nag_cov_to_corr (g02bwc) (PDF version)
g02 Chapter Contents
g02 Chapter Introduction
NAG C Library Manual

NAG Library Function Document

nag_cov_to_corr (g02bwc)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_cov_to_corr (g02bwc) calculates a matrix of Pearson product-moment correlation coefficients from sums of squares and cross-products of deviations about the mean.

2  Specification

#include <nag.h>
#include <nagg02.h>
void  nag_cov_to_corr (Integer m, double r[], NagError *fail)

3  Description

nag_cov_to_corr (g02bwc) 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 nag_sum_sqs (g02buc) or a series of calls to nag_sum_sqs_update (g02btc). 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:     mIntegerInput
On entry: m, the number of variables.
Constraint: m1.
2:     r[m×m+m/2]doubleInput/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-1].
On exit: Pearson product-moment correlation coefficients.
These are stored packed by column corresponding to the input cross-products.
3:     failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

NE_BAD_PARAM
On entry, argument value had an illegal value.
NE_INT
On entry, m=value.
Constraint: m1.
NE_INTERNAL_ERROR
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
NE_ZERO_VARIANCE
On entry, a variable has zero variance.

7  Accuracy

The accuracy of nag_cov_to_corr (g02bwc) is entirely dependent upon the accuracy of the elements of array r.

8  Further Comments

nag_cov_to_corr (g02bwc) 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 functions in this chapter.

9  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 nag_sum_sqs (g02buc). The correlation matrix is then calculated from these values.

9.1  Program Text

Program Text (g02bwce.c)

9.2  Program Data

Program Data (g02bwce.d)

9.3  Program Results

Program Results (g02bwce.r)


nag_cov_to_corr (g02bwc) (PDF version)
g02 Chapter Contents
g02 Chapter Introduction
NAG C Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2012