, s)

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

C Header Interface

#include <nag.h>

void	f06hqf_ (const char pivot, const char direct, const Integer n, Complex alpha, Complex x[], const Integer *incx, double c[], Complex s[], const Charlen length_pivot, const Charlen length_direct)

C++ Header Interface

#include <nag.h>

extern "C" {

void	f06hqf_ (const char pivot, const char direct, const Integer &n, Complex &alpha, Complex x[], const Integer &incx, double c[], Complex s[], const Charlen length_pivot, const Charlen length_direct)

}

3 Description

f06hqf generates the parameters of a complex unitary matrix

P

, of order

n + 1

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

n

-element complex 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 complex 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 \times 2

plane rotation part has the form

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

with

c_{k}

real. The tangent of the rotation,

t_{k}

, is overwritten on

x_{k}

5 Arguments

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'

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'

n

– Integer Input

On entry:

n

, the number of elements in

x

alpha

– Complex (Kind=nag_wp) Input/Output

On entry: the scalar

α

On exit: the scalar

β

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 plane rotations.

incx

– Integer Input

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

x

Constraint:

incx > 0

c (n)

– Real (Kind=nag_wp) array Output

On exit: the values

c_{k}

, the cosines of the rotations.

s (n)

– Complex (Kind=nag_wp) array Output

On exit: the values

s_{k}

, the sines of the rotations.

NAG FL Interface
f06hqf (zsrotg)

▸▿ 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

NAG FL Interfacef06hqf (zsrotg)

▸▿ 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

NAG FL Interface
f06hqf (zsrotg)