NAG Toolbox: nag_stat_quantiles_stream_arbitrary (g01ap)

Purpose

Syntax

Description

References

Parameters

Compulsory Input Parameters

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

On initial entry: must be set to $0$.

Indicates the action required in the current call to nag_stat_quantiles_stream_arbitrary (g01ap).

$\mathbf{ind}=0$

Initialize the communication arrays and attempt to process the first nb values from the data stream. eps, rv and nb must be set and licomm must be at least $10$.

$\mathbf{ind}=1$

Attempt to 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_arbitrary (g01ap) with all other parameters unchanged.

$\mathbf{ind}=2$

Continue calculation following the reallocation of either or both of the communication arrays rcomm and icomm.

$\mathbf{ind}=3$

Calculate the nq $\epsilon$-approximate quantiles specified in q. The calling program must set q and nq and re-enter nag_stat_quantiles_stream_arbitrary (g01ap) with all other parameters unchanged. This option can be chosen only when $\mathbf{np}\ge ⌈\exp \left(1.0\right)/\mathbf{eps}⌉$.

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

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

The dimension of the array rv must be at least $\mathbf{nb}$ if $\mathbf{ind}=0$, $1$ or $2$

If $\mathbf{ind}=0$, $1$ or $2$, the vector containing the current block of data, otherwise rv is not referenced.

3:     $\mathrm{eps}$ – double scalar

Approximation factor $\epsilon$.

Constraint: $\mathbf{eps}>0.0\text{ and }\mathbf{eps}\le 1.0$.

4:     $\mathrm{q}\left(:\right)$ – 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 $\mathit{i}=1,2,\dots ,\mathbf{nq}$.

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

If $\mathbf{ind}=1$ or $2$ then the first $l$ elements of rcomm as supplied to nag_stat_quantiles_stream_arbitrary (g01ap) must be identical to the first $l$ elements of rcomm returned from the last call to nag_stat_quantiles_stream_arbitrary (g01ap), where $l$ is the value of lrcomm used in the last call. In other words, the contents of rcomm must not be altered between calls to this function. If rcomm needs to be reallocated then its contents must be preserved. If $\mathbf{ind}=0$ then rcomm need not be set.

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

If $\mathbf{ind}=1$ or $2$ then the first $l$ elements of icomm as supplied to nag_stat_quantiles_stream_arbitrary (g01ap) must be identical to the first $l$ elements of icomm returned from the last call to nag_stat_quantiles_stream_arbitrary (g01ap), where $l$ is the value of licomm used in the last call. In other words, the contents of icomm must not be altered between calls to this function. If icomm needs to be reallocated then its contents must be preserved. If $\mathbf{ind}=0$ then icomm need not be set.

Optional Input Parameters

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

Default: the dimension of the array rv.

If $\mathbf{ind}=0$, $1$ 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_arbitrary (g01ap).

Constraint: if $\mathbf{ind}=0$, $1$ 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.

The dimension of the array rcomm.

Constraints:

• if $\mathbf{ind}=0$, $\mathbf{lrcomm}\ge 1$;
• otherwise $\mathbf{lrcomm}\ge \mathbf{icomm}\left(1\right)$.

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

Default: the dimension of the array icomm.

The dimension of the array icomm.

Constraints:

• if $\mathbf{ind}=0$, $\mathbf{licomm}\ge 10$;
• otherwise $\mathbf{licomm}\ge \mathbf{icomm}\left(2\right)$.

Output Parameters

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

Indicates output from the call.

$\mathbf{ind}=1$

nag_stat_quantiles_stream_arbitrary (g01ap) has processed np data points and expects to be called again with additional data.

$\mathbf{ind}=2$

Either one or more of the communication arrays rcomm and icomm is too small. The new minimum lengths of rcomm and icomm have been returned in $\mathbf{icomm}\left(1\right)$ and $\mathbf{icomm}\left(2\right)$ respectively. If the new minimum length is greater than the current length then the corresponding communication array needs to be reallocated, its contents preserved and nag_stat_quantiles_stream_arbitrary (g01ap) called again with all other parameters unchanged.

If there is more data to be processed, it is recommended that lrcomm and licomm are made significantly bigger than the minimum to limit the number of reallocations.

$\mathbf{ind}=3$

nag_stat_quantiles_stream_arbitrary (g01ap) has returned the requested $\epsilon$-approximate quantiles in qv. These quantiles are based on np data points.

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

$m$, 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

rcomm holds information required by subsequent calls to nag_stat_quantiles_stream_arbitrary (g01ap)

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

$\mathbf{icomm}\left(1\right)$ holds the minimum required length for rcomm and $\mathbf{icomm}\left(2\right)$ holds the minimum required length for icomm. The remaining elements of icomm are used for communication between subsequent calls to nag_stat_quantiles_stream_arbitrary (g01ap).

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_arbitrary (g01ap) 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: $0.0<\mathbf{eps}\le 1.0$.

   $\mathbf{ifail}=3$

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

   $\mathbf{ifail}=4$

Constraint: $\mathbf{licomm}\ge 10$.

   $\mathbf{ifail}=5$

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

   $\mathbf{ifail}=6$

The contents of icomm have been altered between calls to this function.

   $\mathbf{ifail}=7$

The contents of rcomm have been altered between calls to this function.

   $\mathbf{ifail}=8$

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.

   $\mathbf{ifail}=9$

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

   $\mathbf{ifail}=10$

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: g01ap_example

function g01ap_example


fprintf('g01ap example results\n\n');

n   = 0;
tol = 0.2;
q   = [0.25 0.5 1.0];
nb  = 20;
% For this example we are using a string as the source of data.
datastream = ['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'];

rcomm = zeros(100, 1);
icomm = zeros(400, 1, 'int64');
ind   = int64(0);
repeat = true;
pos    = 0;

while (repeat)
  if (ind==0 || ind==1)
    [rv, new_pos] = textscan(datastream(pos+1:end), '%f', nb);
    pos = pos+new_pos;

    nd = numel(rv{1});
    if nd == 0
      break;
    elseif nd < nb
      nb = nd;
      repeat = false;
    elseif pos == numel(datastream)
      repeat = false;
    end
    n = n+nb;
  end

  [ind, np, qv, rcomm, icomm, ifail] = ...
    g01ap(ind, rv{1}, tol, q, rcomm, icomm);

  % If ind=2, the communication arrays are too small, so extend them
  % and call the routine again with the same rv
  if ind == 2
    if numel(rcomm) < icomm(1)
      rcomm(icomm(1)) = 0;
    end
    if numel(icomm) < icomm(2)
      icomm(icomm(2)) = 0;
    end
  end
end

% Call again to calculate quantiles q
ind = int64(3);
[ind, np, qv, rcomm, icomm, ifail] = ...
  g01ap(ind, 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']);

g01ap example results


Input Data:
 60 observations
 eps =  0.20

Quantile     Result
   0.25       22.49
   0.50       39.54
   1.00       59.95