NAG Toolbox: nag_stat_quantiles_stream_fixed (g01an)

Purpose

Syntax

Description

References

Parameters

Compulsory Input Parameters

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

Indicates the action required in the current call to nag_stat_quantiles_stream_fixed (g01an).

$\mathbf{ind}=0$

Return the required length of rcomm and icomm in $\mathbf{icomm}\left(1\right)$ and $\mathbf{icomm}\left(2\right)$ respectively. n and eps must be set and licomm must be at least $2$.

$\mathbf{ind}=1$

Initialise the communication arrays and process the first nb values from the data stream as supplied in rv.

$\mathbf{ind}=2$

Process the next block of nb values from the data stream. The calling program must update rv and (if required) nb, and re-enter nag_stat_quantiles_stream_fixed (g01an) with all other parameters unchanged.

$\mathbf{ind}=3$

Calculate the nq $\epsilon$-approximate quantiles specified in q. The calling program must set q and nq and re-enter nag_stat_quantiles_stream_fixed (g01an) with all other parameters unchanged. This option can be chosen only when $\mathbf{np}\ge ⌈\exp \left(1.0\right)/\mathbf{eps}⌉$.

Constraint: on entry $\mathbf{ind}=0$, $1$, $2$ or $3$.

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

$n$, the total number of values in the data stream.

Constraint: $\mathbf{n}>0$.

3:     $\mathrm{rv}\left(:\right)$ – double array

The dimension of the array rv must be at least $\mathbf{nb}$ if $\mathbf{ind}=1$ or $2$

If $\mathbf{ind}=1$ or $2$, the vector containing the current block of data, otherwise rv is not referenced.

4:     $\mathrm{eps}$ – double scalar

Approximation factor $\epsilon$.

Constraint: $\mathbf{eps}\ge \exp \left(1.0\right)/\mathbf{n}\text{ and }\mathbf{eps}\le 1.0$.

5:     $\mathrm{q}\left(:\right)$ – double array

The dimension of the array q must be at least $\mathbf{nq}$ if $\mathbf{ind}=3$

If $\mathbf{ind}=3$, the quantiles to be calculated, otherwise q is not referenced. Note that $\mathbf{q}\left(i\right)=0.0$, corresponds to the minimum value and $\mathbf{q}\left(i\right)=1.0$ to the maximum value.

Constraint: if $\mathbf{ind}=3$, $0.0\le \mathbf{q}\left(\mathit{i}\right)\le 1.0$, for $\mathit{i}=1,2,\dots ,\mathbf{nq}$.

6:     $\mathrm{rcomm}\left(\mathbf{lrcomm}\right)$ – double array

Constraint: if $\mathbf{ind}\ne 0$, lrcomm must be at least equal to the value returned in $\mathbf{icomm}\left(1\right)$ by a call to nag_stat_quantiles_stream_fixed (g01an) with $\mathbf{ind}=0$. This will not be more than $x+2\times \min \left(x,⌈x/2.0⌉+1\right)\times {\log }_2\left(\mathbf{n}/x+1.0\right)+1$, where $x=\max \left(1,⌊\log \left(\mathbf{eps}\times \mathbf{n}\right)/\mathbf{eps}⌋\right)$.

7:     $\mathrm{icomm}\left(\mathbf{licomm}\right)$ – int64int32nag_int array

Constraints:

• if $\mathbf{ind}=0$, $\mathbf{licomm}\ge 2$;
• otherwise licomm must be at least equal to the value returned in $\mathbf{icomm}\left(2\right)$ by a call to nag_stat_quantiles_stream_fixed (g01an) with $\mathbf{ind}=0$. This will not be more than $2\times \left(x+2\times \min \left(x,⌈x/2.0⌉+1\right)\times y\right)+y+6$, where $x=\max \left(1,⌊\log \left(\mathbf{eps}\times \mathbf{n}\right)/\mathbf{eps}⌋\right)$ and $y={\log }_2\left(\mathbf{n}/x+1.0\right)+1$.

Optional Input Parameters

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

Default: the dimension of the array rv.

If $\mathbf{ind}=1$ or $2$, the size of the current block of data. The size of blocks of data in array rv can vary; therefore nb can change between calls to nag_stat_quantiles_stream_fixed (g01an).

Constraint: if $\mathbf{ind}=1$ or $2$, $\mathbf{nb}>0$.

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

Default: the dimension of the array q.

If $\mathbf{ind}=3$, the number of quantiles requested, otherwise nq is not referenced.

Constraint: if $\mathbf{ind}=3$, $\mathbf{nq}>0$.

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

Default: the dimension of the array rcomm.

Constraint: if $\mathbf{ind}\ne 0$, lrcomm must be at least equal to the value returned in $\mathbf{icomm}\left(1\right)$ by a call to nag_stat_quantiles_stream_fixed (g01an) with $\mathbf{ind}=0$. This will not be more than $x+2\times \min \left(x,⌈x/2.0⌉+1\right)\times {\log }_2\left(\mathbf{n}/x+1.0\right)+1$, where $x=\max \left(1,⌊\log \left(\mathbf{eps}\times \mathbf{n}\right)/\mathbf{eps}⌋\right)$.

4:     $\mathrm{licomm}$ – int64int32nag_int scalar

Default: the dimension of the array icomm.

Constraints:

• if $\mathbf{ind}=0$, $\mathbf{licomm}\ge 2$;
• otherwise licomm must be at least equal to the value returned in $\mathbf{icomm}\left(2\right)$ by a call to nag_stat_quantiles_stream_fixed (g01an) with $\mathbf{ind}=0$. This will not be more than $2\times \left(x+2\times \min \left(x,⌈x/2.0⌉+1\right)\times y\right)+y+6$, where $x=\max \left(1,⌊\log \left(\mathbf{eps}\times \mathbf{n}\right)/\mathbf{eps}⌋\right)$ and $y={\log }_2\left(\mathbf{n}/x+1.0\right)+1$.

