rename test for coherency with previous renaming of the module

1 files changed, 1847 insertions, 0 deletions

diff --git a/unsupported/test/NonLinearOptimization.cpp b/unsupported/test/NonLinearOptimization.cpp
new file mode 100644
index 000000000..4106c1e38
--- /dev/null
+++ b/unsupported/test/NonLinearOptimization.cpp
@@ -0,0 +1,1847 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Thomas Capricelli <orzel@freehackers.org>
+
+#include <stdio.h>
+
+#include "main.h"
+#include <unsupported/Eigen/NonLinearOptimization>
+
+int fcn_chkder(const VectorXd &x, VectorXd &fvec, MatrixXd &fjac, int iflag)
+{
+    /*      subroutine fcn for chkder example. */
+
+    int i;
+    assert(15 ==  fvec.size());
+    assert(3 ==  x.size());
+    double tmp1, tmp2, tmp3, tmp4;
+    double y[15]={1.4e-1, 1.8e-1, 2.2e-1, 2.5e-1, 2.9e-1, 3.2e-1, 3.5e-1,
+        3.9e-1, 3.7e-1, 5.8e-1, 7.3e-1, 9.6e-1, 1.34, 2.1, 4.39};
+
+
+    if (iflag == 0) 
+        return 0;
+
+    if (iflag != 2) 
+        for (i=0; i<15; i++) {
+            tmp1 = i+1;
+            tmp2 = 16-i-1;
+            tmp3 = tmp1;
+            if (i >= 8) tmp3 = tmp2;
+            fvec[i] = y[i] - (x[0] + tmp1/(x[1]*tmp2 + x[2]*tmp3));
+        }
+    else {
+        for (i = 0; i < 15; i++) {
+            tmp1 = i+1;
+            tmp2 = 16-i-1;
+
+            /* error introduced into next statement for illustration. */
+            /* corrected statement should read    tmp3 = tmp1 . */
+
+            tmp3 = tmp2;
+            if (i >= 8) tmp3 = tmp2;
+            tmp4 = (x[1]*tmp2 + x[2]*tmp3); tmp4=tmp4*tmp4;
+            fjac(i,0) = -1.;
+            fjac(i,1) = tmp1*tmp2/tmp4;
+            fjac(i,2) = tmp1*tmp3/tmp4;
+        }
+    }
+    return 0;
+}
+
+
+void testChkder()
+{
+  const int m=15, n=3;
+  VectorXd x(n), fvec(m), xp, fvecp(m), err;
+  MatrixXd fjac(m,n);
+  VectorXi ipvt;
+
+  /*      the following values should be suitable for */
+  /*      checking the jacobian matrix. */
+  x << 9.2e-1, 1.3e-1, 5.4e-1;
+
+  ei_chkder(x, fvec, fjac, xp, fvecp, 1, err);
+  fcn_chkder(x, fvec, fjac, 1);
+  fcn_chkder(x, fvec, fjac, 2);
+  fcn_chkder(xp, fvecp, fjac, 1);
+  ei_chkder(x, fvec, fjac, xp, fvecp, 2, err);
+
+  fvecp -= fvec;
+
+  // check those
+  VectorXd fvec_ref(m), fvecp_ref(m), err_ref(m);
+  fvec_ref <<
+      -1.181606, -1.429655, -1.606344,
+      -1.745269, -1.840654, -1.921586,
+      -1.984141, -2.022537, -2.468977,
+      -2.827562, -3.473582, -4.437612,
+      -6.047662, -9.267761, -18.91806;
+  fvecp_ref <<
+      -7.724666e-09, -3.432406e-09, -2.034843e-10,
+      2.313685e-09,  4.331078e-09,  5.984096e-09,
+      7.363281e-09,   8.53147e-09,  1.488591e-08,
+      2.33585e-08,  3.522012e-08,  5.301255e-08,
+      8.26666e-08,  1.419747e-07,   3.19899e-07;
+  err_ref <<
+      0.1141397,  0.09943516,  0.09674474,
+      0.09980447,  0.1073116, 0.1220445,
+      0.1526814, 1, 1,
+      1, 1, 1,
+      1, 1, 1;
+
+  VERIFY_IS_APPROX(fvec, fvec_ref);
+  VERIFY_IS_APPROX(fvecp, fvecp_ref);
+  VERIFY_IS_APPROX(err, err_ref);
+}
+
+// Generic functor
+template<typename _Scalar, int NX=Dynamic, int NY=Dynamic>
+struct Functor
+{
+  typedef _Scalar Scalar;
+  enum {
+    InputsAtCompileTime = NX,
+    ValuesAtCompileTime = NY
+  };
+  typedef Matrix<Scalar,InputsAtCompileTime,1> InputType;
+  typedef Matrix<Scalar,ValuesAtCompileTime,1> ValueType;
+  typedef Matrix<Scalar,ValuesAtCompileTime,InputsAtCompileTime> JacobianType;
+  
+  int m_inputs, m_values;
+  
+  Functor() : m_inputs(InputsAtCompileTime), m_values(ValuesAtCompileTime) {}
+  Functor(int inputs, int values) : m_inputs(inputs), m_values(values) {}
+  
+  int inputs() const { return m_inputs; }
+  int values() const { return m_values; }
+
+  // you should define that in the subclass :
+//  void operator() (const InputType& x, ValueType* v, JacobianType* _j=0) const;
+};
+
+struct lmder_functor : Functor<double>
+{
+    lmder_functor(void): Functor<double>(3,15) {}
+    int operator()(const VectorXd &x, VectorXd &fvec) const
+    {
+        double tmp1, tmp2, tmp3;
+        double y[15] = {1.4e-1, 1.8e-1, 2.2e-1, 2.5e-1, 2.9e-1, 3.2e-1, 3.5e-1,
+            3.9e-1, 3.7e-1, 5.8e-1, 7.3e-1, 9.6e-1, 1.34, 2.1, 4.39};
+
+        for (int i = 0; i < values(); i++)
+        {
+            tmp1 = i+1;
+            tmp2 = 16 - i - 1;
+            tmp3 = (i>=8)? tmp2 : tmp1;
+            fvec[i] = y[i] - (x[0] + tmp1/(x[1]*tmp2 + x[2]*tmp3));
+        }
+        return 0;
+    }
+
+    int df(const VectorXd &x, MatrixXd &fjac) const
+    {
+        double tmp1, tmp2, tmp3, tmp4;
+        for (int i = 0; i < values(); i++)
+        {
+            tmp1 = i+1;
+            tmp2 = 16 - i - 1;
+            tmp3 = (i>=8)? tmp2 : tmp1;
+            tmp4 = (x[1]*tmp2 + x[2]*tmp3); tmp4 = tmp4*tmp4;
+            fjac(i,0) = -1;
+            fjac(i,1) = tmp1*tmp2/tmp4;
+            fjac(i,2) = tmp1*tmp3/tmp4;
+        }
+        return 0;
+    }
+};
+
+void testLmder1()
+{
+  int n=3, info;
+
+  VectorXd x;
+
+  /* the following starting values provide a rough fit. */
+  x.setConstant(n, 1.);
+
+  // do the computation
+  lmder_functor functor;
+  LevenbergMarquardt<lmder_functor> lm(functor);
+  info = lm.lmder1(x);
+
+  // check return value
+  VERIFY( 1 == info);
+  VERIFY(lm.nfev==6);
+  VERIFY(lm.njev==5);
+
+  // check norm
+  VERIFY_IS_APPROX(lm.fvec.blueNorm(), 0.09063596);
+
+  // check x
+  VectorXd x_ref(n);
+  x_ref << 0.08241058, 1.133037, 2.343695;
+  VERIFY_IS_APPROX(x, x_ref);
+}
+
+void testLmder()
+{
+  const int m=15, n=3;
+  int info;
+  double fnorm, covfac;
+  VectorXd x;
+
+  /* the following starting values provide a rough fit. */
+  x.setConstant(n, 1.);
+
+  // do the computation
+  lmder_functor functor;
+  LevenbergMarquardt<lmder_functor> lm(functor);
+  info = lm.minimize(x);
+
+  // check return values
+  VERIFY( 1 == info);
+  VERIFY(lm.nfev==6);
+  VERIFY(lm.njev==5);
+
+  // check norm
+  fnorm = lm.fvec.blueNorm();
+  VERIFY_IS_APPROX(fnorm, 0.09063596);
+
+  // check x
+  VectorXd x_ref(n);
+  x_ref << 0.08241058, 1.133037, 2.343695;
+  VERIFY_IS_APPROX(x, x_ref);
+
+  // check covariance
+  covfac = fnorm*fnorm/(m-n);
+  ei_covar(lm.fjac, lm.ipvt); // TODO : move this as a function of lm
+
+  MatrixXd cov_ref(n,n);
+  cov_ref << 
+      0.0001531202,   0.002869941,  -0.002656662,
+      0.002869941,    0.09480935,   -0.09098995,
+      -0.002656662,   -0.09098995,    0.08778727;
+
+//  std::cout << fjac*covfac << std::endl;
+
+  MatrixXd cov;
+  cov =  covfac*lm.fjac.corner<n,n>(TopLeft);
+  VERIFY_IS_APPROX( cov, cov_ref);
+  // TODO: why isn't this allowed ? : 
+  // VERIFY_IS_APPROX( covfac*fjac.corner<n,n>(TopLeft) , cov_ref);
+}
+
+struct hybrj_functor : Functor<double>
+{
+    hybrj_functor(void) : Functor<double>(9,9) {}
+
+    int operator()(const VectorXd &x, VectorXd &fvec)
+    {
+        double temp, temp1, temp2;
+        const int n = x.size();
+        assert(fvec.size()==n);
+        for (int k = 0; k < n; k++)
+        {
+            temp = (3. - 2.*x[k])*x[k];
+            temp1 = 0.;
+            if (k) temp1 = x[k-1];
+            temp2 = 0.;
+            if (k != n-1) temp2 = x[k+1];
+            fvec[k] = temp - temp1 - 2.*temp2 + 1.;
+        }
+        return 0;
+    }
+    int df(const VectorXd &x, MatrixXd &fjac)
+    {
+        const int n = x.size();
+        assert(fjac.rows()==n);
+        assert(fjac.cols()==n);
+        for (int k = 0; k < n; k++)
+        {
+            for (int j = 0; j < n; j++)
+                fjac(k,j) = 0.;
+            fjac(k,k) = 3.- 4.*x[k];
+            if (k) fjac(k,k-1) = -1.;
+            if (k != n-1) fjac(k,k+1) = -2.;
+        }
+        return 0;
+    }
+};
+
+
+void testHybrj1()
+{
+  const int n=9;
+  int info;
+  VectorXd x(n);
+
+  /* the following starting values provide a rough fit. */
+  x.setConstant(n, -1.);
+
+  // do the computation
+  hybrj_functor functor;
+  HybridNonLinearSolver<hybrj_functor> solver(functor);
+  info = solver.hybrj1(x);
+
+  // check return value
