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Thomas Capricelli 2009-08-25 17:25:56 +02:00
parent 493c72ac38
commit d59cc0ad82
7 changed files with 1018 additions and 1068 deletions
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4
unsupported/Eigen/NonLinear
View File

@ -50,10 +50,6 @@ namespace Eigen {
#include "src/NonLinear/chkder.h"
#include "src/NonLinear/hybrd.h"
#include "src/NonLinear/lmstr.h"
#include "src/NonLinear/lmdif.h"
#include "src/NonLinear/HybridNonLinearSolver.h"
#include "src/NonLinear/LevenbergMarquardt.h"

358
unsupported/Eigen/src/NonLinear/HybridNonLinearSolver.h
View File

@ -20,6 +20,23 @@ public:
const Scalar xtol = ei_sqrt(epsilon<Scalar>())
);
int solveNumericalDiff(
Matrix< Scalar, Dynamic, 1 > &x,
const Scalar tol = ei_sqrt(epsilon<Scalar>())
);
int solveNumericalDiff(
Matrix< Scalar, Dynamic, 1 > &x,
int &nfev,
Matrix< Scalar, Dynamic, 1 > &diag,
const int mode=1,
int nb_of_subdiagonals = -1,
int nb_of_superdiagonals = -1,
const int maxfev = 2000,
const Scalar factor = Scalar(100.),
const Scalar xtol = ei_sqrt(epsilon<Scalar>()),
const Scalar epsfcn = Scalar(0.)
);
Matrix< Scalar, Dynamic, 1 > fvec;
Matrix< Scalar, Dynamic, Dynamic > fjac;
Matrix< Scalar, Dynamic, 1 > R;
@ -357,3 +374,344 @@ algo_end:
return info;
}
template<typename FunctorType, typename Scalar>
int HybridNonLinearSolver<FunctorType,Scalar>::solveNumericalDiff(
Matrix< Scalar, Dynamic, 1 > &x,
const Scalar tol
)
{
const int n = x.size();
int info, nfev=0;
Matrix< Scalar, Dynamic, 1> diag;
/* check the input parameters for errors. */
if (n <= 0 || tol < 0.) {
printf("HybridNonLinearSolver::solve() bad args : n,tol,...");
return 0;
}
diag.setConstant(n, 1.);
info = solveNumericalDiff(
x,
nfev,
diag,
2,
-1, -1,
(n+1)*200,
100.,
tol, Scalar(0.)
);
return (info==5)?4:info;
}
template<typename FunctorType, typename Scalar>
int HybridNonLinearSolver<FunctorType,Scalar>::solveNumericalDiff(
Matrix< Scalar, Dynamic, 1 > &x,
int &nfev,
Matrix< Scalar, Dynamic, 1 > &diag,
const int mode,
int nb_of_subdiagonals,
int nb_of_superdiagonals,
const int maxfev,
const Scalar factor,
const Scalar xtol,
const Scalar epsfcn
)
{
const int n = x.size();
Matrix< Scalar, Dynamic, 1 > wa1(n), wa2(n), wa3(n), wa4(n);
if (nb_of_subdiagonals<0) nb_of_subdiagonals = n-1;
if (nb_of_superdiagonals<0) nb_of_superdiagonals = n-1;
qtf.resize(n);
R.resize( (n*(n+1))/2);
fjac.resize(n, n);
fvec.resize(n);
/* Local variables */
int i, j, l, iwa[1];
Scalar sum;
int sing;
int iter;
Scalar temp;
int msum, iflag;
Scalar delta;
int jeval;
int ncsuc;
Scalar ratio;
Scalar fnorm;
Scalar pnorm, xnorm, fnorm1;
int nslow1, nslow2;
int ncfail;
Scalar actred, prered;
int info;
/* Function Body */
info = 0;
iflag = 0;
nfev = 0;
/* check the input parameters for errors. */
if (n <= 0 || xtol < 0. || maxfev <= 0 || nb_of_subdiagonals < 0 || nb_of_superdiagonals < 0 || factor <= 0. )
goto algo_end;
if (mode == 2)
for (j = 0; j < n; ++j)
if (diag[j] <= 0.) goto algo_end;
/* evaluate the function at the starting point */
/* and calculate its norm. */
iflag = functor.f(x, fvec);
nfev = 1;
if (iflag < 0)
goto algo_end;
fnorm = fvec.stableNorm();
/* determine the number of calls to fcn needed to compute */
/* the jacobian matrix. */
/* Computing MIN */
msum = std::min(nb_of_subdiagonals + nb_of_superdiagonals + 1, n);
/* initialize iteration counter and monitors. */
iter = 1;
ncsuc = 0;
ncfail = 0;
nslow1 = 0;
nslow2 = 0;
/* beginning of the outer loop. */
while (true) {
jeval = true;
/* calculate the jacobian matrix. */
iflag = ei_fdjac1(functor, x, fvec, fjac,
nb_of_subdiagonals, nb_of_superdiagonals, epsfcn);
nfev += msum;
if (iflag < 0)
break;
/* compute the qr factorization of the jacobian. */
ei_qrfac<Scalar>(n, n, fjac.data(), fjac.rows(), false, iwa, 1, wa1.data(), wa2.data());
/* on the first iteration and if mode is 1, scale according */
/* to the norms of the columns of the initial jacobian. */
if (iter == 1) {
if (mode != 2)
for (j = 0; j < n; ++j) {
diag[j] = wa2[j];
if (wa2[j] == 0.)
diag[j] = 1.;
}
/* on the first iteration, calculate the norm of the scaled x */
/* and initialize the step bound delta. */
wa3 = diag.cwise() * x;
xnorm = wa3.stableNorm();
delta = factor * xnorm;
if (delta == 0.)
delta = factor;
}
/* form (q transpose)*fvec and store in qtf. */
qtf = fvec;
for (j = 0; j < n; ++j)
if (fjac(j,j) != 0.) {
sum = 0.;
for (i = j; i < n; ++i)
sum += fjac(i,j) * qtf[i];
temp = -sum / fjac(j,j);
for (i = j; i < n; ++i)
qtf[i] += fjac(i,j) * temp;
}
/* copy the triangular factor of the qr factorization into r. */
sing = false;
for (j = 0; j < n; ++j) {
l = j;
if (j)
for (i = 0; i < j; ++i) {
R[l] = fjac(i,j);
l = l + n - i -1;
}
R[l] = wa1[j];
if (wa1[j] == 0.)
sing = true;
}
/* accumulate the orthogonal factor in fjac. */
ei_qform<Scalar>(n, n, fjac.data(), fjac.rows(), wa1.data());
/* rescale if necessary. */
/* Computing MAX */
if (mode != 2)
diag = diag.cwise().max(wa2);
/* beginning of the inner loop. */
while (true) {
/* determine the direction p. */
ei_dogleg<Scalar>(R, diag, qtf, delta, wa1);
/* store the direction p and x + p. calculate the norm of p. */
wa1 = -wa1;
wa2 = x + wa1;
wa3 = diag.cwise() * wa1;
pnorm = wa3.stableNorm();
/* on the first iteration, adjust the initial step bound. */
if (iter == 1)
delta = std::min(delta,pnorm);
/* evaluate the function at x + p and calculate its norm. */
iflag = functor.f(wa2, wa4);
++nfev;
if (iflag < 0)
goto algo_end;
fnorm1 = wa4.stableNorm();
/* compute the scaled actual reduction. */
actred = -1.;
if (fnorm1 < fnorm) /* Computing 2nd power */
actred = 1. - ei_abs2(fnorm1 / fnorm);
/* compute the scaled predicted reduction. */
l = 0;
for (i = 0; i < n; ++i) {
sum = 0.;
for (j = i; j < n; ++j) {
sum += R[l] * wa1[j];
++l;
}
wa3[i] = qtf[i] + sum;
}
temp = wa3.stableNorm();
prered = 0.;
if (temp < fnorm) /* Computing 2nd power */
prered = 1. - ei_abs2(temp / fnorm);
/* compute the ratio of the actual to the predicted */
/* reduction. */
ratio = 0.;
if (prered > 0.)
