NAG Library Routine Document

void	f06qtf_ (const char side, const Integer n, const Integer k1, const Integer k2, double c[], double s[], double a[], const Integer *lda, const Charlen length_side)

3

Description

f06qtf performs one of the transformations

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

where

U

is a given

n

n

real upper triangular matrix,

P

is a given real orthogonal matrix, and

Q

is a real orthogonal 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^{T},

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^{T},

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

4

References

None.

5

Arguments

1: $side$ – 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'

2: $n$ – IntegerInput

On entry:

n

, the order of the matrices

U

and

R

Constraint:

n \geq 0

3: $k1$ – IntegerInput

4: $k2$ – IntegerInput

On entry: the values

k_{1}

and

k_{2}

k1 < 1

k2 \leq k1

k2 > n

, an immediate return is effected.

5: $c (*)$ – Real (Kind=nag_wp) arrayInput/Output

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

k2 - 1

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

6: $s (*)$ – Real (Kind=nag_wp) arrayInput/Output

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

k2 - 1

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

7: $a (lda *)$ – Real (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

8: $lda$ – IntegerInput

On entry: the first dimension of the array a as declared in the (sub)program from which f06qtf is called.

Constraint:

lda \geq \max (1, n)

6

Error Indicators and Warnings

None.

7

Accuracy

Not applicable.

8

Parallelism and Performance

f06qtf 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

f06qtf (dutsqr)

▸▿ 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