当在两个矩阵上执行时，all.equal 在 R 中做了什么

Question

What does all.equal do in R when it is executed on two matrices like bellow? What is Mean relative difference and how is it calculated?

a <-
  matrix(c(4, 1, 1, 4),
         nrow = 2,
         dimnames = list(Guess = c("Milk", "Tea"),
                         Truth = c("Milk", "Tea")))
b <-
matrix(c(2, 3, 3, 2),
       nrow = 2,
       dimnames = list(Guess = c("Milk", "Tea"),
                       Truth = c("Milk", "Tea")))

all.equal(a, b)

Answer 1

For numeric input mean relative difference is calculated as absolute difference between both vectors as compared to first vector. So something like

mean(abs(a-b))/mean(abs(a))
#[1] 0.8

Answer 2

This is a weird behavior. "Istruing" all equal would produce expected output (FALSE). Sorry if I'm not really answering the question.

a <-
  matrix(c(4, 1, 1, 4),
         nrow = 2,
         dimnames = list(Guess = c("Milk", "Tea"),
                         Truth = c("Milk", "Tea")))
b <-
  matrix(c(2, 3, 3, 2),
         nrow = 2,
         dimnames = list(Guess = c("Milk", "Tea"),
                         Truth = c("Milk", "Tea")))

isTRUE(all.equal(a, b))

a <-
  matrix(c(4, 1, 1, 4),
         nrow = 2,
         dimnames = list(Guess = c("Milk", "Tea"),
                         Truth = c("Milk", "Tea")))
b <-
  matrix(c(4, 1, 1, 4),
         nrow = 2,
         dimnames = list(Guess = c("Milk", "Tea"),
                         Truth = c("Milk", "Tea")))

isTRUE(all.equal(a, b))