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eigen/unsupported/test/NonLinear.cpp

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// 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/NonLinear>
int fcn_chkder(int /*m*/, int /*n*/, const double *x, double *fvec, double *fjac, int ldfjac, int iflag)
{
/* subroutine fcn for chkder example. */
int i;
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)
{
/* insert print statements here when nprint is positive. */
return 0;
}
if (iflag != 2)
for (i=1; i<=15; i++)
{
tmp1 = i;
tmp2 = 16 - i;
tmp3 = tmp1;
if (i > 8) tmp3 = tmp2;
fvec[i-1] = y[i-1] - (x[1-1] + tmp1/(x[2-1]*tmp2 + x[3-1]*tmp3));
}
else
{
for (i = 1; i <= 15; i++)
{
tmp1 = i;
tmp2 = 16 - i;
/* error introduced into next statement for illustration. */
/* corrected statement should read tmp3 = tmp1 . */
tmp3 = tmp2;
if (i > 8) tmp3 = tmp2;
tmp4 = (x[2-1]*tmp2 + x[3-1]*tmp3); tmp4=tmp4*tmp4;
fjac[i-1+ ldfjac*(1-1)] = -1.;
fjac[i-1+ ldfjac*(2-1)] = tmp1*tmp2/tmp4;
fjac[i-1+ ldfjac*(3-1)] = tmp1*tmp3/tmp4;
}
}
return 0;
}
void testChkder()
{
int i, m, n, ldfjac;
double x[3], fvec[15], fjac[15*3], xp[3], fvecp[15],
err[15];
m = 15;
n = 3;
/* the following values should be suitable for */
/* checking the jacobian matrix. */
x[1-1] = 9.2e-1;
x[2-1] = 1.3e-1;
x[3-1] = 5.4e-1;
ldfjac = 15;
chkder(m, n, x, fvec, fjac, ldfjac, xp, fvecp, 1, err);
fcn_chkder(m, n, x, fvec, fjac, ldfjac, 1);
fcn_chkder(m, n, x, fvec, fjac, ldfjac, 2);
fcn_chkder(m, n, xp, fvecp, fjac, ldfjac, 1);
chkder(m, n, x, fvec, fjac, ldfjac, xp, fvecp, 2, err);
for (i=1; i<=m; i++)
{
fvecp[i-1] = fvecp[i-1] - fvec[i-1];
}
double 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
};
double 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
};
double err_ref[] = {
0.1141397, 0.09943516, 0.09674474,
0.09980447, 0.1073116, 0.1220445,
0.1526814, 1, 1,
1, 1, 1,
1, 1, 1
};
for (i=1; i<=m; i++) VERIFY_IS_APPROX(fvec[i-1], fvec_ref[i-1]);
for (i=1; i<=m; i++) VERIFY_IS_APPROX(fvecp[i-1], fvecp_ref[i-1]);
for (i=1; i<=m; i++) VERIFY_IS_APPROX(err[i-1], err_ref[i-1]);
}
struct lmder1_functor {
static int f(void * /*p*/, int /*m*/, int /*n*/, const double *x, double *fvec, double *fjac, int ldfjac, int iflag)
{
/* subroutine fcn for lmder1 example. */
int i;
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 != 2)
{
for (i = 1; i <= 15; i++)
{
tmp1 = i;
tmp2 = 16 - i;
tmp3 = tmp1;
if (i > 8) tmp3 = tmp2;
fvec[i-1] = y[i-1] - (x[1-1] + tmp1/(x[2-1]*tmp2 + x[3-1]*tmp3));
}
}
else
{
for ( i = 1; i <= 15; i++)
{
tmp1 = i;
tmp2 = 16 - i;
tmp3 = tmp1;
if (i > 8) tmp3 = tmp2;
tmp4 = (x[2-1]*tmp2 + x[3-1]*tmp3); tmp4 = tmp4*tmp4;
fjac[i-1 + ldfjac*(1-1)] = -1.;