+  VERIFY( 1 == info);
+  VERIFY(solver.nfev==11);
+  VERIFY(solver.njev==1);
+
+  // check norm
+  VERIFY_IS_APPROX(solver.fvec.blueNorm(), 1.192636e-08);
+
+
+// check x
+  VectorXd x_ref(n);
+  x_ref << 
+     -0.5706545,    -0.6816283,    -0.7017325,
+     -0.7042129,     -0.701369,    -0.6918656,
+     -0.665792,    -0.5960342,    -0.4164121;
+  VERIFY_IS_APPROX(x, x_ref);
+}
+
+void testHybrj()
+{
+  const int n=9;
+  int info;
+  VectorXd x(n);
+
+  /* the following starting values provide a rough fit. */
+  x.setConstant(n, -1.);
+
+
+  // do the computation
+  hybrj_functor functor;
+  HybridNonLinearSolver<hybrj_functor> solver(functor);
+  solver.diag.setConstant(n, 1.);
+  info = solver.solve(x, 2);
+
+  // check return value
+  VERIFY( 1 == info);
+  VERIFY(solver.nfev==11);
+  VERIFY(solver.njev==1);
+
+  // check norm
+  VERIFY_IS_APPROX(solver.fvec.blueNorm(), 1.192636e-08);
+
+
+// check x
+  VectorXd x_ref(n);
+  x_ref << 
+     -0.5706545,    -0.6816283,    -0.7017325,
+     -0.7042129,     -0.701369,    -0.6918656,
+     -0.665792,    -0.5960342,    -0.4164121;
+  VERIFY_IS_APPROX(x, x_ref);
+
+}
+
+struct hybrd_functor : Functor<double>
+{
+    hybrd_functor(void) : Functor<double>(9,9) {}
+    int operator()(const VectorXd &x, VectorXd &fvec) const
+    {
+        double temp, temp1, temp2;
+        const int n = x.size();
+
+        assert(fvec.size()==n);
+        for (int k=0; k < n; k++)
+        {
+            temp = (3. - 2.*x[k])*x[k];
+            temp1 = 0.;
+            if (k) temp1 = x[k-1];
+            temp2 = 0.;
+            if (k != n-1) temp2 = x[k+1];
+            fvec[k] = temp - temp1 - 2.*temp2 + 1.;
+        }
+        return 0;
+    }
+};
+
+void testHybrd1()
+{
+  int n=9, info;
+  VectorXd x(n);
+
+  /* the following starting values provide a rough solution. */
+  x.setConstant(n, -1.);
+
+  // do the computation
+  hybrd_functor functor;
+  HybridNonLinearSolver<hybrd_functor> solver(functor);
+  info = solver.hybrd1(x);
+
+  // check return value
+  VERIFY( 1 == info);
+  VERIFY(solver.nfev==20);
+
+  // check norm
+  VERIFY_IS_APPROX(solver.fvec.blueNorm(), 1.192636e-08);
+
+  // check x
+  VectorXd x_ref(n);
+  x_ref << -0.5706545, -0.6816283, -0.7017325, -0.7042129, -0.701369, -0.6918656, -0.665792, -0.5960342, -0.4164121;
+  VERIFY_IS_APPROX(x, x_ref);
+}
+
+void testHybrd()
+{
+  const int n=9;
+  int info;
+  VectorXd x;
+
+  /* the following starting values provide a rough fit. */
+  x.setConstant(n, -1.);
+
+  // do the computation
+  hybrd_functor functor;
+  HybridNonLinearSolver<hybrd_functor> solver(functor);
+  solver.parameters.nb_of_subdiagonals = 1;
+  solver.parameters.nb_of_superdiagonals = 1;
+  solver.diag.setConstant(n, 1.);
+  info = solver.solveNumericalDiff(x, 2);
+
+  // check return value
+  VERIFY( 1 == info);
+  VERIFY(solver.nfev==14);
+
+  // check norm
+  VERIFY_IS_APPROX(solver.fvec.blueNorm(), 1.192636e-08);
+
+  // check x
+  VectorXd x_ref(n);
+  x_ref << 
+      -0.5706545,    -0.6816283,    -0.7017325,
+      -0.7042129,     -0.701369,    -0.6918656,
+      -0.665792,    -0.5960342,    -0.4164121;
+  VERIFY_IS_APPROX(x, x_ref);
+}
+
+struct lmstr_functor : Functor<double>
+{
+    lmstr_functor(void) : Functor<double>(3,15) {}
+    int operator()(const VectorXd &x, VectorXd &fvec)
+    {
+        /*  subroutine fcn for lmstr1 example. */
+        double tmp1, tmp2, tmp3;
+        double y[15]={1.4e-1, 1.8e-1, 2.2e-1, 2.5e-1, 2.9e-1, 3.2e-1, 3.5e-1,
+            3.9e-1, 3.7e-1, 5.8e-1, 7.3e-1, 9.6e-1, 1.34, 2.1, 4.39};
+
+        assert(15==fvec.size());
+        assert(3==x.size());
+
+        for (int i=0; i<15; i++)
+        {
+            tmp1 = i+1;
+            tmp2 = 16 - i - 1;
+            tmp3 = (i>=8)? tmp2 : tmp1;
+            fvec[i] = y[i] - (x[0] + tmp1/(x[1]*tmp2 + x[2]*tmp3));
+        }
+        return 0;
+    }
+    int df(const VectorXd &x, VectorXd &jac_row, int rownb)
+    {
+        assert(x.size()==3);
+        assert(jac_row.size()==x.size());
+        double tmp1, tmp2, tmp3, tmp4;
+
+        int i = rownb-2;
+        tmp1 = i+1;
+        tmp2 = 16 - i - 1;
+        tmp3 = (i>=8)? tmp2 : tmp1;
+        tmp4 = (x[1]*tmp2 + x[2]*tmp3); tmp4 = tmp4*tmp4;
+        jac_row[0] = -1;
+        jac_row[1] = tmp1*tmp2/tmp4;
+        jac_row[2] = tmp1*tmp3/tmp4;
+        return 0;
+    }
+};
+
+void testLmstr1()
+{
+  const int n=3;
+  int info;
+
+  VectorXd x(n);
+
+  /* the following starting values provide a rough fit. */
+  x.setConstant(n, 1.);
+
+  // do the computation
+  lmstr_functor functor;
+  LevenbergMarquardt<lmstr_functor> lm(functor);
+  info = lm.lmstr1(x);
+
+  // check return value
+  VERIFY( 1 == info);
+  VERIFY(lm.nfev==6);
+  VERIFY(lm.njev==5);
+
+  // check norm
+  VERIFY_IS_APPROX(lm.fvec.blueNorm(), 0.09063596);
+
+  // check x
+  VectorXd x_ref(n);
+  x_ref << 0.08241058, 1.133037, 2.343695 ;
+  VERIFY_IS_APPROX(x, x_ref);
+}
+
+void testLmstr()
+{
+  const int n=3;
+  int info;
+  double fnorm;
+  VectorXd x(n);
+
+  /* the following starting values provide a rough fit. */
+  x.setConstant(n, 1.);
+
+  // do the computation
+  lmstr_functor functor;
+  LevenbergMarquardt<lmstr_functor> lm(functor);
+  info = lm.minimizeOptimumStorage(x);
+
+  // check return values
+  VERIFY( 1 == info);
+  VERIFY(lm.nfev==6);
+  VERIFY(lm.njev==5);
+
+  // check norm
+  fnorm = lm.fvec.blueNorm();
+  VERIFY_IS_APPROX(fnorm, 0.09063596);
+
+  // check x
+  VectorXd x_ref(n);
+  x_ref << 0.08241058, 1.133037, 2.343695;
+  VERIFY_IS_APPROX(x, x_ref);
+
+}
+
+struct lmdif_functor : Functor<double>
+{
+    lmdif_functor(void) : Functor<double>(3,15) {}
+    int operator()(const VectorXd &x, VectorXd &fvec) const
+    {
+        int i;
+        double tmp1,tmp2,tmp3;
+        double y[15]={1.4e-1,1.8e-1,2.2e-1,2.5e-1,2.9e-1,3.2e-1,3.5e-1,3.9e-1,
+            3.7e-1,5.8e-1,7.3e-1,9.6e-1,1.34e0,2.1e0,4.39e0};
+
+        assert(x.size()==3);
+        assert(fvec.size()==15);
+        for (i=0; i<15; i++)
+        {
+            tmp1 = i+1;
+            tmp2 = 15 - i;
+            tmp3 = tmp1;
+
+            if (i >= 8) tmp3 = tmp2;
+            fvec[i] = y[i] - (x[0] + tmp1/(x[1]*tmp2 + x[2]*tmp3));
+        }
+        return 0;
+    }
+};
+
+void testLmdif1()
+{
+  const int n=3;
+  int info;
+
+  VectorXd x(n), fvec(15);
+
+  /* the following starting values provide a rough fit. */
+  x.setConstant(n, 1.);
+
+  // do the computation
+  lmdif_functor functor;
+  int nfev;
+  info = LevenbergMarquardt<lmdif_functor>::lmdif1(functor, x, &nfev);
+
+  // check return value
+  VERIFY( 1 == info);
+  VERIFY(nfev==26);
+
+  // check norm
+  functor(x, fvec);
+  VERIFY_IS_APPROX(fvec.blueNorm(), 0.09063596);
+
+  // check x
+  VectorXd x_ref(n);
+  x_ref << 0.0824106, 1.1330366, 2.3436947;
+  VERIFY_IS_APPROX(x, x_ref);
+
+}
+
+void testLmdif()
+{
+  const int m=15, n=3;
+  int info;
+  double fnorm, covfac;
+  VectorXd x(n);
+
+  /* the following starting values provide a rough fit. */
+  x.setConstant(n, 1.);
+
+  // do the computation
+  lmdif_functor functor;
+  NumericalDiff<lmdif_functor> numDiff(functor);
+  LevenbergMarquardt<NumericalDiff<lmdif_functor> > lm(numDiff);
+  info = lm.minimize(x);
+
+  // check return values
+  VERIFY( 1 == info);
+  VERIFY(lm.nfev==26);
+
+  // check norm
+  fnorm = lm.fvec.blueNorm();
+  VERIFY_IS_APPROX(fnorm, 0.09063596);
+
+  // check x
+  VectorXd x_ref(n);
+  x_ref << 0.08241058, 1.133037, 2.343695;
+  VERIFY_IS_APPROX(x, x_ref);
+
+  // check covariance
+  covfac = fnorm*fnorm/(m-n);
+  ei_covar(lm.fjac, lm.ipvt);
+
+  MatrixXd cov_ref(n,n);
+  cov_ref << 
+      0.0001531202,   0.002869942,  -0.002656662,
+      0.002869942,    0.09480937,   -0.09098997,
+      -0.002656662,   -0.09098997,    0.08778729;
+
+//  std::cout << fjac*covfac << std::endl;
+
+  MatrixXd cov;
+  cov =  covfac*lm.fjac.corner<n,n>(TopLeft);
+  VERIFY_IS_APPROX( cov, cov_ref);
+  // TODO: why isn't this allowed ? : 
+  // VERIFY_IS_APPROX( covfac*fjac.corner<n,n>(TopLeft) , cov_ref);
