NAG FL Interface
g02bwf (ssqmat_​to_​corrmat)

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1 Purpose

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 cjk be the cross-product of deviations from the mean, for j=1,2,,m and k=j,,m, then the product-moment correlation coefficient, rjk is given by
rjk=cjkcjjckk .  

4 References

None.

5 Arguments

1: m Integer Input
On entry: m, the number of variables.
Constraint: m1.
2: r((m×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, kj, is stored in r((k×(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 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 −1 is recommended since useful values can be provided in some output arguments even when ifail0 on exit. 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:
Note: in some cases g02bwf may return useful information.
ifail=1
On entry, m=value.
Constraint: m1.
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.

10.1 Program Text

Program Text (g02bwfe.f90)

10.2 Program Data

Program Data (g02bwfe.d)

10.3 Program Results

Program Results (g02bwfe.r)