fjac[i-1 + ldfjac*(2-1)] = tmp1*tmp2/tmp4;
fjac[i-1 + ldfjac*(3-1)] = tmp1*tmp3/tmp4;
}
}
return 0;
}
};
void testLmder1()
{
int m=15, n=3, info;
Eigen::VectorXd x(n), fvec(m);
VectorXi ipvt;
/* the following starting values provide a rough fit. */
x.setConstant(n, 1.);
// do the computation
info = ei_lmder1<lmder1_functor,double>(x, fvec, ipvt);
// check return value
VERIFY( 1 == info);
// check norm
VERIFY_IS_APPROX(fvec.norm(), 0.09063596);
// check x
VectorXd x_ref(n);
x_ref << 0.08241058, 1.133037, 2.343695;
VERIFY_IS_APPROX(x, x_ref);
}
struct lmder_functor {
static int f(void * /*p*/, int /*m*/, int /*n*/, const double *x, double *fvec, double *fjac, int ldfjac, int iflag)
{
/* subroutine fcn for lmder example. */
int i;
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)
{
/* insert print statements here when nprint is positive. */
return 0;
}
if (iflag != 2)
{
for (i=1; i <= 15; i++)
{
tmp1 = i;
tmp2 = 16 - i;
tmp3 = tmp1;
if (i > 8) tmp3 = tmp2;
fvec[i-1] = y[i-1] - (x[1-1] + tmp1/(x[2-1]*tmp2 + x[3-1]*tmp3));
}
}
else
{
for (i=1; i<=15; i++)
{
tmp1 = i;
tmp2 = 16 - i;
tmp3 = tmp1;
if (i > 8) tmp3 = tmp2;
tmp4 = (x[2-1]*tmp2 + x[3-1]*tmp3); tmp4 = tmp4*tmp4;
fjac[i-1 + ldfjac*(1-1)] = -1.;
fjac[i-1 + ldfjac*(2-1)] = tmp1*tmp2/tmp4;
fjac[i-1 + ldfjac*(3-1)] = tmp1*tmp3/tmp4;
};
}
return 0;
}
};
void testLmder()
{
const int m=15, n=3;
int info, nfev, njev;
double fnorm, covfac, covar_ftol;
Eigen::VectorXd x(n), fvec(m), diag(n), wa1;
Eigen::MatrixXd fjac;
VectorXi ipvt;
/* the following starting values provide a rough fit. */
x.setConstant(n, 1.);
// do the computation
info = ei_lmder<lmder_functor, double>(x, fvec, nfev, njev, fjac, ipvt, wa1, diag);
// check return values
VERIFY( 1 == info);
VERIFY(nfev==6);
VERIFY(njev==5);
// check norm
fnorm = fvec.norm();
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
covar_ftol = dpmpar(1);
covfac = fnorm*fnorm/(m-n);
covar(n, fjac.data(), m, ipvt.data(), covar_ftol, wa1.data());
Eigen::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;
Eigen::MatrixXd cov;
cov = covfac*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);
}
int fcn_hybrj1(void * /*p*/, int n, const double *x, double *fvec, double *fjac, int ldfjac,
int iflag)
{
/* subroutine fcn for hybrj1 example. */
int j, k;
double one=1, temp, temp1, temp2, three=3, two=2, zero=0, four=4;
if (iflag != 2)
{
for (k = 1; k <= n; k++)
{
temp = (three - two*x[k-1])*x[k-1];
temp1 = zero;
if (k != 1) temp1 = x[k-1-1];
temp2 = zero;
if (k != n) temp2 = x[k+1-1];
fvec[k-1] = temp - temp1 - two*temp2 + one;
}
}
else
{
for (k = 1; k <= n; k++)
{
for (j = 1; j <= n; j++)
{
fjac[k-1 + ldfjac*(j-1)] = zero;
}
fjac[k-1 + ldfjac*(k-1)] = three - four*x[k-1];
