计算矩阵被积函数R中的多维积分

我试图计算矩阵的二重积分，我希望结果是矩阵

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fn让我们看一个简单的被积函数，我们知道积分的值：

fn <- function(u){
  u %*% t(u) 
}

cubature::cubintegrate(f = fn, lower = c(0,0), upper = c(1,1), method = "cuhre", 
                       fDim = 4)$integral
# [1] 0.3333333 0.2500000 0.2500000 0.3333333

# integral_0^1 integral_0^1 x^2 dxdy = 1/3
# integral_0^1 integral_0^1 x*y dxdy = 1/2*1/2 = 1/4

fn
fn <- function(u){
  u %*% t(u) 
}

cubature::cubintegrate(f = fn, lower = c(0,0), upper = c(1,1), method = "cuhre", 
                       fDim = 4)$integral
# [1] 0.3333333 0.2500000 0.2500000 0.3333333

# integral_0^1 integral_0^1 x^2 dxdy = 1/3
# integral_0^1 integral_0^1 x*y dxdy = 1/2*1/2 = 1/4