Output Parameters

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

Indicates output from a successful call.

$\mathbf{ind}=1$

Lengths of rcomm and icomm have been returned in $\mathbf{icomm}\left(1\right)$ and $\mathbf{icomm}\left(2\right)$ respectively.

$\mathbf{ind}=2$

nag_stat_quantiles_stream_fixed (g01an) has processed np data points and expects to be called again with additional data (i.e., $\mathbf{np}<\mathbf{n}$).

$\mathbf{ind}=3$

nag_stat_quantiles_stream_fixed (g01an) has returned the requested $\epsilon$-approximate quantiles in qv. These quantiles are based on np data points.

$\mathbf{ind}=4$

Routine has processed all n data points (i.e., $\mathbf{np}=\mathbf{n}$).

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

The number of elements processed so far.

3:     $\mathrm{qv}\left(:\right)$ – double array

The dimension of the array qv will be $\mathbf{nq}$ if $\mathbf{ind}=3$

If $\mathbf{ind}=3$, $\mathbf{qv}\left(i\right)$ contains the $\epsilon$-approximate quantiles specified by the value provided in $\mathbf{q}\left(i\right)$.

4:     $\mathrm{rcomm}\left(\mathbf{lrcomm}\right)$ – double array

Communication array, used to store information between calls to nag_stat_quantiles_stream_fixed (g01an).

5:     $\mathrm{icomm}\left(\mathbf{licomm}\right)$ – int64int32nag_int array

Communication array, used to store information between calls to nag_stat_quantiles_stream_fixed (g01an).

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

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

As an out-of-core function nag_stat_quantiles_stream_fixed (g01an) will only perform certain argument checks when a data checkpoint (including completion of data input) is signaled. As such it will usually be inappropriate to halt program execution when an error is detected since any errors may be subsequently resolved without losing any processing already carried out. Therefore setting ifail to a value of $-1\text{ or }1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. When the value $-\mathbf{1}\text{ or }\mathbf{1}$ is used it is essential to test the value of ifail on exit.

Error Indicators and Warnings

   $\mathbf{ifail}=1$

Constraint: $\mathbf{ind}=0$, $1$, $2$ or $3$.

   $\mathbf{ifail}=2$

Constraint: $\mathbf{n}>0$.

   $\mathbf{ifail}=3$

Constraint: $\exp \left(1.0\right)/\mathbf{n}\le \mathbf{eps}\le 1.0$.

   $\mathbf{ifail}=4$

Constraint: if $\mathbf{ind}=1$ or $2$ then $\mathbf{nb}>0$.

   $\mathbf{ifail}=5$

On entry, licomm is too small.

   $\mathbf{ifail}=6$

On entry, lrcomm is too small.

   $\mathbf{ifail}=7$

Number of data elements streamed, $\_$ is not sufficient for a quantile query when .
Supply more data or reprocess the data with a higher eps value.

   $\mathbf{ifail}=8$

Constraint: if $\mathbf{ind}=3$ then $\mathbf{nq}>0$.

   $\mathbf{ifail}=9$

Constraint: if $\mathbf{ind}=3$ then $0.0\le \mathbf{q}\left(i\right)\le 1.0$ for all $i$.

   $\mathbf{ifail}=-99$

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: g01an_example

function g01an_example


fprintf('g01an example results\n\n');

n   = int64(60);
tol = 0.2;
q   = [0.25 0.5 1.0];
rv = { ...
       [34.01, 57.95, 44.88, 22.04, 28.84,  4.43,  0.32, 20.82, ...
	20.53, 13.08,  7.99, 54.03, 23.21, 26.73, 39.72,  0.97],
       [39.05, 38.78, 19.38, 51.34, 24.08, 12.41, 58.11, 35.90, ...
	40.38, 27.41, 19.80,  6.02, 45.33, 36.34, 43.14, 53.84 , ...
	39.49,  9.04, 36.74, 58.72, 59.95, 15.41, 33.05, 39.54],
       [33.24, 58.67, 54.12, 39.48, 43.73, 24.15, 55.72,  8.87],
       [40.47, 46.18, 20.36,  6.95, 36.86, 49.24, 56.83, 43.87, ...
	29.86, 22.49, 25.29, 33.17] ...
     };
% First call to obtain lengths of communication arrays
ind   = int64(0);
icomm = zeros(2, 1, 'int64');
[ind, np, qv, rcomm, icomm, ifail] = ...
  g01an(ind, n, 0, tol, q, 0, icomm);
% Allocate communication arrays
rcomm = zeros(icomm(1), 1);
icomm = zeros(icomm(2), 1, 'int64');

for i=1:numel(rv)
  % Repeat call for every dataset block in rv.
  [ind, np, qv, rcomm, icomm, ifail] = ...
    g01an(ind, n, rv{i}, tol, q, rcomm, icomm);
end

% Call again to calculate quantiles q
ind = int64(3);
[ind, np, qv, rcomm, icomm, ifail] = ...
  g01an(ind, n, 0, tol, q, rcomm, icomm);

% Display results
fprintf('\nInput Data:\n %d observations\n eps = %5.2f\n\n', n, tol);
fprintf('Quantile     Result\n');
fprintf('%7.2f     %7.2f\n', [q; qv']);

g01an example results


Input Data:
 60 observations
 eps =  0.20

Quantile     Result
   0.25       22.49
   0.50       36.86
   1.00       59.95