naginterfaces.library.smooth.data_​order

naginterfaces.library.smooth.data_order(x, y, wt=None)

data_order orders and weights data which is entered unsequentially, weighted or unweighted.

For full information please refer to the NAG Library document for g10za

https://support.nag.com/numeric/nl/nagdoc_30/flhtml/g10/g10zaf.html

Parameters

xfloat, array-like, shape $\left(n\right)$

The values, $x_{\text{i}}$, for $\text{i}=1,2,\dots ,n$.

yfloat, array-like, shape $\left(n\right)$

The values $y_{\text{i}}$, for $\text{i}=1,2,\dots ,n$.

wtNone or float, array-like, shape $\left(n\right)$, optional

If $\text{weight}=\text{'W'}$, $wt$ must contain the $n$ weights. Otherwise $wt$ is not referenced and unit weights are assumed.

Returns

nordint

The number of distinct observations.

xordfloat, ndarray, shape $\left(n\right)$

The first $nord$ elements contain the ordered and distinct $x_i$.

yordfloat, ndarray, shape $\left(n\right)$

The first $nord$ elements contain the values $y^{\prime }$ corresponding to the values in $xord$.

wtordfloat, ndarray, shape $\left(n\right)$

The first $nord$ elements contain the values $w^{\prime }$ corresponding to the values of $xord$ and $yord$.

rssfloat

The within group sum of squares for tied observations.

Raises

NagValueError

(errno $1$)

On entry, $\text{weight}=⟨value⟩$.

Constraint: $\text{weight}=\text{'W'}$ or $\text{'U'}$.

(errno $1$)

On entry, $n=⟨value⟩$.

Constraint: $n\ge 1$.

(errno $2$)

On entry, all weights are zero.

(errno $2$)

On entry, $i=⟨value⟩$ and $wt[i-1]=⟨value⟩$.

Constraint: $wt[i-1]\ge 0.0$.

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.

Given a set of observations $(x_i,y_i)$, for $i=1,2,\dots ,n$, with corresponding weights $w_i$, data_order rearranges the observations so that the $x_i$ are in ascending order.

For any equal $x_i$ in the ordered set, say $x_j=x_{j+1}=\cdots =x_{j+k}$, a single observation $x_j$ is returned with a corresponding $y^{\prime }$ and $w^{\prime }$, calculated as

$$w^{\prime }=\sum _{l=0}^k{w}_{i+l}$$

and

$$y^{\prime }=\frac{{\sum }_{l=0}^k{w}_{i+l}{y}_{i+l}}{w^{\prime }}\text{.}$$

Observations with zero weight are ignored. If no weights are supplied by you, then unit weights are assumed; that is $w_{\text{i}}=1$, for $\text{i}=1,2,\dots ,n$.

In addition, the within group sum of squares is computed for the tied observations using West’s algorithm (see West (1979)).

References

Draper, N R and Smith, H, 1985, Applied Regression Analysis, (2nd Edition), Wiley

West, D H D, 1979, Updating mean and variance estimates: An improved method, Comm. ACM (22), 532–555