NAG Library Routine Document

g03zaf (z_scores)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:     $\mathbf{n}$ – IntegerInput

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

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

2:     $\mathbf{m}$ – IntegerInput

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

Constraint: $\mathbf{m}\ge \mathbf{nvar}$.

3:     $\mathbf{x}\left(\mathbf{ldx},\mathbf{m}\right)$ – 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:     $\mathbf{ldx}$ – 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:     $\mathbf{nvar}$ – IntegerInput

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

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

6:     $\mathbf{isx}\left(\mathbf{m}\right)$ – 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:     $\mathbf{s}\left(\mathbf{m}\right)$ – 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:     $\mathbf{e}\left(\mathbf{m}\right)$ – 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:     $\mathbf{z}\left(\mathbf{ldz},\mathbf{nvar}\right)$ – Real (Kind=nag_wp) arrayOutput

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

10:   $\mathbf{ldz}$ – 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:   $\mathbf{ifail}$ – IntegerInput/Output

On entry: ifail must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this argument you should refer to Section 3.4 in How to Use the NAG Library and its Documentation 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 argument, 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, $\mathbf{ldx}=〈\mathit{\text{value}}〉$ and $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{ldx}\ge \mathbf{n}$.

On entry, $\mathbf{ldz}=〈\mathit{\text{value}}〉$ and $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{ldz}\ge \mathbf{n}$.

On entry, $\mathbf{m}=〈\mathit{\text{value}}〉$ and $\mathbf{nvar}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{m}\ge \mathbf{nvar}$.

On entry, $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{n}\ge 1$.

On entry, $\mathbf{nvar}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{nvar}\ge 1$.

$\mathbf{ifail}=2$

On entry, $\mathbf{nvar}=〈\mathit{\text{value}}〉$ and $〈\mathit{\text{value}}〉$ values of $\mathbf{isx}>0$.
Constraint: exactly nvar elements of $\mathbf{isx}>0$.

$\mathbf{ifail}=3$

On entry, $j=〈\mathit{\text{value}}〉$ and $\mathbf{s}\left(i\right)\le 0.0$.
Constraint: $\mathbf{s}\left(\mathit{j}\right)>0.0$.

$\mathbf{ifail}=-99$

An unexpected error has been triggered by this routine. Please contact NAG.

See Section 3.9 in How to Use the NAG Library and its Documentation for further information.

$\mathbf{ifail}=-399$

Your licence key may have expired or may not have been installed correctly.

See Section 3.8 in How to Use the NAG Library and its Documentation for further information.

$\mathbf{ifail}=-999$

Dynamic memory allocation failed.

See Section 3.7 in How to Use the NAG Library and its Documentation for further information.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (g03zafe.f90)

10.2

Program Data

Program Data (g03zafe.d)

10.3

Program Results

Program Results (g03zafe.r)