void	g10zac (Integer n, const double x[], const double y[], const double weights[], Integer nord, double xord[], double yord[], double wwt[], double rss, NagError *fail)

The function may be called by the names: g10zac, nag_smooth_data_order or nag_order_data.

3 Description

Given a set of observations

(x_{i}, y_{i})

for

i = 1, 2, \dots, n

, with corresponding weights

w_{i}

, g10zac 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} = \dots = x_{j + k}

, a single observation

x_{j}

is returned with a corresponding

y^{'}

and

w^{'}

, calculated as:

w^{'} = \sum_{l = 0}^{k} w_{i + l}

and

y^{'} = \frac{\sum_{l = 0}^{k} w_{i + l} y_{i + l}}{w^{'}} .

Observations with zero weight are ignored. If no weights are supplied by you, then unit weights are assumed; that is

w_{i} = 1

, for

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)).

4 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

5 Arguments

1: $n$ – Integer Input

On entry: the number of observations,

n

Constraint:

n \geq 1

2: $x [n]$ – const double Input

On entry: the values

x_{i}

, for

i = 1, 2, \dots, n

3: $y [n]$ – const double Input

On entry: the values

y_{i}

, for

i = 1, 2, \dots, n

4: $weights [n]$ – const double Input

On entry: weights must contain the

n

weights, if they are required. Otherwise, weights must be set to NULL.

Constraints:

if weights are required, then $weights [i - 1] \geq 0.0$ , for $i = 1, 2, \dots, n$ ;
at least one $weights [i - 1] > 0.0$ , for some $i$ .

5: $nord$ – Integer * Output

On exit: the number of distinct observations.

6: $xord [n]$ – double Output

On exit: the first nord elements contain the ordered and distinct

x_{i}

7: $yord [n]$ – double Output

On exit: the first nord elements contain the values

y^{'}

corresponding to the values in xord.

8: $wwt [n]$ – double Output

On exit: the first nord elements contain the values

w^{'}

corresponding to the values of xord and yord.

9: $rss$ – double * Output

On exit: the within group sum of squares for tied observations.

10: $fail$ – NagError * Input/Output

The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

NE_ALLOC_FAIL: Dynamic memory allocation failed.
NE_ARRAY_CONS: The contents of array weights are not valid.
Constraint: at least one element of weights must be $> 0$ .
NE_INT_ARG_LT: On entry, $n = ⟨ value ⟩$ .
Constraint: $n \geq 1$ .
NE_INTERNAL_ERROR: An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
NE_REAL_ARRAY_CONS: On entry, $weights [⟨ value ⟩] = ⟨ value ⟩$ .
Constraint: $weights [i] \geq 0$ , for $i = 0, 1, \dots, n - 1$ .

7 Accuracy

For a discussion on the accuracy of the algorithm for computing mean and variance see West (1979).

8 Parallelism and Performance

Background information to multithreading can be found in the Multithreading documentation.

g10zac is not threaded in any implementation.

9 Further Comments

g10zac may be used to compute the pure error sum of squares in simple linear regression along with g02dac, see Draper and Smith (1985).

10 Example

A set of unweighted observations are input and g10zac used to produce a set of strictly increasing weighted observations.

g10za: FL CL CPP AD PY MB

NAG CL Interfaceg10zac (data_​order)

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results

NAG CL Interface
g10zac (data_order)