NAG Library Function Document

nag_tabulate_stats (g11bac)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:    $\mathbf{stat}$ – Nag_TableStatsInput

On entry: indicates which statistic is to be computed for the table cells.

$\mathbf{stat}=\mathrm{Nag\_TableStatsNObs}$

The number of observations for each cell.

$\mathbf{stat}=\mathrm{Nag\_TableStatsTotal}$

The total for the variable in y for each cell.

$\mathbf{stat}=\mathrm{Nag\_TableStatsAv}$

The average (mean) for the variable in y for each cell.

$\mathbf{stat}=\mathrm{Nag\_TableStatsVar}$

The variance for the variable in y for each cell.

$\mathbf{stat}=\mathrm{Nag\_TableStatsLarge}$

The largest value for the variable in y for each cell.

$\mathbf{stat}=\mathrm{Nag\_TableStatsSmall}$

The smallest value for the variable in y for each cell.

Constraint: $\mathbf{stat}=\mathrm{Nag\_TableStatsNObs}$, $\mathrm{Nag\_TableStatsTotal}$, $\mathrm{Nag\_TableStatsAv}$, $\mathrm{Nag\_TableStatsVar}$, $\mathrm{Nag\_TableStatsLarge}$ or $\mathrm{Nag\_TableStatsSmall}$.

2:    $\mathbf{update}$ – Nag_TableUpdateInput

On entry: indicates if an existing table is to be updated by further observation.

$\mathbf{update}=\mathrm{Nag\_TableUpdateI}$

The table cells will be initialized to zero before tabulations take place.

$\mathbf{update}=\mathrm{Nag\_TableUpdateU}$

The table input in table will be updated. The arguments ncells, table, count and comm_ar must remain unchanged from the previous call to nag_tabulate_stats (g11bac).

Constraint: $\mathbf{update}=\mathrm{Nag\_TableUpdateI}$ or $\mathrm{Nag\_TableUpdateU}$.

3:    $\mathbf{weight}$ – Nag_WeightstypeInput

On entry: indicates if weights are to be used.

$\mathbf{weight}=\mathrm{Nag\_NoWeights}$

Weights are not used and unit weights are assumed.

$\mathbf{weight}=\mathrm{Nag\_Weights}$ or $\mathrm{Nag\_Weightsvar}$

Weights are used and must be supplied in wt. The only difference between $\mathbf{weight}=\mathrm{Nag\_Weights}$ and $\mathbf{weight}=\mathrm{Nag\_Weightsvar}$ is if the variance is computed.

$\mathbf{weight}=\mathrm{Nag\_Weights}$

The divisor for the variance is the sum of the weights minus one and if $\mathbf{weight}=\mathrm{Nag\_Weightsvar}$, the divisor is the number of observations with nonzero weights minus one. The former is useful if the weights represent the frequency of the observed values.

If $\mathbf{stat}=\mathrm{Nag\_TableStatsTotal}$ or $\mathrm{Nag\_TableStatsAv}$, the weighted total or mean is computed respectively.

If $\mathbf{stat}=\mathrm{Nag\_TableStatsNObs}$, $\mathrm{Nag\_TableStatsLarge}$ or $\mathrm{Nag\_TableStatsSmall}$ the only effect of weights is to eliminate values with zero weights from the computations.

Constraint: $\mathbf{weight}=\mathrm{Nag\_NoWeights}$, $\mathrm{Nag\_Weightsvar}$ or $\mathrm{Nag\_Weights}$.

4:    $\mathbf{n}$ – IntegerInput

On entry: the number of observations.

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

5:    $\mathbf{nfac}$ – IntegerInput

On entry: the number of classifying factors in factor.

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

6:    $\mathbf{sf}\left[\mathbf{nfac}\right]$ – const IntegerInput

On entry: indicates which factors in factor are to be used in the tabulation.

If $\mathbf{sf}\left[i-1\right]>0$ the $i$th factor in factor is included in the tabulation.

