NAG Library Routine Document

g13nbf (cp_pelt_user)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:     $\mathbf{n}$ – IntegerInput

On entry: $n$, the length of the time series.

Constraint: $\mathbf{n}\ge 2$.

2:     $\mathbf{beta}$ – Real (Kind=nag_wp)Input

On entry: $\beta$, the penalty term.

There are a number of standard ways of setting $\beta$, including:

SIC or BIC

$\beta =p\times \log \left(n\right)$ 

AIC

$\beta =2p$ 

Hannan-Quinn

$\beta =2p\times \log \left(\log \left(n\right)\right)$ 

where $p$ is the number of parameters being treated as estimated in each segment. The value of $p$ will depend on the cost function being used.

If no penalty is required then set $\beta =0$. Generally, the smaller the value of $\beta$ the larger the number of suggested change points.

3:     $\mathbf{minss}$ – IntegerInput

On entry: the minimum distance between two change points, that is ${\tau }_i-{\tau }_{i-1}\ge \mathbf{minss}$.

Constraint: $\mathbf{minss}\ge 2$.

4:     $\mathbf{k}$ – Real (Kind=nag_wp)Input

On entry: $K$, the constant value that satisfies equation (2). If $K$ exists, it is unlikely to be unique in such cases, it is recommened that the largest value of $K$, that satisfies equation (2), is chosen. No check is made that $K$ is the correct value for the supplied cost function.

5:     $\mathbf{costfn}$ – Subroutine, supplied by the user.External Procedure

The cost function, $C$. costfn must calculate a vector of costs for a number of segments.

The specification of costfn is:

Fortran Interface

Subroutine costfn ( ts, nr, r, c, y, iuser, ruser, info) Integer, Intent (In) :: ts, nr, r(nr) Integer, Intent (Inout) :: iuser(*), info Real (Kind=nag_wp), Intent (Inout) :: y(*), ruser(*) Real (Kind=nag_wp), Intent (Out) :: c(nr)

C Header Interface

#include <nagmk26.h> void  costfn (const Integer *ts, const Integer *nr, const Integer r[], double c[], double y[], Integer iuser[], double ruser[], Integer *info)

1:     $\mathbf{ts}$ – IntegerInput

On entry: a reference time point.

2:     $\mathbf{nr}$ – IntegerInput

On entry: number of segments being considered.

3:     $\mathbf{r}\left(\mathbf{nr}\right)$ – Integer arrayInput

On entry: time points which, along with ts, define the segments being considered, $0\le \mathbf{r}\left(i\right)\le n$ for $i=1,2,\dots \mathbf{nr}$.

4:     $\mathbf{c}\left(\mathbf{nr}\right)$ – Real (Kind=nag_wp) arrayOutput

On exit: the cost function, $C$, with

$$\mathbf{c}\left(i\right)=\left\{\begin{array}{ll}C\left(y_{r_i:t}\right)& \text{ if }t>r_i,\\ C\left(y_{t:r_i}\right)& \text{ otherwise.}\end{array}\right.$$

where $t=\mathbf{ts}$ and $r_i=\mathbf{r}\left(i\right)$.

It should be noted that if $t>r_i$ for any value of $i$ then it will be true for all values of $i$. Therefore the inequality need only be tested once per call to costfn.

5:     $\mathbf{y}\left(*\right)$ – Real (Kind=nag_wp) arrayUser Data

costfn is called with y as supplied to g13nbf. You are free to use the array y to supply information to costfn.

y is supplied in addition to iuser and ruser for ease of coding as in most cases costfn will require (functions of) the time series, $y$.

6:     $\mathbf{iuser}\left(*\right)$ – Integer arrayUser Workspace

7:     $\mathbf{ruser}\left(*\right)$ – Real (Kind=nag_wp) arrayUser Workspace

costfn is called with the arguments iuser and ruser as supplied to g13nbf. You should use the arrays iuser and ruser to supply information to costfn.

8:     $\mathbf{info}$ – IntegerInput/Output

On entry: $\mathbf{info}=0$.

On exit: set info to a nonzero value if you wish g13nbf to terminate with $\mathbf{ifail}=\mathbf{51}$.

costfn must either be a module subprogram USEd by, or declared as EXTERNAL in, the (sub)program from which g13nbf is called. Arguments denoted as Input must not be changed by this procedure.

Note: costfn should not return floating-point NaN (Not a Number) or infinity values, since these are not handled by g13nbf. If your code inadvertently does return any NaNs or infinities, g13nbf is likely to produce unexpected results.

6:     $\mathbf{ntau}$ – IntegerOutput

On exit: $m$, the number of change points detected.

7:     $\mathbf{tau}\left(\mathbf{n}\right)$ – Integer arrayOutput

On exit: the first $m$ elements of tau hold the location of the change points. The $i$th segment is defined by $y_{\left({\tau }_{i-1}+1\right)}$ to $y_{{\tau }_i}$, where ${\tau }_0=0$ and ${\tau }_i=\mathbf{tau}\left(i\right),1\le i\le m$.

The remainder of tau is used as workspace.

8:     $\mathbf{y}\left(*\right)$ – Real (Kind=nag_wp) arrayUser Data

y is not used by g13nbf, but is passed directly to costfn and may be used to pass information to this routine. y will usually be used to pass (functions of) the time series, $y$ of interest.

9:     $\mathbf{iuser}\left(*\right)$ – Integer arrayUser Workspace

10:   $\mathbf{ruser}\left(*\right)$ – Real (Kind=nag_wp) arrayUser Workspace

iuser and ruser are not used by g13nbf, but are passed directly to costfn and may be used to pass information to this routine.

11:   $\mathbf{ifail}$ – 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

$\mathbf{ifail}=11$

On entry, $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{n}\ge 2$.

$\mathbf{ifail}=31$

On entry, $\mathbf{minss}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{minss}\ge 2$.

$\mathbf{ifail}=51$

User requested termination.

$\mathbf{ifail}=-99$

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 (g13nbfe.f90)

10.2

Program Data

Program Data (g13nbfe.d)

10.3

Program Results

Program Results (g13nbfe.r)