# mxRex09.r   
 #
 # my solutions to 'Some Matrix Exercises in R'
 #
 # (1) Create X
  n <- 7            # arbitrary size
 #
  X <- matrix(c(rep(1,n),(1:n),(1:n)*(1:n)),n,3)
  X
 #  changing to arbitrary degree is harder
  diff(diff(X))
 #
 # (2) Create A
  A <- matrix(c(1,-2,1,rep(0,n-2)),n-2,n,byrow=TRUE)
  A
 #     Multiply AX
  A %*% X
 #
 #
 # (3) Toeplitz matrix
 # first way
  Z <- matrix(0,n,n)          # create zero matrix 
  E <- abs( row(Z) - col(Z) )
  V <- log(1+E)
  V
 # second way
  E <- abs( matrix(1:n,n,n) - matrix(1:n,n,n,byrow=T) )
  V <- log(1+E)
  V
 #
 # (4) V(i,j) = max(i,j)
 #  similar to previous approach
  R <- matrix(1:n,n,n)
  C <- matrix(1:n,n,n,byrow=T) 
  V <- ( (R+C) + abs(R-C) )/2
  V
 # try another way
  V <- pmax(R,C)
  V
 # (5) J(i,j) = 1 only where i+j=n+1
  J <- diag(rep(1,n))[rev(1:n),]
  J
  J <- diag(1,n)[rev(1:n),]
  J
 #
 # (6) K = 2x? matrix of all combinations
  K <- matrix(c(rep((1:3),4),rep((1:4),each=3)),nrow=2,byrow=TRUE)
  K
 #
 # done -- clean up 
   rm(list=ls())
   q()