naginterfaces.library.mv.z_​scores

naginterfaces.library.mv.z_scores(x, nvar, isx, s, e)

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

For full information please refer to the NAG Library document for g03za

https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/g03/g03zaf.html

Parameters

xfloat, array-like, shape $(n,m)$

$x[\text{i}-1,\text{j}-1]$ must contain the $\text{i}$th sample point for the $\text{j}$th variable, $x_{\text{i}\text{j}}$, for $\text{j}=1,2,\dots ,m$, for $\text{i}=1,2,\dots ,n$.

nvarint

$p$, the number of variables to be standardized.

isxint, array-like, shape $\left(m\right)$

$isx[j-1]$ indicates whether or not the observations on the $j$th variable are included in the matrix of standardized values.

If $isx[j-1]\ne 0$, the observations from the $j$th variable are included.

If $isx[j-1]=0$, the observations from the $j$th variable are not included.

sfloat, array-like, shape $\left(m\right)$

If $isx[j-1]\ne 0$, $s[j-1]$ must contain the scaling (standard deviation), ${\sigma }_j$, for the $j$th variable.

If $isx[j-1]=0$, $s[j-1]$ is not referenced.

efloat, array-like, shape $\left(m\right)$

If $isx[j-1]\ne 0$, $e[j-1]$ must contain the location shift (mean), ${\mu }_j$, for the $j$th variable.

If $isx[j-1]=0$, $e[j-1]$ is not referenced.

Returns

zfloat, ndarray, shape $(n,nvar)$

The matrix of standardized values ($z$-scores), $Z$.

Raises

NagValueError

(errno $1$)

On entry, $m=⟨value⟩$ and $nvar=⟨value⟩$.

Constraint: $m\ge nvar$.

(errno $1$)

On entry, $nvar=⟨value⟩$.

Constraint: $nvar\ge 1$.

(errno $1$)

On entry, $n=⟨value⟩$.

Constraint: $n\ge 1$.

(errno $2$)

On entry, $nvar=⟨value⟩$ and $⟨value⟩$ values of $isx>0$.

Constraint: exactly $nvar$ elements of $isx>0$.

(errno $3$)

On entry, $j=⟨value⟩$ and $s[i-1]\le 0.0$.

Constraint: $s\left[\text{j}\right]>0.0$.

Notes

In the NAG Library the traditional C interface for this routine uses a different algorithmic base. Please contact NAG if you have any questions about compatibility.

For a data matrix, $X$, consisting of $n$ observations on $p$ variables, with elements $x_{ij}$, z_scores computes a matrix, $Z$, with elements $z_{ij}$ such that:

$$z_{ij}=\frac{x_{ij}-{\mu }_j}{{\sigma }_j}\text{,}i=1,2,\dots ,n\text{;}j=1,2,\dots ,p\text{,}$$

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.