NAG FL Interface
g02bdf (coeffs_​zero)

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1 Purpose

g02bdf computes means and standard deviations of variables, sums of squares and cross-products about zero, and correlation-like coefficients for a set of data.

2 Specification

Fortran Interface
Subroutine g02bdf ( n, m, x, ldx, xbar, std, sspz, ldsspz, rz, ldrz, ifail)
Integer, Intent (In) :: n, m, ldx, ldsspz, ldrz
Integer, Intent (Inout) :: ifail
Real (Kind=nag_wp), Intent (In) :: x(ldx,m)
Real (Kind=nag_wp), Intent (Inout) :: sspz(ldsspz,m), rz(ldrz,m)
Real (Kind=nag_wp), Intent (Out) :: xbar(m), std(m)
C Header Interface
#include <nag.h>
void  g02bdf_ (const Integer *n, const Integer *m, const double x[], const Integer *ldx, double xbar[], double std[], double sspz[], const Integer *ldsspz, double rz[], const Integer *ldrz, Integer *ifail)
The routine may be called by the names g02bdf or nagf_correg_coeffs_zero.

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.
The quantities calculated are:
  1. (a)Means:
    x¯j=1ni=1nxij,  j=1,2,,m.  
  2. (b)Standard deviations:
    sj=1n- 1 i= 1n (xij-x¯j) 2,   j= 1,2,,m.  
  3. (c)Sums of squares and cross-products about zero:
    S~jk=i=1nxijxik,  j,k=1,2,,m.  
  4. (d)Correlation-like coefficients:
    R~jk=S~jkS~jjS~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 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: x(ldx,m) Real (Kind=nag_wp) array Input
On entry: x(i,j) must be set to the value of xij, 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 g02bdf is called.
Constraint: ldxn.
5: xbar(m) Real (Kind=nag_wp) array Output
On exit: xbar(j) contains the mean value, x¯j, of the jth variable, for j=1,2,,m.
6: std(m) Real (Kind=nag_wp) array Output
On exit: the standard deviation, sj, of the jth variable, for j=1,2,,m.
7: sspz(ldsspz,m) Real (Kind=nag_wp) array Output
On exit: sspz(j,k) is the cross-product about zero, S~jk, for j=1,2,,m and k=1,2,,m.
8: ldsspz Integer Input
On entry: the first dimension of the array sspz as declared in the (sub)program from which g02bdf is called.
Constraint: ldsspzm.
9: rz(ldrz,m) Real (Kind=nag_wp) array Output
On exit: rz(j,k) is the correlation-like coefficient, R~jk, between the jth and kth variables, for j=1,2,,m and k=1,2,,m.
10: ldrz Integer Input
On entry: the first dimension of the array rz as declared in the (sub)program from which g02bdf is called.
Constraint: ldrzm.
11: 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 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, m=value.
Constraint: m2.
ifail=3
On entry, ldrz=value and m=value.
Constraint: ldrzm.
On entry, ldsspz=value and m=value.
Constraint: ldsspzm.
On entry, ldx=value and n=value.
Constraint: ldxn.
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

g02bdf 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

Background information to multithreading can be found in the Multithreading documentation.
g02bdf is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.
g02bdf 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 g02bdf depends on n and m.
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 three variables. 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.

10.1 Program Text

Program Text (g02bdfe.f90)

10.2 Program Data

Program Data (g02bdfe.d)

10.3 Program Results

Program Results (g02bdfe.r)