R 与矩阵

library(Matrix)
A <- matrix(1:18,3,6)
#求秩
rankMatrix(A)
#奇异值分解
svd(A)
#特征值分解（方阵）
B <- matrix(1:9,3)
eigen(B)

library(numDeriv)
sc2.f <- function(x){
  n <- length(x)
  sum((1:n) * (exp(x) - x)) / n
}

sc2.g <- function(x){
  n <- length(x)
  (1:n) * (exp(x) - 1) / n
}

x0 <- rnorm(5)
hess <- hessian(func=sc2.f, x=x0)
hessc <- hessian(func=sc2.f, x=x0, "complex")
all.equal(hess, hessc, tolerance = .Machine$double.eps)

#  Hessian = Jacobian of the gradient
jac  <- jacobian(func=sc2.g, x=x0)
jacc <- jacobian(func=sc2.g, x=x0, "complex")
all.equal(hess, jac, tolerance = .Machine$double.eps)
all.equal(hessc, jacc, tolerance = .Machine$double.eps)