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1848 lines
62 KiB
C++
1848 lines
62 KiB
C++
// This file is part of Eigen, a lightweight C++ template library
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// for linear algebra.
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//
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// Copyright (C) 2009 Thomas Capricelli <orzel@freehackers.org>
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#include <stdio.h>
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#include "main.h"
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#include <unsupported/Eigen/NonLinear>
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int fcn_chkder(const VectorXd &x, VectorXd &fvec, MatrixXd &fjac, int iflag)
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{
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/* subroutine fcn for chkder example. */
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int i;
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assert(15 == fvec.size());
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assert(3 == x.size());
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double tmp1, tmp2, tmp3, tmp4;
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double y[15]={1.4e-1, 1.8e-1, 2.2e-1, 2.5e-1, 2.9e-1, 3.2e-1, 3.5e-1,
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3.9e-1, 3.7e-1, 5.8e-1, 7.3e-1, 9.6e-1, 1.34, 2.1, 4.39};
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if (iflag == 0)
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return 0;
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if (iflag != 2)
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for (i=0; i<15; i++) {
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tmp1 = i+1;
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tmp2 = 16-i-1;
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tmp3 = tmp1;
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if (i >= 8) tmp3 = tmp2;
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fvec[i] = y[i] - (x[0] + tmp1/(x[1]*tmp2 + x[2]*tmp3));
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}
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else {
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for (i = 0; i < 15; i++) {
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tmp1 = i+1;
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tmp2 = 16-i-1;
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/* error introduced into next statement for illustration. */
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/* corrected statement should read tmp3 = tmp1 . */
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tmp3 = tmp2;
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if (i >= 8) tmp3 = tmp2;
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tmp4 = (x[1]*tmp2 + x[2]*tmp3); tmp4=tmp4*tmp4;
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fjac(i,0) = -1.;
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fjac(i,1) = tmp1*tmp2/tmp4;
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fjac(i,2) = tmp1*tmp3/tmp4;
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}
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}
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return 0;
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}
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void testChkder()
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{
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const int m=15, n=3;
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VectorXd x(n), fvec(m), xp, fvecp(m), err;
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MatrixXd fjac(m,n);
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VectorXi ipvt;
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/* the following values should be suitable for */
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/* checking the jacobian matrix. */
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x << 9.2e-1, 1.3e-1, 5.4e-1;
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ei_chkder(x, fvec, fjac, xp, fvecp, 1, err);
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fcn_chkder(x, fvec, fjac, 1);
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fcn_chkder(x, fvec, fjac, 2);
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fcn_chkder(xp, fvecp, fjac, 1);
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ei_chkder(x, fvec, fjac, xp, fvecp, 2, err);
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fvecp -= fvec;
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// check those
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VectorXd fvec_ref(m), fvecp_ref(m), err_ref(m);
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fvec_ref <<
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-1.181606, -1.429655, -1.606344,
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-1.745269, -1.840654, -1.921586,
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-1.984141, -2.022537, -2.468977,
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-2.827562, -3.473582, -4.437612,
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-6.047662, -9.267761, -18.91806;
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fvecp_ref <<
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-7.724666e-09, -3.432406e-09, -2.034843e-10,
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2.313685e-09, 4.331078e-09, 5.984096e-09,
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7.363281e-09, 8.53147e-09, 1.488591e-08,
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2.33585e-08, 3.522012e-08, 5.301255e-08,
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8.26666e-08, 1.419747e-07, 3.19899e-07;
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err_ref <<
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0.1141397, 0.09943516, 0.09674474,
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0.09980447, 0.1073116, 0.1220445,
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0.1526814, 1, 1,
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1, 1, 1,
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1, 1, 1;
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VERIFY_IS_APPROX(fvec, fvec_ref);
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VERIFY_IS_APPROX(fvecp, fvecp_ref);
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VERIFY_IS_APPROX(err, err_ref);
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}
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// Generic functor
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template<typename _Scalar, int NX=Dynamic, int NY=Dynamic>
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struct Functor
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{
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typedef _Scalar Scalar;
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enum {
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InputsAtCompileTime = NX,
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ValuesAtCompileTime = NY
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};
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typedef Matrix<Scalar,InputsAtCompileTime,1> InputType;
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typedef Matrix<Scalar,ValuesAtCompileTime,1> ValueType;
