F06TTF : NAG Library, Mark 25

NAG Library Routine Document

F06TTF

Note: before using this routine, please read the Users' Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details.

1 Purpose

F06TTF performs a

Q R

R Q

factorization of the product of a complex upper triangular matrix and a complex matrix of plane rotations.

2 Specification

3 Description

F06TTF performs one of the transformations

R \leftarrow P U Q^{H} or R \leftarrow Q U P^{H},

where

U

is a given

n

n

complex upper triangular matrix,

P

is a given complex unitary matrix, and

Q

is a complex unitary matrix chosen to make

R

upper triangular. Both

P

and

Q

are represented as sequences of plane rotations in planes

k_{1}

k_{2}

SIDE ='L'

R \leftarrow P U Q^{H},

where

P = P_{k_{2} - 1} \dots P_{k_{1} + 1} P_{k_{1}}

and

Q = Q_{k_{2} - 1} \dots Q_{k_{1} + 1} Q_{k_{1}}

SIDE ='R'

R \leftarrow Q U P^{H},

where

P = P_{k_{1}} P_{k_{1} + 1} \dots P_{k_{2} - 1}

and

Q = Q_{k_{1}} Q_{k_{1} + 1} \dots Q_{k_{2} - 1}

In either case

P_{k}

and

Q_{k}

are rotations in the

(k, k + 1)

plane.

The

2

2

rotation part of

P_{k}

Q_{k}

has the form

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

with

c_{k}

real.

5 Parameters

SIDE

– CHARACTER(1)Input

On entry: specifies whether

P

is applied from the left or the right in the transformation.

$SIDE ='L'$: $P$ is applied from the left.
$SIDE ='R'$: $P$ is applied from the right.

Constraint:

SIDE ='L'

'R'

N

– INTEGERInput

On entry:

n

, the order of the matrices

U

and

R

Constraint:

N \geq 0

K1

– INTEGERInput

K2

– INTEGERInput

On entry: the values

k_{1}

and

k_{2}

K1 < 1

K2 \leq K1

K2 > N

, an immediate return is effected.

C (*)

– REAL (KIND=nag_wp) arrayInput/Output

Note: the dimension of the array C must be at least

K2 - K1

On entry:

C (k)

must hold the cosine of the rotation

P_{k}

, for

k = k_{1}, \dots, k_{2} - 1

On exit:

C (k)

holds the cosine of the rotation

Q_{k}

, for

k = k_{1}, \dots, k_{2} - 1

S (*)

– COMPLEX (KIND=nag_wp) arrayInput/Output

Note: the dimension of the array S must be at least

K2 - K1

On entry:

S (k)

must hold the sine of the rotation

P_{k}

, for

k = k_{1}, \dots, k_{2} - 1

On exit:

S (k)

holds the sine of the rotation

Q_{k}

, for

k = k_{1}, \dots, k_{2} - 1

A (LDA *)

– COMPLEX (KIND=nag_wp) arrayInput/Output

Note: the second dimension of the array A must be at least

N

On entry: the

n

n

upper triangular matrix

U

On exit: the upper triangular matrix

R

LDA

– INTEGERInput

On entry: the first dimension of the array A as declared in the (sub)program from which F06TTF is called.

Constraint:

LDA \geq \max (1, N)

NAG Library Routine Document

F06TTF

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Parameters

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

NAG Library Routine DocumentF06TTF

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Parameters

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

NAG Library Routine Document

F06TTF