fromo (version 0.2.4)

cent_cosums: Multivariate centered sums; join and unjoined.

Description

Compute, join, or unjoin multivariate centered (co-) sums.

Usage

cent_cosums(v, max_order = 2L, na_omit = FALSE)
cent_comoments(v, max_order = 2L, used_df = 0L, na_omit = FALSE)
join_cent_cosums(ret1, ret2)
unjoin_cent_cosums(ret3, ret2)

Value

a multidimensional arry of dimension max_order, each side of length \(1+n\). For the case currently implemented where max_order must be 2, the output is a symmetric matrix, where the element in the 1,1 position is the count of complete) rows of v, the 2:(n+1),1 column is the mean, and the 2:(n+1),2:(n+1) is the co sums matrix, which is the covariance up to scaling by the count. cent_comoments performs this normalization for you.

Arguments

v

an \(m\) by \(n\) matrix, each row an independent observation of some \(n\) variate variable.

max_order

the maximum order of cosum to compute. For now this can only be 2; in the future higher order cosums should be possible.

na_omit

a boolean; if TRUE, then only rows of v with complete observations will be used.

used_df

the number of degrees of freedom consumed, used in the denominator of the centered moments computation. These are subtracted from the number of observations.

ret1

a multdimensional array as output by cent_cosums.

ret2

a multdimensional array as output by cent_cosums.

ret3

a multdimensional array as output by cent_cosums.

Author

Steven E. Pav

References

Terriberry, T. "Computing Higher-Order Moments Online." https://web.archive.org/web/20140423031833/http://people.xiph.org/~tterribe/notes/homs.html

J. Bennett, et. al., "Numerically Stable, Single-Pass, Parallel Statistics Algorithms," Proceedings of IEEE International Conference on Cluster Computing, 2009. tools:::Rd_expr_doi("10.1109/CLUSTR.2009.5289161")

Cook, J. D. "Accurately computing running variance." https://www.johndcook.com/standard_deviation/

Cook, J. D. "Comparing three methods of computing standard deviation." https://www.johndcook.com/blog/2008/09/26/comparing-three-methods-of-computing-standard-deviation/

See Also

cent_sums

Examples

 set.seed(1234)
 x1 <- matrix(rnorm(1e3*5,mean=1),ncol=5)
 x2 <- matrix(rnorm(1e3*5,mean=1),ncol=5)
 max_ord <- 2L
 rs1 <- cent_cosums(x1,max_ord)
 rs2 <- cent_cosums(x2,max_ord)
 rs3 <- cent_cosums(rbind(x1,x2),max_ord)
 rs3alt <- join_cent_cosums(rs1,rs2)
 stopifnot(max(abs(rs3 - rs3alt)) < 1e-7)
 rs1alt <- unjoin_cent_cosums(rs3,rs2)
 rs2alt <- unjoin_cent_cosums(rs3,rs1)
 stopifnot(max(abs(rs1 - rs1alt)) < 1e-7)
 stopifnot(max(abs(rs2 - rs2alt)) < 1e-7)