NAG Library Routine Document

G11BAF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     STAT – CHARACTER(1)Input

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

$\mathbf{STAT}=\text{'N'}$

The number of observations for each cell.

$\mathbf{STAT}=\text{'T'}$

The total for the variable in Y for each cell.

$\mathbf{STAT}=\text{'A'}$

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

$\mathbf{STAT}=\text{'V'}$

The variance for the variable in Y for each cell.

$\mathbf{STAT}=\text{'L'}$

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

$\mathbf{STAT}=\text{'S'}$

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

Constraint: $\mathbf{STAT}=\text{'N'}$, $\text{'T'}$, $\text{'A'}$, $\text{'V'}$, $\text{'L'}$ or $\text{'S'}$.

2:     UPDATE – CHARACTER(1)Input

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

$\mathbf{UPDATE}=\text{'I'}$

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

$\mathbf{UPDATE}=\text{'U'}$

The table input in TABLE will be updated. The parameters NCELLS, TABLE, ICOUNT and AUXT must remain unchanged from the previous call to G11BAF.

Constraint: $\mathbf{UPDATE}=\text{'I'}$ or $\text{'U'}$.

3:     WEIGHT – CHARACTER(1)Input

On entry: indicates if weights are to be used.

$\mathbf{WEIGHT}=\text{'U'}$

Weights are not used and unit weights are assumed.

$\mathbf{WEIGHT}=\text{'W'}$ or $\text{'V'}$

Weights are used and must be supplied in WT. The only difference between $\mathbf{WEIGHT}=\text{'W'}$ and $\mathbf{WEIGHT}=\text{'V'}$ is if the variance is computed.

$\mathbf{WEIGHT}=\text{'W'}$

The divisor for the variance is the sum of the weights minus one and if $\mathbf{WEIGHT}=\text{'V'}$, 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 $\mathbf{STAT}=\text{'T'}$ or $\text{'A'}$, the weighted total or mean is computed respectively.

If $\mathbf{STAT}=\text{'N'}$, $\text{'L'}$ or $\text{'S'}$, the only effect of weights is to eliminate values with zero weights from the computations.

Constraint: $\mathbf{WEIGHT}=\text{'U'}$, $\text{'V'}$ or $\text{'W'}$.

4:     N – INTEGERInput

On entry: the number of observations.

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

5:     NFAC – INTEGERInput

On entry: the number of classifying factors in IFAC.

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

6:     ISF(NFAC) – INTEGER arrayInput

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

If $\mathbf{ISF}\left(i\right)>0$ the $i$th factor in IFAC is included in the tabulation.

Note that if $\mathbf{ISF}\left(\mathit{i}\right)\le 0$, for $\mathit{i}=1,2,\dots ,\mathbf{NFAC}$ then the statistic for the whole sample is calculated and returned in a $1\times 1$ table.

7:     LFAC(NFAC) – INTEGER arrayInput

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

Constraint: if $\mathbf{ISF}\left(\mathit{i}\right)>0$, $\mathbf{LFAC}\left(\mathit{i}\right)\ge 2$, for $\mathit{i}=\mathrm{Ai},\dots ,\mathrm{Ai}$.

8:     IFAC(LDF,NFAC) – INTEGER arrayInput

On entry: the NFAC coded classification factors for the N observations.

Constraint: $1\le \mathbf{IFAC}\left(\mathit{i},\mathit{j}\right)\le \mathbf{LFAC}\left(\mathit{j}\right)$, for $\mathit{i}=1,2,\dots ,\mathbf{N}$ and $\mathit{j}=1,2,\dots ,\mathbf{NFAC}$.

9:     LDF – INTEGERInput

On entry: the first dimension of the array IFAC as declared in the (sub)program from which G11BAF is called.

Constraint: $\mathbf{LDF}\ge \mathbf{N}$.

10:   Y(N) – REAL (KIND=nag_wp) arrayInput

On entry: the variable to be tabulated. If $\mathbf{STAT}=\text{'N'}$, Y is not referenced.

11:   WT($*$) – REAL (KIND=nag_wp) arrayInput

Note: the dimension of the array WT must be at least $\mathbf{N}$ if $\mathbf{WEIGHT}=\text{'W'}$ or $\text{'V'}$, and at least $1$ otherwise.

On entry: if $\mathbf{WEIGHT}=\text{'W'}$ or $\text{'V'}$, WT must contain the N weights. Otherwise WT is not referenced.