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typedef Matrix<Scalar,ValuesAtCompileTime,InputsAtCompileTime> JacobianType;
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int m_inputs, m_values;
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Functor() : m_inputs(InputsAtCompileTime), m_values(ValuesAtCompileTime) {}
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Functor(int inputs, int values) : m_inputs(inputs), m_values(values) {}
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int inputs() const { return m_inputs; }
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int values() const { return m_values; }
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// you should define that in the subclass :
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// void operator() (const InputType& x, ValueType* v, JacobianType* _j=0) const;
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};
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struct lmder_functor : Functor<double>
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{
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lmder_functor(void): Functor<double>(3,15) {}
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int operator()(const VectorXd &x, VectorXd &fvec) const
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{
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double tmp1, tmp2, tmp3;
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double y[15] = {1.4e-1, 1.8e-1, 2.2e-1, 2.5e-1, 2.9e-1, 3.2e-1, 3.5e-1,
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3.9e-1, 3.7e-1, 5.8e-1, 7.3e-1, 9.6e-1, 1.34, 2.1, 4.39};
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for (int i = 0; i < values(); i++)
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{
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tmp1 = i+1;
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tmp2 = 16 - i - 1;
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tmp3 = (i>=8)? tmp2 : tmp1;
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fvec[i] = y[i] - (x[0] + tmp1/(x[1]*tmp2 + x[2]*tmp3));
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}
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return 0;
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}
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int df(const VectorXd &x, MatrixXd &fjac) const
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{
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double tmp1, tmp2, tmp3, tmp4;
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for (int i = 0; i < values(); i++)
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{
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tmp1 = i+1;
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tmp2 = 16 - i - 1;
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tmp3 = (i>=8)? tmp2 : tmp1;
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tmp4 = (x[1]*tmp2 + x[2]*tmp3); tmp4 = tmp4*tmp4;
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fjac(i,0) = -1;
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fjac(i,1) = tmp1*tmp2/tmp4;
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fjac(i,2) = tmp1*tmp3/tmp4;
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}
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return 0;
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}
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};
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void testLmder1()
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{
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int n=3, info;
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VectorXd x;
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/* the following starting values provide a rough fit. */
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x.setConstant(n, 1.);
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// do the computation
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lmder_functor functor;
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LevenbergMarquardt<lmder_functor> lm(functor);
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info = lm.lmder1(x);
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// check return value
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VERIFY( 1 == info);
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VERIFY(lm.nfev==6);
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VERIFY(lm.njev==5);
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// check norm
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VERIFY_IS_APPROX(lm.fvec.blueNorm(), 0.09063596);
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// check x
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VectorXd x_ref(n);
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x_ref << 0.08241058, 1.133037, 2.343695;
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VERIFY_IS_APPROX(x, x_ref);
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}
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void testLmder()
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{
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const int m=15, n=3;
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int info;
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double fnorm, covfac;
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VectorXd x;
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/* the following starting values provide a rough fit. */
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x.setConstant(n, 1.);
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// do the computation
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lmder_functor functor;
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LevenbergMarquardt<lmder_functor> lm(functor);
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info = lm.minimize(x);
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// check return values
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VERIFY( 1 == info);
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VERIFY(lm.nfev==6);
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VERIFY(lm.njev==5);
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// check norm
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fnorm = lm.fvec.blueNorm();
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VERIFY_IS_APPROX(fnorm, 0.09063596);
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// check x
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VectorXd x_ref(n);
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x_ref << 0.08241058, 1.133037, 2.343695;
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VERIFY_IS_APPROX(x, x_ref);
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// check covariance
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covfac = fnorm*fnorm/(m-n);
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ei_covar(lm.fjac, lm.ipvt); // TODO : move this as a function of lm
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MatrixXd cov_ref(n,n);
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cov_ref <<
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0.0001531202, 0.002869941, -0.002656662,
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0.002869941, 0.09480935, -0.09098995,
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-0.002656662, -0.09098995, 0.08778727;
