NAG Library Function Document

nag_best_subset_given_size (h05abc)

1  Purpose

2  Specification

3  Description

4  References

5  Arguments

1:    $\mathbf{mincr}$ – IntegerInput

On entry: flag indicating whether the scoring function $f$ is increasing or decreasing.

$\mathbf{mincr}=1$

$f\left(S_i\right)\le f\left(S_j\right)$, i.e., the subsets with the largest score will be selected.

$\mathbf{mincr}=0$

$f\left(S_i\right)\ge f\left(S_j\right)$, i.e., the subsets with the smallest score will be selected.

For all $S_j\subseteq \Omega$ and $S_i\subseteq S_j$.

Constraint: $\mathbf{mincr}=0$ or $1$.

2:    $\mathbf{m}$ – IntegerInput

On entry: $m$, the number of features in the full feature set.

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

3:    $\mathbf{ip}$ – IntegerInput

On entry: $p$, the number of features in the subset of interest.

Constraint: $1\le \mathbf{ip}\le \mathbf{m}$.

4:    $\mathbf{nbest}$ – IntegerInput

On entry: $n$, the maximum number of best subsets required. The actual number of subsets returned is given by la on final exit. If on final exit $\mathbf{la}\ne \mathbf{nbest}$ then $\mathbf{fail}\mathbf{.}\mathbf{code}=$ NE_TOO_MANY is returned.

Constraint: $\mathbf{nbest}\ge 1$.

5:    $\mathbf{la}$ – Integer *Output

On exit: the number of best subsets returned.

6:    $\mathbf{bscore}\left[\mathbf{nbest}\right]$ – doubleOutput

On exit: holds the score for the la best subsets returned in bz.

7:    $\mathbf{bz}\left[\left(\mathbf{m}-\mathbf{ip}\right)\times \mathbf{nbest}\right]$ – IntegerOutput

Note: where $\mathbf{BZ}\left(i,j\right)$ appears in this document, it refers to the array element $\mathbf{bz}\left[\left(j-1\right)\times \left(\mathbf{m}-\mathbf{ip}\right)+i-1\right]$.

On exit: the $j$th best subset is constructed by dropping the features specified in $\mathbf{BZ}\left(\mathit{i},\mathit{j}\right)$, for $\mathit{i}=1,2,\dots ,\mathbf{m}-\mathbf{ip}$ and $\mathit{j}=1,2,\dots ,\mathbf{la}$, from the set of all features, $\Omega$. The score for the $j$th best subset is given in $\mathbf{bscore}\left[j-1\right]$.

8:    $\mathbf{f}$ – function, supplied by the userExternal Function

f must evaluate the scoring function $f$.

The specification of f is:

void  f (Integer m, Integer drop, Integer lz, const Integer z[], Integer la, const Integer a[], double score[], Nag_Comm *comm, Integer *info)

1:    $\mathbf{m}$ – IntegerInput

On entry: $m=\left|\Omega \right|$, the number of features in the full feature set.

2:    $\mathbf{drop}$ – IntegerInput

On entry: flag indicating whether the intermediate subsets should be constructed by dropping features from the full set ($\mathbf{drop}=1$) or adding features to the empty set ($\mathbf{drop}=0$). See score for additional details.

3:    $\mathbf{lz}$ – IntegerInput

On entry: the number of features stored in z.

4:    $\mathbf{z}\left[\mathbf{lz}\right]$ – const IntegerInput

On entry: $\mathbf{z}\left[\mathit{i}-1\right]$, for $\mathit{i}=1,2,\dots ,\mathbf{lz}$, contains the list of features which, along with those specified in a, define the subsets whose score is required. See score for additional details.

5:    $\mathbf{la}$ – IntegerInput

On entry: if $\mathbf{la}>0$, the number of subsets for which a score must be returned.

If $\mathbf{la}=0$, the score for a single subset should be returned. See score for additional details.

6:    $\mathbf{a}\left[\mathbf{la}\right]$ – const IntegerInput

On entry: $\mathbf{a}\left[\mathit{j}-1\right]$, for $\mathit{j}=1,2,\dots ,\mathbf{la}$, contains the list of features which, along with those specified in z, define the subsets whose score is required. See score for additional details.

7:    $\mathbf{score}\left[\max \left(\mathbf{la},1\right)\right]$ – doubleOutput

On exit: the value $f\left(S_{\mathit{j}}\right)$, for $\mathit{j}=1,2,\dots ,\mathbf{la}$, the score associated with the $j$th subset. $S_j$ is constructed as follows:

$\mathbf{drop}=1$

$S_j$ is constructed by dropping the features specified in the first lz elements of z and the single feature given in $\mathbf{a}\left[j-1\right]$ from the full set of features, $\Omega$. The subset will therefore contain $\mathbf{m}-\mathbf{lz}-1$ features.

$\mathbf{drop}=0$

$S_j$ is constructed by adding the features specified in the first lz elements of z and the single feature specified in $\mathbf{a}\left[j-1\right]$ to the empty set, $\varnothing$. The subset will therefore contain $\mathbf{lz}+1$ features.

