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rloopssum
Émile Boutin
Émile Boutin

Reputation: 23

Double summation to find the variance in R

I don't know how to code this summation in R. As a beginner, I don't know how to code several loops in the same function.

The equation I need to code in R is

enter image description here

Upvotes: 2

Views: 428

Answers (2)

Henry
Henry

Reputation: 6784

Taking josliber's example numbers, this can be done with simple matrix multiplication

alpha <- 1:3
sigma <- 2:4
rho <- cbind(c(1, .2, -.1), c(.2, 1, 0), c(-.1, 0, 1))
t(alpha * sigma) %*% rho %*% (alpha * sigma) 
#      [,1]
# [1,]  184

Upvotes: 3

josliber
josliber

Reputation: 44340

First you might want to make a matrix where element (i,j) is the i^th element of the alpha*sigma vector times the j^th element of that same vector. This can be accomplished with the outer function in R:

alpha <- 1:3
sigma <- 2:4
outer(alpha*sigma, alpha*sigma)
#      [,1] [,2] [,3]
# [1,]    4   12   24
# [2,]   12   36   72
# [3,]   24   72  144

The desired double summation is the sum of all elements in this multiplied element-wise with the matrix containing the rho_ij values, which can be achieved in R with * for element-wise multiplication and sum for summing the element in a matrix:

(rho <- cbind(c(1, .2, -.1), c(.2, 1, 0), c(-.1, 0, 1)))
#      [,1] [,2] [,3]
# [1,]  1.0  0.2 -0.1
# [2,]  0.2  1.0  0.0
# [3,] -0.1  0.0  1.0
sum(outer(alpha*sigma, alpha*sigma) * rho)
# [1] 184

Upvotes: 4

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