NAG Library Routine Document

G10ZAF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     WEIGHT – CHARACTER(1)Input

On entry: indicates whether user-defined weights are to be used.

• If $\mathbf{WEIGHT}=\text{'W'}$, user-defined weights are to be used and must be supplied in WT.
• If $\mathbf{WEIGHT}=\text{'U'}$, the data is treated as unweighted.

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

2:     N – INTEGERInput

On entry: $n$, the number of observations.

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

3:     X(N) – REAL (KIND=nag_wp) arrayInput

On entry: the values, $x_{\mathit{i}}$, for $\mathit{i}=1,2,\dots ,n$.

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

On entry: the values $y_{\mathit{i}}$, for $\mathit{i}=1,2,\dots ,n$.

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

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

On entry: if $\mathbf{WEIGHT}=\text{'W'}$, WT must contain the $n$ weights. Otherwise WT is not referenced and unit weights are assumed.

Constraints:

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

6:     NORD – INTEGEROutput

On exit: the number of distinct observations.

7:     XORD(N) – REAL (KIND=nag_wp) arrayOutput

On exit: the first NORD elements contain the ordered and distinct $x_i$.

8:     YORD(N) – REAL (KIND=nag_wp) arrayOutput

On exit: the first NORD elements contain the values $y^{\prime }$ corresponding to the values in XORD.

9:     WTORD(N) – REAL (KIND=nag_wp) arrayOutput

On exit: the first NORD elements contain the values $w^{\prime }$ corresponding to the values of XORD and YORD.

10:   RSS – REAL (KIND=nag_wp)Output

On exit: the within group sum of squares for tied observations.

11:   IWRK(N) – INTEGER arrayWorkspace

12:   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,	$\mathbf{WEIGHT}\ne \text{'W'}$ or $\text{'U'}$,
or	$\mathbf{N}<1$.

$\mathbf{IFAIL}=2$

On entry,

$\mathbf{WEIGHT}=\text{'W'}$ and at least one element of WT is $<0.0$, or all elements of WT are $0.0$.

7  Accuracy

8  Further Comments

9  Example

9.1  Program Text

Program Text (g10zafe.f90)

9.2  Program Data

Program Data (g10zafe.d)

9.3  Program Results

Program Results (g10zafe.r)