# NAG FL Interfaceg03zaf (z_​scores)

## 1Purpose

g03zaf produces standardized values ($z$-scores) for a data matrix.

## 2Specification

Fortran Interface
 Subroutine g03zaf ( n, m, x, ldx, nvar, isx, s, e, z, ldz,
 Integer, Intent (In) :: n, m, ldx, nvar, isx(m), ldz Integer, Intent (Inout) :: ifail Real (Kind=nag_wp), Intent (In) :: x(ldx,m), s(m), e(m) Real (Kind=nag_wp), Intent (Inout) :: z(ldz,nvar)
#include <nag.h>
 void g03zaf_ (const Integer *n, const Integer *m, const double x[], const Integer *ldx, const Integer *nvar, const Integer isx[], const double s[], const double e[], double z[], const Integer *ldz, Integer *ifail)
The routine may be called by the names g03zaf or nagf_mv_z_scores.

## 3Description

For a data matrix, $X$, consisting of $n$ observations on $p$ variables, with elements ${x}_{ij}$, g03zaf computes a matrix, $Z$, with elements ${z}_{ij}$ such that:
 $zij=xij-μjσj, i=1,2,…,n; j=1,2,…,p,$
where ${\mu }_{j}$ is a location shift and ${\sigma }_{j}$ is a scaling factor. Typically, ${\mu }_{j}$ will be the mean and ${\sigma }_{j}$ will be the standard deviation of the $j$th variable and therefore the elements in column $j$ of $Z$ will have zero mean and unit variance.

None.

## 5Arguments

1: $\mathbf{n}$Integer Input
On entry: $n$, the number of observations in the data matrix.
Constraint: ${\mathbf{n}}\ge 1$.
2: $\mathbf{m}$Integer Input
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) array Input
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: $\mathbf{ldx}$Integer Input
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: $\mathbf{nvar}$Integer Input
On entry: $p$, the number of variables to be standardized.
Constraint: ${\mathbf{nvar}}\ge 1$.
6: $\mathbf{isx}\left({\mathbf{m}}\right)$Integer array Input
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) array Input
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) array Input
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) array Output
On exit: the matrix of standardized values ($z$-scores), $Z$.
10: $\mathbf{ldz}$Integer Input
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: $\mathbf{ifail}$Integer Input/Output
On entry: ifail must be set to $0$, . If you are unfamiliar with this argument you should refer to Section 4 in the Introduction to the NAG Library FL Interface for details.
For environments where it might be inappropriate to halt program execution when an error is detected, the value 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 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).

## 6Error Indicators and Warnings

If on entry ${\mathbf{ifail}}=0$ or $-1$, explanatory error messages are output on the current error message unit (as defined by x04aaf).
Errors or warnings detected by the routine:
${\mathbf{ifail}}=1$
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: ${\mathbf{s}}\left(\mathit{j}\right)>0.0$.
${\mathbf{ifail}}=-99$
See Section 7 in the Introduction to the NAG Library FL Interface for further information.
${\mathbf{ifail}}=-399$
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library FL Interface for further information.
${\mathbf{ifail}}=-999$
Dynamic memory allocation failed.
See Section 9 in the Introduction to the NAG Library FL Interface for further information.

## 7Accuracy

Standard accuracy is achieved.

## 8Parallelism and Performance

g03zaf is not threaded in any implementation.

Means and standard deviations may be obtained using g01atf or g02bxf.

## 10Example

A $4$ by $3$ data matrix is input along with location and scaling values. The first and third columns are scaled and the results printed.

### 10.1Program Text

Program Text (g03zafe.f90)

### 10.2Program Data

Program Data (g03zafe.d)

### 10.3Program Results

Program Results (g03zafe.r)