#
# Rosenbrock function for lecture "Numerical Optimization".
#
# Author: Sangkyun Lee (sangkyun.lee@tu-dortmund.de)
#

#
# Helper functions
#

# Create a column vector (matrix with a single column in R) for the given list l.
# Ex. x = vec(c(1.2, 2.4))
vec <- function(l) {
  len = length(l);
  v <- matrix(l, nrow=len, ncol=1);
  return(v)
}
# Create a matrix for the given list l with the given number of rows(r) and column(r)
# Ex. x = mat(c(1,2,3,4), 2, 2)
mat <- function(l, r, c, byrow=TRUE) {
  len = length(l);
  if(!(len = r*c)) {
    print("Error in mat(): length of l must be r x c")
    return (NULL);
  }
  m <- matrix(l, nrow=r, ncol=c, byrow=byrow);
  return(m)
}

#
# Compute the inverse of a square matrix A
#
inv <- function(A) {
  return(solve(A))
}

#
# Compute the 2-norm of a vector or a matrix
#
norm2 <- function(A) {
  return(norm(A, type="2"))
}

#
# Rosenbrock function (function value, gradient, and Hessian) for a given x = (x1,x2).
# x must be a column vector (a 2x1 matrix in R)
#
f <- function(x) {
  if (!(class(x)=="matrix" && nrow(x)==2 && ncol(x)==1)) {
    print("Error in f(x): x must be 2x1 matrix");
    return (NULL);
  } 
  x1 = x[1];
  x2 = x[2];
  val = 100*(x2-x1^2)^2 + (1-x1)^2;
  return(val);
}

g <- function(x) {
  if (!(class(x)=="matrix" && nrow(x)==2 && ncol(x)==1)) {
    print("Error in f(x): x must be 2x1 matrix");
    return (NULL);
  } 
  x1 = x[1];
  x2 = x[2];
  val = vec( c( -400*(x2-x1^2)*x1 - 2*(1-x1), 200*(x2-x1^2) ) )
  return(val)
}

H <- function(x) {
  if (!(class(x)=="matrix" && nrow(x)==2 && ncol(x)==1)) {
    print("Error in f(x): x must be 2x1 matrix");
    return (NULL);
  } 
  x1 = x[1];
  x2 = x[2];
  val = mat( c( -400*(x2-3*x1^2)+2, -400*x1, -400*x1, 200 ), 2, 2 )
  return(val)
}