g11sbc is a service function which may be used prior to calling g11sac to calculate the frequency distribution of a set of dichotomous score patterns.

2 Specification

#include <nag.h>

void	g11sbc (Nag_OrderType order, Integer p, Integer n, Integer ns, Nag_Boolean x[], Integer pdx, Integer irl[], NagError fail)

The function may be called by the names: g11sbc, nag_contab_binary_service or nag_binary_factor_service.

3 Description

When each of

n

individuals responds to each of

p

dichotomous variables the data assumes the form of the matrix

X

defined below

X = [\begin{array}{l} x_{11} & x_{12} & \dots & x_{1 p} \\ x_{21} & x_{22} & \dots & x_{2 p} \\ ⋮ & ⋮ & ⋮ \\ x_{n 1} & x_{n 2} & \dots & x_{n p} \end{array}] = [\begin{array}{l} {\underset{̲}{x}}_{1} \\ {\underset{̲}{x}}_{2} \\ ⋮ \\ {\underset{̲}{x}}_{n} \end{array}],

where the

x

take the value of

0

1

and

{\underset{̲}{x}}_{l} = (x_{l 1}, x_{l 2}, \dots, x_{l p})

, for

l = 1, 2, \dots, n

, denotes the score pattern of the

l

th individual. g11sbc calculates the number of different score patterns,

s

, and the frequency with which each occurs. This information can then be passed to g11sac.

4 References

None.

5 Arguments

1: $order$ – Nag_OrderType Input

On entry: the order argument specifies the two-dimensional storage scheme being used, i.e., row-major ordering or column-major ordering. C language defined storage is specified by

order = Nag_RowMajor

. See Section 3.1.3 in the Introduction to the NAG Library CL Interface for a more detailed explanation of the use of this argument.

Constraint:

order = Nag_RowMajor

Nag_ColMajor

2: $p$ – Integer Input

On entry:

p

, the number of dichotomous variables.

Constraint:

p \geq 3

3: $n$ – Integer Input

On entry:

n

, the number of individuals in the sample.

Constraint:

n \geq 7

4: $ns$ – Integer * Output

On exit: the number of different score patterns,

s

5: $x [\dim]$ – Nag_Boolean Input/Output

Note: the dimension, dim, of the array x must be at least

$\max (1, pdx \times p)$ when $order = Nag_ColMajor$ ;
$\max (1, n \times pdx)$ when $order = Nag_RowMajor$ .

where

X (i, j)

appears in this document, it refers to the array element

$x [(j - 1) \times pdx + i - 1]$ when $order = Nag_ColMajor$ ;
$x [(i - 1) \times pdx + j - 1]$ when $order = Nag_RowMajor$ .

On entry:

X (i, j)

must be set equal to Nag_TRUE if

x_{i j} = 1

, and Nag_FALSE if

x_{i j} = 0

, for

i = 1, 2, \dots, n

and

j = 1, 2, \dots, p

On exit: the first

s

rows of x contain the

s

different score patterns.

6: $pdx$ – Integer Input

On entry: the stride separating row or column elements (depending on the value of order) in the array x.

Constraints:

if $order = Nag_ColMajor$ , $pdx \geq n$ ;
if $order = Nag_RowMajor$ , $pdx \geq p$ .

7: $irl [n]$ – Integer Output

On exit: the frequency with which the

l

th row of x occurs, for

l = 1, 2, \dots, s

8: $fail$ – 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.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
NE_BAD_PARAM: On entry, argument $〈value〉$ had an illegal value.
NE_INT: On entry, $n = 〈value〉$ .
Constraint: $n \geq 7$ .

On entry, $p = 〈value〉$ .
Constraint: $p \geq 3$ .

On entry, $pdx = 〈value〉$ .
Constraint: $pdx > 0$ .
NE_INT_2: On entry, $pdx = 〈value〉$ and $n = 〈value〉$ .
Constraint: $pdx \geq n$ .

On entry, $pdx = 〈value〉$ and $p = 〈value〉$ .
Constraint: $pdx \geq p$ .
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.
See Section 7.5 in the Introduction to the NAG Library CL Interface for further information.
NE_NO_LICENCE: Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.

7 Accuracy

Exact.

8 Parallelism and Performance

g11sbc is not threaded in any implementation.

9 Further Comments

The time taken by g11sbc is small and increases with

n

10 Example

This example counts the frequencies of different score patterns in the following list:

Score Patterns
000
010
111
000
001
000
000
110
001
011

g11sb: FL CL CPP AD

NAG CL Interfaceg11sbc (binary_​service)

▸▿ 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
g11sbc (binary_service)