NAG CL Interface
g05pvc (kfold_xyw)
1
Purpose
g05pvc generates training and validation datasets suitable for use in crossvalidation or jackknifing.
2
Specification
void 
g05pvc (Integer k,
Integer fold,
Integer n,
Integer m,
Nag_DataByObsOrVar sordx,
double x[],
Integer pdx,
double y[],
double w[],
Integer *nt,
Integer state[],
NagError *fail) 

The function may be called by the names: g05pvc or nag_rand_kfold_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.
g05pvc 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 as follows.
Each of the original $n$ observations is randomly assigned to one of $K$ equally sized groups or folds. For the $k$th sample the validation dataset consists of those observations in group $k$ and the training dataset consists of all those observations not in group $k$. Therefore at most $K$ samples can be generated.
If $n$ is not divisible by $K$ then the observations are assigned to groups as evenly as possible, therefore any group will be at most one observation larger or smaller than any other group.
When using $K=n$ the resulting datasets are suitable for leaveoneout crossvalidation, or the training dataset on its own for jackknifing. When using $K\ne n$ the resulting datasets are suitable for $K$fold crossvalidation. Datasets suitable for reversed crossvalidation can be obtained by switching the training and validation datasets, i.e., use the $k$th group as the training dataset and the rest of the data as the validation dataset.
One of the initialization functions
g05kfc (for a repeatable sequence if computed sequentially) or
g05kgc (for a nonrepeatable sequence) must be called prior to the first call to
g05pvc.
4
References
None.
5
Arguments

1:
$\mathbf{k}$ – Integer
Input

On entry: $K$, the number of folds.
Constraint:
$2\le {\mathbf{k}}\le {\mathbf{n}}$.

2:
$\mathbf{fold}$ – Integer
Input

On entry: the number of the fold to return as the validation dataset.
On the first call to
g05pvc ${\mathbf{fold}}$ should be set to
$1$ and then incremented by one at each subsequent call until all
$K$ sets of training and validation datasets have been produced. See
Section 9 for more details on how a different calling sequence can be used.
Constraint:
$1\le {\mathbf{fold}}\le {\mathbf{k}}$.

3:
$\mathbf{n}$ – Integer
Input

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

4:
$\mathbf{m}$ – Integer
Input

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

5:
$\mathbf{sordx}$ – Nag_DataByObsOrVar
Input

On entry: determines how variables are stored in
x.
Constraint:
${\mathbf{sordx}}=\mathrm{Nag\_DataByVar}$ or $\mathrm{Nag\_DataByObs}$.

6:
$\mathbf{x}\left[\mathit{dim}\right]$ – double
Input/Output

Note: the dimension,
dim, of the array
x
must be at least
 ${\mathbf{pdx}}\times {\mathbf{m}}$ when
${\mathbf{sordx}}=\mathrm{Nag\_DataByVar}$;
 ${\mathbf{pdx}}\times {\mathbf{n}}$ when
${\mathbf{sordx}}=\mathrm{Nag\_DataByObs}$.
The way the data is stored in
x is defined by
sordx.
If ${\mathbf{sordx}}=\mathrm{Nag\_DataByVar}$, ${\mathbf{x}}\left[\left(\mathit{j}1\right)\times {\mathbf{pdx}}+\mathit{i}1\right]$ 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 ${\mathbf{sordx}}=\mathrm{Nag\_DataByObs}$, ${\mathbf{x}}\left[\left(\mathit{i}1\right)\times {\mathbf{pdx}}+\mathit{j}1\right]$ 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: if
${\mathbf{fold}}=1$,
x must hold
${X}_{o}$, the values of
$X$ for the original dataset, otherwise,
x must not be changed since the last call to
g05pvc.
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 ${\mathbf{n}}$.

7:
$\mathbf{pdx}$ – Integer
Input

On entry: the stride separating row elements in the twodimensional data stored in the array
x.
Constraints:
 if ${\mathbf{sordx}}=\mathrm{Nag\_DataByObs}$, ${\mathbf{pdx}}\ge {\mathbf{m}}$;
 otherwise ${\mathbf{pdx}}\ge {\mathbf{n}}$.

