void	g05pwc (Integer nt, Integer n, Integer m, Nag_DataByObsOrVar sordx, double x[], Integer pdx, double y[], double w[], Integer state[], NagError *fail)

The function may be called by the names: g05pwc or nag_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.

g05pwc 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 functions g05kfc (for a repeatable sequence if computed sequentially) or g05kgc (for a non-repeatable sequence) must be called prior to the first call to g05pwc.

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: $sordx$ – Nag_DataByObsOrVar Input

On entry: determines how variables are stored in x.

Constraint:

sordx = Nag_DataByVar

Nag_DataByObs

5: $x [\dim]$ – double Input/Output

Note: the dimension, dim, of the array x must be at least

$pdx \times m$ when $sordx = Nag_DataByVar$ ;
$pdx \times n$ when $sordx = Nag_DataByObs$ .

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

sordx = Nag_DataByVar

x [(j - 1) \times pdx + i - 1]

contains the

i

th observation for the

j

th variable, for

i = 1, 2, \dots, n

and

j = 1, 2, \dots, m

sordx = Nag_DataByObs

x [(i - 1) \times pdx + j - 1]

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 g05pwc.

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: $pdx$ – Integer Input

On entry: the stride separating row elements in the two-dimensional data stored in the array x.

Constraints:

if $sordx = Nag_DataByObs$ , $pdx \geq m$ ;
otherwise $pdx \geq n$ .

7: $y [\dim]$ – double Input/Output

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

$n$ , when $y is not NULL$ ;
otherwise $y$ is not referenced and may be NULL.

If the original dataset does not include

y_{o}

then y must be set to NULL.

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 g05pwc.

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

8: $w [\dim]$ – double Input/Output

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

$n$ , when $w is not NULL$ ;
otherwise $w$ is not referenced and may be NULL.

If the original dataset does not include

w_{o}

then w must be set to NULL.

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 g05pwc.

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

9: $state [\dim]$ – Integer Communication Array

Note: the dimension,

\dim

, of this array is dictated by the requirements of associated functions that must have been previously called. This array MUST be the same array passed as argument state in the previous call to nag_rand_init_repeatable (g05kfc) or nag_rand_init_nonrepeatable (g05kgc).

On entry: contains information on the selected base generator and its current state.

On exit: contains updated information on the state of the generator.

10: $fail$ – NagError * Input/Output

The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

NE_ALLOC_FAIL: Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
NE_ARRAY_SIZE: On entry, $pdx = ⟨ value ⟩$ and $m = ⟨ value ⟩$ .
Constraint: if $sordx = Nag_DataByObs$ , $pdx \geq m$ .

On entry, $pdx = ⟨ value ⟩$ and $n = ⟨ value ⟩$ .
Constraint: if $sordx = Nag_DataByVar$ , $pdx \geq n$ .
NE_BAD_PARAM: On entry, argument $⟨ value ⟩$ had an illegal value.
NE_INT: On entry, $m = ⟨ value ⟩$ .
Constraint: $m \geq 1$ .

On entry, $n = ⟨ value ⟩$ .
Constraint: $n \geq 1$ .
NE_INT_2: On entry, $nt = ⟨ value ⟩$ and $n = ⟨ value ⟩$ .
Constraint: $1 \leq nt \leq n$ .
NE_INTERNAL_ERROR: An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 7.5 in the Introduction to the NAG Library CL Interface for further information.
NE_INVALID_STATE: On entry, state vector has been corrupted or not initialized.
NE_NO_LICENCE: Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.

7 Accuracy

Not applicable.

8 Parallelism and Performance

g05pwc is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.

g05pwc 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 function. Please also consult the Users' Note for your implementation for any additional implementation-specific information.

9 Further Comments

g05pwc will be computationality more efficient if each observation in x is contiguous, that is

sordx = Nag_DataByObs

10 Example

This example uses g05pwc to facilitate repeated random sub-sampling cross-validation.

A set of simulated data is randomly split into a training and validation datasets. g02gbc is used to fit a logistic regression model to each training dataset and then g02gpc 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

NAG CL Interfaceg05pwc (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 CL Interface
g05pwc (subsamp_xyw)