NAG FL Interface
g02bkf (coeffs_​zero_​subset)

1 Purpose

g02bkf computes means and standard deviations, sums of squares and cross-products about zero, and correlation-like coefficients for selected variables.

2 Specification

Fortran Interface
Subroutine g02bkf ( n, m, x, ldx, nvars, kvar, xbar, std, sspz, ldsspz, rz, ldrz, ifail)
Integer, Intent (In) :: n, m, ldx, nvars, kvar(nvars), ldsspz, ldrz
Integer, Intent (Inout) :: ifail
Real (Kind=nag_wp), Intent (In) :: x(ldx,m)
Real (Kind=nag_wp), Intent (Inout) :: sspz(ldsspz,nvars), rz(ldrz,nvars)
Real (Kind=nag_wp), Intent (Out) :: xbar(nvars), std(nvars)
C Header Interface
#include <nag.h>
void  g02bkf_ (const Integer *n, const Integer *m, const double x[], const Integer *ldx, const Integer *nvars, const Integer kvar[], double xbar[], double std[], double sspz[], const Integer *ldsspz, double rz[], const Integer *ldrz, Integer *ifail)
The routine may be called by the names g02bkf or nagf_correg_coeffs_zero_subset.

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,,m m2,  
where xij is the ith observation on the jth variable, together with the subset of these variables, v1,v2,,vp, for which information is required.
The quantities calculated are:
  1. (a)Means:
    x¯j=i=1nxijn,  j=v1,v2,,vp.  
  2. (b)Standard deviations:
    sj=1n- 1 i= 1n xij-x¯j 2,   j=v1,v2,,vp.  
  3. (c)Sums of squares and cross-products about zero:
    S~jk=i=1nxijxik,  j,k=v1,v2,,vp.  
  4. (d)Correlation-like coefficients:
    R~jk=S~jkS~jjS~kk ,   j,k=v1,v2,,vp.  
    If S~jj or S~kk is zero, R~jk is set to zero.

4 References

None.

5 Arguments

1: n Integer Input
On entry: n, the number of observations or cases.
Constraint: n2.
2: m Integer Input
On entry: m, the number of variables.
Constraint: m2.
3: xldxm Real (Kind=nag_wp) array Input
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 Integer Input
On entry: the first dimension of the array x as declared in the (sub)program from which g02bkf is called.
Constraint: ldxn.
5: nvars Integer Input
On entry: p, the number of variables for which information is required.
Constraint: 2nvarsm.
6: kvarnvars Integer array Input
On entry: kvarj must be set to the column number in x of the jth variable for which information is required, for j=1,2,,p.
Constraint: 1kvarjm, for j=1,2,,p.
7: xbarnvars Real (Kind=nag_wp) array Output
On exit: the mean value, x¯j, of the variable specified in kvarj, for j=1,2,,p.
8: stdnvars Real (Kind=nag_wp) array Output
On exit: the standard deviation, sj, of the variable specified in kvarj, for j=1,2,,p.
9: sspzldsspznvars Real (Kind=nag_wp) array Output
On exit: sspzjk is the cross-product about zero, S~jk, for the variables specified in kvarj and kvark, for j=1,2,,p and k=1,2,,p.
10: ldsspz Integer Input
On entry: the first dimension of the array sspz as declared in the (sub)program from which g02bkf is called.
Constraint: ldsspznvars.
11: rzldrznvars Real (Kind=nag_wp) array Output
On exit: rzjk is the correlation-like coefficient, R~jk, between the variables specified in kvarj and kvark, for j=1,2,,p and k=1,2,,p.
12: ldrz Integer Input
On entry: the first dimension of the array rz as declared in the (sub)program from which g02bkf is called.
Constraint: ldrznvars.
13: ifail Integer Input/Output
On entry: ifail must be set to 0, -1 or 1. If you are unfamiliar with this argument you should refer to Section 4 in the Introduction to the NAG Library FL Interface 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=value.
Constraint: n2.
ifail=2
On entry, nvars=value and m=value.
Constraint: nvars2 and nvarsm.
ifail=3
On entry, ldrz=value and nvars=value.
Constraint: ldrznvars.
On entry, ldsspz=value and nvars=value.
Constraint: ldsspznvars.
On entry, ldx=value and n=value.
Constraint: ldxn.
ifail=4
On entry, i=value, kvari=value and m=value.
Constraint: 1kvarim.
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

g02bkf does not use additional precision arithmetic for the accumulation of scalar products, so there may be a loss of significant figures for large n.

8 Parallelism and Performance

g02bkf is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.
g02bkf makes calls to BLAS and/or LAPACK routines, which may be threaded within the vendor library used by this implementation. Consult the documentation for the vendor library for further information.
Please consult the X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this routine. Please also consult the Users' Note for your implementation for any additional implementation-specific information.

9 Further Comments

The time taken by g02bkf depends on n and p.
The routine uses a two-pass algorithm.

9.1 Internal Changes

Internal changes have been made to this routine as follows:
For details of all known issues which have been reported for the NAG Library please refer to the Known Issues.

10 Example

This example reads in a set of data consisting of five observations on each of four variables. The means, standard deviations, sums of squares and cross-products about zero, and correlation-like coefficients for the fourth, first and second variables are then calculated and printed.

10.1 Program Text

Program Text (g02bkfe.f90)

10.2 Program Data

Program Data (g02bkfe.d)

10.3 Program Results

Program Results (g02bkfe.r)