NAG Library Routine Document

Integer, Intent (In)	::	n, k, ldb
Real (Kind=nag_wp), Intent (In)	::	perm(*)
Real (Kind=nag_wp), Intent (Inout)	::	b(ldb,*)
Character (1), Intent (In)	::	side, trans

C Header Interface

#include <nagmk26.h>

void	f06qkf_ (const char side, const char trans, const Integer n, const double perm[], const Integer k, double b[], const Integer *ldb, const Charlen length_side, const Charlen length_trans)

3

Description

f06qkf performs one of the permutation operations

\begin{array}{l} B \leftarrow P^{T} B, & B \leftarrow P B, \\ B \leftarrow B P^{T} or & B \leftarrow B P, \end{array}

where

B

is a real matrix, and

P

is a permutation matrix.

P

is represented in the form

P = P_{1, p_{1}} P_{2, p_{2}} \dots P_{n, p_{n}},

where

P_{i, j}

is the permutation matrix that interchanges items

i

and

j

; that is,

P_{i, j}

is the unit matrix with rows and columns

i

and

j

interchanged. If

i = j

P_{i, j} = I

Let

m

denote the number of rows of

B

side ='L'

, or the number of columns of

B

side ='R'

: the routine does not require

m

to be passed as an argument, but assumes that

m \geq p_{i}

, for

i = 1, 2, \dots, n

This routine requires the indices

p_{i}

to be supplied in a real array (the routine takes the integer part of the array elements); f06qjf performs the same operation with the indices supplied in an integer array.

4

References

None.

5

Arguments

1: $side$ – Character(1)Input

2: $trans$ – Character(1)Input

On entry: specifies the operation to be performed.

$side ='L'$ and $trans ='T'$: $B \leftarrow P^{T} B$ .
$side ='L'$ and $trans ='N'$: $B \leftarrow P B$ .
$side ='R'$ and $trans ='T'$: $B \leftarrow B P^{T}$ .
$side ='R'$ and $trans ='N'$: $B \leftarrow B P$ .

Constraints:

$side ='L'$ or $'R'$ ;
$trans ='N'$ or $'T'$ .

3: $n$ – IntegerInput

On entry:

n

, the number of interchanges in the representation of

P

Constraint:

n \geq 0

4: $perm (*)$ – Real (Kind=nag_wp) arrayInput

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

\max (1, n)

On entry: the

n

indices

p_{i}

which define the interchanges in the representation of

P

. It is usual to have

p_{i} \geq i

, but this is not necessary.

Constraint:

1 \leq perm (i) \leq m

, where

m = \max_{k} \{int perm (k)\}

5: $k$ – IntegerInput

On entry:

k

, the number of columns of

B

side ='L'

, or the number of rows of

B

side ='R'

Constraint:

k \geq 0

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

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

\max (1, k)

side ='L'

and at least

\max (n, \max_{k} \{int perm (k)\})

side ='R'

On entry: the original matrix

B

;

B

m

, where

m = \max_{k} \{int perm (k)\}

k

side ='L'

, or

k

m

, where

m = \max_{k} \{int perm (k)\}

side ='R'

On exit: the permuted matrix

B

7: $ldb$ – IntegerInput

On entry: the first dimension of the array b as declared in the (sub)program from which f06qkf is called.

Constraints:

if $side ='L'$ , $ldb \geq \max (n, m)$ ;
if $side ='R'$ , $ldb \geq \max (1, k)$ .

6

Error Indicators and Warnings

None.

7

Accuracy

Not applicable.

8

Parallelism and Performance

f06qkf 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

f06qkf (dgeapr)

▸▿ 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