NAG Library Routine Document

G03EAF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     UPDATE – CHARACTER(1)Input

On entry: indicates whether or not an existing matrix is to be updated.

$\mathbf{UPDATE}=\text{'U'}$

The matrix $D$ is updated and distances are added to $D$.

$\mathbf{UPDATE}=\text{'I'}$

The matrix $D$ is initialized to zero before the distances are added to $D$.

Constraint: $\mathbf{UPDATE}=\text{'U'}$ or $\text{'I'}$.

2:     DIST – CHARACTER(1)Input

On entry: indicates which type of distances are computed.

$\mathbf{DIST}=\text{'A'}$

Absolute distances.

$\mathbf{DIST}=\text{'E'}$

Euclidean distances.

$\mathbf{DIST}=\text{'S'}$

Euclidean squared distances.

Constraint: $\mathbf{DIST}=\text{'A'}$, $\text{'E'}$ or $\text{'S'}$.

3:     SCAL – CHARACTER(1)Input

On entry: indicates the standardization of the variables to be used.

$\mathbf{SCAL}=\text{'S'}$

Standard deviation.

$\mathbf{SCAL}=\text{'R'}$

Range.

$\mathbf{SCAL}=\text{'G'}$

Standardizations given in array S.

$\mathbf{SCAL}=\text{'U'}$

Unscaled.

Constraint: $\mathbf{SCAL}=\text{'S'}$, $\text{'R'}$, $\text{'G'}$ or $\text{'U'}$.

4:     N – INTEGERInput

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

Constraint: $\mathbf{N}\ge 2$.

5:     M – INTEGERInput

On entry: the total number of variables in array X.

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

6:     X(LDX,M) – REAL (KIND=nag_wp) arrayInput

On entry: $\mathbf{X}\left(\mathit{i},\mathit{j}\right)$ must contain the value of the $\mathit{j}$th variable for the $\mathit{i}$th object, for $\mathit{i}=1,2,\dots ,n$ and $\mathit{j}=1,2,\dots ,\mathbf{M}$.

7:     LDX – INTEGERInput

On entry: the first dimension of the array X as declared in the (sub)program from which G03EAF is called.

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

8:     ISX(M) – INTEGER arrayInput

On entry: $\mathbf{ISX}\left(j\right)$ indicates whether or not the $j$th variable in X is to be included in the distance computations.

If $\mathbf{ISX}\left(\mathit{j}\right)>0$ the $\mathit{j}$th variable is included, for $\mathit{j}=1,2,\dots ,\mathbf{M}$; otherwise it is not referenced.

Constraint: $\mathbf{ISX}\left(\mathit{j}\right)>0$ for at least one $\mathit{j}$, for $\mathit{j}=1,2,\dots ,\mathbf{M}$.

9:     S(M) – REAL (KIND=nag_wp) arrayInput/Output

On entry: if $\mathbf{SCAL}=\text{'G'}$ and $\mathbf{ISX}\left(\mathit{j}\right)>0$ then $\mathbf{S}\left(\mathit{j}\right)$ must contain the scaling for variable $\mathit{j}$, for $\mathit{j}=1,2,\dots ,\mathbf{M}$.

Constraint: if $\mathbf{SCAL}=\text{'G'}$ and $\mathbf{ISX}\left(j\right)>0$, $\mathbf{S}\left(\mathit{j}\right)>0.0$, for $\mathit{j}=1,2,\dots ,\mathbf{M}$.

On exit: if $\mathbf{SCAL}=\text{'S'}$ and $\mathbf{ISX}\left(j\right)>0$ then $\mathbf{S}\left(j\right)$ contains the standard deviation of the variable in the $j$th column of X.

If $\mathbf{SCAL}=\text{'R'}$ and $\mathbf{ISX}\left(j\right)>0$, $\mathbf{S}\left(j\right)$ contains the range of the variable in the $j$th column of X.

If $\mathbf{SCAL}=\text{'U'}$ and $\mathbf{ISX}\left(j\right)>0$, $\mathbf{S}\left(j\right)=1.0$.

If $\mathbf{SCAL}=\text{'G'}$, S is unchanged.

10:   D($\mathbf{N}\times \left(\mathbf{N}-1\right)/2$) – REAL (KIND=nag_wp) arrayInput/Output

On entry: if $\mathbf{UPDATE}=\text{'U'}$, D must contain the strictly lower triangle of the distance matrix $D$ to be updated. $D$ must be stored packed by rows, i.e., $\mathbf{D}\left(\left(i-1\right)\left(i-2\right)/2+j\right)$, $i>j$ must contain $d_{ij}$.

If $\mathbf{UPDATE}=\text{'I'}$, D need not be set.

Constraint: if $\mathbf{UPDATE}=\text{'U'}$, $\mathbf{D}\left(\mathit{j}\right)\ge 0.0$, for $\mathit{j}=1,2,\dots ,n\left(n-1\right)/2$.

On exit: the strictly lower triangle of the distance matrix $D$ stored packed by rows, i.e., $d_{ij}$ is contained in $\mathbf{D}\left(\left(i-1\right)\left(i-2\right)/2+j\right)$, $i>j$.

11:   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,	$\mathbf{N}<2$,
or	$\mathbf{LDX}<\mathbf{N}$,
or	$\mathbf{M}\le 0$,
or	$\mathbf{UPDATE}\ne \text{'I'}$ or $\text{'U'}$,
or	$\mathbf{DIST}\ne \text{'A'}$, $\text{'E'}$ or $\text{'S'}$,
or	$\mathbf{SCAL}\ne \text{'S'}$, $\text{'R'}$, $\text{'G'}$ or $\text{'U'}$.

$\mathbf{IFAIL}=2$

On entry,	$\mathbf{ISX}\left(\mathit{j}\right)\le 0$, for $\mathit{j}=1,2,\dots ,\mathbf{M}$,
or	$\mathbf{UPDATE}=\text{'U'}$ and $\mathbf{D}\left(j\right)<0.0$, for some $j=1,2,\dots ,n\left(n-1\right)/2$,
or	$\mathbf{SCAL}=\text{'S'}$ or $\text{'R'}$ and $\mathbf{X}\left(i,j\right)=\mathbf{X}\left(i+1,j\right)$ for $i=1,2,\dots ,n-1$, for some $j$ with $\mathbf{ISX}\left(i\right)>0$.
or	$\mathbf{S}\left(j\right)\le 0.0$ for some $j$ when $\mathbf{SCAL}=\text{'G'}$ and $\mathbf{ISX}\left(j\right)>0$.

7  Accuracy

8  Further Comments

9  Example

9.1  Program Text

Program Text (g03eafe.f90)

9.2  Program Data

Program Data (g03eafe.d)

9.3  Program Results

Program Results (g03eafe.r)