g02bwf calculates a matrix of Pearson product-moment correlation coefficients from sums of squares and cross-products of deviations about the mean.

2 Specification

Fortran Interface

Subroutine g02bwf (

m, r, ifail)

Integer, Intent (In)	::	m
Integer, Intent (Inout)	::	ifail
Real (Kind=nag_wp), Intent (Inout)	::	r((m*m+m)/2)

C Header Interface

#include <nag.h>

void	g02bwf_ (const Integer m, double r[], Integer ifail)

The routine may be called by the names g02bwf or nagf_correg_ssqmat_to_corrmat.

3 Description

g02bwf calculates a matrix of Pearson product-moment correlation coefficients from sums of squares and cross-products about the mean for observations on

m

variables which can be computed by a single call to g02buf or a series of calls to g02btf. The sums of squares and cross-products are stored in an array packed by column and are overwritten by the correlation coefficients.

Let

c_{j k}

be the cross-product of deviations from the mean, for

j = 1, 2, \dots, m

and

k = j, \dots, m

, then the product-moment correlation coefficient,

r_{j k}

is given by

r_{j k} = \frac{c_{j k}}{\sqrt{c_{j j} c_{k k}}} .

4 References

None.

5 Arguments

1: $m$ – Integer Input: On entry: $m$ , the number of variables.

Constraint: $m \geq 1$ .
2: $r ((m \times m + m) / 2)$ – Real (Kind=nag_wp) array Input/Output: On entry: contains the upper triangular part of the sums of squares and cross-products matrix of deviations from the mean. These are stored packed by column, i.e., the cross-product between variable $j$ and $k$ , $k \geq j$ , is stored in $r ((k \times (k - 1) / 2 + j))$ .

On exit: the Pearson product-moment correlation coefficients.
These are stored packed by column corresponding to the input cross-products.
3: $ifail$ – 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, because for this routine the values of the output arguments may be useful even if $ifail \neq 0$ on exit, the recommended value is $- 1$ . 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:

Note: in some cases g02bwf may return useful information.

$ifail = 1$: On entry, $m = 〈value〉$ .
Constraint: $m \geq 1$ .

$ifail = 2$: A variable has a zero variance. All correlations involving the variable with zero variance will be returned as zero.

$ifail = - 99$: 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

The accuracy of g02bwf is entirely dependent upon the accuracy of the elements of array r.

8 Parallelism and Performance

g02bwf is not threaded in any implementation.

9 Further Comments

g02bwf may also be used to calculate the correlations between parameter estimates from the variance-covariance matrix of the parameter estimates as is given by several routines in this chapter.

10 Example

A program to calculate the correlation matrix from raw data. The sum of squares and cross-products about the mean are calculated from the raw data by a call to g02buf. The correlation matrix is then calculated from these values.

Interfaces: FL CL AD

NAG FL Interface Introduction

G02 (Correg) Chapter Contents

G02 (Correg) Chapter Introduction

g02bw: FL CL AD

NAG FL Interfaceg02bwf (ssqmat_​to_​corrmat)

▸▿ 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
g02bwf (ssqmat_to_corrmat)