diag.rb

# Create a diagonal matrix given a vector (or an array), placing the entries
# of the vector on the diagonal of the matrix.
# For example, diag([1,2,3]) would give:
# [ 1 0 0 ]
# [ 0 2 0 ]
# [ 0 0 3 ]
# That would actually be a 2D matrix like this [[1, 0, 0], [0, 2, 0], [0, 0, 3]]
# The array returned has to be converted to a matrix by doing 
#  Matrix[ *diag(vector) ]
def diag(vector)
  n = vector.size
  matrix = []
  n.times do |i|
    matrix << Array.new(n) { |x| (x == i) ? vector[x] : 0 }
  end
  matrix
end