NAG Toolbox: nag_contab_tabulate_stat (g11ba)

Purpose

Syntax

Description

References

Parameters

Compulsory Input Parameters

1:     $\mathrm{stat}$ – string (length ≥ 1)

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:     $\mathrm{update}$ – string (length ≥ 1)

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 arguments ncells, table, icount and auxt must remain unchanged from the previous call to nag_contab_tabulate_stat (g11ba).

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

3:     $\mathrm{weight}$ – string (length ≥ 1)

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:     $\mathrm{isf}\left(\mathbf{nfac}\right)$ – int64int32nag_int array

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.

5:     $\mathrm{lfac}\left(\mathbf{nfac}\right)$ – int64int32nag_int array

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 $\mathit{i}=\mathrm{Ai},\dots ,\mathrm{Ai}$.

6:     $\mathrm{ifac}\left(\mathit{ldf},\mathbf{nfac}\right)$ – int64int32nag_int array

ldf, the first dimension of the array, must satisfy the constraint $\mathit{ldf}\ge \mathbf{n}$.

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 $\mathit{j}=1,2,\dots ,\mathbf{nfac}$.

7:     $\mathrm{y}\left(\mathbf{n}\right)$ – double array

The variable to be tabulated. If $\mathbf{stat}=\text{'N'}$, y is not referenced.

8:     $\mathrm{wt}\left(:\right)$ – double array

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

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 $\mathit{i}=\mathrm{Ai},\dots ,\mathrm{Ai}$.

9:     $\mathrm{table}\left(\mathbf{maxt}\right)$ – double array

If $\mathbf{update}=\text{'U'}$, table must be unchanged from the previous call to nag_contab_tabulate_stat (g11ba), otherwise table need not be set.

10:   $\mathrm{ncells}$ – int64int32nag_int scalar

If $\mathbf{update}=\text{'U'}$, ncells must be unchanged from the previous call to nag_contab_tabulate_stat (g11ba), otherwise ncells need not be set.

11:   $\mathrm{icount}\left(\mathbf{maxt}\right)$ – int64int32nag_int array

If $\mathbf{update}=\text{'U'}$, icount must be unchanged from the previous call to nag_contab_tabulate_stat (g11ba), otherwise icount need not be set.

12:   $\mathrm{auxt}\left(:\right)$ – double array

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

If $\mathbf{update}=\text{'U'}$, auxt must be unchanged from the previous call to nag_contab_tabulate_stat (g11ba), otherwise auxt need not be set.

Optional Input Parameters

1:     $\mathrm{n}$ – int64int32nag_int scalar

Default: the dimension of the array y and the first dimension of the array ifac. (An error is raised if these dimensions are not equal.)

The number of observations.

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

2:     $\mathrm{nfac}$ – int64int32nag_int scalar

Default: the dimension of the arrays isf, lfac and the second dimension of the array ifac. (An error is raised if these dimensions are not equal.)

The number of classifying factors in ifac.

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

3:     $\mathrm{maxt}$ – int64int32nag_int scalar

Default: the dimension of the arrays table, icount. (An error is raised if these dimensions are not equal.)

The maximum size of the table to be computed.

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

Output Parameters

1:     $\mathrm{table}\left(\mathbf{maxt}\right)$ – double array

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 Further Comments.

2:     $\mathrm{ncells}$ – int64int32nag_int scalar

The number of cells in the table.

3:     $\mathrm{ndim}$ – int64int32nag_int scalar

The number of factors defining the table.

4:     $\mathrm{idim}\left(\mathbf{nfac}\right)$ – int64int32nag_int array

The first ndim elements contain the number of levels for the factors defining the table.

5:     $\mathrm{icount}\left(\mathbf{maxt}\right)$ – int64int32nag_int array

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.

