NAG Library Routine Document

F01CRF

+− Contents

1 Purpose

2 Specification

3 Description

4 References

5 Parameters

6 Error Indicators and Warnings

7 Accuracy

8 Further Comments

+− 9 Example

9.1 Program Text

9.2 Program Data

9.3 Program Results

1 Purpose

F01CRF transposes a rectangular matrix in-situ.

2 Specification

SUBROUTINE F01CRF (

A, M, N, MN, MOVE, LMOVE, IFAIL)

INTEGER	M, N, MN, MOVE(LMOVE), LMOVE, IFAIL
REAL (KIND=nag_wp)	A(MN)

3 Description

F01CRF requires that the elements of an

m

n

matrix

A

are stored consecutively by columns in a one-dimensional array. It reorders the elements so that on exit the array holds the transpose of

A

stored in the same way. For example, if

m = 4

and

n = 3

, on entry the array must hold:

a_{11} a_{21} a_{31} a_{41} a_{12} a_{22} a_{32} a_{42} a_{13} a_{23} a_{33} a_{43}

and on exit it holds

a_{11} a_{12} a_{13} a_{21} a_{22} a_{23} a_{31} a_{32} a_{33} a_{41} a_{42} a_{43} .

4 References

Cate E G and Twigg D W (1977) Algorithm 513: Analysis of in-situ transposition ACM Trans. Math. Software 3 104–110

5 Parameters

1: A(MN) – REAL (KIND=nag_wp) arrayInput/Output: On entry: the elements of the $m$ by $n$ matrix $A$ , stored by columns.

On exit: the elements of the transpose matrix, also stored by columns.
2: M – INTEGERInput: On entry: $m$ , the number of rows of the matrix $A$ .
3: N – INTEGERInput: On entry: $n$ , the number of columns of the matrix $A$ .
4: MN – INTEGERInput: On entry: $n$ , the value $m \times n$ .
5: MOVE(LMOVE) – INTEGER arrayWorkspace
6: LMOVE – INTEGERInput: On entry: the dimension of the array MOVE as declared in the (sub)program from which F01CRF is called.

Suggested value: $LMOVE = (m + n) / 2$ .
Constraint: $LMOVE \geq 1$ .
7: IFAIL – INTEGERInput/Output: On entry: IFAIL must be set to $0$ , $- 1 or 1$ . If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction for details.
For environments where it might be inappropriate to halt program execution when an error is detected, the value $- 1 or 1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this parameter, the recommended value is $0$ . When the value $- 1 or 1$ is used it is essential to test the value of IFAIL on exit.

On exit: $IFAIL = 0$ unless the routine detects an error or a warning has been flagged (see Section 6).

6 Error Indicators and Warnings

If on entry

IFAIL = 0

- 1

, explanatory error messages are output on the current error message unit (as defined by X04AAF).

Errors or warnings detected by the routine:

$IFAIL = 1$

On entry,

MN \neq M \times N

$IFAIL = 2$

On entry,

LMOVE \leq 0

$IFAIL < 0$: A serious error has occurred. Check all subroutine calls and array sizes. Seek expert help.

7 Accuracy

Exact results are produced.

8 Further Comments

The time taken by F01CRF is approximately proportional to

m n

9 Example

This example transposes a

7

3

matrix and prints out, for convenience, its transpose.

NAG Library Routine DocumentF01CRF