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// std::cout << fjac*covfac << std::endl;
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MatrixXd cov;
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cov = covfac*lm.fjac.corner<n,n>(TopLeft);
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VERIFY_IS_APPROX( cov, cov_ref);
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// TODO: why isn't this allowed ? :
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// VERIFY_IS_APPROX( covfac*fjac.corner<n,n>(TopLeft) , cov_ref);
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}
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struct hybrj_functor : Functor<double>
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{
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hybrj_functor(void) : Functor<double>(9,9) {}
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int operator()(const VectorXd &x, VectorXd &fvec)
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{
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double temp, temp1, temp2;
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const int n = x.size();
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assert(fvec.size()==n);
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for (int k = 0; k < n; k++)
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{
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temp = (3. - 2.*x[k])*x[k];
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temp1 = 0.;
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if (k) temp1 = x[k-1];
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temp2 = 0.;
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if (k != n-1) temp2 = x[k+1];
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fvec[k] = temp - temp1 - 2.*temp2 + 1.;
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}
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return 0;
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}
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int df(const VectorXd &x, MatrixXd &fjac)
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{
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const int n = x.size();
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assert(fjac.rows()==n);
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assert(fjac.cols()==n);
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for (int k = 0; k < n; k++)
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{
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for (int j = 0; j < n; j++)
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fjac(k,j) = 0.;
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fjac(k,k) = 3.- 4.*x[k];
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if (k) fjac(k,k-1) = -1.;
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if (k != n-1) fjac(k,k+1) = -2.;
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}
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return 0;
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}
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};
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void testHybrj1()
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{
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const int n=9;
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int info;
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VectorXd x(n);
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/* the following starting values provide a rough fit. */
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x.setConstant(n, -1.);
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// do the computation
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hybrj_functor functor;
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HybridNonLinearSolver<hybrj_functor> solver(functor);
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info = solver.hybrj1(x);
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// check return value
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VERIFY( 1 == info);
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VERIFY(solver.nfev==11);
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VERIFY(solver.njev==1);
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// check norm
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VERIFY_IS_APPROX(solver.fvec.blueNorm(), 1.192636e-08);
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// check x
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VectorXd x_ref(n);
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x_ref <<
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-0.5706545, -0.6816283, -0.7017325,
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-0.7042129, -0.701369, -0.6918656,
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-0.665792, -0.5960342, -0.4164121;
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VERIFY_IS_APPROX(x, x_ref);
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}
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void testHybrj()
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{
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const int n=9;
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int info;
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VectorXd x(n);
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/* the following starting values provide a rough fit. */
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x.setConstant(n, -1.);
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// do the computation
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hybrj_functor functor;
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HybridNonLinearSolver<hybrj_functor> solver(functor);
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solver.diag.setConstant(n, 1.);
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info = solver.solve(x, 2);
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// check return value
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VERIFY( 1 == info);
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VERIFY(solver.nfev==11);
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VERIFY(solver.njev==1);
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// check norm
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VERIFY_IS_APPROX(solver.fvec.blueNorm(), 1.192636e-08);
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// check x
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VectorXd x_ref(n);
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x_ref <<
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-0.5706545, -0.6816283, -0.7017325,
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-0.7042129, -0.701369, -0.6918656,
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-0.665792, -0.5960342, -0.4164121;
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VERIFY_IS_APPROX(x, x_ref);
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}
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struct hybrd_functor : Functor<double>
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{
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hybrd_functor(void) : Functor<double>(9,9) {}
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int operator()(const VectorXd &x, VectorXd &fvec) const
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{
