linear_algebra_stats: Simple Linear Algebra Functions for Statistics

In broadcast: Broadcasted Array Operations Like 'NumPy'

Simple Linear Algebra Functions for Statistics

Description

'broadcast' provides some simple Linear Algebra Functions for Statistics:
cinv();
sd_lc().

Usage

cinv(x)

sd_lc(X, vc, bad_rp = NaN)

Arguments

x	a real symmetric positive-definite square matrix.
X	a numeric (or logical) matrix of multipliers/constants
vc	the variance-covariance matrix for the (correlated) random variables.
bad_rp	if vc is not a Positive (semi-) Definite matrix, give here the value to replace bad standard deviations with.

Details

cinv()
cinv() computes the Choleski inverse of a real symmetric positive-definite square matrix.

sd_lc()
Given the linear combination X %*% b, where:

• X is a matrix of multipliers/constants;

• b is a vector of (correlated) random variables;

• vc is the symmetric variance-covariance matrix for b;

sd_lc(X, vc) computes the standard deviations for the linear combination X %*% b, without making needless copies.
sd_lc(X, vc) will use much less memory than a base 'R' approach.
sd_lc(X, vc) may possibly, but not necessarily, be faster than a base 'R' approach (depending on the Linear Algebra Library used for base 'R').

Value

For cinv():
A matrix.

For sd_lc():
A vector of standard deviations.

References

John A. Rice (2007), Mathematical Statistics and Data Analysis (6th Edition)

See Also

chol, chol2inv

Examples

vc <- datasets::ability.cov$cov
X <- matrix(rnorm(100), 100, ncol(vc))

solve(vc)
cinv(vc) # faster than `solve()`, but only works on positive definite matrices
all(round(solve(vc), 6) == round(cinv(vc), 6)) # they're the same

sd_lc(X, vc)

     

broadcast documentation built on Sept. 15, 2025, 5:08 p.m.