naginterfaces.library.correg.ssqmat_​to_​corrmat

naginterfaces.library.correg.ssqmat_to_corrmat(m, r)

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

For full information please refer to the NAG Library document for g02bw

https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/g02/g02bwf.html

Parameters

mint

$m$, the number of variables.

rfloat, array-like, shape $\left((m\times m+m)/2\right)$

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 $k$, $k\ge j$, is stored in $r[(k\times (k-1)/2+j)-1]$.

Returns

rfloat, ndarray, shape $\left((m\times m+m)/2\right)$

The Pearson product-moment correlation coefficients.

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

Raises

NagValueError

(errno $1$)

On entry, $m=⟨value⟩$.

Constraint: $m\ge 1$.

Warns

NagAlgorithmicWarning

(errno $2$)

A variable has a zero variance. All correlations involving the variable with zero variance will be returned as zero.

Notes

ssqmat_to_corrmat 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 ssqmat() or a series of calls to ssqmat_update(). The sums of squares and cross-products are stored in an array packed by column and are overwritten by the correlation coefficients.

Let $c_{jk}$ be the cross-product of deviations from the mean, for $\text{k}=j,\dots ,m$, for $\text{j}=1,2,\dots ,m$, then the product-moment correlation coefficient, $r_{jk}$ is given by

$$r_{jk}=\frac{c_{jk}}{\sqrt{c_{jj}{c}_{kk}}}\text{.}$$