ratio = actred / prered;
/* update the step bound. */
if (ratio < Scalar(.1)) {
ncsuc = 0;
++ncfail;
delta = Scalar(.5) * delta;
} else {
ncfail = 0;
++ncsuc;
if (ratio >= Scalar(.5) || ncsuc > 1) /* Computing MAX */
delta = std::max(delta, pnorm / Scalar(.5));
if (ei_abs(ratio - 1.) <= Scalar(.1)) {
delta = pnorm / Scalar(.5);
}
}
/* test for successful iteration. */
if (ratio >= Scalar(1e-4)) {
/* successful iteration. update x, fvec, and their norms. */
x = wa2;
wa2 = diag.cwise() * x;
fvec = wa4;
xnorm = wa2.stableNorm();
fnorm = fnorm1;
++iter;
}
/* determine the progress of the iteration. */
++nslow1;
if (actred >= Scalar(.001))
nslow1 = 0;
if (jeval)
++nslow2;
if (actred >= Scalar(.1))
nslow2 = 0;
/* test for convergence. */
if (delta <= xtol * xnorm || fnorm == 0.)
info = 1;
if (info != 0)
goto algo_end;
/* tests for termination and stringent tolerances. */
if (nfev >= maxfev)
info = 2;
/* Computing MAX */
if (Scalar(.1) * std::max(Scalar(.1) * delta, pnorm) <= epsilon<Scalar>() * xnorm)
info = 3;
if (nslow2 == 5)
info = 4;
if (nslow1 == 10)
info = 5;
if (info != 0)
goto algo_end;
/* criterion for recalculating jacobian approximation */
/* by forward differences. */
if (ncfail == 2)
break;
/* calculate the rank one modification to the jacobian */
/* and update qtf if necessary. */
for (j = 0; j < n; ++j) {
sum = wa4.dot(fjac.col(j));
wa2[j] = (sum - wa3[j]) / pnorm;
wa1[j] = diag[j] * (diag[j] * wa1[j] / pnorm);
if (ratio >= Scalar(1e-4))
qtf[j] = sum;
}
/* compute the qr factorization of the updated jacobian. */
ei_r1updt<Scalar>(n, n, R.data(), R.size(), wa1.data(), wa2.data(), wa3.data(), &sing);
ei_r1mpyq<Scalar>(n, n, fjac.data(), fjac.rows(), wa2.data(), wa3.data());
ei_r1mpyq<Scalar>(1, n, qtf.data(), 1, wa2.data(), wa3.data());
/* end of the inner loop. */
jeval = false;
}
/* end of the outer loop. */
}
algo_end:
/* termination, either normal or user imposed. */
if (iflag < 0)
info = iflag;
return info;
}

648
unsupported/Eigen/src/NonLinear/LevenbergMarquardt.h
View File

@ -24,6 +24,42 @@ public:
const Scalar gtol = Scalar(0.)
);
int minimizeNumericalDiff(
Matrix< Scalar, Dynamic, 1 > &x,
const Scalar tol = ei_sqrt(epsilon<Scalar>())
);
int minimizeNumericalDiff(
Matrix< Scalar, Dynamic, 1 > &x,
int &nfev,
Matrix< Scalar, Dynamic, 1 > &diag,
const int mode=1,
const Scalar factor = Scalar(100.),
const int maxfev = 400,
const Scalar ftol = ei_sqrt(epsilon<Scalar>()),
const Scalar xtol = ei_sqrt(epsilon<Scalar>()),
const Scalar gtol = Scalar(0.),
const Scalar epsfcn = Scalar(0.)
);
int minimizeOptimumStorage(
Matrix< Scalar, Dynamic, 1 > &x,
const Scalar tol = ei_sqrt(epsilon<Scalar>())
);
int minimizeOptimumStorage(
Matrix< Scalar, Dynamic, 1 > &x,
int &nfev,
int &njev,
Matrix< Scalar, Dynamic, 1 > &diag,
const int mode=1,
const Scalar factor = Scalar(100.),
const int maxfev = 400,
const Scalar ftol = ei_sqrt(epsilon<Scalar>()),
const Scalar xtol = ei_sqrt(epsilon<Scalar>()),
const Scalar gtol = Scalar(0.)
);
Matrix< Scalar, Dynamic, 1 > fvec;
Matrix< Scalar, Dynamic, Dynamic > fjac;
VectorXi ipvt;
@ -330,3 +366,615 @@ algo_end:
info = iflag;
return info;
}
template<typename FunctorType, typename Scalar>
int LevenbergMarquardt<FunctorType,Scalar>::minimizeNumericalDiff(
Matrix< Scalar, Dynamic, 1 > &x,
const Scalar tol
)
{
const int n = x.size();
const int m = functor.nbOfFunctions();
int info, nfev=0;
Matrix< Scalar, Dynamic, Dynamic > fjac(m, n);
Matrix< Scalar, Dynamic, 1> diag, qtf;
VectorXi ipvt;
/* check the input parameters for errors. */
if (n <= 0 || m < n || tol < 0.) {
printf("ei_lmder1 bad args : m,n,tol,...");
return 0;
}
info = minimizeNumericalDiff(
x,
nfev,
diag,
1,
100.,
(n+1)*200,
tol, tol, Scalar(0.), Scalar(0.)
);
return (info==8)?4:info;
}
template<typename FunctorType, typename Scalar>
int LevenbergMarquardt<FunctorType,Scalar>::minimizeNumericalDiff(
Matrix< Scalar, Dynamic, 1 > &x,
int &nfev,
Matrix< Scalar, Dynamic, 1 > &diag,
const int mode,
const Scalar factor,
const int maxfev,
const Scalar ftol,
const Scalar xtol,
const Scalar gtol,
const Scalar epsfcn
)
{
const int n = x.size();
const int m = functor.nbOfFunctions();
Matrix< Scalar, Dynamic, 1 > wa1(n), wa2(n), wa3(n), wa4(m);
fvec.resize(m);
ipvt.resize(n);
fjac.resize(m, n);
diag.resize(n);
qtf.resize(n);
/* Local variables */
int i, j, l;
Scalar par, sum;
int iter;
Scalar temp, temp1, temp2;
int iflag;
Scalar delta;
Scalar ratio;
Scalar fnorm, gnorm;
Scalar pnorm, xnorm, fnorm1, actred, dirder, prered;
int info;
/* Function Body */
info = 0;
iflag = 0;
nfev = 0;
/* check the input parameters for errors. */
if (n <= 0 || m < n || ftol < 0. || xtol < 0. || gtol < 0. || maxfev <= 0 || factor <= 0.)
goto algo_end;
if (mode == 2)
for (j = 0; j < n; ++j)
if (diag[j] <= 0.) goto algo_end;
/* evaluate the function at the starting point */
/* and calculate its norm. */
iflag = functor.f(x, fvec);
nfev = 1;
if (iflag < 0)
goto algo_end;
fnorm = fvec.stableNorm();
/* initialize levenberg-marquardt parameter and iteration counter. */
par = 0.;
iter = 1;
/* beginning of the outer loop. */
while (true) {
/* calculate the jacobian matrix. */
iflag = ei_fdjac2(functor, x, fvec, fjac, epsfcn);
nfev += n;
if (iflag < 0)
break;
/* compute the qr factorization of the jacobian. */
ei_qrfac<Scalar>(m, n, fjac.data(), fjac.rows(), true, ipvt.data(), n, wa1.data(), wa2.data());
ipvt.cwise()-=1; // qrfac() creates ipvt with fortran convetion (1->n), convert it to c (0->n-1)
/* on the first iteration and if mode is 1, scale according */
/* to the norms of the columns of the initial jacobian. */
if (iter == 1) {
if (mode != 2)
for (j = 0; j < n; ++j) {
diag[j] = wa2[j];
if (wa2[j] == 0.)