Constraint: if $\mathbf{WEIGHT}=\text{'W'}$ or $\text{'V'}$, $\mathbf{WT}\left(\mathit{i}\right)\ge 0.0$, for $\mathit{i}=\mathrm{Ai},\dots ,\mathrm{Ai}$.

12:   TABLE(MAXT) – REAL (KIND=nag_wp) arrayInput/Output

On entry: if $\mathbf{UPDATE}=\text{'U'}$, TABLE must be unchanged from the previous call to G11BAF, 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 IFAC changes faster. For further details see Section 8.

13:   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:   NCELLS – INTEGERInput/Output

On entry: if $\mathbf{UPDATE}=\text{'U'}$, NCELLS must be unchanged from the previous call to G11BAF, otherwise NCELLS need not be set.

On exit: the number of cells in the table.

15:   NDIM – INTEGEROutput

On exit: the number of factors defining the table.

16:   IDIM(NFAC) – INTEGER arrayOutput

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

17:   ICOUNT(MAXT) – INTEGER arrayInput/Output

On entry: if $\mathbf{UPDATE}=\text{'U'}$, ICOUNT must be unchanged from the previous call to G11BAF, otherwise ICOUNT 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 $\mathbf{STAT}=\text{'N'}$ this is the same as is returned in TABLE.

18:   AUXT($*$) – REAL (KIND=nag_wp) arrayInput/Output

Note: the dimension of the array AUXT must be at least $\mathbf{NCELLS}$ if $\mathbf{STAT}=\text{'A'}$, $2\times \mathbf{NCELLS}$ if $\mathbf{STAT}=\text{'V'}$, and at least $1$ otherwise.

On entry: if $\mathbf{UPDATE}=\text{'U'}$, AUXT must be unchanged from the previous call to G11BAF, otherwise AUXT need not be set.

On exit: if $\mathbf{STAT}=\text{'A'}$ or $\text{'V'}$, 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 $\mathbf{STAT}=\text{'V'}$, the second set of NCELLS values hold the table of cell means. Otherwise AUXT is not referenced.

19:   IWK($2\times \mathbf{NFAC}$) – INTEGER arrayWorkspace

20:   IFAIL – INTEGERInput/Output

On entry: IFAIL must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction for details.

For environments where it might be inappropriate to halt program execution when an error is detected, the value $-1\text{ or }1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this parameter, the recommended value is $0$. When the value $-\mathbf{1}\text{ or }\mathbf{1}$ is used it is essential to test the value of IFAIL on exit.

On exit: $\mathbf{IFAIL}=\mathbf{0}$ unless the routine detects an error or a warning has been flagged (see Section 6).

6  Error Indicators and Warnings

$\mathbf{IFAIL}=1$

On entry,	$\mathbf{N}<2$,
or	$\mathbf{NFAC}<1$,
or	$\mathbf{LDF}<\mathbf{N}$,
or	$\mathbf{UPDATE}\ne \text{'I'}$ or $\text{'U'}$,
or	$\mathbf{WEIGHT}\ne \text{'U'}$, $\text{'W'}$ or $\text{'V'}$,
or	$\mathbf{STAT}\ne \text{'N'}$, $\text{'T'}$, $\text{'A'}$, $\text{'V'}$, $\text{'L'}$ or $\text{'S'}$.

$\mathbf{IFAIL}=2$

On entry,	$\mathbf{ISF}\left(i\right)>0$ and $\mathbf{LFAC}\left(i\right)<2$, for some $i$,
or	$\mathbf{IFAC}\left(i,j\right)<1$, for some $i,j$,
or	$\mathbf{IFAC}\left(i,j\right)>\mathbf{LFAC}\left(j\right)$ for some $i,j$,
or	MAXT is too small,
or	$\mathbf{WEIGHT}=\text{'W'}$ or $\text{'V'}$ and $\mathbf{WT}\left(i\right)<0.0$, for some $i$.

$\mathbf{IFAIL}=3$

$\mathbf{STAT}=\text{'V'}$ and the divisor for the variance is $\le 0.0$.

$\mathbf{IFAIL}=4$

$\mathbf{UPDATE}=\text{'U'}$ and at least one of NCELLS, TABLE, AUXT or ICOUNT have been changed since previous call to G11BAF.

7  Accuracy

8  Further Comments

9  Example

9.1  Program Text

Program Text (g11bafe.f90)

9.2  Program Data

Program Data (g11bafe.d)

9.3  Program Results

Program Results (g11bafe.r)