+}
+
+struct chwirut2_functor : Functor<double>
+{
+    chwirut2_functor(void) : Functor<double>(3,54) {}
+    static const double m_x[54];
+    static const double m_y[54];
+    int operator()(const VectorXd &b, VectorXd &fvec)
+    {
+        int i;
+
+        assert(b.size()==3);
+        assert(fvec.size()==54);
+        for(i=0; i<54; i++) {
+            double x = m_x[i];
+            fvec[i] = exp(-b[0]*x)/(b[1]+b[2]*x) - m_y[i];
+        }
+        return 0;
+    }
+    int df(const VectorXd &b, MatrixXd &fjac)
+    {
+        assert(b.size()==3);
+        assert(fjac.rows()==54);
+        assert(fjac.cols()==3);
+        for(int i=0; i<54; i++) {
+            double x = m_x[i];
+            double factor = 1./(b[1]+b[2]*x);
+            double e = exp(-b[0]*x);
+            fjac(i,0) = -x*e*factor;
+            fjac(i,1) = -e*factor*factor;
+            fjac(i,2) = -x*e*factor*factor;
+        }
+        return 0;
+    }
+};
+const double chwirut2_functor::m_x[54] = { 0.500E0, 1.000E0, 1.750E0, 3.750E0, 5.750E0, 0.875E0, 2.250E0, 3.250E0, 5.250E0, 0.750E0, 1.750E0, 2.750E0, 4.750E0, 0.625E0, 1.250E0, 2.250E0, 4.250E0, .500E0, 3.000E0, .750E0, 3.000E0, 1.500E0, 6.000E0, 3.000E0, 6.000E0, 1.500E0, 3.000E0, .500E0, 2.000E0, 4.000E0, .750E0, 2.000E0, 5.000E0, .750E0, 2.250E0, 3.750E0, 5.750E0, 3.000E0, .750E0, 2.500E0, 4.000E0, .750E0, 2.500E0, 4.000E0, .750E0, 2.500E0, 4.000E0, .500E0, 6.000E0, 3.000E0, .500E0, 2.750E0, .500E0, 1.750E0};
+const double chwirut2_functor::m_y[54] = { 92.9000E0 ,57.1000E0 ,31.0500E0 ,11.5875E0 ,8.0250E0 ,63.6000E0 ,21.4000E0 ,14.2500E0 ,8.4750E0 ,63.8000E0 ,26.8000E0 ,16.4625E0 ,7.1250E0 ,67.3000E0 ,41.0000E0 ,21.1500E0 ,8.1750E0 ,81.5000E0 ,13.1200E0 ,59.9000E0 ,14.6200E0 ,32.9000E0 ,5.4400E0 ,12.5600E0 ,5.4400E0 ,32.0000E0 ,13.9500E0 ,75.8000E0 ,20.0000E0 ,10.4200E0 ,59.5000E0 ,21.6700E0 ,8.5500E0 ,62.0000E0 ,20.2000E0 ,7.7600E0 ,3.7500E0 ,11.8100E0 ,54.7000E0 ,23.7000E0 ,11.5500E0 ,61.3000E0 ,17.7000E0 ,8.7400E0 ,59.2000E0 ,16.3000E0 ,8.6200E0 ,81.0000E0 ,4.8700E0 ,14.6200E0 ,81.7000E0 ,17.1700E0 ,81.3000E0 ,28.9000E0  };
+
+// http://www.itl.nist.gov/div898/strd/nls/data/chwirut2.shtml
+void testNistChwirut2(void)
+{
+  const int n=3;
+  int info;
+
+  VectorXd x(n);
+
+  /*
+   * First try
+   */
+  x<< 0.1, 0.01, 0.02;
+  // do the computation
+  chwirut2_functor functor;
+  LevenbergMarquardt<chwirut2_functor> lm(functor);
+  info = lm.minimize(x);
+
+  // check return value
+  VERIFY( 1 == info); 
+  VERIFY( 10 == lm.nfev); 
+  VERIFY( 8 == lm.njev); 
+  // check norm^2
+  VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 5.1304802941E+02); 
+  // check x
+  VERIFY_IS_APPROX(x[0], 1.6657666537E-01);
+  VERIFY_IS_APPROX(x[1], 5.1653291286E-03);
+  VERIFY_IS_APPROX(x[2], 1.2150007096E-02);
+
+  /*
+   * Second try
+   */
+  x<< 0.15, 0.008, 0.010;
+  // do the computation
+  lm.resetParameters();
+  lm.parameters.ftol = 1.E6*epsilon<double>();
+  lm.parameters.xtol = 1.E6*epsilon<double>();
+  info = lm.minimize(x);
+
+  // check return value
+  VERIFY( 1 == info); 
+  VERIFY( 7 == lm.nfev); 
+  VERIFY( 6 == lm.njev); 
+  // check norm^2
+  VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 5.1304802941E+02); 
+  // check x
+  VERIFY_IS_APPROX(x[0], 1.6657666537E-01);
+  VERIFY_IS_APPROX(x[1], 5.1653291286E-03);
+  VERIFY_IS_APPROX(x[2], 1.2150007096E-02);
+}
+
+
+struct misra1a_functor : Functor<double>
+{
+    misra1a_functor(void) : Functor<double>(2,14) {}
+    static const double m_x[14];
+    static const double m_y[14];
+    int operator()(const VectorXd &b, VectorXd &fvec)
+    {
+        assert(b.size()==2);
+        assert(fvec.size()==14);
+        for(int i=0; i<14; i++) {
+            fvec[i] = b[0]*(1.-exp(-b[1]*m_x[i])) - m_y[i] ;
+        }
+        return 0;
+    }
+    int df(const VectorXd &b, MatrixXd &fjac)
+    {
+        assert(b.size()==2);
+        assert(fjac.rows()==14);
+        assert(fjac.cols()==2);
+        for(int i=0; i<14; i++) {
+            fjac(i,0) = (1.-exp(-b[1]*m_x[i]));
+            fjac(i,1) = (b[0]*m_x[i]*exp(-b[1]*m_x[i]));
+        }
+        return 0;
+    }
+};
+const double misra1a_functor::m_x[14] = { 77.6E0, 114.9E0, 141.1E0, 190.8E0, 239.9E0, 289.0E0, 332.8E0, 378.4E0, 434.8E0, 477.3E0, 536.8E0, 593.1E0, 689.1E0, 760.0E0};
+const double misra1a_functor::m_y[14] = { 10.07E0, 14.73E0, 17.94E0, 23.93E0, 29.61E0, 35.18E0, 40.02E0, 44.82E0, 50.76E0, 55.05E0, 61.01E0, 66.40E0, 75.47E0, 81.78E0};
+
+// http://www.itl.nist.gov/div898/strd/nls/data/misra1a.shtml
+void testNistMisra1a(void)
+{
+  const int n=2;
+  int info;
+
+  VectorXd x(n);
+
+  /*
+   * First try
+   */
+  x<< 500., 0.0001;
+  // do the computation
+  misra1a_functor functor;
+  LevenbergMarquardt<misra1a_functor> lm(functor);
+  info = lm.minimize(x);
+
+  // check return value
+  VERIFY( 1 == info); 
+  VERIFY( 19 == lm.nfev); 
+  VERIFY( 15 == lm.njev); 
+  // check norm^2
+  VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 1.2455138894E-01); 
+  // check x
+  VERIFY_IS_APPROX(x[0], 2.3894212918E+02);
+  VERIFY_IS_APPROX(x[1], 5.5015643181E-04);
+
+  /*
+   * Second try
+   */
+  x<< 250., 0.0005;
+  // do the computation
+  info = lm.minimize(x);
+
+  // check return value
+  VERIFY( 1 == info); 
+  VERIFY( 5 == lm.nfev); 
+  VERIFY( 4 == lm.njev); 
+  // check norm^2
+  VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 1.2455138894E-01); 
+  // check x
+  VERIFY_IS_APPROX(x[0], 2.3894212918E+02);
+  VERIFY_IS_APPROX(x[1], 5.5015643181E-04);
+}
+
+struct hahn1_functor : Functor<double>
+{
+    hahn1_functor(void) : Functor<double>(7,236) {}
+    static const double m_x[236];
+    int operator()(const VectorXd &b, VectorXd &fvec)
+    {
+        static const double m_y[236] = { .591E0 , 1.547E0 , 2.902E0 , 2.894E0 , 4.703E0 , 6.307E0 , 7.03E0  , 7.898E0 , 9.470E0 , 9.484E0 , 10.072E0 , 10.163E0 , 11.615E0 , 12.005E0 , 12.478E0 , 12.982E0 , 12.970E0 , 13.926E0 , 14.452E0 , 14.404E0 , 15.190E0 , 15.550E0 , 15.528E0 , 15.499E0 , 16.131E0 , 16.438E0 , 16.387E0 , 16.549E0 , 16.872E0 , 16.830E0 , 16.926E0 , 16.907E0 , 16.966E0 , 17.060E0 , 17.122E0 , 17.311E0 , 17.355E0 , 17.668E0 , 17.767E0 , 17.803E0 , 17.765E0 , 17.768E0 , 17.736E0 , 17.858E0 , 17.877E0 , 17.912E0 , 18.046E0 , 18.085E0 , 18.291E0 , 18.357E0 , 18.426E0 , 18.584E0 , 18.610E0 , 18.870E0 , 18.795E0 , 19.111E0 , .367E0 , .796E0 , 0.892E0 , 1.903E0 , 2.150E0 , 3.697E0 , 5.870E0 , 6.421E0 , 7.422E0 , 9.944E0 , 11.023E0 , 11.87E0  , 12.786E0 , 14.067E0 , 13.974E0 , 14.462E0 , 14.464E0 , 15.381E0 , 15.483E0 , 15.59E0  , 16.075E0 , 16.347E0 , 16.181E0 , 16.915E0 , 17.003E0 , 16.978E0 , 17.756E0 , 17.808E0 , 17.868E0 , 18.481E0 , 18.486E0 , 19.090E0 , 16.062E0 , 16.337E0 , 16.345E0 , 16.388E0 , 17.159E0 , 17.116E0 , 17.164E0 , 17.123E0 , 17.979E0 , 17.974E0 , 18.007E0 , 17.993E0 , 18.523E0 , 18.669E0 , 18.617E0 , 19.371E0 , 19.330E0 , 0.080E0 , 0.248E0 , 1.089E0 , 1.418E0 , 2.278E0 , 3.624E0 , 4.574E0 , 5.556E0 , 7.267E0 , 7.695E0 , 9.136E0 , 9.959E0 , 9.957E0 , 11.600E0 , 13.138E0 , 13.564E0 , 13.871E0 , 13.994E0 , 14.947E0 , 15.473E0 , 15.379E0 , 15.455E0 , 15.908E0 , 16.114E0 , 17.071E0 , 17.135E0 , 17.282E0 , 17.368E0 , 17.483E0 , 17.764E0 , 18.185E0 , 18.271E0 , 18.236E0 , 18.237E0 , 18.523E0 , 18.627E0 , 18.665E0 , 19.086E0 , 0.214E0 , 0.943E0 , 1.429E0 , 2.241E0 , 2.951E0 , 3.782E0 , 4.757E0 , 5.602E0 , 7.169E0 , 8.920E0 , 10.055E0 , 12.035E0 , 12.861E0 , 13.436E0 , 14.167E0 , 14.755E0 , 15.168E0 , 15.651E0 , 15.746E0 , 16.216E0 , 16.445E0 , 16.965E0 , 17.121E0 , 17.206E0 , 17.250E0 , 17.339E0 , 17.793E0 , 18.123E0 , 18.49E0  , 18.566E0 , 18.645E0 , 18.706E0 , 18.924E0 , 19.1E0   , 0.375E0 , 0.471E0 , 1.504E0 , 2.204E0 , 2.813E0 , 4.765E0 , 9.835E0 , 10.040E0 , 11.946E0 , 12.596E0 , 13.303E0 , 13.922E0 , 14.440E0 , 14.951E0 , 15.627E0 , 15.639E0 , 15.814E0 , 16.315E0 , 16.334E0 , 16.430E0 , 16.423E0 , 17.024E0 , 17.009E0 , 17.165E0 , 17.134E0 , 17.349E0 , 17.576E0 , 17.848E0 , 18.090E0 , 18.276E0 , 18.404E0 , 18.519E0 , 19.133E0 , 19.074E0 , 19.239E0 , 19.280E0 , 19.101E0 , 19.398E0 , 19.252E0 , 19.89E0  , 20.007E0 , 19.929E0 , 19.268E0 , 19.324E0 , 20.049E0 , 20.107E0 , 20.062E0 , 20.065E0 , 19.286E0 , 19.972E0 , 20.088E0 , 20.743E0 , 20.83E0  , 20.935E0 , 21.035E0 , 20.93E0  , 21.074E0 , 21.085E0 , 20.935E0 };
