Computes a correlation matrix from a sum of squares matrix

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NAG[g02bwc] NAG[nag_cov_to_corr] - Computes a correlation matrix from a sum of squares matrix

Calling Sequence

g02bwc(m, r, 'fail'=fail)

nag_cov_to_corr(. . .)

Parameters

m - integer;

On entry: , the number of variables.

Constraint: . .

r - Vector(1.., datatype=float[8]);

Note: the dimension, dim, of the array r must be at least .

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 and , , is stored in .

On exit: Pearson product-moment correlation coefficients.

These are stored packed by column corresponding to the input cross-products.

'fail'=fail - table; (optional)

The NAG error argument, see the documentation for NagError.

Description

	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.

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 variables which can be computed by a single call to g02buc (nag_sum_sqs) or a series of calls to g02btc (nag_sum_sqs_update). The sums of squares and cross-products are stored in an array packed by column and are overwritten by the correlation coefficients.

Let be the cross-product of deviations from the mean for variables ; , then the product-moment correlation coefficient, is given by

r[j*k] = c[j*k]/sqrt(c[j*j]*c[k*k])

	Error Indicators and Warnings
	"NE_BAD_PARAM" On entry, argument had an illegal value. "NE_INT" On entry, . Constraint: . "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 consult NAG for assistance. "NE_ZERO_VARIANCE" On entry, a variable has zero variance.

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

	Further Comments
	nag_cov_to_corr (g02bwc) may also be used to calculate the correlations between argument estimates from the variance-covariance matrix of the argument estimates as is given by several functions in this chapter.

Examples

>	m := 3: r := Vector([8.75689620235916, 3.697844992253459, 1.59053509294466, 4.070728079123907, 1.686058157917487, 1.929668337915273], datatype=float[8]): NAG:-g02bwc(m, r):