diag[j] = 1.;
}
/* on the first iteration, calculate the norm of the scaled x */
/* and initialize the step bound delta. */
wa3 = diag.cwise() * x;
xnorm = wa3.stableNorm();
delta = factor * xnorm;
if (delta == 0.)
delta = factor;
}
/* form (q transpose)*fvec and store the first n components in */
/* qtf. */
wa4 = fvec;
for (j = 0; j < n; ++j) {
if (fjac(j,j) != 0.) {
sum = 0.;
for (i = j; i < m; ++i)
sum += fjac(i,j) * wa4[i];
temp = -sum / fjac(j,j);
for (i = j; i < m; ++i)
wa4[i] += fjac(i,j) * temp;
}
fjac(j,j) = wa1[j];
qtf[j] = wa4[j];
}
/* compute the norm of the scaled gradient. */
gnorm = 0.;
if (fnorm != 0.)
for (j = 0; j < n; ++j) {
l = ipvt[j];
if (wa2[l] != 0.) {
sum = 0.;
for (i = 0; i <= j; ++i)
sum += fjac(i,j) * (qtf[i] / fnorm);
/* Computing MAX */
gnorm = std::max(gnorm, ei_abs(sum / wa2[l]));
}
}
/* test for convergence of the gradient norm. */
if (gnorm <= gtol)
info = 4;
if (info != 0)
break;
/* rescale if necessary. */
if (mode != 2) /* Computing MAX */
diag = diag.cwise().max(wa2);
/* beginning of the inner loop. */
do {
/* determine the levenberg-marquardt parameter. */
ei_lmpar<Scalar>(fjac, ipvt, diag, qtf, delta, par, wa1, wa2);
/* store the direction p and x + p. calculate the norm of p. */
wa1 = -wa1;
wa2 = x + wa1;
wa3 = diag.cwise() * wa1;
pnorm = wa3.stableNorm();
/* on the first iteration, adjust the initial step bound. */
if (iter == 1)
delta = std::min(delta,pnorm);
/* evaluate the function at x + p and calculate its norm. */
iflag = functor.f(wa2, wa4);
++nfev;
if (iflag < 0)
goto algo_end;
fnorm1 = wa4.stableNorm();
/* compute the scaled actual reduction. */
actred = -1.;
if (Scalar(.1) * fnorm1 < fnorm) /* Computing 2nd power */
actred = 1. - ei_abs2(fnorm1 / fnorm);
/* compute the scaled predicted reduction and */
/* the scaled directional derivative. */
wa3.fill(0.);
for (j = 0; j < n; ++j) {
l = ipvt[j];
temp = wa1[l];
for (i = 0; i <= j; ++i)
wa3[i] += fjac(i,j) * temp;
}
temp1 = ei_abs2(wa3.stableNorm() / fnorm);
temp2 = ei_abs2(ei_sqrt(par) * pnorm / fnorm);
/* Computing 2nd power */
prered = temp1 + temp2 / Scalar(.5);
dirder = -(temp1 + temp2);
/* compute the ratio of the actual to the predicted */
/* reduction. */
ratio = 0.;
if (prered != 0.)
ratio = actred / prered;
/* update the step bound. */
if (ratio <= Scalar(.25)) {
if (actred >= 0.)
temp = Scalar(.5);
if (actred < 0.)
temp = Scalar(.5) * dirder / (dirder + Scalar(.5) * actred);
if (Scalar(.1) * fnorm1 >= fnorm || temp < Scalar(.1))
temp = Scalar(.1);
/* Computing MIN */
delta = temp * std::min(delta, pnorm / Scalar(.1));
par /= temp;
} else if (!(par != 0. && ratio < Scalar(.75))) {
delta = pnorm / Scalar(.5);
par = Scalar(.5) * par;
}
/* test for successful iteration. */
if (ratio >= Scalar(1e-4)) {
/* successful iteration. update x, fvec, and their norms. */
x = wa2;
wa2 = diag.cwise() * x;
fvec = wa4;
xnorm = wa2.stableNorm();
fnorm = fnorm1;
++iter;
}
/* tests for convergence. */
if (ei_abs(actred) <= ftol && prered <= ftol && Scalar(.5) * ratio <= 1.)
info = 1;
if (delta <= xtol * xnorm)
info = 2;
if (ei_abs(actred) <= ftol && prered <= ftol && Scalar(.5) * ratio <= 1. && info == 2)
info = 3;
if (info != 0)
goto algo_end;
/* tests for termination and stringent tolerances. */
if (nfev >= maxfev)
info = 5;
if (ei_abs(actred) <= epsilon<Scalar>() && prered <= epsilon<Scalar>() && Scalar(.5) * ratio <= 1.)
info = 6;
if (delta <= epsilon<Scalar>() * xnorm)
info = 7;
if (gnorm <= epsilon<Scalar>())
info = 8;
if (info != 0)
goto algo_end;
/* end of the inner loop. repeat if iteration unsuccessful. */
} while (ratio < Scalar(1e-4));
/* end of the outer loop. */
}
algo_end:
/* termination, either normal or user imposed. */
if (iflag < 0)
info = iflag;
return info;
}
template<typename FunctorType, typename Scalar>
int LevenbergMarquardt<FunctorType,Scalar>::minimizeOptimumStorage(
Matrix< Scalar, Dynamic, 1 > &x,
const Scalar tol
)
{
const int n = x.size();
const int m = functor.nbOfFunctions();
int info, nfev=0, njev=0;
Matrix< Scalar, Dynamic, Dynamic > fjac(m, n);
Matrix< Scalar, Dynamic, 1> diag, qtf;
VectorXi ipvt;
/* check the input parameters for errors. */
if (n <= 0 || m < n || tol < 0.) {
printf("LevenbergMarquardtOptimumStorage::minimize() bad args : m,n,tol,...");
return 0;
}
info = minimizeOptimumStorage(
x,
nfev, njev,
diag,
1,
100.,
(n+1)*100,
tol, tol, Scalar(0.)
);
return (info==8)?4:info;
}
template<typename FunctorType, typename Scalar>
int LevenbergMarquardt<FunctorType,Scalar>::minimizeOptimumStorage(
Matrix< Scalar, Dynamic, 1 > &x,
int &nfev,
int &njev,
Matrix< Scalar, Dynamic, 1 > &diag,
const int mode,
const Scalar factor,
const int maxfev,
const Scalar ftol,
const Scalar xtol,
const Scalar gtol
)
{
const int n = x.size();
const int m = functor.nbOfFunctions();
Matrix< Scalar, Dynamic, 1 > wa1(n), wa2(n), wa3(n), wa4(m);
fvec.resize(m);
ipvt.resize(n);
fjac.resize(m, n);
diag.resize(n);
qtf.resize(n);
/* Local variables */
int i, j, l;
Scalar par, sum;
int sing, iter;
Scalar temp, temp1, temp2;
int iflag;
Scalar delta;
Scalar ratio;
Scalar fnorm, gnorm;
Scalar pnorm, xnorm, fnorm1, actred, dirder, prered;
int info;
/* Function Body */
info = 0;
iflag = 0;
nfev = 0;
njev = 0;
/* check the input parameters for errors. */
if (n <= 0 || m < n || ftol < 0. || xtol < 0. || gtol < 0. || maxfev <= 0 || factor <= 0.)