+
+        //        int called=0; printf("call hahn1_functor with  iflag=%d, called=%d\n", iflag, called); if (iflag==1) called++;
+
+        assert(b.size()==7);
+        assert(fvec.size()==236);
+        for(int i=0; i<236; i++) {
+            double x=m_x[i], xx=x*x, xxx=xx*x;
+            fvec[i] = (b[0]+b[1]*x+b[2]*xx+b[3]*xxx) / (1.+b[4]*x+b[5]*xx+b[6]*xxx) - m_y[i];
+        }
+        return 0;
+    }
+
+    int df(const VectorXd &b, MatrixXd &fjac)
+    {
+        assert(b.size()==7);
+        assert(fjac.rows()==236);
+        assert(fjac.cols()==7);
+        for(int i=0; i<236; i++) {
+            double x=m_x[i], xx=x*x, xxx=xx*x;
+            double fact = 1./(1.+b[4]*x+b[5]*xx+b[6]*xxx);
+            fjac(i,0) = 1.*fact;
+            fjac(i,1) = x*fact;
+            fjac(i,2) = xx*fact;
+            fjac(i,3) = xxx*fact;
+            fact = - (b[0]+b[1]*x+b[2]*xx+b[3]*xxx) * fact * fact;
+            fjac(i,4) = x*fact;
+            fjac(i,5) = xx*fact;
+            fjac(i,6) = xxx*fact;
+        }
+        return 0;
+    }
+};
+const double hahn1_functor::m_x[236] = { 24.41E0 , 34.82E0 , 44.09E0 , 45.07E0 , 54.98E0 , 65.51E0 , 70.53E0 , 75.70E0 , 89.57E0 , 91.14E0 , 96.40E0 , 97.19E0 , 114.26E0 , 120.25E0 , 127.08E0 , 133.55E0 , 133.61E0 , 158.67E0 , 172.74E0 , 171.31E0 , 202.14E0 , 220.55E0 , 221.05E0 , 221.39E0 , 250.99E0 , 268.99E0 , 271.80E0 , 271.97E0 , 321.31E0 , 321.69E0 , 330.14E0 , 333.03E0 , 333.47E0 , 340.77E0 , 345.65E0 , 373.11E0 , 373.79E0 , 411.82E0 , 419.51E0 , 421.59E0 , 422.02E0 , 422.47E0 , 422.61E0 , 441.75E0 , 447.41E0 , 448.7E0  , 472.89E0 , 476.69E0 , 522.47E0 , 522.62E0 , 524.43E0 , 546.75E0 , 549.53E0 , 575.29E0 , 576.00E0 , 625.55E0 , 20.15E0 , 28.78E0 , 29.57E0 , 37.41E0 , 39.12E0 , 50.24E0 , 61.38E0 , 66.25E0 , 73.42E0 , 95.52E0 , 107.32E0 , 122.04E0 , 134.03E0 , 163.19E0 , 163.48E0 , 175.70E0 , 179.86E0 , 211.27E0 , 217.78E0 , 219.14E0 , 262.52E0 , 268.01E0 , 268.62E0 , 336.25E0 , 337.23E0 , 339.33E0 , 427.38E0 , 428.58E0 , 432.68E0 , 528.99E0 , 531.08E0 , 628.34E0 , 253.24E0 , 273.13E0 , 273.66E0 , 282.10E0 , 346.62E0 , 347.19E0 , 348.78E0 , 351.18E0 , 450.10E0 , 450.35E0 , 451.92E0 , 455.56E0 , 552.22E0 , 553.56E0 , 555.74E0 , 652.59E0 , 656.20E0 , 14.13E0 , 20.41E0 , 31.30E0 , 33.84E0 , 39.70E0 , 48.83E0 , 54.50E0 , 60.41E0 , 72.77E0 , 75.25E0 , 86.84E0 , 94.88E0 , 96.40E0 , 117.37E0 , 139.08E0 , 147.73E0 , 158.63E0 , 161.84E0 , 192.11E0 , 206.76E0 , 209.07E0 , 213.32E0 , 226.44E0 , 237.12E0 , 330.90E0 , 358.72E0 , 370.77E0 , 372.72E0 , 396.24E0 , 416.59E0 , 484.02E0 , 495.47E0 , 514.78E0 , 515.65E0 , 519.47E0 , 544.47E0 , 560.11E0 , 620.77E0 , 18.97E0 , 28.93E0 , 33.91E0 , 40.03E0 , 44.66E0 , 49.87E0 , 55.16E0 , 60.90E0 , 72.08E0 , 85.15E0 , 97.06E0 , 119.63E0 , 133.27E0 , 143.84E0 , 161.91E0 , 180.67E0 , 198.44E0 , 226.86E0 , 229.65E0 , 258.27E0 , 273.77E0 , 339.15E0 , 350.13E0 , 362.75E0 , 371.03E0 , 393.32E0 , 448.53E0 , 473.78E0 , 511.12E0 , 524.70E0 , 548.75E0 , 551.64E0 , 574.02E0 , 623.86E0 , 21.46E0 , 24.33E0 , 33.43E0 , 39.22E0 , 44.18E0 , 55.02E0 , 94.33E0 , 96.44E0 , 118.82E0 , 128.48E0 , 141.94E0 , 156.92E0 , 171.65E0 , 190.00E0 , 223.26E0 , 223.88E0 , 231.50E0 , 265.05E0 , 269.44E0 , 271.78E0 , 273.46E0 , 334.61E0 , 339.79E0 , 349.52E0 , 358.18E0 , 377.98E0 , 394.77E0 , 429.66E0 , 468.22E0 , 487.27E0 , 519.54E0 , 523.03E0 , 612.99E0 , 638.59E0 , 641.36E0 , 622.05E0 , 631.50E0 , 663.97E0 , 646.9E0  , 748.29E0 , 749.21E0 , 750.14E0 , 647.04E0 , 646.89E0 , 746.9E0  , 748.43E0 , 747.35E0 , 749.27E0 , 647.61E0 , 747.78E0 , 750.51E0 , 851.37E0 , 845.97E0 , 847.54E0 , 849.93E0 , 851.61E0 , 849.75E0 , 850.98E0 , 848.23E0};
+
+// http://www.itl.nist.gov/div898/strd/nls/data/hahn1.shtml
+void testNistHahn1(void)
+{
+  const int  n=7;
+  int info;
+
+  VectorXd x(n);
+
+  /*
+   * First try
+   */
+  x<< 10., -1., .05, -.00001, -.05, .001, -.000001;
+  // do the computation
+  hahn1_functor functor;
+  LevenbergMarquardt<hahn1_functor> lm(functor);
+  info = lm.minimize(x);
+
+  // check return value
+  VERIFY( 1 == info); 
+  VERIFY( 11== lm.nfev); 
+  VERIFY( 10== lm.njev); 
+  // check norm^2
+  VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 1.5324382854E+00); 
+  // check x
+  VERIFY_IS_APPROX(x[0], 1.0776351733E+00  );
+  VERIFY_IS_APPROX(x[1],-1.2269296921E-01  );
+  VERIFY_IS_APPROX(x[2], 4.0863750610E-03  );
+  VERIFY_IS_APPROX(x[3],-1.426264e-06); // shoulde be : -1.4262662514E-06
+  VERIFY_IS_APPROX(x[4],-5.7609940901E-03  );
+  VERIFY_IS_APPROX(x[5], 2.4053735503E-04  );
+  VERIFY_IS_APPROX(x[6],-1.2314450199E-07  );
+
+  /*
+   * Second try
+   */
+  x<< .1, -.1, .005, -.000001, -.005, .0001, -.0000001;
+  // do the computation
+  info = lm.minimize(x);
+
+  // check return value
+  VERIFY( 1 == info); 
+  VERIFY( 11 == lm.nfev); 
+  VERIFY( 10 == lm.njev); 
+  // check norm^2
+  VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 1.5324382854E+00); 
+  // check x
+  VERIFY_IS_APPROX(x[0], 1.077640); // should be :  1.0776351733E+00
+  VERIFY_IS_APPROX(x[1], -0.1226933); // should be : -1.2269296921E-01
+  VERIFY_IS_APPROX(x[2], 0.004086383); // should be : 4.0863750610E-03
+  VERIFY_IS_APPROX(x[3], -1.426277e-06); // shoulde be : -1.4262662514E-06
+  VERIFY_IS_APPROX(x[4],-5.7609940901E-03  );
+  VERIFY_IS_APPROX(x[5], 0.00024053772); // should be : 2.4053735503E-04 
+  VERIFY_IS_APPROX(x[6], -1.231450e-07); // should be : -1.2314450199E-07
+
+}
+
+struct misra1d_functor : Functor<double>
+{
+    misra1d_functor(void) : Functor<double>(2,14) {}
+    static const double x[14];
+    static const double y[14];
+    int operator()(const VectorXd &b, VectorXd &fvec)
+    {
+        assert(b.size()==2);
+        assert(fvec.size()==14);
+        for(int i=0; i<14; i++) {
+            fvec[i] = b[0]*b[1]*x[i]/(1.+b[1]*x[i]) - y[i];
+        }
+        return 0;
+    }
+    int df(const VectorXd &b, MatrixXd &fjac)
+    {
+        assert(b.size()==2);
+        assert(fjac.rows()==14);
+        assert(fjac.cols()==2);
+        for(int i=0; i<14; i++) {
+            double den = 1.+b[1]*x[i];
+            fjac(i,0) = b[1]*x[i] / den;
+            fjac(i,1) = b[0]*x[i]*(den-b[1]*x[i])/den/den;
+        }
+        return 0;
+    }
+};
+const double misra1d_functor::x[14] = { 77.6E0, 114.9E0, 141.1E0, 190.8E0, 239.9E0, 289.0E0, 332.8E0, 378.4E0, 434.8E0, 477.3E0, 536.8E0, 593.1E0, 689.1E0, 760.0E0};
+const double misra1d_functor::y[14] = { 10.07E0, 14.73E0, 17.94E0, 23.93E0, 29.61E0, 35.18E0, 40.02E0, 44.82E0, 50.76E0, 55.05E0, 61.01E0, 66.40E0, 75.47E0, 81.78E0};
+
+// http://www.itl.nist.gov/div898/strd/nls/data/misra1d.shtml
+void testNistMisra1d(void)
+{
+  const int n=2;
+  int info;
+
+  VectorXd x(n);
+
+  /*
+   * First try
+   */
+  x<< 500., 0.0001;
+  // do the computation
+  misra1d_functor functor;
+  LevenbergMarquardt<misra1d_functor> lm(functor);
+  info = lm.minimize(x);
+
+  // check return value
+  VERIFY( 3 == info); 
+  VERIFY( 9 == lm.nfev); 
+  VERIFY( 7 == lm.njev); 
+  // check norm^2
+  VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 5.6419295283E-02); 
+  // check x
+  VERIFY_IS_APPROX(x[0], 4.3736970754E+02);
+  VERIFY_IS_APPROX(x[1], 3.0227324449E-04);
+
+  /*
+   * Second try
+   */
+  x<< 450., 0.0003;
+  // do the computation
+  info = lm.minimize(x);
+
+  // check return value
+  VERIFY( 1 == info); 
+  VERIFY( 4 == lm.nfev); 
+  VERIFY( 3 == lm.njev); 
+  // check norm^2
+  VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 5.6419295283E-02); 
+  // check x
+  VERIFY_IS_APPROX(x[0], 4.3736970754E+02);
+  VERIFY_IS_APPROX(x[1], 3.0227324449E-04);
+}
+
+
+struct lanczos1_functor : Functor<double>
+{
+    lanczos1_functor(void) : Functor<double>(6,24) {}
+    static const double x[24];
+    static const double y[24];