if (k != 1) fjac[k-1 + ldfjac*(k-1-1)] = -one;
if (k != n) fjac[k-1 + ldfjac*(k+1-1)] = -two;
}
}
return 0;
}
void testHybrj1()
{
int j, n, ldfjac, info, lwa;
double tol, fnorm;
double x[9], fvec[9], fjac[9*9], wa[99];
n = 9;
/* the following starting values provide a rough solution. */
for (j=1; j<=9; j++)
{
x[j-1] = -1.;
}
ldfjac = 9;
lwa = 99;
/* set tol to the square root of the machine precision. */
/* unless high solutions are required, */
/* this is the recommended setting. */
tol = sqrt(dpmpar(1));
info = hybrj1(fcn_hybrj1, 0, n, x, fvec, fjac, ldfjac, tol, wa, lwa);
fnorm = enorm(n, fvec);
VERIFY_IS_APPROX(fnorm, 1.192636e-08);
VERIFY(info==1);
double x_ref[] = {
-0.5706545, -0.6816283, -0.7017325,
-0.7042129, -0.701369, -0.6918656,
-0.665792, -0.5960342, -0.4164121
};
for (j=1; j<=n; j++) VERIFY_IS_APPROX(x[j-1], x_ref[j-1]);
}
int fcn_hybrj(void * /*p*/, int n, const double *x, double *fvec, double *fjac, int ldfjac,
int iflag)
{
/* subroutine fcn for hybrj example. */
int j, k;
double one=1, temp, temp1, temp2, three=3, two=2, zero=0, four=4;
if (iflag == 0)
{
/* insert print statements here when nprint is positive. */
return 0;
}
if (iflag != 2)
{
for (k=1; k <= n; k++)
{
temp = (three - two*x[k-1])*x[k-1];
temp1 = zero;
if (k != 1) temp1 = x[k-1-1];
temp2 = zero;
if (k != n) temp2 = x[k+1-1];
fvec[k-1] = temp - temp1 - two*temp2 + one;
}
}
else
{
for (k = 1; k <= n; k++)
{
for (j=1; j <= n; j++)
{
fjac[k-1 + ldfjac*(j-1)] = zero;
}
fjac[k-1 + ldfjac*(k-1)] = three - four*x[k-1];
if (k != 1) fjac[k-1 + ldfjac*(k-1-1)] = -one;
if (k != n) fjac[k-1 + ldfjac*(k+1-1)] = -two;
}
}
return 0;
}
void testHybrj()
{
int j, n, ldfjac, maxfev, mode, nprint, info, nfev, njev, lr;
double xtol, factor, fnorm;
double x[9], fvec[9], fjac[9*9], diag[9], r[45], qtf[9],
wa1[9], wa2[9], wa3[9], wa4[9];
n = 9;
/* the following starting values provide a rough solution. */
for (j=1; j<=9; j++)
{
x[j-1] = -1.;
}
ldfjac = 9;
lr = 45;
/* set xtol to the square root of the machine precision. */
/* unless high solutions are required, */
/* this is the recommended setting. */
xtol = sqrt(dpmpar(1));
maxfev = 1000;
mode = 2;
for (j=1; j<=9; j++)
{
diag[j-1] = 1.;
}
factor = 1.e2;
nprint = 0;
info = hybrj(fcn_hybrj, 0, n, x, fvec, fjac, ldfjac, xtol, maxfev, diag,
mode, factor, nprint, &nfev, &njev, r, lr, qtf,
wa1, wa2, wa3, wa4);
fnorm = enorm(n, fvec);
VERIFY_IS_APPROX(fnorm, 1.192636e-08);
VERIFY(nfev==11);
VERIFY(njev==1);
VERIFY(info==1);
double x_ref[] = {
-0.5706545, -0.6816283, -0.7017325,
-0.7042129, -0.701369, -0.6918656,
-0.665792, -0.5960342, -0.4164121
};
for (j=1; j<=n; j++) VERIFY_IS_APPROX(x[j-1], x_ref[j-1]);
}
struct hybrd1_functor {
