g11sbf is a service routine which may be used prior to calling g11saf to calculate the frequency distribution of a set of dichotomous score patterns.

2 Specification

Fortran Interface

Subroutine g11sbf (

ip, n, ns, x, ldx, irl, ifail)

Integer, Intent (In)	::	ip, n, ldx
Integer, Intent (Inout)	::	ifail
Integer, Intent (Out)	::	ns, irl(n)
Logical, Intent (Inout)	::	x(ldx,ip)

C Header Interface

#include <nag.h>

void	g11sbf_ (const Integer ip, const Integer n, Integer ns, logical x[], const Integer ldx, Integer irl[], Integer *ifail)

The routine may be called by the names g11sbf or nagf_contab_binary_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. g11sbf calculates the number of different score patterns,

s

, and the frequency with which each occurs. This information can then be passed to g11saf.

4 References

None.

5 Arguments

1: $ip$ – Integer Input: On entry: $p$ , the number of dichotomous variables.

Constraint: $ip \geq 3$ .
2: $n$ – Integer Input: On entry: $n$ , the number of individuals in the sample.

Constraint: $n \geq 7$ .
3: $ns$ – Integer Output: On exit: the number of different score patterns, $s$ .
4: $x (ldx, ip)$ – Logical array Input/Output: On entry: $x (i, j)$ must be set equal to .TRUE. if $x_{i j} = 1$ , and .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.
5: $ldx$ – Integer Input: On entry: the first dimension of the array x as declared in the (sub)program from which g11sbf is called.

Constraint: $ldx \geq n$ .
6: $irl (n)$ – Integer array Output: On exit: the frequency with which the $l$ th row of x occurs, for $l = 1, 2, \dots, s$ .
7: $ifail$ – Integer Input/Output: On entry: ifail must be set to $0$ , $−1$ or $1$ to set behaviour on detection of an error; these values have no effect when no error is detected.
A value of $0$ causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of $−1$ means that an error message is printed while a value of $1$ means that it is not.

If halting is not appropriate, the value $−1$ or $1$ is recommended. If message printing is undesirable, then the value $1$ is recommended. Otherwise, the value $0$ is recommended. When the value $- 1$ or $1$ is used it is essential to test the value of ifail on exit.

On exit: $ifail = 0$ unless the routine detects an error or a warning has been flagged (see Section 6).

6 Error Indicators and Warnings

If on entry

ifail = 0

−1

, explanatory error messages are output on the current error message unit (as defined by x04aaf).

Errors or warnings detected by the routine:

$ifail = 1$: On entry, $ip = ⟨ value ⟩$ .
Constraint: $ip \geq 3$ .

On entry, $ldx = ⟨ value ⟩$ and $n = ⟨ value ⟩$ .
Constraint: $ldx \geq n$ .

On entry, $n = ⟨ value ⟩$ .
Constraint: $n \geq 7$ .

$ifail = - 99$: An unexpected error has been triggered by this routine. Please contact NAG.
See Section 7 in the Introduction to the NAG Library FL Interface for further information.

$ifail = - 399$: 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.

$ifail = - 999$: Dynamic memory allocation failed.
See Section 9 in the Introduction to the NAG Library FL Interface for further information.

7 Accuracy

Exact.

8 Parallelism and Performance

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

g11sbf is not threaded in any implementation.

9 Further Comments

The time taken by g11sbf 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 PY MB

NAG FL Interfaceg11sbf (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 FL Interface
g11sbf (binary_service)