# naginterfaces.library.correg.corrmat¶

naginterfaces.library.correg.corrmat(x, nonzwt='W', wt=None)[source]

corrmat calculates the sample means, the standard deviations, the variance-covariance matrix, and the matrix of Pearson product-moment correlation coefficients for a set of data. Weights may be used.

For full information please refer to the NAG Library document for g02bx

https://www.nag.com/numeric/nl/nagdoc_27.1/flhtml/g02/g02bxf.html

Parameters
xfloat, array-like, shape

must contain the th observation for the th variable, for , for .

nonzwtstr, length 1, optional

The variance calculation uses a divisor which is either the number of weights or the number of nonzero weights.

wtNone or float, array-like, shape , optional

, the optional frequency weighting for each observation, with . Usually will be an integral value corresponding to the number of observations associated with the th data value, or zero if the th data value is to be ignored. If , is set to for all .

Returns
xbarfloat, ndarray, shape

The sample means. contains the mean of the th variable.

stdfloat, ndarray, shape

The standard deviations. contains the standard deviation for the th variable.

vfloat, ndarray, shape

The variance-covariance matrix. contains the covariance between variables and , for , for .

rfloat, ndarray, shape

The matrix of Pearson product-moment correlation coefficients. contains the correlation coefficient between variables and .

Raises
NagValueError
(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: , or

(errno )

On entry, at least one value of is negative.

Constraint: , for .

(errno )

On entry, observations have nonzero weight.

Constraint: at least two observations must have a nonzero weight.

(errno )

On entry, Sum of the weights is .

Constraint: Sum of the weights must be greater than .

Warns
NagAlgorithmicWarning
(errno )

A variable has a zero variance. In this case and are returned as calculated but will contain zero for any correlation involving a variable with zero variance.

Notes

For observations on variables the one-pass algorithm of West (1979) as implemented in ssqmat() is used to compute the means, the standard deviations, the variance-covariance matrix, and the Pearson product-moment correlation matrix for selected variables. Suitables weights may be used to indicate multiple observations and to remove missing values. The quantities are defined by:

1. The means

1. The variance-covariance matrix

1. The standard deviations

1. The Pearson product-moment correlation coefficients

where is the value of the th observation on the th variable and is the weight for the th observation which will be in the unweighted case.

Note that the denominator for the variance-covariance is , so the weights should be scaled so that the sum of weights reflects the true sample size.

References

Chan, T F, Golub, G H and Leveque, R J, 1982, Updating Formulae and a Pairwise Algorithm for Computing Sample Variances, Compstat, Physica-Verlag

West, D H D, 1979, Updating mean and variance estimates: An improved method, Comm. ACM (22), 532–555