static int f(void * /*p*/, int n, const double *x, double *fvec, int /*iflag*/)
{
/* subroutine fcn for hybrd1 example. */
int k;
double one=1, temp, temp1, temp2, three=3, two=2, zero=0;
for (k=1; k <= n; k++)
{
temp = (three - two*x[k-1])*x[k-1];
temp1 = zero;
if (k != 1) temp1 = x[k-1-1];
temp2 = zero;
if (k != n) temp2 = x[k+1-1];
fvec[k-1] = temp - temp1 - two*temp2 + one;
}
return 0;
}
};
void testHybrd1()
{
int n=9, info;
Eigen::VectorXd x(n), fvec(n);
/* the following starting values provide a rough solution. */
x.setConstant(n, -1.);
// do the computation
info = ei_hybrd1<hybrd1_functor,double>(x, fvec);
// check return value
VERIFY( 1 == info);
// check norm
VERIFY_IS_APPROX(fvec.norm(), 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 {
static int f(void * /*p*/, int n, const double *x, double *fvec, int iflag)
{
/* subroutine fcn for hybrd example. */
int k;
double one=1, temp, temp1, temp2, three=3, two=2, zero=0;
if (iflag == 0)
{
/* insert print statements here when nprint is positive. */
return 0;
}
for (k=1; k<=n; k++)
{
temp = (three - two*x[k-1])*x[k-1];
temp1 = zero;
if (k != 1) temp1 = x[k-1-1];
temp2 = zero;
if (k != n) temp2 = x[k+1-1];
fvec[k-1] = temp - temp1 - two*temp2 + one;
}
return 0;
}
};
void testHybrd()
{
const int n=9;
int info, nfev, ml, mu, mode;
Eigen::VectorXd x(n), fvec, diag(n), R, qtf;
Eigen::MatrixXd fjac;
VectorXi ipvt;
/* the following starting values provide a rough fit. */
x.setConstant(n, -1.);
ml = 1;
mu = 1;
mode = 2;
diag.setConstant(n, 1.);
// do the computation
info = ei_hybrd<hybrd_functor, double>(x,fvec, nfev, fjac, R, qtf, diag, mode, ml, mu);
// check return value
VERIFY( 1 == info);
VERIFY(nfev==14);
// check norm
VERIFY_IS_APPROX(fvec.norm(), 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);
}
int fcn_lmstr1(void * /*p*/, int /*m*/, int /*n*/, const double *x, double *fvec, double *fjrow, int iflag)
{
/* subroutine fcn for lmstr1 example. */
int i;
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 < 2)
{
for (i=1; i<=15; i++)
{
tmp1=i;
tmp2 = 16-i;
tmp3 = tmp1;
if (i > 8) tmp3 = tmp2;
fvec[i-1] = y[i-1] - (x[1-1] + tmp1/(x[2-1]*tmp2 + x[3-1]*tmp3));
}
}
else
{
i = iflag - 1;
tmp1 = i;
tmp2 = 16 - i;
tmp3 = tmp1;
if (i > 8) tmp3 = tmp2;
tmp4 = (x[2-1]*tmp2 + x[3-1]*tmp3); tmp4=tmp4*tmp4;
fjrow[1-1] = -1;
fjrow[2-1] = tmp1*tmp2/tmp4;
fjrow[3-1] = tmp1*tmp3/tmp4;
}
return 0;
}
void testLmstr1()
{
int m, n, ldfjac, info, lwa, ipvt[3];
double tol, fnorm;
double x[30], fvec[15], fjac[9], wa[30];
m = 15;
n = 3;
/* the following starting values provide a rough fit. */
x[0] = 1.;
x[1] = 1.;
x[2] = 1.;
ldfjac = 3;
lwa = 30;
/* set tol to the square root of the machine precision.