goto algo_end;
if (mode == 2)
for (j = 0; j < n; ++j)
if (diag[j] <= 0.) goto algo_end;
/* evaluate the function at the starting point */
/* and calculate its norm. */
iflag = functor.f(x, fvec);
nfev = 1;
if (iflag < 0)
goto algo_end;
fnorm = fvec.stableNorm();
/* initialize levenberg-marquardt parameter and iteration counter. */
par = 0.;
iter = 1;
/* beginning of the outer loop. */
while (true) {
/* compute the qr factorization of the jacobian matrix */
/* calculated one row at a time, while simultaneously */
/* forming (q transpose)*fvec and storing the first */
/* n components in qtf. */
qtf.fill(0.);
fjac.fill(0.);
iflag = 2;
for (i = 0; i < m; ++i) {
if (functor.df(x, wa3, iflag) < 0)
break;
temp = fvec[i];
ei_rwupdt<Scalar>(n, fjac.data(), fjac.rows(), wa3.data(), qtf.data(), &temp, wa1.data(), wa2.data());
++iflag;
}
++njev;
/* if the jacobian is rank deficient, call qrfac to */
/* reorder its columns and update the components of qtf. */
sing = false;
for (j = 0; j < n; ++j) {
if (fjac(j,j) == 0.) {
sing = true;
}
ipvt[j] = j;
wa2[j] = fjac.col(j).start(j).stableNorm();
}
if (sing) {
ipvt.cwise()+=1;
ei_qrfac<Scalar>(n, n, fjac.data(), fjac.rows(), true, ipvt.data(), n, wa1.data(), wa2.data());
ipvt.cwise()-=1; // qrfac() creates ipvt with fortran convetion (1->n), convert it to c (0->n-1)
for (j = 0; j < n; ++j) {
if (fjac(j,j) != 0.) {
sum = 0.;
for (i = j; i < n; ++i)
sum += fjac(i,j) * qtf[i];
temp = -sum / fjac(j,j);
for (i = j; i < n; ++i)
qtf[i] += fjac(i,j) * temp;
}
fjac(j,j) = wa1[j];
}
}
/* on the first iteration and if mode is 1, scale according */
/* to the norms of the columns of the initial jacobian. */
if (iter == 1) {
if (mode != 2)
for (j = 0; j < n; ++j) {
diag[j] = wa2[j];
if (wa2[j] == 0.)
diag[j] = 1.;
}
/* on the first iteration, calculate the norm of the scaled x */
/* and initialize the step bound delta. */
wa3 = diag.cwise() * x;
xnorm = wa3.stableNorm();
delta = factor * xnorm;
if (delta == 0.)
delta = factor;
}
/* compute the norm of the scaled gradient. */
gnorm = 0.;
if (fnorm != 0.)
for (j = 0; j < n; ++j) {
l = ipvt[j];
if (wa2[l] != 0.) {
sum = 0.;
for (i = 0; i <= j; ++i)
sum += fjac(i,j) * (qtf[i] / fnorm);
/* Computing MAX */
gnorm = std::max(gnorm, ei_abs(sum / wa2[l]));
}
}
/* test for convergence of the gradient norm. */
if (gnorm <= gtol)
info = 4;
if (info != 0)
break;
/* rescale if necessary. */
if (mode != 2) /* Computing MAX */
diag = diag.cwise().max(wa2);
/* beginning of the inner loop. */
do {
/* determine the levenberg-marquardt parameter. */
ei_lmpar<Scalar>(fjac, ipvt, diag, qtf, delta, par, wa1, wa2);
/* store the direction p and x + p. calculate the norm of p. */
wa1 = -wa1;
wa2 = x + wa1;
wa3 = diag.cwise() * wa1;
pnorm = wa3.stableNorm();
/* on the first iteration, adjust the initial step bound. */
if (iter == 1)
delta = std::min(delta,pnorm);
/* evaluate the function at x + p and calculate its norm. */
iflag = functor.f(wa2, wa4);
++nfev;
if (iflag < 0)
goto algo_end;
fnorm1 = wa4.stableNorm();
/* compute the scaled actual reduction. */
actred = -1.;
if (Scalar(.1) * fnorm1 < fnorm) /* Computing 2nd power */
actred = 1. - ei_abs2(fnorm1 / fnorm);
/* compute the scaled predicted reduction and */
/* the scaled directional derivative. */
wa3.fill(0.);
for (j = 0; j < n; ++j) {
l = ipvt[j];
temp = wa1[l];
for (i = 0; i <= j; ++i)
wa3[i] += fjac(i,j) * temp;
}
temp1 = ei_abs2(wa3.stableNorm() / fnorm);
temp2 = ei_abs2(ei_sqrt(par) * pnorm / fnorm);
/* Computing 2nd power */
prered = temp1 + temp2 / Scalar(.5);
dirder = -(temp1 + temp2);
/* compute the ratio of the actual to the predicted */
/* reduction. */
ratio = 0.;
if (prered != 0.)
ratio = actred / prered;
/* update the step bound. */
if (ratio <= Scalar(.25)) {
if (actred >= 0.)
temp = Scalar(.5);
if (actred < 0.)
temp = Scalar(.5) * dirder / (dirder + Scalar(.5) * actred);
if (Scalar(.1) * fnorm1 >= fnorm || temp < Scalar(.1))
temp = Scalar(.1);
/* Computing MIN */
delta = temp * std::min(delta, pnorm / Scalar(.1));
par /= temp;
} else if (!(par != 0. && ratio < Scalar(.75))) {
delta = pnorm / Scalar(.5);
par = Scalar(.5) * par;
}
/* test for successful iteration. */
if (ratio >= Scalar(1e-4)) {
/* successful iteration. update x, fvec, and their norms. */
x = wa2;
wa2 = diag.cwise() * x;
fvec = wa4;
xnorm = wa2.stableNorm();
fnorm = fnorm1;
++iter;
}
/* tests for convergence. */
if (ei_abs(actred) <= ftol && prered <= ftol && Scalar(.5) * ratio <= 1.)
info = 1;
if (delta <= xtol * xnorm)
info = 2;
if (ei_abs(actred) <= ftol && prered <= ftol && Scalar(.5) * ratio <= 1. && info == 2)
info = 3;
if (info != 0)
goto algo_end;
/* tests for termination and stringent tolerances. */
if (nfev >= maxfev)
info = 5;
if (ei_abs(actred) <= epsilon<Scalar>() && prered <= epsilon<Scalar>() && Scalar(.5) * ratio <= 1.)
info = 6;
if (delta <= epsilon<Scalar>() * xnorm)
info = 7;
if (gnorm <= epsilon<Scalar>())
info = 8;
if (info != 0)
goto algo_end;
/* end of the inner loop. repeat if iteration unsuccessful. */
} while (ratio < Scalar(1e-4));
/* end of the outer loop. */
}
algo_end:
/* termination, either normal or user imposed. */
if (iflag < 0)
info = iflag;
return info;
}

374
unsupported/Eigen/src/NonLinear/hybrd.h
View File

@ -1,374 +0,0 @@
template<typename FunctorType, typename Scalar=double>
class HybridNonLinearSolverNumericalDiff
{
public:
HybridNonLinearSolverNumericalDiff(const FunctorType &_functor)
: functor(_functor) {}
int solve(
Matrix< Scalar, Dynamic, 1 > &x,
const Scalar tol = ei_sqrt(epsilon<Scalar>())
);
int solve(
Matrix< Scalar, Dynamic, 1 > &x,
int &nfev,
Matrix< Scalar, Dynamic, 1 > &diag,
const int mode=1,
int nb_of_subdiagonals = -1,
int nb_of_superdiagonals = -1,
const int maxfev = 2000,
const Scalar factor = Scalar(100.),
const Scalar xtol = ei_sqrt(epsilon<Scalar>()),
const Scalar epsfcn = Scalar(0.)