+    int operator()(const VectorXd &b, VectorXd &fvec)
+    {
+        assert(b.size()==6);
+        assert(fvec.size()==24);
+        for(int i=0; i<24; i++)
+            fvec[i] = b[0]*exp(-b[1]*x[i]) + b[2]*exp(-b[3]*x[i]) + b[4]*exp(-b[5]*x[i])  - y[i];
+        return 0;
+    }
+    int df(const VectorXd &b, MatrixXd &fjac)
+    {
+        assert(b.size()==6);
+        assert(fjac.rows()==24);
+        assert(fjac.cols()==6);
+        for(int i=0; i<24; i++) {
+            fjac(i,0) = exp(-b[1]*x[i]);
+            fjac(i,1) = -b[0]*x[i]*exp(-b[1]*x[i]);
+            fjac(i,2) = exp(-b[3]*x[i]);
+            fjac(i,3) = -b[2]*x[i]*exp(-b[3]*x[i]);
+            fjac(i,4) = exp(-b[5]*x[i]);
+            fjac(i,5) = -b[4]*x[i]*exp(-b[5]*x[i]);
+        }
+        return 0;
+    }
+};
+const double lanczos1_functor::x[24] = { 0.000000000000E+00, 5.000000000000E-02, 1.000000000000E-01, 1.500000000000E-01, 2.000000000000E-01, 2.500000000000E-01, 3.000000000000E-01, 3.500000000000E-01, 4.000000000000E-01, 4.500000000000E-01, 5.000000000000E-01, 5.500000000000E-01, 6.000000000000E-01, 6.500000000000E-01, 7.000000000000E-01, 7.500000000000E-01, 8.000000000000E-01, 8.500000000000E-01, 9.000000000000E-01, 9.500000000000E-01, 1.000000000000E+00, 1.050000000000E+00, 1.100000000000E+00, 1.150000000000E+00 };
+const double lanczos1_functor::y[24] = { 2.513400000000E+00 ,2.044333373291E+00 ,1.668404436564E+00 ,1.366418021208E+00 ,1.123232487372E+00 ,9.268897180037E-01 ,7.679338563728E-01 ,6.388775523106E-01 ,5.337835317402E-01 ,4.479363617347E-01 ,3.775847884350E-01 ,3.197393199326E-01 ,2.720130773746E-01 ,2.324965529032E-01 ,1.996589546065E-01 ,1.722704126914E-01 ,1.493405660168E-01 ,1.300700206922E-01 ,1.138119324644E-01 ,1.000415587559E-01 ,8.833209084540E-02 ,7.833544019350E-02 ,6.976693743449E-02 ,6.239312536719E-02 };
+
+// http://www.itl.nist.gov/div898/strd/nls/data/lanczos1.shtml
+void testNistLanczos1(void)
+{
+  const int n=6;
+  int info;
+
+  VectorXd x(n);
+
+  /*
+   * First try
+   */
+  x<< 1.2, 0.3, 5.6, 5.5, 6.5, 7.6;
+  // do the computation
+  lanczos1_functor functor;
+  LevenbergMarquardt<lanczos1_functor> lm(functor);
+  info = lm.minimize(x);
+
+  // check return value
+  VERIFY( 2 == info); 
+  VERIFY( 79 == lm.nfev); 
+  VERIFY( 72 == lm.njev); 
+  // check norm^2
+  VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 1.429604433690E-25);  // should be 1.4307867721E-25, but nist results are on 128-bit floats
+  // check x
+  VERIFY_IS_APPROX(x[0], 9.5100000027E-02 );
+  VERIFY_IS_APPROX(x[1], 1.0000000001E+00 );
+  VERIFY_IS_APPROX(x[2], 8.6070000013E-01 );
+  VERIFY_IS_APPROX(x[3], 3.0000000002E+00 );
+  VERIFY_IS_APPROX(x[4], 1.5575999998E+00 );
+  VERIFY_IS_APPROX(x[5], 5.0000000001E+00 );
+
+  /*
+   * Second try
+   */
+  x<< 0.5, 0.7, 3.6, 4.2, 4., 6.3;
+  // do the computation
+  info = lm.minimize(x);
+
+  // check return value
+  VERIFY( 2 == info); 
+  VERIFY( 9 == lm.nfev); 
+  VERIFY( 8 == lm.njev); 
+  // check norm^2
+  VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 1.43049947737308E-25);  // should be 1.4307867721E-25, but nist results are on 128-bit floats
+  // check x
+  VERIFY_IS_APPROX(x[0], 9.5100000027E-02 );
+  VERIFY_IS_APPROX(x[1], 1.0000000001E+00 );
+  VERIFY_IS_APPROX(x[2], 8.6070000013E-01 );
+  VERIFY_IS_APPROX(x[3], 3.0000000002E+00 );
+  VERIFY_IS_APPROX(x[4], 1.5575999998E+00 );
+  VERIFY_IS_APPROX(x[5], 5.0000000001E+00 );
+
+}
+
+struct rat42_functor : Functor<double>
+{
+    rat42_functor(void) : Functor<double>(3,9) {}
+    static const double x[9];
+    static const double y[9];
+    int operator()(const VectorXd &b, VectorXd &fvec)
+    {
+        assert(b.size()==3);
+        assert(fvec.size()==9);
+        for(int i=0; i<9; i++) {
+            fvec[i] = b[0] / (1.+exp(b[1]-b[2]*x[i])) - y[i];
+        }
+        return 0;
+    }
+
+    int df(const VectorXd &b, MatrixXd &fjac)
+    {
+        assert(b.size()==3);
+        assert(fjac.rows()==9);
+        assert(fjac.cols()==3);
+        for(int i=0; i<9; i++) {
+            double e = exp(b[1]-b[2]*x[i]);
+            fjac(i,0) = 1./(1.+e);
+            fjac(i,1) = -b[0]*e/(1.+e)/(1.+e);
+            fjac(i,2) = +b[0]*e*x[i]/(1.+e)/(1.+e);
+        }
+        return 0;
+    }
+};
+const double rat42_functor::x[9] = { 9.000E0, 14.000E0, 21.000E0, 28.000E0, 42.000E0, 57.000E0, 63.000E0, 70.000E0, 79.000E0 };
+const double rat42_functor::y[9] = { 8.930E0 ,10.800E0 ,18.590E0 ,22.330E0 ,39.350E0 ,56.110E0 ,61.730E0 ,64.620E0 ,67.080E0 };
+
+// http://www.itl.nist.gov/div898/strd/nls/data/ratkowsky2.shtml
+void testNistRat42(void)
+{
+  const int n=3;
+  int info;
+
+  VectorXd x(n);
+
+  /*
+   * First try
+   */
+  x<< 100., 1., 0.1;
+  // do the computation
+  rat42_functor functor;
+  LevenbergMarquardt<rat42_functor> lm(functor);
+  info = lm.minimize(x);
+
+  // check return value
+  VERIFY( 1 == info); 
+  VERIFY( 10 == lm.nfev); 
+  VERIFY( 8 == lm.njev); 
+  // check norm^2
+  VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 8.0565229338E+00);
+  // check x
+  VERIFY_IS_APPROX(x[0], 7.2462237576E+01);
+  VERIFY_IS_APPROX(x[1], 2.6180768402E+00);
+  VERIFY_IS_APPROX(x[2], 6.7359200066E-02);
+
+  /*
+   * Second try
+   */
+  x<< 75., 2.5, 0.07;
+  // do the computation
+  info = lm.minimize(x);
+
+  // check return value
+  VERIFY( 1 == info); 
+  VERIFY( 6 == lm.nfev); 
+  VERIFY( 5 == lm.njev); 
+  // check norm^2
+  VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 8.0565229338E+00);
+  // check x
+  VERIFY_IS_APPROX(x[0], 7.2462237576E+01);
+  VERIFY_IS_APPROX(x[1], 2.6180768402E+00);
+  VERIFY_IS_APPROX(x[2], 6.7359200066E-02);
+}
+
+struct MGH10_functor : Functor<double>
+{
+    MGH10_functor(void) : Functor<double>(3,16) {}
+    static const double x[16];
+    static const double y[16];
+    int operator()(const VectorXd &b, VectorXd &fvec)
+    {
+        assert(b.size()==3);
+        assert(fvec.size()==16);
+        for(int i=0; i<16; i++)
+            fvec[i] =  b[0] * exp(b[1]/(x[i]+b[2])) - y[i];
+        return 0;
+    }
+    int df(const VectorXd &b, MatrixXd &fjac)
+    {
+        assert(b.size()==3);
+        assert(fjac.rows()==16);
+        assert(fjac.cols()==3);
+        for(int i=0; i<16; i++) {
+            double factor = 1./(x[i]+b[2]);
+            double e = exp(b[1]*factor);
+            fjac(i,0) = e;
+            fjac(i,1) = b[0]*factor*e;
+            fjac(i,2) = -b[1]*b[0]*factor*factor*e;
+        }
+        return 0;
+    }
+};
+const double MGH10_functor::x[16] = { 5.000000E+01, 5.500000E+01, 6.000000E+01, 6.500000E+01, 7.000000E+01, 7.500000E+01, 8.000000E+01, 8.500000E+01, 9.000000E+01, 9.500000E+01, 1.000000E+02, 1.050000E+02, 1.100000E+02, 1.150000E+02, 1.200000E+02, 1.250000E+02 };
+const double MGH10_functor::y[16] = { 3.478000E+04, 2.861000E+04, 2.365000E+04, 1.963000E+04, 1.637000E+04, 1.372000E+04, 1.154000E+04, 9.744000E+03, 8.261000E+03, 7.030000E+03, 6.005000E+03, 5.147000E+03, 4.427000E+03, 3.820000E+03, 3.307000E+03, 2.872000E+03 };
+
+// http://www.itl.nist.gov/div898/strd/nls/data/mgh10.shtml
+void testNistMGH10(void)
+{
+  const int n=3;
+  int info;
+
+  VectorXd x(n);
+
+  /*
+   * First try
+   */
+  x<< 2., 400000., 25000.;
+  // do the computation
+  MGH10_functor functor;
+  LevenbergMarquardt<MGH10_functor> lm(functor);
+  info = lm.minimize(x);
+
+  // check return value
+  VERIFY( 2 == info); 
+  VERIFY( 285 == lm.nfev); 
+  VERIFY( 250 == lm.njev); 
+  // check norm^2
+  VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 8.7945855171E+01);
+  // check x
+  VERIFY_IS_APPROX(x[0], 5.6096364710E-03);
+  VERIFY_IS_APPROX(x[1], 6.1813463463E+03);
+  VERIFY_IS_APPROX(x[2], 3.4522363462E+02);
+
+  /*
+   * Second try
+   */
+  x<< 0.02, 4000., 250.;
+  // do the computation
+  info = lm.minimize(x);
+
+  // check return value
+  VERIFY( 2 == info); 
+  VERIFY( 126 == lm.nfev); 
+  VERIFY( 116 == lm.njev); 
+  // check norm^2
+  VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 8.7945855171E+01);
