cent_cosums {fromo}

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)

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.

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.

Note

The moment computations provided by fromo are numerically robust, but will often not provide the same results as the 'standard' implementations, due to differences in roundoff. We make every attempt to balance speed and robustness. User assumes all risk from using the fromo package.

Author(s)

Steven E. Pav [e-mail]

References

Terriberry, T. "Computing Higher-Order Moments Online." 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. https://www.semanticscholar.org/paper/Numerically-stable-single-pass-parallel-statistics-Bennett-Grout/a83ed72a5ba86622d5eb6395299b46d51c901265

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

Cook, J. D. "Comparing three methods of computing standard deviation." http://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)