NAG Library Routine Document

G01ATF

1 Purpose

2 Specification

3 Description

4 References

5 Parameters

1:   NB – INTEGERInput

On entry: $b$, the number of observations in the current block of data. The size of the block of data supplied in X and WT can vary; therefore NB can change between calls to G01ATF.

Constraint: $\mathbf{NB}\ge 0$.

2:   X(NB) – REAL (KIND=nag_wp) arrayInput

On entry: the current block of observations, corresponding to $x_{\mathit{i}}$, for $\mathit{i}=k+1,\dots ,k+b$, where $k$ is the number of observations processed so far and $b$ is the size of the current block of data.

3:   IWT – INTEGERInput

On entry: indicates whether user-supplied weights are provided:

$\mathbf{IWT}=1$

User-supplied weights are given in the array WT.

$\mathbf{IWT}=0$

$w_i=1$, for all $i$, so no user-supplied weights are given and WT is not referenced.

Constraint: $\mathbf{IWT}=0$ or $1$.

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

Note: the dimension of the array WT must be at least $\mathbf{NB}$ if $\mathbf{IWT}=1$.

On entry: if $\mathbf{IWT}=1$, WT must contain the user-supplied weights corresponding to the block of data supplied in X, that is $w_{\mathit{i}}$, for $\mathit{i}=k+1,\dots ,k+b$.

Constraint: if $\mathbf{IWT}=1$, $\mathbf{WT}\left(\mathit{i}\right)\ge 0$, for $\mathit{i}=1,2,\dots ,\mathbf{NB}$.

5:   PN – INTEGERInput/Output

On entry: the number of valid observations processed so far, that is the number of observations with $w_i>0$, for $\mathit{i}=1,2,\dots ,k$. On the first call to G01ATF, or when starting to summarise a new dataset, PN must be set to $0$.

If $\mathbf{PN}\ne 0$, it must be the same value as returned by the last call to G01ATF.

On exit: the updated number of valid observations processed, that is the number of observations with $w_i>0$, for $\mathit{i}=1,2,\dots ,k+b$.

Constraint: $\mathbf{PN}\ge 0$.

6:   XMEAN – REAL (KIND=nag_wp)Output

On exit: $\stackrel{-}{x}$, the mean of the first $k+b$ observations.

7:   XSD – REAL (KIND=nag_wp)Output

On exit: $s_2$, the standard deviation of the first $k+b$ observations.

8:   XSKEW – REAL (KIND=nag_wp)Output

On exit: $s_3$, the coefficient of skewness for the first $k+b$ observations.

9:   XKURT – REAL (KIND=nag_wp)Output

On exit: $s_4$, the coefficient of kurtosis for the first $k+b$ observations.

10:   XMIN – REAL (KIND=nag_wp)Output

On exit: the smallest value in the first $k+b$ observations.

11:   XMAX – REAL (KIND=nag_wp)Output

On exit: the largest value in the first $k+b$ observations.

12:   RCOMM($20$) – REAL (KIND=nag_wp) arrayCommunication Array

On entry: communication array, used to store information between calls to G01ATF. If $\mathbf{PN}=0$, RCOMM need not be initialized, otherwise it must be unchanged since the last call to this routine.

On exit: the updated communication array. The first five elements of RCOMM hold information that may be of interest with

$$\begin{array}{ccc}\mathbf{RCOMM}\left(1\right)& =& \sum _{\mathit{i}=1}^{k+b}{w}_i\\ \mathbf{RCOMM}\left(2\right)& =& {\left(\sum _{\mathit{i}=1}^{k+b}{w}_i\right)}^2-\sum _{\mathit{i}=1}^{k+b}{w}_i^2\\ \mathbf{RCOMM}\left(3\right)& =& \sum _{\mathit{i}=1}^{k+b}{w}_i{\left(x_i-\stackrel{-}{x}\right)}^2\\ \mathbf{RCOMM}\left(4\right)& =& \sum _{\mathit{i}=1}^{k+b}{w}_i{\left(x_i-\stackrel{-}{x}\right)}^3\\ \mathbf{RCOMM}\left(5\right)& =& \sum _{\mathit{i}=1}^{k+b}{w}_i{\left(x_i-\stackrel{-}{x}\right)}^4\end{array}$$

the remaining elements of RCOMM are used for workspace and so are undefined.

13:   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

$\mathbf{IFAIL}=11$

On entry, $\mathbf{NB}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{NB}\ge 0$.

$\mathbf{IFAIL}=31$

On entry, $\mathbf{IWT}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{IWT}=0$ or $1$.

$\mathbf{IFAIL}=41$

On entry, $\mathbf{WT}\left(⟨\mathit{\text{value}}⟩\right)=⟨\mathit{\text{value}}⟩$.
Constraint: if $\mathbf{IWT}=1$ then $\mathbf{WT}\left(\mathit{i}\right)\ge 0$, for $\mathit{i}=1,2,\dots ,\mathbf{NB}$.

$\mathbf{IFAIL}=51$

On entry, $\mathbf{PN}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{PN}\ge 0$.

$\mathbf{IFAIL}=52$

On entry, $\mathbf{PN}=⟨\mathit{\text{value}}⟩$.
On exit from previous call, $\mathbf{PN}=⟨\mathit{\text{value}}⟩$.
Constraint: if $\mathbf{PN}>0$, PN must be unchanged since previous call.

$\mathbf{IFAIL}=53$

On entry, the number of valid observations is zero.

$\mathbf{IFAIL}=71$

On exit we were unable to calculate XSKEW or XKURT. A value of $0$ has been returned.

$\mathbf{IFAIL}=72$

On exit we were unable to calculate XSD, XSKEW or XKURT. A value of $0$ has been returned.

$\mathbf{IFAIL}=121$

RCOMM has been corrupted between calls.

7 Accuracy

8 Further Comments

9 Example

9.1 Program Text

Program Text (g01atfe.f90)

9.2 Program Data

Program Data (g01atfe.d)

9.3 Program Results

Program Results (g01atfe.r)