NAG Library Routine Document
g05pwf
(subsamp_xyw)
1
Purpose
g05pwf generates a dataset suitable for use with repeated random subsampling validation.
2
Specification
Fortran Interface
Subroutine g05pwf ( 
nt,
n,
m,
sordx,
x,
ldx,
usey,
y,
usew,
w,
state,
ifail) 
Integer, Intent (In)  :: 
nt,
n,
m,
sordx,
ldx,
usey,
usew  Integer, Intent (Inout)  :: 
state(*),
ifail  Real (Kind=nag_wp), Intent (Inout)  :: 
x(ldx,*),
y(*),
w(*) 

C Header Interface
#include nagmk26.h
void 
g05pwf_ (
const Integer *nt,
const Integer *n,
const Integer *m,
const Integer *sordx,
double x[],
const Integer *ldx,
const Integer *usey,
double y[],
const Integer *usew,
double w[],
Integer state[],
Integer *ifail) 

3
Description
Let ${X}_{o}$ denote a matrix of $n$ observations on $m$ variables and ${y}_{o}$ and ${w}_{o}$ each denote a vector of length $n$. For example, ${X}_{o}$ might represent a matrix of independent variables, ${y}_{o}$ the dependent variable and ${w}_{o}$ the associated weights in a weighted regression.
g05pwf generates a series of training datasets, denoted by the matrix, vector, vector triplet $\left({X}_{t},{y}_{t},{w}_{t}\right)$ of ${n}_{t}$ observations, and validation datasets, denoted $\left({X}_{v},{y}_{v},{w}_{v}\right)$ with ${n}_{v}$ observations. These training and validation datasets are generated by randomly assigning each observation to either the training dataset or the validation dataset.
The resulting datasets are suitable for use with repeated random subsampling validation.
One of the initialization routines
g05kff (for a repeatable sequence if computed sequentially) or
g05kgf (for a nonrepeatable sequence) must be called prior to the first call to
g05pwf.
4
References
None.
5
Arguments
 1: $\mathbf{nt}$ – IntegerInput

On entry: ${n}_{t}$, the number of observations in the training dataset.
Constraint:
$1\le {\mathbf{nt}}\le {\mathbf{n}}$.
 2: $\mathbf{n}$ – IntegerInput

On entry: $n$, the number of observations.
Constraint:
${\mathbf{n}}\ge 1$.
 3: $\mathbf{m}$ – IntegerInput

On entry: $m$, the number of variables.
Constraint:
${\mathbf{m}}\ge 1$.
 4: $\mathbf{sordx}$ – IntegerInput

On entry: determines how variables are stored in
x.
Constraint:
${\mathbf{sordx}}=1$ or $2$.
 5: $\mathbf{x}\left({\mathbf{ldx}},*\right)$ – Real (Kind=nag_wp) arrayInput/Output

Note: the second dimension of the array
x
must be at least
${\mathbf{m}}$ if
${\mathbf{sordx}}=1$ and at least
${\mathbf{n}}$ if
${\mathbf{sordx}}=2$.
The way the data is stored in
x is defined by
sordx.
If ${\mathbf{sordx}}=1$, ${\mathbf{x}}\left(\mathit{i},\mathit{j}\right)$ contains the $\mathit{i}$th observation for the $\mathit{j}$th variable, for $i=1,2,\dots ,{\mathbf{n}}$ and $j=1,2,\dots ,{\mathbf{m}}$.
If ${\mathbf{sordx}}=2$, ${\mathbf{x}}\left(\mathit{j},\mathit{i}\right)$ contains the $\mathit{i}$th observation for the $\mathit{j}$th variable, for $i=1,2,\dots ,{\mathbf{n}}$ and $j=1,2,\dots ,{\mathbf{m}}$.
On entry:
x must hold
${X}_{o}$, the values of
$X$ for the original dataset. This may be the same
x as returned by a previous call to
g05pwf.
On exit: values of $X$ for the training and validation datasets, with ${X}_{t}$ held in observations $1$ to ${\mathbf{nt}}$ and ${X}_{v}$ in observations ${\mathbf{nt}}+1$ to ${\mathbf{n}}$.
 6: $\mathbf{ldx}$ – IntegerInput

On entry: the first dimension of the array
x as declared in the (sub)program from which
g05pwf is called.
Constraints:
 if ${\mathbf{sordx}}=2$, ${\mathbf{ldx}}\ge {\mathbf{m}}$;
 otherwise ${\mathbf{ldx}}\ge {\mathbf{n}}$.
 7: $\mathbf{usey}$ – IntegerInput

On entry: if ${\mathbf{usey}}=1$, the original dataset includes ${y}_{o}$ and ${y}_{o}$ will be processed alongside ${X}_{o}$.
Constraint:
${\mathbf{usey}}=0$ or $1$.
 8: $\mathbf{y}\left(*\right)$ – Real (Kind=nag_wp) arrayInput/Output

