G02BEF (PDF version)
G02 Chapter Contents
G02 Chapter Introduction
NAG Library Manual

NAG Library Routine Document

G02BEF

Note:  before using this routine, please read the Users' Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details.

 Contents

    1  Purpose
    7  Accuracy

1  Purpose

G02BEF computes means and standard deviations of variables, sums of squares and cross-products about zero, and correlation-like coefficients for a set of data omitting completely any cases with a missing observation for any variable.

2  Specification

SUBROUTINE G02BEF ( N, M, X, LDX, MISS, XMISS, XBAR, STD, SSPZ, LDSSPZ, RZ, LDRZ, NCASES, IFAIL)
INTEGER  N, M, LDX, MISS(M), LDSSPZ, LDRZ, NCASES, IFAIL
REAL (KIND=nag_wp)  X(LDX,M), XMISS(M), XBAR(M), STD(M), SSPZ(LDSSPZ,M), RZ(LDRZ,M)

3  Description

The input data consists of n observations for each of m variables, given as an array
xij,  i=1,2,,n n2,j=1,2,,mm2,  
where xij is the ith observation on the jth variable. In addition, each of the m variables may optionally have associated with it a value which is to be considered as representing a missing observation for that variable; the missing value for the jth variable is denoted by xmj. Missing values need not be specified for all variables.
Let wi=0 if observation i contains a missing value for any of those variables for which missing values have been declared, i.e., if xij=xmj for any j for which an xmj has been assigned (see also Section 7); and wi=1 otherwise, for i=1,2,,n.
The quantities calculated are:
(a) Means:
x-j=i=1nwixij i=1nwi ,  j=1,2,,m.  
(b) Standard deviations:
sj= i= 1nwi xij-x-j 2 i= 1nwi- 1 ,   j= 1,2,,m.  
(c) Sums of squares and cross-products about zero:
S~jk=i=1nwixijxik,  j,k=1,2,,m.  
(d) Correlation-like coefficients:
R~jk=S~jkS~jj S~kk ,   j,k= 1,2,,m.  
If S~jj or S~kk is zero, R~jk is set to zero.

4  References

None.

5  Arguments

1:     N – INTEGERInput
On entry: n, the number of observations or cases.
Constraint: N2.
2:     M – INTEGERInput
On entry: m, the number of variables.
Constraint: M2.
3:     XLDXM – REAL (KIND=nag_wp) arrayInput
On entry: Xij must be set to xij, the value of the ith observation on the jth variable, for i=1,2,,n and j=1,2,,m.
4:     LDX – INTEGERInput
On entry: the first dimension of the array X as declared in the (sub)program from which G02BEF is called.
Constraint: LDXN.
5:     MISSM – INTEGER arrayInput/Output
On entry: MISSj must be set equal to 1 if a missing value, xmj, is to be specified for the jth variable in the array X, or set equal to 0 otherwise. Values of MISS must be given for all m variables in the array X.
On exit: the array MISS is overwritten by the routine, and the information it contained on entry is lost.
6:     XMISSM – REAL (KIND=nag_wp) arrayInput/Output
On entry: XMISSj must be set to the missing value, xmj, to be associated with the jth variable in the array X, for those variables for which missing values are specified by means of the array MISS (see Section 7).
On exit: the array XMISS is overwritten by the routine, and the information it contained on entry is lost.
7:     XBARM – REAL (KIND=nag_wp) arrayOutput
On exit: the mean value, x-j, of the jth variable, for j=1,2,,m.
8:     STDM – REAL (KIND=nag_wp) arrayOutput
On exit: the standard deviation, sj, of the jth variable, for j=1,2,,m.
9:     SSPZLDSSPZM – REAL (KIND=nag_wp) arrayOutput
On exit: SSPZjk is the cross-product about zero, S~jk, for j=1,2,,m and k=1,2,,m.
10:   LDSSPZ – INTEGERInput
On entry: the first dimension of the array SSPZ as declared in the (sub)program from which G02BEF is called.
Constraint: LDSSPZM.
11:   RZLDRZM – REAL (KIND=nag_wp) arrayOutput
On exit: RZjk is the correlation-like coefficient, R~jk, between the jth and kth variables, for j=1,2,,m and k=1,2,,m.
12:   LDRZ – INTEGERInput
On entry: the first dimension of the array RZ as declared in the (sub)program from which G02BEF is called.
Constraint: LDRZM.
13:   NCASES – INTEGEROutput
On exit: the number of cases actually used in the calculations (when cases involving missing values have been eliminated).
14:   IFAIL – INTEGERInput/Output
On entry: IFAIL must be set to 0, -1​ or ​1. If you are unfamiliar with this argument you should refer to Section 3.4 in How to Use the NAG Library and its Documentation for details.
For environments where it might be inappropriate to halt program execution when an error is detected, the value -1​ or ​1 is recommended. If the output of error messages is undesirable, then the value 1 is recommended. Otherwise, if you are not familiar with this argument, the recommended value is 0. 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 or -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,N<2.
IFAIL=2
On entry,M<2.
IFAIL=3
On entry,LDX<N,
orLDSSPZ<M,
orLDRZ<M.
IFAIL=4
After observations with missing values were omitted, no cases remained.
IFAIL=5
After observations with missing values were omitted, only one case remained.
IFAIL=-99
An unexpected error has been triggered by this routine. Please contact NAG.
See Section 3.9 in How to Use the NAG Library and its Documentation for further information.
IFAIL=-399
Your licence key may have expired or may not have been installed correctly.
See Section 3.8 in How to Use the NAG Library and its Documentation for further information.
IFAIL=-999
Dynamic memory allocation failed.
See Section 3.7 in How to Use the NAG Library and its Documentation for further information.

7  Accuracy

G02BEF does not use additional precision arithmetic for the accumulation of scalar products, so there may be a loss of significant figures for large n.
You are warned of the need to exercise extreme care in your selection of missing values. G02BEF treats all values in the inclusive range 1±0.1X02BEF-2×xmj, where xmj is the missing value for variable j specified in XMISS.
You must therefore ensure that the missing value chosen for each variable is sufficiently different from all valid values for that variable so that none of the valid values fall within the range indicated above.

8  Parallelism and Performance

G02BEF is not threaded in any implementation.

9  Further Comments

The time taken by G02BEF depends on n and m, and the occurrence of missing values.
The routine uses a two-pass algorithm.

10  Example

This example reads in a set of data consisting of five observations on each of three variables. Missing values of 0.0 are declared for the first and third variables; no missing value is specified for the second variable. The means, standard deviations, sums of squares and cross-products about zero, and correlation-like coefficients for all three variables are then calculated and printed, omitting completely all cases containing missing values; cases 3 and 4 are therefore eliminated, leaving only three cases in the calculations.

10.1  Program Text

Program Text (g02befe.f90)

10.2  Program Data

Program Data (g02befe.d)

10.3  Program Results

Program Results (g02befe.r)


G02BEF (PDF version)
G02 Chapter Contents
G02 Chapter Introduction
NAG Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2016