NAG Library Routine Document

g01amf (quantiles)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:     $\mathbf{n}$ – IntegerInput

On entry: the number of elements in the input vector rv.

Constraint: $\mathbf{n}>0$.

2:     $\mathbf{rv}\left(\mathbf{n}\right)$ – Real (Kind=nag_wp) arrayInput/Output

On entry: the vector whose quantiles are to be determined.

On exit: the order of the elements in rv is not, in general, preserved.

3:     $\mathbf{nq}$ – IntegerInput

On entry: the number of quantiles requested.

Constraint: $\mathbf{nq}>0$.

4:     $\mathbf{q}\left(\mathbf{nq}\right)$ – Real (Kind=nag_wp) arrayInput

On entry: the quantiles to be calculated, in ascending order. Note that these must be between $0.0$ and $1.0$, with $0.0$ returning the smallest element and $1.0$ the largest.

Constraints:

• $0.0\le \mathbf{q}\left(\mathit{i}\right)\le 1.0$, for $\mathit{i}=1,2,\dots ,\mathbf{nq}$;
• $\mathbf{q}\left(\mathit{i}\right)\le \mathbf{q}\left(\mathit{i}+1\right)$, for $\mathit{i}=1,2,\dots ,\mathbf{nq}-1$.

5:     $\mathbf{qv}\left(\mathbf{nq}\right)$ – Real (Kind=nag_wp) arrayOutput

On exit: $\mathbf{qv}\left(i\right)$ contains the quantile specified by the value provided in $\mathbf{q}\left(i\right)$, or an interpolated value if the quantile falls between two data values.

6:     $\mathbf{ifail}$ – 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).

6

Error Indicators and Warnings

$\mathbf{ifail}=1$

On entry, $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{n}>0$.

$\mathbf{ifail}=2$

On entry, $\mathbf{nq}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{nq}>0$.

$\mathbf{ifail}=3$

On entry, an element of q was less than $0.0$ or greater than $1.0$.

$\mathbf{ifail}=4$

On entry, q was not in ascending order.

$\mathbf{ifail}=5$

Internal error. Please contact NAG.

$\mathbf{ifail}=-99$

An unexpected error has been triggered by this routine. Please contact NAG.

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.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (g01amfe.f90)

10.2

Program Data

Program Data (g01amfe.d)

10.3

Program Results

Program Results (g01amfe.r)