Note that if $\mathbf{sf}\left[i-1\right]\le 0$ for $i=1,2,\dots ,\mathbf{nfac}$ then the statistic for the whole sample is calculated and returned in a 1 by 1 table.

7:    $\mathbf{lfac}\left[\mathbf{nfac}\right]$ – const IntegerInput

On entry: the number of levels of the classifying factors in factor.

Constraint: if $\mathbf{sf}\left[i-1\right]>0$, $\mathbf{lfac}\left[\mathit{i}-1\right]\ge 2$, for $\mathit{i}=1,2,\dots ,\mathbf{nfac}$.

8:    $\mathbf{factor}\left[\mathbf{n}\times \mathbf{tdf}\right]$ – const IntegerInput

On entry: the nfac coded classification factors for the n observations.

Constraint: $1\le \mathbf{factor}\left[\left(\mathit{i}-1\right)\times \mathbf{tdf}+\mathit{j}-1\right]\le \mathbf{lfac}\left[\mathit{j}-1\right]$, for $\mathit{i}=1,2,\dots ,\mathbf{n}$ and $\mathit{j}=1,2,\dots ,\mathbf{nfac}$.

9:    $\mathbf{tdf}$ – IntegerInput

On entry: the stride separating matrix column elements in the array factor.

Constraint: $\mathbf{tdf}\ge \mathbf{nfac}$.

10:  $\mathbf{y}\left[\mathbf{n}\right]$ – const doubleInput

On entry: the variable to be tabulated.

If $\mathbf{stat}=\mathrm{Nag\_TableStatsNObs}$, y is not referenced.

11:  $\mathbf{wt}\left[\mathbf{n}\right]$ – const doubleInput

On entry: if $\mathbf{weight}=\mathrm{Nag\_Weights}$ or $\mathrm{Nag\_Weightsvar}$, wt must contain the n weights. Otherwise wt is not referenced and can be set to null, (double *)0.

Constraint: if $\mathbf{weight}=\mathrm{Nag\_Weights}$ or $\mathrm{Nag\_Weightsvar}$, $\mathbf{wt}\left[\mathit{i}-1\right]\ge 0.0$, for $\mathit{i}=1,2,\dots ,\mathbf{n}$.

12:  $\mathbf{table}\left[\mathbf{maxt}\right]$ – doubleInput/Output

On entry: if $\mathbf{update}=\mathrm{Nag\_TableUpdateU}$, table must be unchanged from the previous call to nag_tabulate_stats (g11bac), otherwise table need not be set.

On exit: the computed table. The ncells cells of the table are stored so that for any two factors the index relating to the factor referred to later in lfac and factor changes faster. For further details see Section 9.

13:  $\mathbf{maxt}$ – IntegerInput

On entry: the maximum size of the table to be computed.

Constraint: $\mathbf{maxt}\ge$ product of the levels of the factors included in the tabulation.

14:  $\mathbf{ncells}$ – Integer *Input/Output

On entry: if $\mathbf{update}=\mathrm{Nag\_TableUpdateU}$, ncells must be unchanged from the previous call to nag_tabulate_stats (g11bac), otherwise ncells need not be set.

On exit: the number of cells in the table.

15:  $\mathbf{ndim}$ – Integer *Output

On exit: the number of factors defining the table.

16:  $\mathbf{idim}\left[\mathbf{nfac}\right]$ – IntegerOutput

On exit: the first ndim elements contain the number of levels for the factors defining the table.

17:  $\mathbf{count}\left[\mathbf{maxt}\right]$ – IntegerInput/Output

On entry: if $\mathbf{update}=\mathrm{Nag\_TableUpdateU}$, count must be unchanged from the previous call to nag_tabulate_stats (g11bac), otherwise count need not be set.

On exit: a table containing the number of observations contributing to each cell of the table, stored identically to table. Note if $\mathbf{stat}=\mathrm{Nag\_TableStatsNObs}$ this is the same as is returned in table.