+  // check x
+  VERIFY_IS_APPROX(x[0], 5.6096364710E-03);
+  VERIFY_IS_APPROX(x[1], 6.1813463463E+03);
+  VERIFY_IS_APPROX(x[2], 3.4522363462E+02);
+}
+
+
+struct BoxBOD_functor : Functor<double>
+{
+    BoxBOD_functor(void) : Functor<double>(2,6) {}
+    static const double x[6];
+    int operator()(const VectorXd &b, VectorXd &fvec)
+    {
+        static const double y[6] = { 109., 149., 149., 191., 213., 224. };
+        assert(b.size()==2);
+        assert(fvec.size()==6);
+        for(int i=0; i<6; i++)
+            fvec[i] =  b[0]*(1.-exp(-b[1]*x[i])) - y[i];
+        return 0;
+    }
+    int df(const VectorXd &b, MatrixXd &fjac)
+    {
+        assert(b.size()==2);
+        assert(fjac.rows()==6);
+        assert(fjac.cols()==2);
+        for(int i=0; i<6; i++) {
+            double e = exp(-b[1]*x[i]);
+            fjac(i,0) = 1.-e;
+            fjac(i,1) = b[0]*x[i]*e;
+        }
+        return 0;
+    }
+};
+const double BoxBOD_functor::x[6] = { 1., 2., 3., 5., 7., 10. };
+
+// http://www.itl.nist.gov/div898/strd/nls/data/boxbod.shtml
+void testNistBoxBOD(void)
+{
+  const int n=2;
+  int info;
+
+  VectorXd x(n);
+
+  /*
+   * First try
+   */
+  x<< 1., 1.;
+  // do the computation
+  BoxBOD_functor functor;
+  LevenbergMarquardt<BoxBOD_functor> lm(functor);
+  lm.parameters.ftol = 1.E6*epsilon<double>();
+  lm.parameters.xtol = 1.E6*epsilon<double>();
+  lm.parameters.factor = 10.;
+  info = lm.minimize(x);
+
+  // check return value
+  VERIFY( 1 == info); 
+  VERIFY( 31 == lm.nfev); 
+  VERIFY( 25  == lm.njev); 
+  // check norm^2
+  VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 1.1680088766E+03);
+  // check x
+  VERIFY_IS_APPROX(x[0], 2.1380940889E+02);
+  VERIFY_IS_APPROX(x[1], 5.4723748542E-01);
+
+  /*
+   * Second try
+   */
+  x<< 100., 0.75;
+  // do the computation
+  lm.resetParameters();
+  lm.parameters.ftol = epsilon<double>();
+  lm.parameters.xtol = epsilon<double>();
+  info = lm.minimize(x);
+
+  // check return value
+  VERIFY( 1 == info); 
+  VERIFY( 15 == lm.nfev); 
+  VERIFY( 14 == lm.njev); 
+  // check norm^2
+  VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 1.1680088766E+03);
+  // check x
+  VERIFY_IS_APPROX(x[0], 2.1380940889E+02);
+  VERIFY_IS_APPROX(x[1], 5.4723748542E-01);
+}
+
+struct MGH17_functor : Functor<double>
+{
+    MGH17_functor(void) : Functor<double>(5,33) {}
+    static const double x[33];
+    static const double y[33];
+    int operator()(const VectorXd &b, VectorXd &fvec)
+    {
+        assert(b.size()==5);
+        assert(fvec.size()==33);
+        for(int i=0; i<33; i++) 
+            fvec[i] =  b[0] + b[1]*exp(-b[3]*x[i]) +  b[2]*exp(-b[4]*x[i]) - y[i];
+        return 0;
+    }
+    int df(const VectorXd &b, MatrixXd &fjac)
+    {
+        assert(b.size()==5);
+        assert(fjac.rows()==33);
+        assert(fjac.cols()==5);
+        for(int i=0; i<33; i++) {
+            fjac(i,0) = 1.;
+            fjac(i,1) = exp(-b[3]*x[i]);
+            fjac(i,2) = exp(-b[4]*x[i]);
+            fjac(i,3) = -x[i]*b[1]*exp(-b[3]*x[i]);
+            fjac(i,4) = -x[i]*b[2]*exp(-b[4]*x[i]);
+        }
+        return 0;
+    }
+};
+const double MGH17_functor::x[33] = { 0.000000E+00, 1.000000E+01, 2.000000E+01, 3.000000E+01, 4.000000E+01, 5.000000E+01, 6.000000E+01, 7.000000E+01, 8.000000E+01, 9.000000E+01, 1.000000E+02, 1.100000E+02, 1.200000E+02, 1.300000E+02, 1.400000E+02, 1.500000E+02, 1.600000E+02, 1.700000E+02, 1.800000E+02, 1.900000E+02, 2.000000E+02, 2.100000E+02, 2.200000E+02, 2.300000E+02, 2.400000E+02, 2.500000E+02, 2.600000E+02, 2.700000E+02, 2.800000E+02, 2.900000E+02, 3.000000E+02, 3.100000E+02, 3.200000E+02 };
+const double MGH17_functor::y[33] = { 8.440000E-01, 9.080000E-01, 9.320000E-01, 9.360000E-01, 9.250000E-01, 9.080000E-01, 8.810000E-01, 8.500000E-01, 8.180000E-01, 7.840000E-01, 7.510000E-01, 7.180000E-01, 6.850000E-01, 6.580000E-01, 6.280000E-01, 6.030000E-01, 5.800000E-01, 5.580000E-01, 5.380000E-01, 5.220000E-01, 5.060000E-01, 4.900000E-01, 4.780000E-01, 4.670000E-01, 4.570000E-01, 4.480000E-01, 4.380000E-01, 4.310000E-01, 4.240000E-01, 4.200000E-01, 4.140000E-01, 4.110000E-01, 4.060000E-01 };
+
+// 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 = epsilon<double>();
+  lm.parameters.xtol = epsilon<double>();
+  lm.parameters.maxfev = 1000;
+  info = lm.minimize(x);
+
+  // check return value
+  VERIFY( 1 == info); 
+  VERIFY( 599 == lm.nfev); 
+  VERIFY( 544 == lm.njev); 
+  // 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);
+
+  /*
+   * 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( 1 == info); 
+  VERIFY( 18 == lm.nfev); 
+  VERIFY( 15 == lm.njev); 
+  // 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);
+}
+
+struct MGH09_functor : Functor<double>
+{
+    MGH09_functor(void) : Functor<double>(4,11) {}
+    static const double _x[11];
+    static const double y[11];
+    int operator()(const VectorXd &b, VectorXd &fvec)
+    {
+        assert(b.size()==4);
+        assert(fvec.size()==11);
+        for(int i=0; i<11; i++) {
+            double x = _x[i], xx=x*x;
+            fvec[i] = b[0]*(xx+x*b[1])/(xx+x*b[2]+b[3]) - y[i];
+        }
+        return 0;
+    }
+    int df(const VectorXd &b, MatrixXd &fjac)
+    {
+        assert(b.size()==4);
+        assert(fjac.rows()==11);
+        assert(fjac.cols()==4);
+        for(int i=0; i<11; i++) {
+            double x = _x[i], xx=x*x;
+            double factor = 1./(xx+x*b[2]+b[3]);
+            fjac(i,0) = (xx+x*b[1]) * factor;
+            fjac(i,1) = b[0]*x* factor;
+            fjac(i,2) = - b[0]*(xx+x*b[1]) * x * factor * factor;
+            fjac(i,3) = - b[0]*(xx+x*b[1]) * factor * factor;
+        }
+        return 0;
+    }
+};
+const double MGH09_functor::_x[11] = { 4., 2., 1., 5.E-1 , 2.5E-01, 1.670000E-01, 1.250000E-01,  1.E-01, 8.330000E-02, 7.140000E-02, 6.250000E-02 };
+const double MGH09_functor::y[11] = { 1.957000E-01, 1.947000E-01, 1.735000E-01, 1.600000E-01, 8.440000E-02, 6.270000E-02, 4.560000E-02, 3.420000E-02, 3.230000E-02, 2.350000E-02, 2.460000E-02 };
+
+// http://www.itl.nist.gov/div898/strd/nls/data/mgh09.shtml
+void testNistMGH09(void)
+{
+  const int n=4;
+  int info;
+
+  VectorXd x(n);
+
+  /*
+   * First try
+   */
+  x<< 25., 39, 41.5, 39.;
+  // do the computation
+  MGH09_functor functor;
+  LevenbergMarquardt<MGH09_functor> lm(functor);
+  lm.parameters.maxfev = 1000;
+  info = lm.minimize(x);
+
+  // check return value
+  VERIFY( 1 == info); 
+  VERIFY( 503== lm.nfev); 
+  VERIFY( 385 == lm.njev); 
+  // check norm^2
+  VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 3.0750560385E-04);
+  // check x
+  VERIFY_IS_APPROX(x[0], 0.19280624); // should be 1.9280693458E-01
+  VERIFY_IS_APPROX(x[1], 0.19129774); // should be 1.9128232873E-01
+  VERIFY_IS_APPROX(x[2], 0.12305940); // should be 1.2305650693E-01
+  VERIFY_IS_APPROX(x[3], 0.13606946); // should be 1.3606233068E-01
+
+  /*
+   * Second try
+   */
+  x<< 0.25, 0.39, 0.415, 0.39;
+  // do the computation
+  lm.resetParameters();
+  info = lm.minimize(x);
+
+  // check return value
+  VERIFY( 1 == info); 
+  VERIFY( 18 == lm.nfev); 
+  VERIFY( 16 == lm.njev); 
+  // check norm^2
+  VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 3.0750560385E-04);
+  // check x
+  VERIFY_IS_APPROX(x[0], 0.19280781); // should be 1.9280693458E-01
+  VERIFY_IS_APPROX(x[1], 0.19126265); // should be 1.9128232873E-01
+  VERIFY_IS_APPROX(x[2], 0.12305280); // should be 1.2305650693E-01
+  VERIFY_IS_APPROX(x[3], 0.13605322); // should be 1.3606233068E-01
+}
+
+
+
+struct Bennett5_functor : Functor<double>
+{
+    Bennett5_functor(void) : Functor<double>(3,154) {}
+    static const double x[154];
+    static const double y[154];
+    int operator()(const VectorXd &b, VectorXd &fvec)
+    {
+        assert(b.size()==3);
+        assert(fvec.size()==154);
+        for(int i=0; i<154; i++)
+            fvec[i] = b[0]* pow(b[1]+x[i],-1./b[2]) - y[i];
+        return 0;
+    }
+    int df(const VectorXd &b, MatrixXd &fjac)
+    {
+        assert(b.size()==3);