);
Matrix< Scalar, Dynamic, 1 > fvec;
Matrix< Scalar, Dynamic, Dynamic > fjac;
Matrix< Scalar, Dynamic, 1 > R;
Matrix< Scalar, Dynamic, 1 > qtf;
private:
const FunctorType &functor;
};
template<typename FunctorType, typename Scalar>
int HybridNonLinearSolverNumericalDiff<FunctorType,Scalar>::solve(
Matrix< Scalar, Dynamic, 1 > &x,
const Scalar tol
)
{
const int n = x.size();
int info, nfev=0;
Matrix< Scalar, Dynamic, 1> diag;
/* check the input parameters for errors. */
if (n <= 0 || tol < 0.) {
printf("HybridNonLinearSolver::solve() bad args : n,tol,...");
return 0;
}
diag.setConstant(n, 1.);
info = solve(
x,
nfev,
diag,
2,
-1, -1,
(n+1)*200,
100.,
tol, Scalar(0.)
);
return (info==5)?4:info;
}
template<typename FunctorType, typename Scalar>
int HybridNonLinearSolverNumericalDiff<FunctorType,Scalar>::solve(
Matrix< Scalar, Dynamic, 1 > &x,
int &nfev,
Matrix< Scalar, Dynamic, 1 > &diag,
const int mode,
int nb_of_subdiagonals,
int nb_of_superdiagonals,
const int maxfev,
const Scalar factor,
const Scalar xtol,
const Scalar epsfcn
)
{
const int n = x.size();
Matrix< Scalar, Dynamic, 1 > wa1(n), wa2(n), wa3(n), wa4(n);
if (nb_of_subdiagonals<0) nb_of_subdiagonals = n-1;
if (nb_of_superdiagonals<0) nb_of_superdiagonals = n-1;
qtf.resize(n);
R.resize( (n*(n+1))/2);
fjac.resize(n, n);
fvec.resize(n);
/* Local variables */
int i, j, l, iwa[1];
Scalar sum;
int sing;
int iter;
Scalar temp;
int msum, iflag;
Scalar delta;
int jeval;
int ncsuc;
Scalar ratio;
Scalar fnorm;
Scalar pnorm, xnorm, fnorm1;
int nslow1, nslow2;
int ncfail;
Scalar actred, prered;
int info;
/* Function Body */
info = 0;
iflag = 0;
nfev = 0;
/* check the input parameters for errors. */
if (n <= 0 || xtol < 0. || maxfev <= 0 || nb_of_subdiagonals < 0 || nb_of_superdiagonals < 0 || factor <= 0. )
goto algo_end;
if (mode == 2)
for (j = 0; j < n; ++j)
if (diag[j] <= 0.) goto algo_end;
/* evaluate the function at the starting point */
/* and calculate its norm. */
iflag = functor.f(x, fvec);
nfev = 1;
if (iflag < 0)
goto algo_end;
fnorm = fvec.stableNorm();
/* determine the number of calls to fcn needed to compute */
/* the jacobian matrix. */
/* Computing MIN */
msum = std::min(nb_of_subdiagonals + nb_of_superdiagonals + 1, n);
/* initialize iteration counter and monitors. */
iter = 1;
ncsuc = 0;
ncfail = 0;
nslow1 = 0;
nslow2 = 0;
/* beginning of the outer loop. */
while (true) {
jeval = true;
/* calculate the jacobian matrix. */
iflag = ei_fdjac1(functor, x, fvec, fjac,
nb_of_subdiagonals, nb_of_superdiagonals, epsfcn);
nfev += msum;
if (iflag < 0)
break;
/* compute the qr factorization of the jacobian. */
ei_qrfac<Scalar>(n, n, fjac.data(), fjac.rows(), false, iwa, 1, wa1.data(), wa2.data());
/* on the first iteration and if mode is 1, scale according */
/* to the norms of the columns of the initial jacobian. */
if (iter == 1) {
if (mode != 2)
for (j = 0; j < n; ++j) {
diag[j] = wa2[j];
if (wa2[j] == 0.)
diag[j] = 1.;
}
/* on the first iteration, calculate the norm of the scaled x */
/* and initialize the step bound delta. */
wa3 = diag.cwise() * x;
xnorm = wa3.stableNorm();
delta = factor * xnorm;
if (delta == 0.)
delta = factor;
}
/* form (q transpose)*fvec and store in qtf. */
qtf = fvec;
for (j = 0; j < n; ++j)
if (fjac(j,j) != 0.) {
sum = 0.;
for (i = j; i < n; ++i)
sum += fjac(i,j) * qtf[i];
temp = -sum / fjac(j,j);
for (i = j; i < n; ++i)
qtf[i] += fjac(i,j) * temp;
}
/* copy the triangular factor of the qr factorization into r. */
sing = false;
for (j = 0; j < n; ++j) {
l = j;
if (j)
for (i = 0; i < j; ++i) {
R[l] = fjac(i,j);
l = l + n - i -1;
}
R[l] = wa1[j];
if (wa1[j] == 0.)
sing = true;
}
/* accumulate the orthogonal factor in fjac. */
ei_qform<Scalar>(n, n, fjac.data(), fjac.rows(), wa1.data());
/* rescale if necessary. */
/* Computing MAX */
if (mode != 2)
diag = diag.cwise().max(wa2);
/* beginning of the inner loop. */
while (true) {
/* determine the direction p. */
ei_dogleg<Scalar>(R, diag, qtf, delta, wa1);
/* store the direction p and x + p. calculate the norm of p. */
wa1 = -wa1;
wa2 = x + wa1;
wa3 = diag.cwise() * wa1;
pnorm = wa3.stableNorm();
/* on the first iteration, adjust the initial step bound. */
if (iter == 1)
delta = std::min(delta,pnorm);
/* evaluate the function at x + p and calculate its norm. */
iflag = functor.f(wa2, wa4);
++nfev;
if (iflag < 0)
goto algo_end;
fnorm1 = wa4.stableNorm();
/* compute the scaled actual reduction. */
actred = -1.;
if (fnorm1 < fnorm) /* Computing 2nd power */
actred = 1. - ei_abs2(fnorm1 / fnorm);
/* compute the scaled predicted reduction. */
l = 0;
for (i = 0; i < n; ++i) {
sum = 0.;
for (j = i; j < n; ++j) {
sum += R[l] * wa1[j];
++l;
}
wa3[i] = qtf[i] + sum;
}
temp = wa3.stableNorm();
prered = 0.;
if (temp < fnorm) /* Computing 2nd power */
prered = 1. - ei_abs2(temp / fnorm);
/* compute the ratio of the actual to the predicted */
/* reduction. */
ratio = 0.;
if (prered > 0.)
ratio = actred / prered;
/* update the step bound. */
if (ratio < Scalar(.1)) {
ncsuc = 0;
++ncfail;
delta = Scalar(.5) * delta;
} else {
ncfail = 0;
++ncsuc;
if (ratio >= Scalar(.5) || ncsuc > 1) /* Computing MAX */
delta = std::max(delta, pnorm / Scalar(.5));
if (ei_abs(ratio - 1.) <= Scalar(.1)) {
delta = pnorm / Scalar(.5);
}
}
/* test for successful iteration. */
if (ratio >= Scalar(1e-4)) {
/* successful iteration. update x, fvec, and their norms. */
x = wa2;
wa2 = diag.cwise() * x;
fvec = wa4;
xnorm = wa2.stableNorm();
fnorm = fnorm1;
++iter;
}
/* determine the progress of the iteration. */
++nslow1;
if (actred >= Scalar(.001))
nslow1 = 0;
if (jeval)
++nslow2;
if (actred >= Scalar(.1))
nslow2 = 0;
/* test for convergence. */
if (delta <= xtol * xnorm || fnorm == 0.)