Note: the dimension of the array
y
must be at least
${\mathbf{n}}$ if
${\mathbf{usey}}=1$.
If
${\mathbf{usey}}=0$,
y is not referenced on entry and will not be modified on exit.
On entry:
y must hold
${y}_{o}$, the values of
$y$ for the original dataset. This may be the same
y as returned by a previous call to
g05pwf.
On exit: values of $y$ for the training and validation datasets, with ${y}_{t}$ held in elements $1$ to ${\mathbf{nt}}$ and ${y}_{v}$ in elements ${\mathbf{nt}}+1$ to ${\mathbf{n}}$.
 9: $\mathbf{usew}$ – IntegerInput

On entry: if ${\mathbf{usew}}=1$, the original dataset includes ${w}_{o}$ and ${w}_{o}$ will be processed alongside ${X}_{o}$.
Constraint:
${\mathbf{usew}}=0$ or $1$.
 10: $\mathbf{w}\left(*\right)$ – Real (Kind=nag_wp) arrayInput/Output

Note: the dimension of the array
w
must be at least
${\mathbf{n}}$ if
${\mathbf{usew}}=1$.
If
${\mathbf{usew}}=0$,
w is not referenced on entry or and will not be modified on exit.
On entry:
w must hold
${w}_{o}$, the values of
$w$ for the original dataset. This may be the same
w as returned by a previous call to
g05pwf.
On exit: values of $w$ for the training and validation datasets, with ${w}_{t}$ held in elements $1$ to ${\mathbf{nt}}$ and ${w}_{v}$ in elements ${\mathbf{nt}}+1$ to ${\mathbf{n}}$.
 11: $\mathbf{state}\left(*\right)$ – Integer arrayCommunication Array

Note: the actual argument supplied
must be the array
state supplied to the initialization routines
g05kff or
g05kgf.
On entry: contains information on the selected base generator and its current state.
On exit: contains updated information on the state of the generator.
 12: $\mathbf{ifail}$ – 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
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:
 ${\mathbf{ifail}}=11$

On entry, ${\mathbf{nt}}=\u2329\mathit{\text{value}}\u232a$ and ${\mathbf{n}}=\u2329\mathit{\text{value}}\u232a$.
Constraint: $1\le {\mathbf{nt}}\le {\mathbf{n}}$.
 ${\mathbf{ifail}}=21$

On entry, ${\mathbf{n}}=\u2329\mathit{\text{value}}\u232a$.
Constraint: ${\mathbf{n}}\ge 1$.
 ${\mathbf{ifail}}=31$

On entry, ${\mathbf{m}}=\u2329\mathit{\text{value}}\u232a$.
Constraint: ${\mathbf{m}}\ge 1$.
 ${\mathbf{ifail}}=41$

On entry, ${\mathbf{sordx}}=\u2329\mathit{\text{value}}\u232a$.
Constraint: ${\mathbf{sordx}}=1$ or $2$.
 ${\mathbf{ifail}}=61$

On entry, ${\mathbf{ldx}}=\u2329\mathit{\text{value}}\u232a$ and ${\mathbf{n}}=\u2329\mathit{\text{value}}\u232a$.
Constraint: if ${\mathbf{sordx}}=1$, ${\mathbf{ldx}}\ge {\mathbf{n}}$.
 ${\mathbf{ifail}}=62$

On entry, ${\mathbf{ldx}}=\u2329\mathit{\text{value}}\u232a$ and ${\mathbf{m}}=\u2329\mathit{\text{value}}\u232a$.
Constraint: if ${\mathbf{sordx}}=2$, ${\mathbf{ldx}}\ge {\mathbf{m}}$.
 ${\mathbf{ifail}}=71$

Constraint: ${\mathbf{usey}}=0$ or $1$.
 ${\mathbf{ifail}}=91$

Constraint: ${\mathbf{usew}}=0$ or $1$.
 ${\mathbf{ifail}}=111$

On entry,
state vector has been corrupted or not initialized.
 ${\mathbf{ifail}}=99$
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
Not applicable.
8
Parallelism and Performance
g05pwf is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.
g05pwf makes calls to BLAS and/or LAPACK routines, which may be threaded within the vendor library used by this implementation. Consult the documentation for the vendor library for further information.
Please consult the
X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this routine. Please also consult the
Users' Note for your implementation for any additional implementationspecific information.
g05pwf will be computationality more efficient if each observation in
x is contiguous, that is
${\mathbf{sordx}}=2$.
10
Example
This example uses g05pwf to facilitate repeated random subsampling crossvalidation.
A set of simulated data is randomly split into a training and validation datasets.
g02gbf is used to fit a logistic regression model to each training dataset and then
g02gpf is used to predict the response for the observations in the validation dataset. This process is repeated
$10$ times.
The counts of true and false positives and negatives along with the sensitivity and specificity is then reported.
10.1
Program Text
Program Text (g05pwfe.f90)
10.2
Program Data
Program Data (g05pwfe.d)
10.3
Program Results
Program Results (g05pwfe.r)