6:     $\mathrm{auxt}\left(:\right)$ – double array

The dimension of the array auxt will be $\mathbf{ncells}$ if $\mathbf{stat}=\text{'A'}$, $2\times \mathbf{ncells}$ if $\mathbf{stat}=\text{'V'}$ and $1$ otherwise

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.

7:     $\mathrm{ifail}$ – int64int32nag_int scalar

$\mathbf{ifail}=\mathbf{0}$ unless the function detects an error (see Error Indicators and Warnings).

Error Indicators and Warnings

   $\mathbf{ifail}=1$

On entry,	$\mathbf{n}<2$,
or	$\mathbf{nfac}<1$,
or	$\mathit{ldf}<\mathbf{n}$,
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 nag_contab_tabulate_stat (g11ba).

   $\mathbf{ifail}=-99$

An unexpected error has been triggered by this routine. Please contact NAG.

   $\mathbf{ifail}=-399$

Your licence key may have expired or may not have been installed correctly.

   $\mathbf{ifail}=-999$

Dynamic memory allocation failed.

Accuracy

Further Comments

Example

Open in the MATLAB editor: g11ba_example

function g11ba_example


fprintf('g11ba example results\n\n');

ifac = [int64(1),1,1; 1,2,1; 1,3,1; 1,1,2; 1,2,2; 1,3,2;
                 1,1,3; 1,2,3; 1,3,3; 1,1,4; 1,2,4; 1,3,4;
                 1,1,5; 1,2,5; 1,3,5; 1,1,6; 1,2,6; 1,3,6;
                 2,1,1; 2,2,1; 2,3,1; 2,1,2; 2,2,2; 2,3,2;
                 2,1,3; 2,2,3; 2,3,3; 2,1,4; 2,2,4; 2,3,4;
                 2,1,5; 2,2,5; 2,3,5; 2,1,6; 2,2,6; 2,3,6;
                 3,1,1; 3,2,1; 3,3,1; 3,1,2; 3,2,2; 3,3,2;
                 3,1,3; 3,2,3; 3,3,3; 3,1,4; 3,2,4; 3,3,4;
                 3,1,5; 3,2,5; 3,3,5; 3,1,6; 3,2,6; 3,3,6];
y   = [            274;   361;   253;   325;   317;   339;
                   326;   402;   336;   379;   345;   361;
                   352;   334;   318;   339;   393;   358;
                   350;   340;   203;   397;   356;   298;
                   382;   376;   355;   418;   387;   379;
                   432;   339;   293;   322;   417;   342;
                    82;   297;   133;   306;   352;   361;
                   220;   333;   270;   388;   379;   274;
                   336;   307;   266;   389;   333;   353];

weight = 'U';
wt     = [];

stat   = 'A';
update = 'I';
lfac   = [int64(3); 3; 6];
isf    = [int64(0); 1; 1];
maxt   = prod(lfac(isf~=0));

table  = zeros(maxt,1);
icount = zeros(maxt,1,'int64');
auxt   = zeros(2*maxt,1);
ncells = int64(0);

% Compute table
[table, ncells, ndim, idim, icount, auxt, ifail] = ...
  g11ba( ...
         stat, update, weight, isf, lfac, ifac, y, wt, ...
         table, ncells, icount, auxt);

% Display results
fprintf(' Table\n\n');
ncol = idim(ndim);
nrow = ncells/ncol;
table  = transpose(reshape(table,[ncol,nrow]));
icount = transpose(reshape(icount,[ncol,nrow]));
for i = 1:nrow
  row = [table(i,:); double(icount(i,:))];
  fprintf('%8.2f(%2d)', row);
  fprintf('\n');
end

g11ba example results

 Table

  235.33( 3)  342.67( 3)  309.33( 3)  395.00( 3)  373.33( 3)  350.00( 3)
  332.67( 3)  341.67( 3)  370.33( 3)  370.33( 3)  326.67( 3)  381.00( 3)
  196.33( 3)  332.67( 3)  320.33( 3)  338.00( 3)  292.33( 3)  351.00( 3)