/*************************************************
 *            BEGIN RVL UNIT TEST 5              *
 * Test of Functional, CheckGradient and other   *
 * methods - Functional implements               *
 *          f(x) = (|x|^2)^2                     *
 *************************************************/

1. construct 5D RnSpace, random input Vector x, write out:

Vector Object
member of space:
RnSpace: simple dense vector space
dimension = 5
data container:
RnArray Local Data Container object
length = 5
samples: 
data[0] = 0.108797
data[1] = 0.728763
data[2] = 0.109489
data[3] = 0.131133
data[4] = 0.924143

2. compute value of f(x) = 2.03392
   compare to result of independent computation
   using RVL::Vector::inner = 2.03392

3. construct random direction vector:
Vector Object
member of space:
RnSpace: simple dense vector space
dimension = 5
data container:
RnArray Local Data Container object
length = 5
samples: 
data[0] = 0.312103
data[1] = 0.523156
data[2] = 0.26092
data[3] = 0.851918
data[4] = 0.940463

4. check gradient against finite difference approximation
   of directional derivative in direction p, using checkGradient.
   output: last column should converge to 2.0, indicating 2nd
   order convergence of centered diff. approx. to dir.  deriv.,
   computed as inner product of gradient and direction.
   convergence will start to degrade as relative error gets close
   to level of 32 bit machine precision, i.e. 10^{-5 or 6}.
   precise specs: success if convergence rate estimate >= 1.95
   test history reported in ut5.rpt

GradientTest returned true - success

/*************************************************
 *              END RVL UNIT TEST 5              *
 *************************************************/