In both cases the individual features are referenced by the integers $1$ to m with $1$ indicating the first feature, $2$ the second, etc., for some arbitrary ordering of the features, chosen by you prior to calling nag_best_subset_given_size (h05abc). For example, $1$ might refer to the first variable in a particular set of data, $2$ the second, etc..

If $\mathbf{la}=0$, the score for a single subset should be returned. This subset is constructed by adding or removing only those features specified in the first lz elements of z. If $\mathbf{lz}=0$, this subset will either be $\Omega$ or $\varnothing$.

8:    $\mathbf{comm}$ – Nag_Comm *

Pointer to structure of type Nag_Comm; the following members are relevant to f.

user – double *

iuser – Integer *

p – Pointer 

The type Pointer will be void *. Before calling nag_best_subset_given_size (h05abc) you may allocate memory and initialize these pointers with various quantities for use by f when called from nag_best_subset_given_size (h05abc) (see Section 3.2.1.1 in the Essential Introduction).

9:    $\mathbf{info}$ – Integer *Input/Output

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

On exit: set info to a nonzero value if you wish nag_best_subset_given_size (h05abc) to terminate with $\mathbf{fail}\mathbf{.}\mathbf{code}=$ NE_USER_STOP.

9:    $\mathbf{mincnt}$ – IntegerInput

On entry: $k$, the minimum number of times the effect of each feature, $x_i$, must have been observed before $f\left(S-\left\{x_i\right\}\right)$ is estimated from $f\left(S\right)$ as opposed to being calculated directly.

If $k=0$ then $f\left(S-\left\{x_i\right\}\right)$ is never estimated. If $\mathbf{mincnt}<0$ then $k$ is set to $1$.

10:  $\mathbf{gamma}$ – doubleInput

On entry: $\gamma$, the scaling factor used when estimating scores. If $\mathbf{gamma}<0$ then $\gamma =1$ is used.

11:  $\mathbf{acc}\left[2\right]$ – const doubleInput

On entry: a measure of the accuracy of the scoring function, $f$.

Letting $a_i={\epsilon }_1\left|f\left(S_i\right)\right|+{\epsilon }_2$, then when confirming whether the scoring function is strictly increasing or decreasing (as described in mincr), or when assessing whether a node defined by subset $S_i$ can be trimmed, then any values in the range $f\left(S_i\right)\pm a_i$ are treated as being numerically equivalent.

If $0\le \mathbf{acc}\left[0\right]\le 1$ then ${\epsilon }_1=\mathbf{acc}\left[0\right]$, otherwise ${\epsilon }_1=0$.

If $\mathbf{acc}\left[1\right]\ge 0$ then ${\epsilon }_2=\mathbf{acc}\left[1\right]$, otherwise ${\epsilon }_2=0$.

In most situations setting both ${\epsilon }_1$ and ${\epsilon }_2$ to zero should be sufficient. Using a nonzero value, when one is not required, can significantly increase the number of subsets that need to be evaluated.

12:  $\mathbf{comm}$ – Nag_Comm *

The NAG communication argument (see Section 3.2.1.1 in the Essential Introduction).

13:  $\mathbf{fail}$ – NagError *Input/Output

The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.
See Section 3.2.1.2 in the Essential Introduction for further information.

NE_BAD_PARAM

On entry, argument $〈\mathit{\text{value}}〉$ had an illegal value.

NE_INT

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

On entry, $\mathbf{mincr}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{mincr}=0$ or $1$.

On entry, $\mathbf{nbest}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{nbest}\ge 1$.

NE_INT_2

On entry, $\mathbf{ip}=〈\mathit{\text{value}}〉$ and $\mathbf{m}=〈\mathit{\text{value}}〉$.
Constraint: $1\le \mathbf{ip}\le \mathbf{m}$.

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.

An unexpected error has been triggered by this function. Please contact NAG.
See Section 3.6.6 in the Essential Introduction for further information.

NE_NO_LICENCE

Your licence key may have expired or may not have been installed correctly.
See Section 3.6.5 in the Essential Introduction for further information.

NE_REAL

On exit from f, $\mathbf{score}\left[〈\mathit{\text{value}}〉\right]=〈\mathit{\text{value}}〉$, which is inconsistent with the score for the parent node. Score for the parent node is $〈\mathit{\text{value}}〉$.

NE_TOO_MANY

On entry, $\mathbf{nbest}=〈\mathit{\text{value}}〉$.
But only $〈\mathit{\text{value}}〉$ best subsets could be calculated.

NE_USER_STOP

A nonzero value for info has been returned: $\mathbf{info}=〈\mathit{\text{value}}〉$.

7  Accuracy

8  Parallelism and Performance

9  Further Comments

10  Example

10.1  Program Text

Program Text (h05abce.c)

10.2  Program Data

Program Data (h05abce.d)

10.3  Program Results

Program Results (h05abce.r)