# NAG FL Interfacem01zcf (permute_​decompose)

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## 1Purpose

m01zcf decomposes a permutation into cycles, as an aid to reordering ranked data.

## 2Specification

Fortran Interface
 Subroutine m01zcf ( m1, m2,
 Integer, Intent (In) :: m1, m2 Integer, Intent (Inout) :: iperm(m2), ifail Integer, Intent (Out) :: icycl(m2)
#include <nag.h>
 void m01zcf_ (Integer iperm[], const Integer *m1, const Integer *m2, Integer icycl[], Integer *ifail)
The routine may be called by the names m01zcf or nagf_sort_permute_decompose.

## 3Description

m01zcf is provided as an aid to reordering arbitrary data structures without using additional storage. However, you should consider carefully whether it is necessary to rearrange yourr data, or whether it would be simpler and more efficient to refer to the data in sorted order using an index vector, or to create a copy of the data in sorted order.
To rearrange data into a different order without using additional storage, the simplest method is to decompose the permutation which specifies the new order into cycles and then to do a cyclic permutation of the data items in each cycle. (This is the method used by the reordering routines m01eaf, m01ebf, m01ecf and m01edf.) Given a vector IRANK which specifies the ranks of the data (as generated by the routines m01daf, m01dbf, m01dcf, m01def, m01dff, m01djf, m01dkf and m01dzf), m01zcf generates a new vector icycl, in which the permutation is represented in its component cycles, with the first element of each cycle negated. For example, the permutation
 $5 7 4 2 1 6 3$
is composed of the cycles
 $( 1 5 ) ( 2 7 3 4 ) ( 6 )$
and the vector icycl generated by m01zcf contains
 $−1 5 −2 7 3 4 −6$
In order to rearrange the data according to the specified ranks:
• item $6$ must be left in place;
• items $1$ and $5$ must be interchanged;
• items $4$, $2$, $7$ and $3$ must be moved right one place round the cycle.
The complete rearrangement can be achieved by the following code:
```do k = m1, m2
i = icycl(k)
if (i < 0) then
j = -i
else
[swap items i and j]
end if
end do```

None.

## 5Arguments

1: $\mathbf{iperm}\left({\mathbf{m2}}\right)$Integer array Input/Output
On entry: elements ${\mathbf{m1}}$ to ${\mathbf{m2}}$ of iperm must contain a permutation of the integers m1 to m2.
On exit: is used as internal workpsace prior to being restored and hence is unchanged.
2: $\mathbf{m1}$Integer Input
3: $\mathbf{m2}$Integer Input
On entry: m1 and m2 must specify the range of elements used in the array iperm and the range of values in the permutation, as specified under iperm.
Constraint: $0<{\mathbf{m1}}\le {\mathbf{m2}}$.
4: $\mathbf{icycl}\left({\mathbf{m2}}\right)$Integer array Output
On exit: elements ${\mathbf{m1}}$ to ${\mathbf{m2}}$ of icycl contain a representation of the permutation as a list of cycles, with the first integer in each cycle negated. (See Section 3.)
5: $\mathbf{ifail}$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 $-\mathbf{1}$ 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, ${\mathbf{m1}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{m1}}\ge 1$.
On entry, ${\mathbf{m1}}=⟨\mathit{\text{value}}⟩$ and ${\mathbf{m2}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{m1}}\le {\mathbf{m2}}$.
On entry, ${\mathbf{m2}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{m2}}\ge 1$.
${\mathbf{ifail}}=2$
${\mathbf{iperm}}\left({\mathbf{m1}}:{\mathbf{m2}}\right)$ does not contain a permutation of the integers m1 to m2. ${\mathbf{iperm}}\left(I\right)$ contains an out-of-range value: $I=⟨\mathit{\text{value}}⟩$, ${\mathbf{iperm}}\left(I\right)=⟨\mathit{\text{value}}⟩$.
${\mathbf{ifail}}=3$
${\mathbf{iperm}}\left({\mathbf{m1}}:{\mathbf{m2}}\right)$ does not contain a permutation of the integers m1 to m2. iperm contains a repeated value: $⟨\mathit{\text{value}}⟩$.
${\mathbf{ifail}}=-99$
See Section 7 in the Introduction to the NAG Library FL Interface for further information.
${\mathbf{ifail}}=-399$
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.
${\mathbf{ifail}}=-999$
Dynamic memory allocation failed.
See Section 9 in the Introduction to the NAG Library FL Interface for further information.

Not applicable.

## 8Parallelism and Performance

m01zcf is not threaded in any implementation.

None.

## 10Example

This example reads a matrix of real numbers and rearranges its columns so that the elements of the $l$th row are in ascending order. To do this, the program first calls m01djf to rank the elements of the $l$th row, and then calls m01zcf to decompose the rank vector into cycles. It then rearranges the columns using the framework of code suggested in Section 3. The value of $l$ is read from the data file.

### 10.1Program Text

Program Text (m01zcfe.f90)

### 10.2Program Data

Program Data (m01zcfe.d)

### 10.3Program Results

Program Results (m01zcfe.r)