NAG Toolbox: nag_smooth_data_order (g10za)

Purpose

Syntax

Description

References

Parameters

Compulsory Input Parameters

1:     $\mathrm{x}\left(\mathbf{n}\right)$ – double array

The values, $x_{\mathit{i}}$, for $\mathit{i}=1,2,\dots ,n$.

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

The values $y_{\mathit{i}}$, for $\mathit{i}=1,2,\dots ,n$.

Optional Input Parameters

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

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

$n$, the number of observations.

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

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

The dimension of the array wt must be at least $\mathbf{n}$ if $\mathit{weight}=\text{'W'}$

If $\mathit{weight}=\text{'W'}$, wt must contain the $n$ weights. Otherwise wt is not referenced and unit weights are assumed.

Constraints:

• if $\mathit{weight}=\text{'W'}$, $\mathbf{wt}\left(\mathit{i}\right)>0.0$, for $\mathit{i}=1,2,\dots ,n$;
• if $\mathit{weight}=\text{'W'}$, ${\sum }_{i=1}^n\mathbf{wt}\left(i\right)>0$.

Output Parameters

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

The number of distinct observations.

2:     $\mathrm{xord}\left(\mathbf{n}\right)$ – double array

The first nord elements contain the ordered and distinct $x_i$.

3:     $\mathrm{yord}\left(\mathbf{n}\right)$ – double array

The first nord elements contain the values $y^{\prime }$ corresponding to the values in xord.

4:     $\mathrm{wtord}\left(\mathbf{n}\right)$ – double array

The first nord elements contain the values $w^{\prime }$ corresponding to the values of xord and yord.

5:     $\mathrm{rss}$ – double scalar

The within group sum of squares for tied observations.

6:     $\mathrm{ifail}$ – 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,	$\mathit{weight}\ne \text{'W'}$ or $\text{'U'}$,
or	$\mathbf{n}<1$.

   $\mathbf{ifail}=2$

On entry,

$\mathit{weight}=\text{'W'}$ and at least one element of wt is $<0.0$, or all elements of wt are $0.0$.

   $\mathbf{ifail}=-99$

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: g10za_example

function g10za_example


fprintf('g10za example results\n\n');

x = [1; 3; 5; 5; 3; 4; 9; 6; 9; 9];
y = [4; 4; 1; 2; 5; 3; 4; 9; 7; 4];

% Reorder data
[nord, xord, yord, wtord, rss, ifail] =  ...
  g10za(x, y);

% Display results
fprintf('Number of distinct observations = %7d\n', nord);
fprintf('Residual sum of squares         = %13.5f\n\n', rss);
fprintf('%16s%18s%19s\n', 'x', 'y', 'wt');
results = [xord(1:nord) yord(1:nord) wtord(1:nord)];
fprintf('%17.1f%18.1f%18.1f\n', results');

g10za example results

Number of distinct observations =       6
Residual sum of squares         =       7.00000

               x                 y                 wt
              1.0               4.0               1.0
              3.0               4.5               2.0
              4.0               3.0               1.0
              5.0               1.5               2.0
              6.0               9.0               1.0
              9.0               5.0               3.0