info = 1;
if (info != 0)
goto algo_end;
/* tests for termination and stringent tolerances. */
if (nfev >= maxfev)
info = 2;
/* Computing MAX */
if (Scalar(.1) * std::max(Scalar(.1) * delta, pnorm) <= epsilon<Scalar>() * xnorm)
info = 3;
if (nslow2 == 5)
info = 4;
if (nslow1 == 10)
info = 5;
if (info != 0)
goto algo_end;
/* criterion for recalculating jacobian approximation */
/* by forward differences. */
if (ncfail == 2)
break;
/* calculate the rank one modification to the jacobian */
/* and update qtf if necessary. */
for (j = 0; j < n; ++j) {
sum = wa4.dot(fjac.col(j));
wa2[j] = (sum - wa3[j]) / pnorm;
wa1[j] = diag[j] * (diag[j] * wa1[j] / pnorm);
if (ratio >= Scalar(1e-4))
qtf[j] = sum;
}
/* compute the qr factorization of the updated jacobian. */
ei_r1updt<Scalar>(n, n, R.data(), R.size(), wa1.data(), wa2.data(), wa3.data(), &sing);
ei_r1mpyq<Scalar>(n, n, fjac.data(), fjac.rows(), wa2.data(), wa3.data());
ei_r1mpyq<Scalar>(1, n, qtf.data(), 1, wa2.data(), wa3.data());
/* end of the inner loop. */
jeval = false;
}
/* end of the outer loop. */
}
algo_end:
/* termination, either normal or user imposed. */
if (iflag < 0)
info = iflag;
return info;
}

330
unsupported/Eigen/src/NonLinear/lmdif.h
View File

@ -1,330 +0,0 @@
template<typename FunctorType, typename Scalar=double>
class LevenbergMarquardtNumericalDiff
{
public:
LevenbergMarquardtNumericalDiff(const FunctorType &_functor)
: functor(_functor) {}
int minimize(
Matrix< Scalar, Dynamic, 1 > &x,
const Scalar tol = ei_sqrt(epsilon<Scalar>())
);
int minimize(
Matrix< Scalar, Dynamic, 1 > &x,
int &nfev,
Matrix< Scalar, Dynamic, 1 > &diag,
const int mode=1,
const Scalar factor = Scalar(100.),
const int maxfev = 400,
const Scalar ftol = ei_sqrt(epsilon<Scalar>()),
const Scalar xtol = ei_sqrt(epsilon<Scalar>()),
const Scalar gtol = Scalar(0.),
const Scalar epsfcn = Scalar(0.)
);
Matrix< Scalar, Dynamic, 1 > fvec;
Matrix< Scalar, Dynamic, Dynamic > fjac;
VectorXi ipvt;
Matrix< Scalar, Dynamic, 1 > qtf;
private:
const FunctorType &functor;
};
template<typename FunctorType, typename Scalar>
int LevenbergMarquardtNumericalDiff<FunctorType,Scalar>::minimize(
Matrix< Scalar, Dynamic, 1 > &x,
const Scalar tol
)
{
const int n = x.size();
const int m = functor.nbOfFunctions();
int info, nfev=0;
Matrix< Scalar, Dynamic, Dynamic > fjac(m, n);
Matrix< Scalar, Dynamic, 1> diag, qtf;
VectorXi ipvt;
/* check the input parameters for errors. */
if (n <= 0 || m < n || tol < 0.) {
printf("ei_lmder1 bad args : m,n,tol,...");
return 0;
}
info = minimize(
x,
nfev,
diag,
1,
100.,
(n+1)*200,
tol, tol, Scalar(0.), Scalar(0.)
);
return (info==8)?4:info;
}
template<typename FunctorType, typename Scalar>
int LevenbergMarquardtNumericalDiff<FunctorType,Scalar>::minimize(
Matrix< Scalar, Dynamic, 1 > &x,
int &nfev,
Matrix< Scalar, Dynamic, 1 > &diag,
const int mode,
const Scalar factor,
const int maxfev,
const Scalar ftol,
const Scalar xtol,
const Scalar gtol,
const Scalar epsfcn
)
{
const int n = x.size();
const int m = functor.nbOfFunctions();
Matrix< Scalar, Dynamic, 1 > wa1(n), wa2(n), wa3(n), wa4(m);
fvec.resize(m);
ipvt.resize(n);
fjac.resize(m, n);
diag.resize(n);
qtf.resize(n);
/* Local variables */
int i, j, l;
Scalar par, sum;
int iter;
Scalar temp, temp1, temp2;
int iflag;
Scalar delta;
Scalar ratio;
Scalar fnorm, gnorm;
Scalar pnorm, xnorm, fnorm1, actred, dirder, prered;
int info;
/* Function Body */
info = 0;
iflag = 0;
nfev = 0;
/* check the input parameters for errors. */
if (n <= 0 || m < n || ftol < 0. || xtol < 0. || gtol < 0. || maxfev <= 0 || factor <= 0.)
goto algo_end;
if (mode == 2)
for (j = 0; j < n; ++j)
if (diag[j] <= 0.) goto algo_end;
/* evaluate the function at the starting point */
/* and calculate its norm. */
iflag = functor.f(x, fvec);
nfev = 1;
if (iflag < 0)
goto algo_end;
fnorm = fvec.stableNorm();
/* initialize levenberg-marquardt parameter and iteration counter. */
par = 0.;
iter = 1;
/* beginning of the outer loop. */
while (true) {
/* calculate the jacobian matrix. */
iflag = ei_fdjac2(functor, x, fvec, fjac, epsfcn);
nfev += n;
if (iflag < 0)
break;
/* compute the qr factorization of the jacobian. */
ei_qrfac<Scalar>(m, n, fjac.data(), fjac.rows(), true, ipvt.data(), n, wa1.data(), wa2.data());
ipvt.cwise()-=1; // qrfac() creates ipvt with fortran convetion (1->n), convert it to c (0->n-1)
/* on the first iteration and if mode is 1, scale according */
/* to the norms of the columns of the initial jacobian. */
if (iter == 1) {
if (mode != 2)
for (j = 0; j < n; ++j) {
diag[j] = wa2[j];
if (wa2[j] == 0.)
diag[j] = 1.;
}
/* on the first iteration, calculate the norm of the scaled x */
/* and initialize the step bound delta. */
wa3 = diag.cwise() * x;
xnorm = wa3.stableNorm();
delta = factor * xnorm;
if (delta == 0.)
delta = factor;
}
/* form (q transpose)*fvec and store the first n components in */
/* qtf. */
wa4 = fvec;
for (j = 0; j < n; ++j) {
if (fjac(j,j) != 0.) {
sum = 0.;
for (i = j; i < m; ++i)
sum += fjac(i,j) * wa4[i];
temp = -sum / fjac(j,j);
for (i = j; i < m; ++i)
wa4[i] += fjac(i,j) * temp;
}
fjac(j,j) = wa1[j];
qtf[j] = wa4[j];
}
/* compute the norm of the scaled gradient. */
gnorm = 0.;
if (fnorm != 0.)
