# Description:
# Solves the minimum norm of a singular linear least squares problem.
#
# The objective function for this problem is
#       f(x) = (x(1) + x(2) - 1)^2 + (x(1) + x(2) - 2)^2
#
# The partial of f with respect to x(1) or with respect to x(2) is
#       (x(1) + x(2) - 1) + (x(1) + x(2) - 2)
#
# The function f is convex, it is minimized when its partials are zero; i.e.,
#       2 * x(1) + 2 * x(2) - 3 = 0
#       x(2) = 1.5 - x(1)
#
# linlsq will return the x that minimizes |x|^2 subject to x(2) = 1.5 - x(1)
#       g(x(1)) = |x|^2 = x(1)^2 + x(2)^2 = x(1)^2 + (1.5 - x(1))^2
#       g'(x(1)) = 2 * x(1) + 2 * (1.5 - x(1)) = 0 implies that x(1) = .75
#
#
# f(x) = | A * x - b |^2 where A and b are defined as
#
clear
A = { [1., 1.], [1., 1.] }
b = {1., 2.}
eps = 1e-7
x = linlsq(A, b, eps)
print "x =", x
	  

x = {
   0.75000
   0.75000
}