+        assert(fjac.rows()==154);
+        assert(fjac.cols()==3);
+        for(int i=0; i<154; i++) {
+            double e = pow(b[1]+x[i],-1./b[2]);
+            fjac(i,0) = e;
+            fjac(i,1) = - b[0]*e/b[2]/(b[1]+x[i]);
+            fjac(i,2) = b[0]*e*log(b[1]+x[i])/b[2]/b[2];
+        }
+        return 0;
+    }
+};
+const double Bennett5_functor::x[154] = { 7.447168E0, 8.102586E0, 8.452547E0, 8.711278E0, 8.916774E0, 9.087155E0, 9.232590E0, 9.359535E0, 9.472166E0, 9.573384E0, 9.665293E0, 9.749461E0, 9.827092E0, 9.899128E0, 9.966321E0, 10.029280E0, 10.088510E0, 10.144430E0, 10.197380E0, 10.247670E0, 10.295560E0, 10.341250E0, 10.384950E0, 10.426820E0, 10.467000E0, 10.505640E0, 10.542830E0, 10.578690E0, 10.613310E0, 10.646780E0, 10.679150E0, 10.710520E0, 10.740920E0, 10.770440E0, 10.799100E0, 10.826970E0, 10.854080E0, 10.880470E0, 10.906190E0, 10.931260E0, 10.955720E0, 10.979590E0, 11.002910E0, 11.025700E0, 11.047980E0, 11.069770E0, 11.091100E0, 11.111980E0, 11.132440E0, 11.152480E0, 11.172130E0, 11.191410E0, 11.210310E0, 11.228870E0, 11.247090E0, 11.264980E0, 11.282560E0, 11.299840E0, 11.316820E0, 11.333520E0, 11.349940E0, 11.366100E0, 11.382000E0, 11.397660E0, 11.413070E0, 11.428240E0, 11.443200E0, 11.457930E0, 11.472440E0, 11.486750E0, 11.500860E0, 11.514770E0, 11.528490E0, 11.542020E0, 11.555380E0, 11.568550E0, 11.581560E0, 11.594420E0, 11.607121E0, 11.619640E0, 11.632000E0, 11.644210E0, 11.656280E0, 11.668200E0, 11.679980E0, 11.691620E0, 11.703130E0, 11.714510E0, 11.725760E0, 11.736880E0, 11.747890E0, 11.758780E0, 11.769550E0, 11.780200E0, 11.790730E0, 11.801160E0, 11.811480E0, 11.821700E0, 11.831810E0, 11.841820E0, 11.851730E0, 11.861550E0, 11.871270E0, 11.880890E0, 11.890420E0, 11.899870E0, 11.909220E0, 11.918490E0, 11.927680E0, 11.936780E0, 11.945790E0, 11.954730E0, 11.963590E0, 11.972370E0, 11.981070E0, 11.989700E0, 11.998260E0, 12.006740E0, 12.015150E0, 12.023490E0, 12.031760E0, 12.039970E0, 12.048100E0, 12.056170E0, 12.064180E0, 12.072120E0, 12.080010E0, 12.087820E0, 12.095580E0, 12.103280E0, 12.110920E0, 12.118500E0, 12.126030E0, 12.133500E0, 12.140910E0, 12.148270E0, 12.155570E0, 12.162830E0, 12.170030E0, 12.177170E0, 12.184270E0, 12.191320E0, 12.198320E0, 12.205270E0, 12.212170E0, 12.219030E0, 12.225840E0, 12.232600E0, 12.239320E0, 12.245990E0, 12.252620E0, 12.259200E0, 12.265750E0, 12.272240E0 };
+const double Bennett5_functor::y[154] = { -34.834702E0 ,-34.393200E0 ,-34.152901E0 ,-33.979099E0 ,-33.845901E0 ,-33.732899E0 ,-33.640301E0 ,-33.559200E0 ,-33.486801E0 ,-33.423100E0 ,-33.365101E0 ,-33.313000E0 ,-33.260899E0 ,-33.217400E0 ,-33.176899E0 ,-33.139198E0 ,-33.101601E0 ,-33.066799E0 ,-33.035000E0 ,-33.003101E0 ,-32.971298E0 ,-32.942299E0 ,-32.916302E0 ,-32.890202E0 ,-32.864101E0 ,-32.841000E0 ,-32.817799E0 ,-32.797501E0 ,-32.774300E0 ,-32.757000E0 ,-32.733799E0 ,-32.716400E0 ,-32.699100E0 ,-32.678799E0 ,-32.661400E0 ,-32.644001E0 ,-32.626701E0 ,-32.612202E0 ,-32.597698E0 ,-32.583199E0 ,-32.568699E0 ,-32.554298E0 ,-32.539799E0 ,-32.525299E0 ,-32.510799E0 ,-32.499199E0 ,-32.487598E0 ,-32.473202E0 ,-32.461601E0 ,-32.435501E0 ,-32.435501E0 ,-32.426800E0 ,-32.412300E0 ,-32.400799E0 ,-32.392101E0 ,-32.380501E0 ,-32.366001E0 ,-32.357300E0 ,-32.348598E0 ,-32.339901E0 ,-32.328400E0 ,-32.319698E0 ,-32.311001E0 ,-32.299400E0 ,-32.290699E0 ,-32.282001E0 ,-32.273300E0 ,-32.264599E0 ,-32.256001E0 ,-32.247299E0 ,-32.238602E0 ,-32.229900E0 ,-32.224098E0 ,-32.215401E0 ,-32.203800E0 ,-32.198002E0 ,-32.189400E0 ,-32.183601E0 ,-32.174900E0 ,-32.169102E0 ,-32.163300E0 ,-32.154598E0 ,-32.145901E0 ,-32.140099E0 ,-32.131401E0 ,-32.125599E0 ,-32.119801E0 ,-32.111198E0 ,-32.105400E0 ,-32.096699E0 ,-32.090900E0 ,-32.088001E0 ,-32.079300E0 ,-32.073502E0 ,-32.067699E0 ,-32.061901E0 ,-32.056099E0 ,-32.050301E0 ,-32.044498E0 ,-32.038799E0 ,-32.033001E0 ,-32.027199E0 ,-32.024300E0 ,-32.018501E0 ,-32.012699E0 ,-32.004002E0 ,-32.001099E0 ,-31.995300E0 ,-31.989500E0 ,-31.983700E0 ,-31.977900E0 ,-31.972099E0 ,-31.969299E0 ,-31.963501E0 ,-31.957701E0 ,-31.951900E0 ,-31.946100E0 ,-31.940300E0 ,-31.937401E0 ,-31.931601E0 ,-31.925800E0 ,-31.922899E0 ,-31.917101E0 ,-31.911301E0 ,-31.908400E0 ,-31.902599E0 ,-31.896900E0 ,-31.893999E0 ,-31.888201E0 ,-31.885300E0 ,-31.882401E0 ,-31.876600E0 ,-31.873699E0 ,-31.867901E0 ,-31.862101E0 ,-31.859200E0 ,-31.856300E0 ,-31.850500E0 ,-31.844700E0 ,-31.841801E0 ,-31.838900E0 ,-31.833099E0 ,-31.830200E0 ,-31.827299E0 ,-31.821600E0 ,-31.818701E0 ,-31.812901E0 ,-31.809999E0 ,-31.807100E0 ,-31.801300E0 ,-31.798401E0 ,-31.795500E0 ,-31.789700E0 ,-31.786800E0 };
+
+// http://www.itl.nist.gov/div898/strd/nls/data/bennett5.shtml
+void testNistBennett5(void)
+{
+  const int  n=3;
+  int info;
+
+  VectorXd x(n);
+
+  /*
+   * First try
+   */
+  x<< -2000., 50., 0.8;
+  // do the computation
+  Bennett5_functor functor;
+  LevenbergMarquardt<Bennett5_functor> lm(functor);
+  lm.parameters.maxfev = 1000;
+  info = lm.minimize(x);
+
+  // check return value
+  VERIFY( 1 == info); 
+  VERIFY( 758 == lm.nfev); 
+  VERIFY( 744 == lm.njev); 
+  // check norm^2
+  VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 5.2404744073E-04);
+  // check x
+  VERIFY_IS_APPROX(x[0], -2.5235058043E+03);
+  VERIFY_IS_APPROX(x[1], 4.6736564644E+01);
+  VERIFY_IS_APPROX(x[2], 9.3218483193E-01);
+  /*
+   * Second try
+   */
+  x<< -1500., 45., 0.85;
+  // do the computation
+  lm.resetParameters();
+  info = lm.minimize(x);
+
+  // check return value
+  VERIFY( 1 == info); 
+  VERIFY( 203 == lm.nfev); 
+  VERIFY( 192 == lm.njev); 
+  // check norm^2
+  VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 5.2404744073E-04);
+  // check x
+  VERIFY_IS_APPROX(x[0], -2523.3007865); // should be -2.5235058043E+03
+  VERIFY_IS_APPROX(x[1], 46.735705771); // should be 4.6736564644E+01);
+  VERIFY_IS_APPROX(x[2], 0.93219881891); // should be 9.3218483193E-01);
+}
+
+struct thurber_functor : Functor<double>
+{
+    thurber_functor(void) : Functor<double>(7,37) {}
+    static const double _x[37];
+    static const double _y[37];
+    int operator()(const VectorXd &b, VectorXd &fvec)
+    {
+        //        int called=0; printf("call hahn1_functor with  iflag=%d, called=%d\n", iflag, called); if (iflag==1) called++;
+        assert(b.size()==7);
+        assert(fvec.size()==37);
+        for(int i=0; i<37; i++) {
+            double x=_x[i], xx=x*x, xxx=xx*x;
+            fvec[i] = (b[0]+b[1]*x+b[2]*xx+b[3]*xxx) / (1.+b[4]*x+b[5]*xx+b[6]*xxx) - _y[i];
+        }
+        return 0;
+    }
+    int df(const VectorXd &b, MatrixXd &fjac)
+    {
+        assert(b.size()==7);
+        assert(fjac.rows()==37);
+        assert(fjac.cols()==7);
+        for(int i=0; i<37; i++) {
+            double x=_x[i], xx=x*x, xxx=xx*x;
+            double fact = 1./(1.+b[4]*x+b[5]*xx+b[6]*xxx);
+            fjac(i,0) = 1.*fact;
+            fjac(i,1) = x*fact;
+            fjac(i,2) = xx*fact;
+            fjac(i,3) = xxx*fact;
+            fact = - (b[0]+b[1]*x+b[2]*xx+b[3]*xxx) * fact * fact;
+            fjac(i,4) = x*fact;
+            fjac(i,5) = xx*fact;
+            fjac(i,6) = xxx*fact;
+        }
+        return 0;
+    }
+};
+const double thurber_functor::_x[37] = { -3.067E0, -2.981E0, -2.921E0, -2.912E0, -2.840E0, -2.797E0, -2.702E0, -2.699E0, -2.633E0, -2.481E0, -2.363E0, -2.322E0, -1.501E0, -1.460E0, -1.274E0, -1.212E0, -1.100E0, -1.046E0, -0.915E0, -0.714E0, -0.566E0, -0.545E0, -0.400E0, -0.309E0, -0.109E0, -0.103E0, 0.010E0, 0.119E0, 0.377E0, 0.790E0, 0.963E0, 1.006E0, 1.115E0, 1.572E0, 1.841E0, 2.047E0, 2.200E0 };
+const double thurber_functor::_y[37] = { 80.574E0, 84.248E0, 87.264E0, 87.195E0, 89.076E0, 89.608E0, 89.868E0, 90.101E0, 92.405E0, 95.854E0, 100.696E0, 101.060E0, 401.672E0, 390.724E0, 567.534E0, 635.316E0, 733.054E0, 759.087E0, 894.206E0, 990.785E0, 1090.109E0, 1080.914E0, 1122.643E0, 1178.351E0, 1260.531E0, 1273.514E0, 1288.339E0, 1327.543E0, 1353.863E0, 1414.509E0, 1425.208E0, 1421.384E0, 1442.962E0, 1464.350E0, 1468.705E0, 1447.894E0, 1457.628E0};
+
+// http://www.itl.nist.gov/div898/strd/nls/data/thurber.shtml
