Matrix multiplication of random variables.
x %**% y
# S3 method for rvar
matrixOps(x, y)(multiple options) The object to be postmultiplied by y:
If a vector is used, it is treated as a row vector.
(multiple options) The object to be premultiplied by x:
If a vector is used, it is treated as a column vector.
An rvar representing the matrix product of x and y.
If x or y are vectors, they are converted into matrices prior to multiplication, with x
converted to a row vector and y to a column vector. Numerics and logicals can be multiplied
by rvars and are broadcasted across all draws of the rvar argument. Tensor multiplication
is used to efficiently multiply matrices across draws, so if either x or y is an rvar,
x %**% y will be much faster than rdo(x %*% y).
In R >= 4.3, you can also use %*% in place of %**% for matrix multiplication
of rvars. In R < 4.3, S3 classes cannot properly override %*%, so
you must use %**% for matrix multiplication of rvars.
# d has mu (mean vector of length 3) and Sigma (3x3 covariance matrix)
d <- as_draws_rvars(example_draws("multi_normal"))
d$Sigma
#> rvar<100,4>[3,3] mean ± sd:
#> [,1] [,2] [,3]
#> [1,] 1.28 ± 0.17 0.53 ± 0.20 -0.40 ± 0.28
#> [2,] 0.53 ± 0.20 3.67 ± 0.45 -2.10 ± 0.48
#> [3,] -0.40 ± 0.28 -2.10 ± 0.48 8.12 ± 0.95
# trivial example: multiplication by a non-random matrix
d$Sigma %**% diag(1:3)
#> rvar<100,4>[3,3] mean ± sd:
#> [,1] [,2] [,3]
#> [1,] 1.28 ± 0.17 1.05 ± 0.40 -1.21 ± 0.85
#> [2,] 0.53 ± 0.20 7.33 ± 0.89 -6.30 ± 1.44
#> [3,] -0.40 ± 0.28 -4.20 ± 0.96 24.35 ± 2.84
# Decompose Sigma into R s.t. R'R = Sigma ...
R <- chol(d$Sigma)
# ... and recreate Sigma using matrix multiplication
t(R) %**% R
#> rvar<100,4>[3,3] mean ± sd:
#> [,1] [,2] [,3]
#> [1,] 1.28 ± 0.17 0.53 ± 0.20 -0.40 ± 0.28
#> [2,] 0.53 ± 0.20 3.67 ± 0.45 -2.10 ± 0.48
#> [3,] -0.40 ± 0.28 -2.10 ± 0.48 8.12 ± 0.95