# Calculate integrations
# INPUT:
# rands: random points as a matrix
# with dim rows and n cloumns
# integrand: the integrand expression
# constrains: inequalities which variables should satisfy
calculate <- function(rands, area, integrand, constrains)
{
n <- dim(rands)[2]
dim <- dim(rands)[1]
x <- rands[1,]
if (dim>1){y <- rands[2,]}
if (dim>2){z <- rands[3,]}
# eval constrains
c_num <- length(constrains)
constrains_eval = rep(1, n)
for (i in 1:c_num){
constrains_eval = constrains_eval*eval(parse(text=constrains[i]))
}
return(area * sum(eval(integrand)*constrains_eval)/n)
}
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