unless high precision solutions are required,
this is the recommended setting. */
tol = sqrt(dpmpar(1));
info = lmstr1(fcn_lmstr1, 0, m, n,
x, fvec, fjac, ldfjac,
tol, ipvt, wa, lwa);
fnorm = enorm(m, fvec);
VERIFY_IS_APPROX(fnorm, 0.09063596);
VERIFY(info==1);
double x_ref[] = {0.08241058, 1.133037, 2.343695 };
for (m=1; m<=3; m++) VERIFY_IS_APPROX(x[m-1], x_ref[m-1]);
}
int fcn_lmstr(void * /*p*/, int /*m*/, int /*n*/, const double *x, double *fvec, double *fjrow, int iflag)
{
/* subroutine fcn for lmstr example. */
int i;
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)
{
/* insert print statements here when nprint is positive. */
return 0;
}
if (iflag < 2)
{
for (i = 1; i <= 15; i++)
{
tmp1 = i;
tmp2 = 16 - i;
tmp3 = tmp1;
if (i > 8) tmp3 = tmp2;
fvec[i-1] = y[i-1] - (x[1-1] + tmp1/(x[2-1]*tmp2 + x[3-1]*tmp3));
}
}
else
{
i = iflag - 1;
tmp1 = i;
tmp2 = 16 - i;
tmp3 = tmp1;
if (i > 8) tmp3 = tmp2;
tmp4 = (x[2-1]*tmp2 + x[3-1]*tmp3); tmp4 = tmp4*tmp4;
fjrow[1-1] = -1.;
fjrow[2-1] = tmp1*tmp2/tmp4;
fjrow[3-1] = tmp1*tmp3/tmp4;
}
return 0;
}
void testLmstr()
{
int j, m, n, ldfjac, maxfev, mode, nprint, info, nfev, njev;
int ipvt[3];
double ftol, xtol, gtol, factor, fnorm;
double x[3], fvec[15], fjac[3*3], diag[3], qtf[3],
wa1[3], wa2[3], wa3[3], wa4[15];
m = 15;
n = 3;
/* the following starting values provide a rough fit. */
x[1-1] = 1.;
x[2-1] = 1.;
x[3-1] = 1.;
ldfjac = 3;
/* set ftol and xtol to the square root of the machine */
/* and gtol to zero. unless high solutions are */
/* required, these are the recommended settings. */
ftol = sqrt(dpmpar(1));
xtol = sqrt(dpmpar(1));
gtol = 0.;
maxfev = 400;
mode = 1;
factor = 1.e2;
nprint = 0;
info = lmstr(fcn_lmstr, 0, m, n, x, fvec, fjac, ldfjac, ftol, xtol, gtol,
maxfev, diag, mode, factor, nprint, &nfev, &njev,
ipvt, qtf, wa1, wa2, wa3, wa4);
fnorm = enorm(m, fvec);
VERIFY_IS_APPROX(fnorm, 0.09063596);
VERIFY(nfev==6);
VERIFY(njev==5);
VERIFY(info==1);
double x_ref[] = {0.08241058, 1.133037, 2.343695 };
for (j=1; j<=n; j++) VERIFY_IS_APPROX(x[j-1], x_ref[j-1]);
}
int fcn_lmdif1(void * /*p*/, int /*m*/, int /*n*/, const double *x, double *fvec, int /*iflag*/)
{
/* function fcn for lmdif1 example */
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};
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()
{
int m, n, info, lwa, iwa[3];
double tol, fnorm, x[3], fvec[15], wa[75];
m = 15;
n = 3;
/* the following starting values provide a rough fit. */
x[0] = 1.e0;
x[1] = 1.e0;
x[2] = 1.e0;
lwa = 75;
/* set tol to the square root of the machine precision. unless high
precision solutions are required, this is the recommended
setting. */
tol = sqrt(dpmpar(1));
info = lmdif1(fcn_lmdif1, 0, m, n, x, fvec, tol, iwa, wa, lwa);
fnorm = enorm(m, fvec);
VERIFY_IS_APPROX(fnorm, 0.09063596);
VERIFY(info==1);
double x_ref[] = {0.0824106, 1.1330366, 2.3436947 };
int j;
for (j=1; j<=n; j++) VERIFY_IS_APPROX(x[j-1], x_ref[j-1]);
}
int fcn_lmdif(void * /*p*/, int /*m*/, int /*n*/, const double *x, double *fvec, int iflag)
{
/* subroutine fcn for lmdif example. */
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, 1.34, 2.1, 4.39};
if (iflag == 0)
{
/* insert print statements here when nprint is positive. */
