naginterfaces.library.correg.ssqmat_update¶
- naginterfaces.library.correg.ssqmat_update(wt, x, sw, xbar, c, mean='M')[source]¶
ssqmat_update
updates the sample means and sums of squares and cross-products, or sums of squares and cross-products of deviations about the mean, for a new observation. The data may be weighted.For full information please refer to the NAG Library document for g02bt
https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/g02/g02btf.html
- Parameters
- wtfloat
The weight to use for the current observation, .
For unweighted means and cross-products set .
The use of a suitable negative value of , e.g., will have the effect of deleting the observation.
- xfloat, array-like, shape
must contain the value of the th variable for the current observation, .
- swfloat
The sum of weights for the previous observations, .
The update procedure is initialized.
All elements of and are set to zero.
- xbarfloat, array-like, shape
If , is initialized, otherwise must contain the weighted mean of the th variable for the previous observations, , for .
- cfloat, array-like, shape
If , must contain the upper triangular part of the matrix of weighted sums of squares and cross-products or weighted sums of squares and cross-products of deviations about the mean. It is stored packed form by column, i.e., the cross-product between the th and th variable, , is stored in .
- meanstr, length 1, optional
Indicates whether
ssqmat_update
is to calculate sums of squares and cross-products, or sums of squares and cross-products of deviations about the mean.The sums of squares and cross-products of deviations about the mean are calculated.
The sums of squares and cross-products are calculated.
- Returns
- swfloat
Contains the updated sum of weights, .
- xbarfloat, ndarray, shape
contains the weighted mean of the th variable, , for .
- cfloat, ndarray, shape
The update sums of squares and cross-products stored as on input.
- Raises
- NagValueError
- (errno )
On entry, .
Constraint: .
- (errno )
On entry, .
Constraint: .
- (errno )
On entry, .
Constraint: .
- (errno )
On entry, .
Constraint: .
- (errno )
On entry, .
Constraint: or .
- Notes
ssqmat_update
is an adaptation of West’s WV2 algorithm; see West (1979). This function updates the weighted means of variables and weighted sums of squares and cross-products or weighted sums of squares and cross-products of deviations about the mean for observations on variables , for . For the first observations let the mean of the th variable be , the cross-product about the mean for the th and th variables be and the sum of weights be . These are updated by the th observation, , for , with weight as follows:and
The algorithm is initialized by taking , the first observation and .
For the unweighted case and for all .
- 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