Function testNistMGH17

python/include/unsupported/test/NonLinearOptimization.cpp:1329–1386

http://www.itl.nist.gov/div898/strd/nls/data/mgh17.shtml

// http://www.itl.nist.gov/div898/strd/nls/data/mgh17.shtml
void testNistMGH17(void)
{
  const int n=5;
  int info;

  VectorXd x(n);

  /*
   * First try
   */
  x<< 50., 150., -100., 1., 2.;
  // do the computation
  MGH17_functor functor;
  LevenbergMarquardt<MGH17_functor> lm(functor);
  lm.parameters.ftol = NumTraits<double>::epsilon();
  lm.parameters.xtol = NumTraits<double>::epsilon();
  lm.parameters.maxfev = 1000;
  info = lm.minimize(x);

  // check norm^2
  VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 5.4648946975E-05);
  // check x
  VERIFY_IS_APPROX(x[0], 3.7541005211E-01);
  VERIFY_IS_APPROX(x[1], 1.9358469127E+00);
  VERIFY_IS_APPROX(x[2], -1.4646871366E+00);
  VERIFY_IS_APPROX(x[3], 1.2867534640E-02);
  VERIFY_IS_APPROX(x[4], 2.2122699662E-02);
  
  // check return value
  VERIFY_IS_EQUAL(info, 2); 
  ++g_test_level;
  VERIFY_IS_EQUAL(lm.nfev, 602);  // 602
  VERIFY_IS_EQUAL(lm.njev, 545);  // 545
  --g_test_level;
  VERIFY(lm.nfev < 602 * LM_EVAL_COUNT_TOL);
  VERIFY(lm.njev < 545 * LM_EVAL_COUNT_TOL);

  /*
   * Second try
   */
  x<< 0.5  ,1.5  ,-1   ,0.01 ,0.02;
  // do the computation
  lm.resetParameters();
  info = lm.minimize(x);

  // check return value
  VERIFY_IS_EQUAL(info, 1);
  VERIFY_IS_EQUAL(lm.nfev, 18);
  VERIFY_IS_EQUAL(lm.njev, 15);
  // check norm^2
  VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 5.4648946975E-05);
  // check x
  VERIFY_IS_APPROX(x[0], 3.7541005211E-01);
  VERIFY_IS_APPROX(x[1], 1.9358469127E+00);
  VERIFY_IS_APPROX(x[2], -1.4646871366E+00);
  VERIFY_IS_APPROX(x[3], 1.2867534640E-02);
  VERIFY_IS_APPROX(x[4], 2.2122699662E-02);
}