NAG Library Routine Document

G03ZAF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     N – INTEGERInput

On entry: $n$, the number of observations in the data matrix.

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

2:     M – INTEGERInput

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

Constraint: $\mathbf{M}\ge \mathbf{NVAR}$.

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

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

4:     LDX – INTEGERInput

On entry: the first dimension of the array X as declared in the (sub)program from which G03ZAF is called.

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

5:     NVAR – INTEGERInput

On entry: $p$, the number of variables to be standardized.

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

6:     ISX(M) – INTEGER arrayInput

On entry: $\mathbf{ISX}\left(j\right)$ indicates whether or not the observations on the $j$th variable are included in the matrix of standardized values.

If $\mathbf{ISX}\left(j\right)\ne 0$, the observations from the $j$th variable are included.

If $\mathbf{ISX}\left(j\right)=0$, the observations from the $j$th variable are not included.

Constraint: $\mathbf{ISX}\left(j\right)\ne 0$ for NVAR values of $j$.

7:     S(M) – REAL (KIND=nag_wp) arrayInput

On entry: if $\mathbf{ISX}\left(j\right)\ne 0$, $\mathbf{S}\left(j\right)$ must contain the scaling (standard deviation), ${\sigma }_j$, for the $j$th variable.

If $\mathbf{ISX}\left(j\right)=0$, $\mathbf{S}\left(j\right)$ is not referenced.

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

8:     E(M) – REAL (KIND=nag_wp) arrayInput

On entry: if $\mathbf{ISX}\left(j\right)\ne 0$, $\mathbf{E}\left(j\right)$ must contain the location shift (mean), ${\mu }_j$, for the $j$th variable.

If $\mathbf{ISX}\left(j\right)=0$, $\mathbf{E}\left(j\right)$ is not referenced.

9:     Z(LDZ,NVAR) – REAL (KIND=nag_wp) arrayOutput

On exit: the matrix of standardized values ($z$-scores), $Z$.

10:   LDZ – INTEGERInput

On entry: the first dimension of the array Z as declared in the (sub)program from which G03ZAF is called.

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

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,	$\mathbf{N}<1$,
or	$\mathbf{NVAR}<1$,
or	$\mathbf{M}<\mathbf{NVAR}$,
or	$\mathbf{LDX}<\mathbf{N}$,
or	$\mathbf{LDZ}<\mathbf{N}$.

$\mathbf{IFAIL}=2$

On entry,

there are not precisely NVAR elements of $\mathbf{ISX}\ne 0$.

$\mathbf{IFAIL}=3$

On entry,

$\mathbf{ISX}\left(j\right)\ne 0$ and $\mathbf{S}\left(j\right)\le 0.0$ for some $j$.

7  Accuracy

8  Further Comments

9  Example

9.1  Program Text

Program Text (g03zafe.f90)

9.2  Program Data

Program Data (g03zafe.d)

9.3  Program Results

Program Results (g03zafe.r)