8:
$\mathbf{y}\left[\mathit{dim}\right]$ – double
Input/Output

Note: the dimension,
dim, of the array
y
must be at least
 ${\mathbf{n}}$, when ${\mathbf{y}}\phantom{\rule{0.25em}{0ex}}\text{is not}\phantom{\rule{0.25em}{0ex}}\mathbf{NULL}$;
 otherwise ${\mathbf{y}}$ 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: if
${\mathbf{fold}}\ne 1$,
y must not be changed since the last call to
g05pvc.
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:
$\mathbf{w}\left[\mathit{dim}\right]$ – double
Input/Output

Note: the dimension,
dim, of the array
w
must be at least
 ${\mathbf{n}}$, when ${\mathbf{w}}\phantom{\rule{0.25em}{0ex}}\text{is not}\phantom{\rule{0.25em}{0ex}}\mathbf{NULL}$;
 otherwise ${\mathbf{w}}$ 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: if
${\mathbf{fold}}\ne 1$,
w must not be changed since the last call to
g05pvc.
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 ${\mathbf{n}}$.

10:
$\mathbf{nt}$ – Integer *
Output

On exit: ${n}_{t}$, the number of observations in the training dataset.

11:
$\mathbf{state}\left[\mathit{dim}\right]$ – Integer
Communication Array
Note: the dimension,
$\mathit{dim}$, 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.

12:
$\mathbf{fail}$ – 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, ${\mathbf{pdx}}=\u2329\mathit{\text{value}}\u232a$ and ${\mathbf{m}}=\u2329\mathit{\text{value}}\u232a$.
Constraint: if ${\mathbf{sordx}}=\mathrm{Nag\_DataByObs}$, ${\mathbf{pdx}}\ge {\mathbf{m}}$.
On entry, ${\mathbf{pdx}}=\u2329\mathit{\text{value}}\u232a$ and ${\mathbf{n}}=\u2329\mathit{\text{value}}\u232a$.
Constraint: if ${\mathbf{sordx}}=\mathrm{Nag\_DataByVar}$, ${\mathbf{pdx}}\ge {\mathbf{n}}$.
 NE_BAD_PARAM

On entry, argument $\u2329\mathit{\text{value}}\u232a$ had an illegal value.
 NE_INT

On entry, ${\mathbf{m}}=\u2329\mathit{\text{value}}\u232a$.
Constraint: ${\mathbf{m}}\ge 1$.
On entry, ${\mathbf{n}}=\u2329\mathit{\text{value}}\u232a$.
Constraint: ${\mathbf{n}}\ge 1$.
 NE_INT_2

On entry, ${\mathbf{fold}}=\u2329\mathit{\text{value}}\u232a$ and ${\mathbf{k}}=\u2329\mathit{\text{value}}\u232a$.
Constraint: $1\le {\mathbf{fold}}\le {\mathbf{k}}$.
On entry, ${\mathbf{k}}=\u2329\mathit{\text{value}}\u232a$ and ${\mathbf{n}}=\u2329\mathit{\text{value}}\u232a$.
Constraint: $2\le {\mathbf{k}}\le {\mathbf{n}}$.
 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.
 NW_POTENTIAL_PROBLEM

More than $50\%$ of the data did not move when the data was shuffled. $\u2329\mathit{\text{value}}\u232a$ of the $\u2329\mathit{\text{value}}\u232a$ observations stayed put.
7
Accuracy
Not applicable.
8
Parallelism and Performance
g05pvc is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.
g05pvc 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 implementationspecific information.
g05pvc will be computationality more efficient if each observation in
x is contiguous, that is
${\mathbf{sordx}}=\mathrm{Nag\_DataByObs}$.
Because of the way
g05pvc stores the data you should usually generate the
$K$ training and validation datasets in order, i.e., set
${\mathbf{fold}}=1$ on the first call and increment it by one at each subsequent call. However, there are times when a different calling sequence would be beneficial, for example, when performing different crossvalidation analyses on different threads. This is possible, as long as the following is borne in mind:
 g05pvc must be called with ${\mathbf{fold}}=1$ first.
 Other than the first set, you can obtain the training and validation dataset in any order, but for a given x you can only obtain each once.
For example, if you have three threads, you would call
g05pvc once with
${\mathbf{fold}}=1$. You would then copy the
x returned onto each thread and generate the remaing
${\mathbf{k}}1$ sets of data by splitting them between the threads. For example, the first thread runs with
${\mathbf{fold}}=2,\dots ,{L}_{1}$, the second with
${\mathbf{fold}}={L}_{1}+1,\dots ,{L}_{2}$ and the third with
${\mathbf{fold}}={L}_{2}+1,\dots ,{\mathbf{k}}$.
10
Example
This example uses g05pvc to facilitate $K$fold crossvalidation.
A set of simulated data is split into
$5$ 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.
The counts of true and false positives and negatives along with the sensitivity and specificity is then reported.
10.1
Program Text
10.2
Program Data
10.3
Program Results