F01CRF (PDF version)
F01 Chapter Contents
F01 Chapter Introduction
NAG Library Manual

NAG Library Routine Document


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.

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

F01CRF transposes a rectangular matrix in-situ.

2  Specification

REAL (KIND=nag_wp)  A(MN)

3  Description

F01CRF requires that the elements of an m by 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:
and on exit it holds
a11 a12 a13 a21 a22 a23 a31 a32 a33 a41 a42 a43.

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×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: LMOVE1.
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 or -1, explanatory error messages are output on the current error message unit (as defined by X04AAF).
Errors or warnings detected by the routine:
On entry,MNM×N.
On entry,LMOVE0.
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 mn.

9  Example

This example transposes a 7 by 3 matrix and prints out, for convenience, its transpose.

9.1  Program Text

Program Text (f01crfe.f90)

9.2  Program Data

Program Data (f01crfe.d)

9.3  Program Results

Program Results (f01crfe.r)

F01CRF (PDF version)
F01 Chapter Contents
F01 Chapter Introduction
NAG Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2012