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double temp, temp1, temp2;
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const int n = x.size();
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assert(fvec.size()==n);
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for (int k=0; k < n; k++)
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{
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temp = (3. - 2.*x[k])*x[k];
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temp1 = 0.;
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if (k) temp1 = x[k-1];
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temp2 = 0.;
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if (k != n-1) temp2 = x[k+1];
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fvec[k] = temp - temp1 - 2.*temp2 + 1.;
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}
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return 0;
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}
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};
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void testHybrd1()
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{
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int n=9, info;
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VectorXd x(n);
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/* the following starting values provide a rough solution. */
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x.setConstant(n, -1.);
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// do the computation
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hybrd_functor functor;
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HybridNonLinearSolver<hybrd_functor> solver(functor);
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info = solver.hybrd1(x);
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// check return value
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VERIFY( 1 == info);
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VERIFY(solver.nfev==20);
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// check norm
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VERIFY_IS_APPROX(solver.fvec.blueNorm(), 1.192636e-08);
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// check x
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VectorXd x_ref(n);
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x_ref << -0.5706545, -0.6816283, -0.7017325, -0.7042129, -0.701369, -0.6918656, -0.665792, -0.5960342, -0.4164121;
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VERIFY_IS_APPROX(x, x_ref);
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}
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void testHybrd()
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{
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const int n=9;
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int info;
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VectorXd x;
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/* the following starting values provide a rough fit. */
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x.setConstant(n, -1.);
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// do the computation
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hybrd_functor functor;
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HybridNonLinearSolver<hybrd_functor> solver(functor);
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solver.parameters.nb_of_subdiagonals = 1;
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solver.parameters.nb_of_superdiagonals = 1;
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solver.diag.setConstant(n, 1.);
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info = solver.solveNumericalDiff(x, 2);
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// check return value
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VERIFY( 1 == info);
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VERIFY(solver.nfev==14);
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// check norm
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VERIFY_IS_APPROX(solver.fvec.blueNorm(), 1.192636e-08);
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// check x
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VectorXd x_ref(n);
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x_ref <<
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-0.5706545, -0.6816283, -0.7017325,
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-0.7042129, -0.701369, -0.6918656,
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-0.665792, -0.5960342, -0.4164121;
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VERIFY_IS_APPROX(x, x_ref);
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}
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struct lmstr_functor : Functor<double>
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{
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lmstr_functor(void) : Functor<double>(3,15) {}
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int operator()(const VectorXd &x, VectorXd &fvec)
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{
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/* subroutine fcn for lmstr1 example. */
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double tmp1, tmp2, tmp3;
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double y[15]={1.4e-1, 1.8e-1, 2.2e-1, 2.5e-1, 2.9e-1, 3.2e-1, 3.5e-1,
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3.9e-1, 3.7e-1, 5.8e-1, 7.3e-1, 9.6e-1, 1.34, 2.1, 4.39};
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assert(15==fvec.size());
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assert(3==x.size());
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for (int i=0; i<15; i++)
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{
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tmp1 = i+1;
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tmp2 = 16 - i - 1;
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tmp3 = (i>=8)? tmp2 : tmp1;
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fvec[i] = y[i] - (x[0] + tmp1/(x[1]*tmp2 + x[2]*tmp3));
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}
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return 0;
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}
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int df(const VectorXd &x, VectorXd &jac_row, int rownb)
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{
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assert(x.size()==3);
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assert(jac_row.size()==x.size());
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double tmp1, tmp2, tmp3, tmp4;
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int i = rownb-2;
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tmp1 = i+1;
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tmp2 = 16 - i - 1;
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tmp3 = (i>=8)? tmp2 : tmp1;
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tmp4 = (x[1]*tmp2 + x[2]*tmp3); tmp4 = tmp4*tmp4;
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jac_row[0] = -1;
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jac_row[1] = tmp1*tmp2/tmp4;
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jac_row[2] = tmp1*tmp3/tmp4;
