knitr::opts_chunk$set( message = FALSE, warning = FALSE, error = FALSE, tidy = FALSE, cache = FALSE )
Version 2.0 integrates two well-known cubature libraries in one place:
It also provides a single function cubintegrate
that allows one to
call all methods in a uniform fashion, as I explain below.
N.B. One has to be aware that there are cases where one library will integrate a function while the other won't, and in some cases, provide somewhat different answers. That still makes sense and depends on the underlying methodology used.
Following a suggestion by Simen Guare, we now have a function
cubintegrate
that can be used to try out various integration methods
easily. Some examples.
library(cubature) m <- 3 sigma <- diag(3) sigma[2,1] <- sigma[1, 2] <- 3/5 ; sigma[3,1] <- sigma[1, 3] <- 1/3 sigma[3,2] <- sigma[2, 3] <- 11/15 logdet <- sum(log(eigen(sigma, symmetric = TRUE, only.values = TRUE)$values)) my_dmvnorm <- function (x, mean, sigma, logdet) { x <- matrix(x, ncol = length(x)) distval <- stats::mahalanobis(x, center = mean, cov = sigma) exp(-(3 * log(2 * pi) + logdet + distval)/2) }
First we try the scalar invocation with hcubature
.
cubintegrate(f = my_dmvnorm, lower = rep(-0.5, 3), upper = c(1, 4, 2), method = "pcubature", mean = rep(0, m), sigma = sigma, logdet = logdet)
We can compare that with Cuba's cuhre
.
cubintegrate(f = my_dmvnorm, lower = rep(-0.5, 3), upper = c(1, 4, 2), method = "cuhre", mean = rep(0, m), sigma = sigma, logdet = logdet)
The Cuba routine can take various further arguments; see for example,
the help on cuhre
. Such arguments can be directly passed to
cubintegrate
.
cubintegrate(f = my_dmvnorm, lower = rep(-0.5, 3), upper = c(1, 4, 2), method = "cuhre", mean = rep(0, m), sigma = sigma, logdet = logdet, flags = list(verbose = 2))
As there are many such method-specific arguments, you may find the
function default_args()
useful.
str(default_args())
cubintegrate
provides vector intefaces too: the parameter nVec
is
by default 1, indicating a scalar interface. Any value > 1 results in
a vectorized call. So f
has to be constructed appropriately, thus:
my_dmvnorm_v <- function (x, mean, sigma, logdet) { distval <- stats::mahalanobis(t(x), center = mean, cov = sigma) exp(matrix(-(3 * log(2 * pi) + logdet + distval)/2, ncol = ncol(x))) }
Here, the two underlying C libraries differ. The cubature library
manages the number of points used in vectorization dynamically and
this number can even vary from call to call. So any value of nVec
greater than 1 is merely a flag to use vectorization. The Cuba C
library on the other hand, will use the actual value of nVec
.
cubintegrate(f = my_dmvnorm_v, lower = rep(-0.5, 3), upper = c(1, 4, 2), method = "pcubature", mean = rep(0, m), sigma = sigma, logdet = logdet, nVec = 128)
cubintegrate(f = my_dmvnorm_v, lower = rep(-0.5, 3), upper = c(1, 4, 2), method = "cuhre", mean = rep(0, m), sigma = sigma, logdet = logdet, nVec = 128)
sessionInfo()
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