# NAG Library Routine Document

## 1Purpose

f01crf transposes a rectangular matrix in-situ.

## 2Specification

Fortran Interface
 Subroutine f01crf ( a, m, n, mn, move,
 Integer, Intent (In) :: m, n, mn, lmove Integer, Intent (Inout) :: ifail Integer, Intent (Out) :: move(lmove) Real (Kind=nag_wp), Intent (Inout) :: a(mn)
#include nagmk26.h
 void f01crf_ (double a[], const Integer *m, const Integer *n, const Integer *mn, Integer move[], const Integer *lmove, Integer *ifail)

## 3Description

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:
 $a11 a21 a31 a41 a12 a22 a32 a42 a13 a23 a33 a43$
and on exit it holds
 $a11 a12 a13 a21 a22 a23 a31 a32 a33 a41 a42 a43.$

## 4References

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

## 5Arguments

1:     $\mathbf{a}\left({\mathbf{mn}}\right)$ – 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:     $\mathbf{m}$ – IntegerInput
On entry: $m$, the number of rows of the matrix $A$.
3:     $\mathbf{n}$ – IntegerInput
On entry: $n$, the number of columns of the matrix $A$.
4:     $\mathbf{mn}$ – IntegerInput
On entry: $n$, the value $m×n$.
5:     $\mathbf{move}\left({\mathbf{lmove}}\right)$ – Integer arrayWorkspace
6:     $\mathbf{lmove}$ – IntegerInput
On entry: the dimension of the array move as declared in the (sub)program from which f01crf is called.
Suggested value: ${\mathbf{lmove}}=\left(m+n\right)/2$.
Constraint: ${\mathbf{lmove}}\ge 1$.
7:     $\mathbf{ifail}$ – IntegerInput/Output
On entry: ifail must be set to $0$, $-1\text{​ or ​}1$. If you are unfamiliar with this argument you should refer to Section 3.4 in How to Use the NAG Library and its Documentation for details.
For environments where it might be inappropriate to halt program execution when an error is detected, the value $-1\text{​ or ​}1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this argument, the recommended value is $0$. When the value $-\mathbf{1}\text{​ or ​}\mathbf{1}$ is used it is essential to test the value of ifail on exit.
On exit: ${\mathbf{ifail}}={\mathbf{0}}$ unless the routine detects an error or a warning has been flagged (see Section 6).

## 6Error Indicators and Warnings

If on entry ${\mathbf{ifail}}=0$ or $-1$, explanatory error messages are output on the current error message unit (as defined by x04aaf).
Errors or warnings detected by the routine:
${\mathbf{ifail}}=1$
 On entry, ${\mathbf{mn}}\ne {\mathbf{m}}×{\mathbf{n}}$.
${\mathbf{ifail}}=2$
 On entry, ${\mathbf{lmove}}\le 0$.
${\mathbf{ifail}}<0$
A serious error has occurred. Check all subroutine calls and array sizes. Seek expert help.
${\mathbf{ifail}}=-99$
See Section 3.9 in How to Use the NAG Library and its Documentation for further information.
${\mathbf{ifail}}=-399$
Your licence key may have expired or may not have been installed correctly.
See Section 3.8 in How to Use the NAG Library and its Documentation for further information.
${\mathbf{ifail}}=-999$
Dynamic memory allocation failed.
See Section 3.7 in How to Use the NAG Library and its Documentation for further information.

## 7Accuracy

Exact results are produced.

## 8Parallelism and Performance

f01crf is not threaded in any implementation.

The time taken by f01crf is approximately proportional to $mn$.

## 10Example

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

### 10.1Program Text

Program Text (f01crfe.f90)

### 10.2Program Data

Program Data (f01crfe.d)

### 10.3Program Results

Program Results (f01crfe.r)

© The Numerical Algorithms Group Ltd, Oxford, UK. 2017