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return 0;
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}
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};
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void testLmstr1()
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{
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const int n=3;
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int info;
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VectorXd x(n);
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/* the following starting values provide a rough fit. */
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x.setConstant(n, 1.);
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// do the computation
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lmstr_functor functor;
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LevenbergMarquardt<lmstr_functor> lm(functor);
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info = lm.lmstr1(x);
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// check return value
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VERIFY( 1 == info);
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VERIFY(lm.nfev==6);
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VERIFY(lm.njev==5);
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// check norm
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VERIFY_IS_APPROX(lm.fvec.blueNorm(), 0.09063596);
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|
// 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};
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|
|
// 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 );
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|
VERIFY_IS_APPROX(x[3],-1.426264e-06); // shoulde be : -1.4262662514E-06
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|
VERIFY_IS_APPROX(x[4],-5.7609940901E-03 );
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|
VERIFY_IS_APPROX(x[5], 2.4053735503E-04 );
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|
VERIFY_IS_APPROX(x[6],-1.2314450199E-07 );
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|
|
|
/*
|
|
* 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
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|
VERIFY_IS_APPROX(x[1], -0.1226933); // should be : -1.2269296921E-01
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|
VERIFY_IS_APPROX(x[2], 0.004086383); // should be : 4.0863750610E-03
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|
VERIFY_IS_APPROX(x[3], -1.426277e-06); // shoulde be : -1.4262662514E-06
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VERIFY_IS_APPROX(x[4],-5.7609940901E-03 );
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|
VERIFY_IS_APPROX(x[5], 0.00024053772); // should be : 2.4053735503E-04
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VERIFY_IS_APPROX(x[6], -1.231450e-07); // should be : -1.2314450199E-07
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|
|
}
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|
|
struct misra1d_functor : Functor<double>
|
|
{
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|
misra1d_functor(void) : Functor<double>(2,14) {}
|
|
static const double x[14];
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|
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];
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|
}
|
|
return 0;
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|
}
|
|
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};
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|
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};
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|
|
// 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_NonLinear()
|
|
{
|
|
// Tests using the examples provided by (c)minpack
|
|
CALL_SUBTEST(testChkder());
|
|
CALL_SUBTEST(testLmder1());
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CALL_SUBTEST(testLmder());
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CALL_SUBTEST(testHybrj1());
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CALL_SUBTEST(testHybrj());
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CALL_SUBTEST(testHybrd1());
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CALL_SUBTEST(testHybrd());
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CALL_SUBTEST(testLmstr1());
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CALL_SUBTEST(testLmstr());
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CALL_SUBTEST(testLmdif1());
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CALL_SUBTEST(testLmdif());
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|
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// NIST tests, level of difficulty = "Lower"
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CALL_SUBTEST(testNistMisra1a());
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CALL_SUBTEST(testNistChwirut2());
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|
|
|
// NIST tests, level of difficulty = "Average"
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|
CALL_SUBTEST(testNistHahn1());
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CALL_SUBTEST(testNistMisra1d());
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CALL_SUBTEST(testNistMGH17());
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CALL_SUBTEST(testNistLanczos1());
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|
|
|
// NIST tests, level of difficulty = "Higher"
|
|
CALL_SUBTEST(testNistRat42());
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|
CALL_SUBTEST(testNistMGH10());
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|
CALL_SUBTEST(testNistBoxBOD());
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|
CALL_SUBTEST(testNistMGH09());
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|
CALL_SUBTEST(testNistBennett5());
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|
CALL_SUBTEST(testNistThurber());
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|
CALL_SUBTEST(testNistRat43());
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|
CALL_SUBTEST(testNistEckerle4());
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|
}
|
|
|
|
/*
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|
* Can be useful for debugging...
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|
printf("info, nfev, njev : %d, %d, %d\n", info, lm.nfev, lm.njev);
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printf("info, nfev : %d, %d\n", info, lm.nfev);
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printf("info, nfev, njev : %d, %d, %d\n", info, solver.nfev, solver.njev);
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printf("info, nfev : %d, %d\n", info, solver.nfev);
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|
printf("x[0] : %.32g\n", x[0]);
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|
printf("x[1] : %.32g\n", x[1]);
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|
printf("x[2] : %.32g\n", x[2]);
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|
printf("x[3] : %.32g\n", x[3]);
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|
printf("fvec.blueNorm() : %.32g\n", solver.fvec.blueNorm());
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|
printf("fvec.blueNorm() : %.32g\n", lm.fvec.blueNorm());
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|
*/
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|