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 <nag.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)

The routine may be called by the names g05pwf or nagf_rand_subsamp_xyw.

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

(X_{t}, y_{t}, w_{t})

n_{t}

observations, and validation datasets, denoted

(X_{v}, y_{v}, w_{v})

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 sub-sampling validation.

One of the initialization routines g05kff (for a repeatable sequence if computed sequentially) or g05kgf (for a non-repeatable sequence) must be called prior to the first call to g05pwf.

4 References

None.

5 Arguments

1: $nt$ – Integer Input

On entry:

n_{t}

, the number of observations in the training dataset.

Constraint:

1 \leq nt \leq n

2: $n$ – Integer Input

On entry:

n

, the number of observations.

Constraint:

n \geq 1

3: $m$ – Integer Input

On entry:

m

, the number of variables.

Constraint:

m \geq 1

4: $sordx$ – Integer Input

On entry: determines how variables are stored in x.

Constraint:

sordx = 1

2

5: $x (ldx, *)$ – Real (Kind=nag_wp) array Input/Output

Note: the second dimension of the array x must be at least

m

sordx = 1

and at least

n

sordx = 2

The way the data is stored in x is defined by sordx.

sordx = 1

x (i, j)

contains the

i

th observation for the

j

th variable, for

i = 1, 2, \dots, n

and

j = 1, 2, \dots, m

sordx = 2

x (j, i)

contains the

i

th observation for the

j

th variable, for

i = 1, 2, \dots, n

and

j = 1, 2, \dots, m

On entry: x must hold

X_{o}

, the values of

X

for the original dataset. This may be the same x as updated by a previous call to g05pwf.

On exit: values of

X

for the training and validation datasets, with

X_{t}

held in observations

1

nt

and

X_{v}

in observations

nt + 1

n

6: $ldx$ – Integer Input

On entry: the first dimension of the array x as declared in the (sub)program from which g05pwf is called.

Constraints:

if $sordx = 2$ , $ldx \geq m$ ;
otherwise $ldx \geq n$ .

7: $usey$ – Integer Input

On entry: if

usey = 1

, the original dataset includes

y_{o}

and

y_{o}

will be processed alongside

X_{o}

Constraint:

usey = 0

1

8: $y (*)$ – Real (Kind=nag_wp) array Input/Output

Note: the dimension of the array y must be at least

n

usey = 1

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 updated by a previous call to g05pwf.

On exit: values of

y

for the training and validation datasets, with

y_{t}

held in elements

1

nt

and

y_{v}

in elements

nt + 1

n

9: $usew$ – Integer Input

On entry: if

usew = 1

, the original dataset includes

w_{o}

and

w_{o}

will be processed alongside

X_{o}

Constraint:

usew = 0

1

10: $w (*)$ – Real (Kind=nag_wp) array Input/Output

Note: the dimension of the array w must be at least

n

usew = 1

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 updated by a previous call to g05pwf.

On exit: values of

w

for the training and validation datasets, with

w_{t}

held in elements

1

nt

and

w_{v}

in elements

nt + 1

n

11: $state (*)$ – Integer array Communication 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: $ifail$ – Integer Input/Output

On entry: ifail must be set to

0

−1

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

1

is recommended. If message printing is undesirable, then the value

1

is recommended. Otherwise, the value

0

is recommended. When the value $- 1$ or $1$ is used it is essential to test the value of ifail on exit.

On exit:

ifail = 0

unless the routine detects an error or a warning has been flagged (see Section 6).

6 Error Indicators and Warnings

If on entry

ifail = 0

−1

, explanatory error messages are output on the current error message unit (as defined by x04aaf).

Errors or warnings detected by the routine:

$ifail = 11$: On entry, $nt = ⟨ value ⟩$ and $n = ⟨ value ⟩$ .
Constraint: $1 \leq nt \leq n$ .

$ifail = 21$: On entry, $n = ⟨ value ⟩$ .
Constraint: $n \geq 1$ .

$ifail = 31$: On entry, $m = ⟨ value ⟩$ .
Constraint: $m \geq 1$ .

$ifail = 41$: On entry, $sordx = ⟨ value ⟩$ .
Constraint: $sordx = 1$ or $2$ .

$ifail = 61$: On entry, $ldx = ⟨ value ⟩$ and $n = ⟨ value ⟩$ .
Constraint: if $sordx = 1$ , $ldx \geq n$ .

$ifail = 62$: On entry, $ldx = ⟨ value ⟩$ and $m = ⟨ value ⟩$ .
Constraint: if $sordx = 2$ , $ldx \geq m$ .

$ifail = 71$: Constraint: $usey = 0$ or $1$ .

$ifail = 91$: Constraint: $usew = 0$ or $1$ .

$ifail = 111$: On entry, state vector has been corrupted or not initialized.

$ifail = - 99$: An unexpected error has been triggered by this routine. Please contact NAG.
See Section 7 in the Introduction to the NAG Library FL Interface for further information.

$ifail = - 399$: 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.

$ifail = - 999$: Dynamic memory allocation failed.
See Section 9 in the Introduction to the NAG Library FL Interface for further information.

7 Accuracy

Not applicable.

8 Parallelism and Performance

Background information to multithreading can be found in the Multithreading documentation.

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 implementation-specific information.

9 Further Comments

g05pwf will be computationality more efficient if each observation in x is contiguous, that is

sordx = 2

10 Example

This example uses g05pwf to facilitate repeated random sub-sampling cross-validation.

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.

g05pw: FL CL CPP AD PY MB

NAG FL Interfaceg05pwf (subsamp_​xyw)

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results

NAG FL Interface
g05pwf (subsamp_xyw)