return 0;
}
for (i = 1; i <= 15; i++)
{
tmp1 = i;
tmp2 = 16 - i;
tmp3 = tmp1;
if (i > 8) tmp3 = tmp2;
fvec[i-1] = y[i-1] - (x[1-1] + tmp1/(x[2-1]*tmp2 + x[3-1]*tmp3));
}
return 0;
}
void testLmdif()
{
int i, j, m, n, maxfev, mode, nprint, info, nfev, ldfjac;
int ipvt[3];
double ftol, xtol, gtol, epsfcn, factor, fnorm;
double x[3], fvec[15], diag[3], fjac[15*3], qtf[3],
wa1[3], wa2[3], wa3[3], wa4[15];
double covfac;
m = 15;
n = 3;
/* the following starting values provide a rough fit. */
x[1-1] = 1.;
x[2-1] = 1.;
x[3-1] = 1.;
ldfjac = 15;
/* set ftol and xtol to the square root of the machine */
/* and gtol to zero. unless high solutions are */
/* required, these are the recommended settings. */
ftol = sqrt(dpmpar(1));
xtol = sqrt(dpmpar(1));
gtol = 0.;
maxfev = 800;
epsfcn = 0.;
mode = 1;
factor = 1.e2;
nprint = 0;
info = lmdif(fcn_lmdif, 0, m, n, x, fvec, ftol, xtol, gtol, maxfev, epsfcn,
diag, mode, factor, nprint, &nfev, fjac, ldfjac,
ipvt, qtf, wa1, wa2, wa3, wa4);
fnorm = enorm(m, fvec);
VERIFY_IS_APPROX(fnorm, 0.09063596);
VERIFY(nfev==21);
VERIFY(info==1);
double x_ref[] = {0.08241058, 1.133037, 2.343695 };
for (j=1; j<=n; j++) VERIFY_IS_APPROX(x[j-1], x_ref[j-1]);
ftol = dpmpar(1);
covfac = fnorm*fnorm/(m-n);
covar(n, fjac, ldfjac, ipvt, ftol, wa1);
double cov_ref[] = {
0.0001531202, 0.002869942, -0.002656662,
0.002869942, 0.09480937, -0.09098997,
-0.002656662, -0.09098997, 0.08778729
};
for (i=1; i<=n; i++)
for (j=1; j<=n; j++)
VERIFY_IS_APPROX(fjac[(i-1)*ldfjac+j-1]*covfac, cov_ref[(i-1)*3+(j-1)]);
}
struct misra1a_functor {
static int f(void * /*p*/, int m, int n, const double *b, double *fvec, double *fjac, int ldfjac, int iflag)
{
static const double 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};
static const double 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};
int i;
assert(m==14);
assert(n==2);
assert(ldfjac==14);
if (iflag != 2) {// compute fvec at x
for(i=0; i<14; i++) {
fvec[i] = b[0]*(1.-exp(-b[1]*x[i])) - y[i] ;
}
}
else { // compute fjac at x
for(i=0; i<14; i++) {
fjac[i+ldfjac*0] = (1.-exp(-b[1]*x[i]));
fjac[i+ldfjac*1] = (b[0]*x[i]*exp(-b[1]*x[i]));
}
}
return 0;
}
};
// http://www.itl.nist.gov/div898/strd/nls/data/misra1a.shtml
void testNistMisra1a(void)
{
const int m=14, n=2;
int info, nfev, njev;
Eigen::VectorXd x(n), fvec(m), wa1, diag;
Eigen::MatrixXd fjac;
VectorXi ipvt;
/*
* First try
*/
x<< 500., 0.0001;
// do the computation
info = ei_lmder<misra1a_functor, double>(x, fvec, nfev, njev, fjac, ipvt, wa1, diag);
// check return value
VERIFY( 1 == info);
VERIFY( 19 == nfev);
VERIFY( 15 == njev);
// check norm^2
VERIFY_IS_APPROX(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 = ei_lmder<misra1a_functor, double>(x, fvec, nfev, njev, fjac, ipvt, wa1, diag);
// check return value
VERIFY( 1 == info);
VERIFY( 5 == nfev);
VERIFY( 4 == njev);
// check norm^2
VERIFY_IS_APPROX(fvec.squaredNorm(), 1.2455138894E-01);
// check x
VERIFY_IS_APPROX(x[0], 2.3894212918E+02);
VERIFY_IS_APPROX(x[1], 5.5015643181E-04);
}
void test_NonLinear()
{
CALL_SUBTEST(testNistMisra1a());
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());
}
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