for (j = 0; j < n; ++j) {
l = ipvt[j];
if (wa2[l] != 0.) {
sum = 0.;
for (i = 0; i <= j; ++i)
sum += fjac(i,j) * (qtf[i] / fnorm);
/* Computing MAX */
gnorm = std::max(gnorm, ei_abs(sum / wa2[l]));
}
}
/* test for convergence of the gradient norm. */
if (gnorm <= gtol)
info = 4;
if (info != 0)
break;
/* rescale if necessary. */
if (mode != 2) /* Computing MAX */
diag = diag.cwise().max(wa2);
/* beginning of the inner loop. */
do {
/* determine the levenberg-marquardt parameter. */
ei_lmpar<Scalar>(fjac, ipvt, diag, qtf, delta, par, wa1, wa2);
/* store the direction p and x + p. calculate the norm of p. */
wa1 = -wa1;
wa2 = x + wa1;
wa3 = diag.cwise() * wa1;
pnorm = wa3.stableNorm();
/* on the first iteration, adjust the initial step bound. */
if (iter == 1)
delta = std::min(delta,pnorm);
/* evaluate the function at x + p and calculate its norm. */
iflag = functor.f(wa2, wa4);
++nfev;
if (iflag < 0)
goto algo_end;
fnorm1 = wa4.stableNorm();
/* compute the scaled actual reduction. */
actred = -1.;
if (Scalar(.1) * fnorm1 < fnorm) /* Computing 2nd power */
actred = 1. - ei_abs2(fnorm1 / fnorm);
/* compute the scaled predicted reduction and */
/* the scaled directional derivative. */
wa3.fill(0.);
for (j = 0; j < n; ++j) {
l = ipvt[j];
temp = wa1[l];
for (i = 0; i <= j; ++i)
wa3[i] += fjac(i,j) * temp;
}
temp1 = ei_abs2(wa3.stableNorm() / fnorm);
temp2 = ei_abs2(ei_sqrt(par) * pnorm / fnorm);
/* Computing 2nd power */
prered = temp1 + temp2 / Scalar(.5);
dirder = -(temp1 + temp2);
/* compute the ratio of the actual to the predicted */
/* reduction. */
ratio = 0.;
if (prered != 0.)
ratio = actred / prered;
/* update the step bound. */
if (ratio <= Scalar(.25)) {
if (actred >= 0.)
temp = Scalar(.5);
if (actred < 0.)
temp = Scalar(.5) * dirder / (dirder + Scalar(.5) * actred);
if (Scalar(.1) * fnorm1 >= fnorm || temp < Scalar(.1))
temp = Scalar(.1);
/* Computing MIN */
delta = temp * std::min(delta, pnorm / Scalar(.1));
par /= temp;
} else if (!(par != 0. && ratio < Scalar(.75))) {
delta = pnorm / Scalar(.5);
par = Scalar(.5) * par;
}
/* test for successful iteration. */
if (ratio >= Scalar(1e-4)) {
/* successful iteration. update x, fvec, and their norms. */
x = wa2;
wa2 = diag.cwise() * x;
fvec = wa4;
xnorm = wa2.stableNorm();
fnorm = fnorm1;
++iter;
}
/* tests for convergence. */
if (ei_abs(actred) <= ftol && prered <= ftol && Scalar(.5) * ratio <= 1.)
info = 1;
if (delta <= xtol * xnorm)
info = 2;
if (ei_abs(actred) <= ftol && prered <= ftol && Scalar(.5) * ratio <= 1. && info == 2)
info = 3;
if (info != 0)
goto algo_end;
/* tests for termination and stringent tolerances. */
if (nfev >= maxfev)
info = 5;
if (ei_abs(actred) <= epsilon<Scalar>() && prered <= epsilon<Scalar>() && Scalar(.5) * ratio <= 1.)
info = 6;
if (delta <= epsilon<Scalar>() * xnorm)
info = 7;
if (gnorm <= epsilon<Scalar>())
info = 8;
if (info != 0)
goto algo_end;
/* end of the inner loop. repeat if iteration unsuccessful. */
} while (ratio < Scalar(1e-4));
/* end of the outer loop. */
}
algo_end:
/* termination, either normal or user imposed. */
if (iflag < 0)
info = iflag;
return info;
}

348
unsupported/Eigen/src/NonLinear/lmstr.h
View File

@ -1,348 +0,0 @@
template<typename FunctorType, typename Scalar=double>
class LevenbergMarquardtOptimumStorage
{
public:
LevenbergMarquardtOptimumStorage(const FunctorType &_functor)
: functor(_functor) {}
int minimize(
Matrix< Scalar, Dynamic, 1 > &x,
const Scalar tol = ei_sqrt(epsilon<Scalar>())
);
int minimize(
Matrix< Scalar, Dynamic, 1 > &x,
int &nfev,
int &njev,
Matrix< Scalar, Dynamic, 1 > &diag,
const int mode=1,
const Scalar factor = Scalar(100.),
const int maxfev = 400,
const Scalar ftol = ei_sqrt(epsilon<Scalar>()),
const Scalar xtol = ei_sqrt(epsilon<Scalar>()),
const Scalar gtol = Scalar(0.)
);
Matrix< Scalar, Dynamic, 1 > fvec;
Matrix< Scalar, Dynamic, Dynamic > fjac;
VectorXi ipvt;
Matrix< Scalar, Dynamic, 1 > qtf;
private:
const FunctorType &functor;
};
template<typename FunctorType, typename Scalar>
int LevenbergMarquardtOptimumStorage<FunctorType,Scalar>::minimize(
Matrix< Scalar, Dynamic, 1 > &x,
const Scalar tol
)
{
const int n = x.size();
const int m = functor.nbOfFunctions();
int info, nfev=0, njev=0;
Matrix< Scalar, Dynamic, Dynamic > fjac(m, n);
Matrix< Scalar, Dynamic, 1> diag, qtf;
VectorXi ipvt;
/* check the input parameters for errors. */
if (n <= 0 || m < n || tol < 0.) {
printf("LevenbergMarquardtOptimumStorage::minimize() bad args : m,n,tol,...");
return 0;
}
info = minimize(
x,
nfev, njev,
diag,
1,
100.,
(n+1)*100,
tol, tol, Scalar(0.)
);
return (info==8)?4:info;
}
template<typename FunctorType, typename Scalar>
int LevenbergMarquardtOptimumStorage<FunctorType,Scalar>::minimize(
Matrix< Scalar, Dynamic, 1 > &x,
int &nfev,
int &njev,
Matrix< Scalar, Dynamic, 1 > &diag,
const int mode,
const Scalar factor,
const int maxfev,
const Scalar ftol,
const Scalar xtol,
const Scalar gtol
)
{
const int n = x.size();
const int m = functor.nbOfFunctions();
Matrix< Scalar, Dynamic, 1 > wa1(n), wa2(n), wa3(n), wa4(m);
fvec.resize(m);
ipvt.resize(n);
fjac.resize(m, n);
diag.resize(n);
qtf.resize(n);
/* Local variables */
int i, j, l;
Scalar par, sum;
int sing, iter;
Scalar temp, temp1, temp2;
int iflag;
Scalar delta;
Scalar ratio;
Scalar fnorm, gnorm;
Scalar pnorm, xnorm, fnorm1, actred, dirder, prered;
int info;
/* Function Body */
info = 0;
iflag = 0;
nfev = 0;
njev = 0;
/* check the input parameters for errors. */
if (n <= 0 || m < n || ftol < 0. || xtol < 0. || gtol < 0. || maxfev <= 0 || factor <= 0.)
