NAG FL Interface
f01crf (real_​gen_​trans_​inplace)

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1 Purpose

f01crf transposes a rectangular matrix in-situ.

2 Specification

Fortran Interface
Subroutine f01crf ( a, m, n, mn, move, lmove, ifail)
Integer, Intent (In) :: m, n, mn, lmove
Integer, Intent (Inout) :: ifail
Integer, Intent (Out) :: move(lmove)
Real (Kind=nag_wp), Intent (Inout) :: a(mn)
C Header Interface
#include <nag.h>
void  f01crf_ (double a[], const Integer *m, const Integer *n, const Integer *mn, Integer move[], const Integer *lmove, Integer *ifail)
The routine may be called by the names f01crf or nagf_matop_real_gen_trans_inplace.

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:
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 Arguments

1: a(mn) Real (Kind=nag_wp) array Input/Output
On entry: the elements of the m×n matrix A, stored by columns.
On exit: the elements of the transpose matrix, also stored by columns.
2: m Integer Input
On entry: m, the number of rows of the matrix A.
3: n Integer Input
On entry: n, the number of columns of the matrix A.
4: mn Integer Input
On entry: mn, the value m×n.
5: move(lmove) Integer array Workspace
6: lmove Integer Input
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 Integer Input/Output
On entry: ifail must be set to 0, −1 or 1 to set behaviour on detection of an error; these values have no effect when no error is detected.
A value of 0 causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of −1 means that an error message is printed while a value of 1 means that it is not.
If halting is not appropriate, the value −1 or 1 is recommended. If message printing is undesirable, then the value 1 is recommended. Otherwise, the value 0 is recommended. 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, m=value, n=value and mn=value.
Constraint: mn=m×n.
On entry, lmove=value.
Constraint: lmove>0.
A serious internal error has occurred in f01crf.
An unexpected error has been triggered by this routine. Please contact NAG.
See Section 7 in the Introduction to the NAG Library FL Interface for further information.
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library FL Interface for further information.
Dynamic memory allocation failed.
See Section 9 in the Introduction to the NAG Library FL Interface for further information.

7 Accuracy

Exact results are produced.

8 Parallelism and Performance

Background information to multithreading can be found in the Multithreading documentation.
f01crf is not threaded in any implementation.

9 Further Comments

The time taken by f01crf is approximately proportional to mn.

10 Example

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

10.1 Program Text

Program Text (f01crfe.f90)

10.2 Program Data

Program Data (f01crfe.d)

10.3 Program Results

Program Results (f01crfe.r)