f06qxf : NAG Library, Mark 26

f06qxf applies a sequence of plane rotations to a real rectangular matrix.

Specification

Fortran Interface

Subroutine f06qxf (

side, pivot, direct, m, n, k1, k2, c, s, a, lda)

Integer, Intent (In)	::	m, n, k1, k2, lda
Real (Kind=nag_wp), Intent (In)	::	c(k2-1), s(k2-1)
Real (Kind=nag_wp), Intent (Inout)	::	a(lda,*)
Character (1), Intent (In)	::	side, pivot, direct

C Header Interface

#include nagmk26.h

void	f06qxf_ ( const char side, const char pivot, const char direct, const Integer m, const Integer n, const Integer k1, const Integer k2, const double c[], const double s[], double a[], const Integer lda, const Charlen length_side, const Charlen length_pivot, const Charlen length_direct)

Description

f06qxf performs the transformation

A \leftarrow P A or A \leftarrow A P^{T},

where

A

is an

m

n

real matrix and

P

is a real orthogonal matrix, defined as a sequence of plane rotations,

P_{k}

, applied in planes

k_{1}

k_{2}

The

2

2

plane rotation part of

P_{k}

is assumed to have the form

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

Arguments

side

– Character(1)Input

On entry: specifies whether

A

is operated on from the left or the right.

$side ='L'$: $A$ is pre-multiplied from the left.
$side ='R'$: $A$ is post-multiplied from the right.

Constraint:

side ='L'

'R'

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.
$pivot ='T'$ (top pivot): $P_{k}$ rotates the $(k_{1}, k + 1)$ plane.
$pivot ='B'$ (bottom pivot): $P_{k}$ rotates the $(k, k_{2})$ plane.

Constraint:

pivot ='V'

'T'

'B'

direct

– Character(1)Input

On entry: specifies the sequence direction.

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

Constraint:

direct ='F'

'B'

m

– IntegerInput

On entry:

m

, the number of rows of the matrix

A

m < 1

, an immediate return is effected.

Constraint:

m \geq 0

n

– IntegerInput

On entry:

n

, the number of columns of the matrix

A

n < 1

, an immediate return is effected.

Constraint:

n \geq 0

k1

– IntegerInput

k2

– IntegerInput

On entry: the values

k_{1}

and

k_{2}

k1 < 1

k2 \leq k1

, or

side ='L'

and

k2 > m

, or

side ='R'

and

k2 > n

, an immediate return is effected.

c (k2 - 1)

– Real (Kind=nag_wp) arrayInput

On entry:

c (k)

must hold

c_{k}

, the cosine of the rotation

P_{k}

, for

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

s (k2 - 1)

– Real (Kind=nag_wp) arrayInput

On entry:

s (k)

must hold

s_{k}

, the sine of the rotation

P_{k}

, for

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

10:

a (lda *)

– Real (Kind=nag_wp) arrayInput/Output

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

n

On entry: the

m

n

matrix

A

On exit: the transformed matrix

A

11:

lda

– IntegerInput

On entry: the first dimension of the array a as declared in the (sub)program from which f06qxf is called.

Constraint:

lda \geq \max (1, m)

NAG Library Routine Document

f06qxf (dgesrc)

▸▿ 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 Library Routine Document

f06qxf (dgesrc)

▸▿ 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