F06VKF : NAG Library, Mark 24

NAG Library Routine Document

F06VKF

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

F06VKF permutes the rows or columns of a complex rectangular matrix using a real array of permutations.

2 Specification

3 Description

F06VKF 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 complex 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); F06VJF performs the same operation with the indices supplied in an integer array.

5 Parameters

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

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,

*

) – COMPLEX (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 (1, \max_{k} \{int PERM (k)\})

SIDE ='R'

On entry: the original matrix

B

;

B

m

k

SIDE ='L'

, or

k

m

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 F06VKF is called.

Constraints:

if $SIDE ='L'$ , $LDB \geq \max (1, m)$ ;
if $SIDE ='R'$ , $LDB \geq \max (1, K)$ .

NAG Library Routine Document

F06VKF

+− Contents

1 Purpose

2 Specification

3 Description

4 References

5 Parameters

6 Error Indicators and Warnings

7 Accuracy

8 Further Comments

9 Example

NAG Library Routine DocumentF06VKF

+− Contents

1 Purpose

2 Specification

3 Description

4 References

5 Parameters

6 Error Indicators and Warnings

7 Accuracy

8 Further Comments

9 Example

NAG Library Routine Document

F06VKF