Function testNistRat43

python/include/unsupported/test/NonLinearOptimization.cpp:1688–1739

http://www.itl.nist.gov/div898/strd/nls/data/ratkowsky3.shtml

// http://www.itl.nist.gov/div898/strd/nls/data/ratkowsky3.shtml
void testNistRat43(void)
{
  const int n=4;
  int info;

  VectorXd x(n);

  /*
   * First try
   */
  x<< 100., 10., 1., 1.;
  // do the computation
  rat43_functor functor;
  LevenbergMarquardt<rat43_functor> lm(functor);
  lm.parameters.ftol = 1.E6*NumTraits<double>::epsilon();
  lm.parameters.xtol = 1.E6*NumTraits<double>::epsilon();
  info = lm.minimize(x);

  // check return value
  VERIFY_IS_EQUAL(info, 1);
  VERIFY_IS_EQUAL(lm.nfev, 27);
  VERIFY_IS_EQUAL(lm.njev, 20);
  // check norm^2
  VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 8.7864049080E+03);
  // check x
  VERIFY_IS_APPROX(x[0], 6.9964151270E+02);
  VERIFY_IS_APPROX(x[1], 5.2771253025E+00);
  VERIFY_IS_APPROX(x[2], 7.5962938329E-01);
  VERIFY_IS_APPROX(x[3], 1.2792483859E+00);

  /*
   * Second try
   */
  x<< 700., 5., 0.75, 1.3;
  // do the computation
  lm.resetParameters();
  lm.parameters.ftol = 1.E5*NumTraits<double>::epsilon();
  lm.parameters.xtol = 1.E5*NumTraits<double>::epsilon();
  info = lm.minimize(x);

  // check return value
  VERIFY_IS_EQUAL(info, 1);
  VERIFY_IS_EQUAL(lm.nfev, 9);
  VERIFY_IS_EQUAL(lm.njev, 8);
  // check norm^2
  VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 8.7864049080E+03);
  // check x
  VERIFY_IS_APPROX(x[0], 6.9964151270E+02);
  VERIFY_IS_APPROX(x[1], 5.2771253025E+00);
  VERIFY_IS_APPROX(x[2], 7.5962938329E-01);
  VERIFY_IS_APPROX(x[3], 1.2792483859E+00);
}