18:  $\mathbf{comm\_ar}[*]$ – doubleInput/Output

On entry: if $\mathbf{update}=\mathrm{Nag\_TableUpdateU}$, comm_ar must be unchanged from the previous call to nag_tabulate_stats (g11bac), otherwise comm_ar need not be set.

On exit: if $\mathbf{stat}=\mathrm{Nag\_TableStatsAv}$ or $\mathrm{Nag\_TableStatsVar}$, the first ncells values hold the table containing the sum of the weights for the observations contributing to each cell, stored identically to table. If $\mathbf{stat}=\mathrm{Nag\_TableStatsVar}$, then the second set of ncells values hold the table of cell means. Otherwise comm_ar is not referenced.

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

The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

6

Error Indicators and Warnings

NE_2_INT_ARG_LT

On entry, $\mathbf{tdf}=〈\mathit{\text{value}}〉$ while $\mathbf{nfac}=〈\mathit{\text{value}}〉$. These arguments must satisfy $\mathbf{tdf}\ge \mathbf{nfac}$.

NE_2_INT_ARRAY_CONS

On entry, $\mathbf{sf}\left[〈\mathit{\text{value}}〉\right]=〈\mathit{\text{value}}〉$ while $\mathbf{lfac}\left[0\right]=〈\mathit{\text{value}}〉$.
Constraint: if $\mathbf{sf}\left[i\right]>0$, $\mathbf{lfac}\left[i\right]\ge 2$ for $i=0,1,\dots ,\mathbf{nfac}$.

NE_2D_1D_INT_ARRAYS_CONS

On entry, $\mathbf{factor}\left[\left(〈\mathit{\text{value}}〉\right)\times \mathbf{tdf}+〈\mathit{\text{value}}〉\right]=〈\mathit{\text{value}}〉$ while $\mathbf{lfac}\left[0\right]=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{factor}\left[\left(\mathit{i}\right)\times \mathbf{tdf}+\mathit{j}\right]\le \mathbf{lfac}\left[\mathit{j}\right]$, for $\mathit{i}=0,1,\dots ,\mathbf{n}-1$ and $\mathit{j}=0,1,\dots ,\mathbf{nfac}-1$.

NE_2D_INT_ARRAY_CONS

On entry, $\mathbf{factor}\left[\left(〈\mathit{\text{value}}〉\right)\times \mathbf{tdf}+〈\mathit{\text{value}}〉\right]=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{factor}\left[\left(\mathit{i}\right)\times \mathbf{tdf}+\mathit{j}\right]\ge 1$, for $\mathit{i}=0,1,\dots ,\mathbf{n}-1$ and $\mathit{j}=0,1,\dots ,\mathbf{nfac}-1$.

NE_ALLOC_FAIL

Dynamic memory allocation failed.

NE_BAD_PARAM

On entry, argument stat had an illegal value.

On entry, argument update had an illegal value.

On entry, argument weight had an illegal value.

NE_G11BA_CHANGED

$\mathbf{update}=\mathrm{Nag\_TableUpdateU}$ and at least one of ncells, table, comm_ar or count have been changed since previous call to nag_tabulate_stats (g11bac).

NE_INT_ARG_LT

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

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

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.

NE_MAXT

The maximum size of the table to be computed, maxt is too small.

NE_REAL_ARRAY_CONS

On entry, $\mathbf{wt}\left[〈\mathit{\text{value}}〉\right]=〈\mathit{\text{value}}〉$.
Constraint: if $\mathbf{weight}=\mathrm{Nag\_Weights}$ or $\mathrm{Nag\_Weightsvar}$, $\mathbf{wt}\left[i\right]\ge 0.0$.

NE_VAR_DIV

$\mathbf{stat}=\mathrm{Nag\_TableStatsVar}$ and the divisor for the variance $\le 0.0$.

NE_WT_ARGS

The wt array argument must not be NULL when the weight argument indicates weights.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (g11bace.c)

10.2

Program Data

Program Data (g11bace.d)

10.3

Program Results

Program Results (g11bace.r)