+void testNistThurber(void)
+{
+  const int n=7;
+  int info;
+
+  VectorXd x(n);
+
+  /*
+   * First try
+   */
+  x<< 1000 ,1000 ,400 ,40 ,0.7,0.3,0.0 ;
+  // do the computation
+  thurber_functor functor;
+  LevenbergMarquardt<thurber_functor> lm(functor);
+  lm.parameters.ftol = 1.E4*epsilon<double>();
+  lm.parameters.xtol = 1.E4*epsilon<double>();
+  info = lm.minimize(x);
+
+  // check return value
+  VERIFY( 1 == info); 
+  VERIFY( 39 == lm.nfev); 
+  VERIFY( 36== lm.njev); 
+  // check norm^2
+  VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 5.6427082397E+03); 
+  // check x
+  VERIFY_IS_APPROX(x[0], 1.2881396800E+03);
+  VERIFY_IS_APPROX(x[1], 1.4910792535E+03);
+  VERIFY_IS_APPROX(x[2], 5.8323836877E+02);
+  VERIFY_IS_APPROX(x[3], 7.5416644291E+01);
+  VERIFY_IS_APPROX(x[4], 9.6629502864E-01);
+  VERIFY_IS_APPROX(x[5], 3.9797285797E-01);
+  VERIFY_IS_APPROX(x[6], 4.9727297349E-02);
+
+  /*
+   * Second try
+   */
+  x<< 1300 ,1500 ,500  ,75   ,1    ,0.4  ,0.05  ;
+  // do the computation
+  lm.resetParameters();
+  lm.parameters.ftol = 1.E4*epsilon<double>();
+  lm.parameters.xtol = 1.E4*epsilon<double>();
+  info = lm.minimize(x);
+
+  // check return value
+  VERIFY( 1 == info); 
+  VERIFY( 29 == lm.nfev); 
+  VERIFY( 28 == lm.njev); 
+  // check norm^2
+  VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 5.6427082397E+03); 
+  // check x
+  VERIFY_IS_APPROX(x[0], 1.2881396800E+03);
+  VERIFY_IS_APPROX(x[1], 1.4910792535E+03);
+  VERIFY_IS_APPROX(x[2], 5.8323836877E+02);
+  VERIFY_IS_APPROX(x[3], 7.5416644291E+01);
+  VERIFY_IS_APPROX(x[4], 9.6629502864E-01);
+  VERIFY_IS_APPROX(x[5], 3.9797285797E-01);
+  VERIFY_IS_APPROX(x[6], 4.9727297349E-02);
+}
+
+struct rat43_functor : Functor<double>
+{
+    rat43_functor(void) : Functor<double>(4,15) {}
+    static const double x[15];
+    static const double y[15];
+    int operator()(const VectorXd &b, VectorXd &fvec)
+    {
+        assert(b.size()==4);
+        assert(fvec.size()==15);
+        for(int i=0; i<15; i++)
+            fvec[i] = b[0] * pow(1.+exp(b[1]-b[2]*x[i]),-1./b[3]) - y[i];
+        return 0;
+    }
+    int df(const VectorXd &b, MatrixXd &fjac)
+    {
+        assert(b.size()==4);
+        assert(fjac.rows()==15);
+        assert(fjac.cols()==4);
+        for(int i=0; i<15; i++) {
+            double e = exp(b[1]-b[2]*x[i]);
+            double power = -1./b[3];
+            fjac(i,0) = pow(1.+e, power);
+            fjac(i,1) = power*b[0]*e*pow(1.+e, power-1.);
+            fjac(i,2) = -power*b[0]*e*x[i]*pow(1.+e, power-1.);
+            fjac(i,3) = b[0]*power*power*log(1.+e)*pow(1.+e, power);
+        }
+        return 0;
+    }
+};
+const double rat43_functor::x[15] = { 1., 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12., 13., 14., 15. };
+const double rat43_functor::y[15] = { 16.08, 33.83, 65.80, 97.20, 191.55, 326.20, 386.87, 520.53, 590.03, 651.92, 724.93, 699.56, 689.96, 637.56, 717.41 };
+
+// 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*epsilon<double>();
+  lm.parameters.xtol = 1.E6*epsilon<double>();
+  info = lm.minimize(x);
+
+  // check return value
+  VERIFY( 1 == info); 
+  VERIFY( 27 == lm.nfev); 
+  VERIFY( 20 == lm.njev); 
+  // 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*epsilon<double>();
+  lm.parameters.xtol = 1.E5*epsilon<double>();
+  info = lm.minimize(x);
+
+  // check return value
+  VERIFY( 1 == info); 
+  VERIFY( 9 == lm.nfev); 
+  VERIFY( 8 == lm.njev); 
+  // 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);
+}
+
+
+
+struct eckerle4_functor : Functor<double>
+{
+    eckerle4_functor(void) : Functor<double>(3,35) {}
+    static const double x[35];
+    static const double y[35];
+    int operator()(const VectorXd &b, VectorXd &fvec)
+    {
+        assert(b.size()==3);
+        assert(fvec.size()==35);
+        for(int i=0; i<35; i++)
+            fvec[i] = b[0]/b[1] * exp(-0.5*(x[i]-b[2])*(x[i]-b[2])/(b[1]*b[1])) - y[i];
+        return 0;
+    }
+    int df(const VectorXd &b, MatrixXd &fjac)
+    {
+        assert(b.size()==3);
+        assert(fjac.rows()==35);
+        assert(fjac.cols()==3);
+        for(int i=0; i<35; i++) {
+            double b12 = b[1]*b[1];
+            double e = exp(-0.5*(x[i]-b[2])*(x[i]-b[2])/b12);
+            fjac(i,0) = e / b[1];
+            fjac(i,1) = ((x[i]-b[2])*(x[i]-b[2])/b12-1.) * b[0]*e/b12;
+            fjac(i,2) = (x[i]-b[2])*e*b[0]/b[1]/b12;
+        }
+        return 0;
+    }
+};
+const double eckerle4_functor::x[35] = { 400.0, 405.0, 410.0, 415.0, 420.0, 425.0, 430.0, 435.0, 436.5, 438.0, 439.5, 441.0, 442.5, 444.0, 445.5, 447.0, 448.5, 450.0, 451.5, 453.0, 454.5, 456.0, 457.5, 459.0, 460.5, 462.0, 463.5, 465.0, 470.0, 475.0, 480.0, 485.0, 490.0, 495.0, 500.0};
+const double eckerle4_functor::y[35] = { 0.0001575, 0.0001699, 0.0002350, 0.0003102, 0.0004917, 0.0008710, 0.0017418, 0.0046400, 0.0065895, 0.0097302, 0.0149002, 0.0237310, 0.0401683, 0.0712559, 0.1264458, 0.2073413, 0.2902366, 0.3445623, 0.3698049, 0.3668534, 0.3106727, 0.2078154, 0.1164354, 0.0616764, 0.0337200, 0.0194023, 0.0117831, 0.0074357, 0.0022732, 0.0008800, 0.0004579, 0.0002345, 0.0001586, 0.0001143, 0.0000710 };
+
+// http://www.itl.nist.gov/div898/strd/nls/data/eckerle4.shtml
+void testNistEckerle4(void)
+{
+  const int n=3;
+  int info;
+
+  VectorXd x(n);
+
+  /*
+   * First try
+   */
+  x<< 1., 10., 500.;
+  // do the computation
+  eckerle4_functor functor;
+  LevenbergMarquardt<eckerle4_functor> lm(functor);
+  info = lm.minimize(x);
+
+  // check return value
+  VERIFY( 1 == info); 
+  VERIFY( 18 == lm.nfev); 
+  VERIFY( 15 == lm.njev); 
+  // check norm^2
+  VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 1.4635887487E-03);
+  // check x
+  VERIFY_IS_APPROX(x[0], 1.5543827178);
+  VERIFY_IS_APPROX(x[1], 4.0888321754);
+  VERIFY_IS_APPROX(x[2], 4.5154121844E+02);
+
+  /*
+   * Second try
+   */
+  x<< 1.5, 5., 450.;
+  // do the computation
+  info = lm.minimize(x);
+
+  // check return value
+  VERIFY( 1 == info); 
+  VERIFY( 7 == lm.nfev); 
+  VERIFY( 6 == lm.njev); 
+  // check norm^2
+  VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 1.4635887487E-03);
+  // check x
+  VERIFY_IS_APPROX(x[0], 1.5543827178);
+  VERIFY_IS_APPROX(x[1], 4.0888321754);
+  VERIFY_IS_APPROX(x[2], 4.5154121844E+02);
+}
+
+void test_NonLinearOptimization()
+{
+    // Tests using the examples provided by (c)minpack
+    CALL_SUBTEST(testChkder());
+    CALL_SUBTEST(testLmder1());
+    CALL_SUBTEST(testLmder());
+    CALL_SUBTEST(testHybrj1());
+    CALL_SUBTEST(testHybrj());
+    CALL_SUBTEST(testHybrd1());
+    CALL_SUBTEST(testHybrd());
+    CALL_SUBTEST(testLmstr1());
+    CALL_SUBTEST(testLmstr());
+    CALL_SUBTEST(testLmdif1());
+    CALL_SUBTEST(testLmdif());
+
+    // NIST tests, level of difficulty = "Lower"
+    CALL_SUBTEST(testNistMisra1a());
+    CALL_SUBTEST(testNistChwirut2());
+
+    // NIST tests, level of difficulty = "Average"
+    CALL_SUBTEST(testNistHahn1());
+    CALL_SUBTEST(testNistMisra1d());
+    CALL_SUBTEST(testNistMGH17());
+    CALL_SUBTEST(testNistLanczos1());
+
+    // NIST tests, level of difficulty = "Higher"
+    CALL_SUBTEST(testNistRat42());
+    CALL_SUBTEST(testNistMGH10());
+    CALL_SUBTEST(testNistBoxBOD());
+    CALL_SUBTEST(testNistMGH09());
+    CALL_SUBTEST(testNistBennett5());
+    CALL_SUBTEST(testNistThurber());
+    CALL_SUBTEST(testNistRat43());
+    CALL_SUBTEST(testNistEckerle4());
+}
+
+/*
+ * Can be useful for debugging...
+  printf("info, nfev, njev : %d, %d, %d\n", info, lm.nfev, lm.njev);
+  printf("info, nfev : %d, %d\n", info, lm.nfev);
+  printf("info, nfev, njev : %d, %d, %d\n", info, solver.nfev, solver.njev);
+  printf("info, nfev : %d, %d\n", info, solver.nfev);
+  printf("x[0] : %.32g\n", x[0]);
+  printf("x[1] : %.32g\n", x[1]);
+  printf("x[2] : %.32g\n", x[2]);
+  printf("x[3] : %.32g\n", x[3]);
+  printf("fvec.blueNorm() : %.32g\n", solver.fvec.blueNorm());
+  printf("fvec.blueNorm() : %.32g\n", lm.fvec.blueNorm());
+*/
+