NAG FL Interfacem01daf (realvec_​rank)

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1Purpose

m01daf ranks a vector of real numbers in ascending or descending order.

2Specification

Fortran Interface
 Subroutine m01daf ( rv, m1, m2,
 Integer, Intent (In) :: m1, m2 Integer, Intent (Inout) :: ifail Integer, Intent (Out) :: irank(m2) Real (Kind=nag_wp), Intent (In) :: rv(m2) Character (1), Intent (In) :: order
#include <nag.h>
 void m01daf_ (const double rv[], const Integer *m1, const Integer *m2, const char *order, Integer irank[], Integer *ifail, const Charlen length_order)
The routine may be called by the names m01daf or nagf_sort_realvec_rank.

3Description

m01daf uses a variant of list-merging, as described on pages 165–166 in Knuth (1973). The routine takes advantage of natural ordering in the data, and uses a simple list insertion in a preparatory pass to generate ordered lists of length at least $10$. The ranking is stable: equal elements preserve their ordering in the input data.

4References

Knuth D E (1973) The Art of Computer Programming (Volume 3) (2nd Edition) Addison–Wesley

5Arguments

1: $\mathbf{rv}\left({\mathbf{m2}}\right)$Real (Kind=nag_wp) array Input
On entry: elements ${\mathbf{m1}}$ to ${\mathbf{m2}}$ of rv must contain real values to be ranked.
2: $\mathbf{m1}$Integer Input
On entry: the index of the first element of rv to be ranked.
Constraint: ${\mathbf{m1}}>0$.
3: $\mathbf{m2}$Integer Input
On entry: the index of the last element of rv to be ranked.
Constraint: ${\mathbf{m2}}\ge {\mathbf{m1}}$.
4: $\mathbf{order}$Character(1) Input
On entry: if ${\mathbf{order}}=\text{'A'}$, the values will be ranked in ascending (i.e., nondecreasing) order.
If ${\mathbf{order}}=\text{'D'}$, into descending order.
Constraint: ${\mathbf{order}}=\text{'A'}$ or $\text{'D'}$.
5: $\mathbf{irank}\left({\mathbf{m2}}\right)$Integer array Output
On exit: elements ${\mathbf{m1}}$ to ${\mathbf{m2}}$ of irank contain the ranks of the corresponding elements of rv. Note that the ranks are in the range m1 to m2: thus, if ${\mathbf{rv}}\left(i\right)$ is the first element in the rank order, ${\mathbf{irank}}\left(i\right)$ is set to m1.
6: $\mathbf{ifail}$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: ${\mathbf{m2}}\ge 1$.
${\mathbf{ifail}}=2$
On entry, order has an illegal value: ${\mathbf{order}}=⟨\mathit{\text{value}}⟩$.
${\mathbf{ifail}}=-99$
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

m01daf is not threaded in any implementation.

The average time taken by the routine is approximately proportional to $n×\mathrm{log}\left(n\right)$, where $n={\mathbf{m2}}-{\mathbf{m1}}+1$.

10Example

Example 1 reads a list of real numbers and ranks them in ascending order.
Example 2 calculates weighted quantiles by ranking data, inverting the permutation to obtain indices of sorted data and using a binary search.

10.1Program Text

Program Text (m01dafe.f90)

10.2Program Data

Program Data (m01dafe.d)

10.3Program Results

Program Results (m01dafe.r)