goto algo_end;
if (mode == 2)
for (j = 0; j < n; ++j)
if (diag[j] <= 0.) goto algo_end;
/* evaluate the function at the starting point */
/* and calculate its norm. */
iflag = functor.f(x, fvec);
nfev = 1;
if (iflag < 0)
goto algo_end;
fnorm = fvec.stableNorm();
/* initialize levenberg-marquardt parameter and iteration counter. */
par = 0.;
iter = 1;
/* beginning of the outer loop. */
while (true) {
/* compute the qr factorization of the jacobian matrix */
/* calculated one row at a time, while simultaneously */
/* forming (q transpose)*fvec and storing the first */
/* n components in qtf. */
qtf.fill(0.);
fjac.fill(0.);
iflag = 2;
for (i = 0; i < m; ++i) {
if (functor.df(x, wa3, iflag) < 0)
break;
temp = fvec[i];
ei_rwupdt<Scalar>(n, fjac.data(), fjac.rows(), wa3.data(), qtf.data(), &temp, wa1.data(), wa2.data());
++iflag;
}
++njev;
/* if the jacobian is rank deficient, call qrfac to */
/* reorder its columns and update the components of qtf. */
sing = false;
for (j = 0; j < n; ++j) {
if (fjac(j,j) == 0.) {
sing = true;
}
ipvt[j] = j;
wa2[j] = fjac.col(j).start(j).stableNorm();
}
if (sing) {
ipvt.cwise()+=1;
ei_qrfac<Scalar>(n, n, fjac.data(), fjac.rows(), true, ipvt.data(), n, wa1.data(), wa2.data());
ipvt.cwise()-=1; // qrfac() creates ipvt with fortran convetion (1->n), convert it to c (0->n-1)
for (j = 0; j < n; ++j) {
if (fjac(j,j) != 0.) {
sum = 0.;
for (i = j; i < n; ++i)
sum += fjac(i,j) * qtf[i];
temp = -sum / fjac(j,j);
for (i = j; i < n; ++i)
qtf[i] += fjac(i,j) * temp;
}
fjac(j,j) = wa1[j];
}
}
/* on the first iteration and if mode is 1, scale according */
/* to the norms of the columns of the initial jacobian. */
if (iter == 1) {
if (mode != 2)
for (j = 0; j < n; ++j) {
diag[j] = wa2[j];
if (wa2[j] == 0.)
diag[j] = 1.;
}
/* on the first iteration, calculate the norm of the scaled x */
/* and initialize the step bound delta. */
wa3 = diag.cwise() * x;
xnorm = wa3.stableNorm();
delta = factor * xnorm;
if (delta == 0.)
delta = factor;
}
/* compute the norm of the scaled gradient. */
gnorm = 0.;
if (fnorm != 0.)
for (j = 0; j < n; ++j) {
l = ipvt[j];
if (wa2[l] != 0.) {
sum = 0.;
for (i = 0; i <= j; ++i)
sum += fjac(i,j) * (qtf[i] / fnorm);
/* Computing MAX */
gnorm = std::max(gnorm, ei_abs(sum / wa2[l]));
}
}
/* test for convergence of the gradient norm. */
if (gnorm <= gtol)
info = 4;
if (info != 0)
break;
/* rescale if necessary. */
if (mode != 2) /* Computing MAX */
diag = diag.cwise().max(wa2);
/* beginning of the inner loop. */
do {
/* determine the levenberg-marquardt parameter. */
ei_lmpar<Scalar>(fjac, ipvt, diag, qtf, delta, par, wa1, wa2);
/* store the direction p and x + p. calculate the norm of p. */
wa1 = -wa1;
wa2 = x + wa1;
wa3 = diag.cwise() * wa1;
pnorm = wa3.stableNorm();
/* on the first iteration, adjust the initial step bound. */
if (iter == 1)
delta = std::min(delta,pnorm);
/* evaluate the function at x + p and calculate its norm. */
iflag = functor.f(wa2, wa4);
++nfev;
if (iflag < 0)
goto algo_end;
fnorm1 = wa4.stableNorm();
/* compute the scaled actual reduction. */
actred = -1.;
if (Scalar(.1) * fnorm1 < fnorm) /* Computing 2nd power */
actred = 1. - ei_abs2(fnorm1 / fnorm);
/* compute the scaled predicted reduction and */
/* the scaled directional derivative. */
wa3.fill(0.);
for (j = 0; j < n; ++j) {
l = ipvt[j];
temp = wa1[l];
for (i = 0; i <= j; ++i)
wa3[i] += fjac(i,j) * temp;
}
temp1 = ei_abs2(wa3.stableNorm() / fnorm);
temp2 = ei_abs2(ei_sqrt(par) * pnorm / fnorm);
/* Computing 2nd power */
prered = temp1 + temp2 / Scalar(.5);
dirder = -(temp1 + temp2);
/* compute the ratio of the actual to the predicted */
/* reduction. */
ratio = 0.;
if (prered != 0.)
ratio = actred / prered;
/* update the step bound. */
if (ratio <= Scalar(.25)) {
if (actred >= 0.)
temp = Scalar(.5);
if (actred < 0.)
temp = Scalar(.5) * dirder / (dirder + Scalar(.5) * actred);
if (Scalar(.1) * fnorm1 >= fnorm || temp < Scalar(.1))
temp = Scalar(.1);
/* Computing MIN */
delta = temp * std::min(delta, pnorm / Scalar(.1));
par /= temp;
} else if (!(par != 0. && ratio < Scalar(.75))) {
delta = pnorm / Scalar(.5);
par = Scalar(.5) * par;
}
/* test for successful iteration. */
if (ratio >= Scalar(1e-4)) {
/* successful iteration. update x, fvec, and their norms. */
x = wa2;
wa2 = diag.cwise() * x;
fvec = wa4;
xnorm = wa2.stableNorm();
fnorm = fnorm1;
++iter;
}
/* tests for convergence. */
if (ei_abs(actred) <= ftol && prered <= ftol && Scalar(.5) * ratio <= 1.)
info = 1;
if (delta <= xtol * xnorm)
info = 2;
if (ei_abs(actred) <= ftol && prered <= ftol && Scalar(.5) * ratio <= 1. && info == 2)
info = 3;
if (info != 0)
goto algo_end;
/* tests for termination and stringent tolerances. */
if (nfev >= maxfev)
info = 5;
if (ei_abs(actred) <= epsilon<Scalar>() && prered <= epsilon<Scalar>() && Scalar(.5) * ratio <= 1.)
info = 6;
if (delta <= epsilon<Scalar>() * xnorm)
info = 7;
if (gnorm <= epsilon<Scalar>())
info = 8;
if (info != 0)
goto algo_end;
/* end of the inner loop. repeat if iteration unsuccessful. */
} while (ratio < Scalar(1e-4));
/* end of the outer loop. */
}
algo_end:
/* termination, either normal or user imposed. */
if (iflag < 0)
info = iflag;
return info;
}

24
unsupported/test/NonLinear.cpp
View File

@ -354,8 +354,8 @@ void testHybrd1()
// do the computation
hybrd_functor functor;
HybridNonLinearSolverNumericalDiff<hybrd_functor> solver(functor);
info = solver.solve(x);
HybridNonLinearSolver<hybrd_functor> solver(functor);
info = solver.solveNumericalDiff(x);
// check return value
VERIFY( 1 == info);
@ -385,8 +385,8 @@ void testHybrd()
// do the computation
hybrd_functor functor;
HybridNonLinearSolverNumericalDiff<hybrd_functor> solver(functor);
info = solver.solve(x, nfev, diag, mode, ml, mu);
HybridNonLinearSolver<hybrd_functor> solver(functor);
info = solver.solveNumericalDiff(x, nfev, diag, mode, ml, mu);
// check return value
VERIFY( 1 == info);
@ -456,8 +456,8 @@ void testLmstr1()
// do the computation
lmstr_functor functor;
LevenbergMarquardtOptimumStorage<lmstr_functor> lm(functor);
info = lm.minimize(x);
LevenbergMarquardt<lmstr_functor> lm(functor);
info = lm.minimizeOptimumStorage(x);
// check return value
VERIFY( 1 == info);
@ -483,8 +483,8 @@ void testLmstr()
// do the computation
lmstr_functor functor;
LevenbergMarquardtOptimumStorage<lmstr_functor> lm(functor);
info = lm.minimize(x, nfev, njev, diag);
LevenbergMarquardt<lmstr_functor> lm(functor);
info = lm.minimizeOptimumStorage(x, nfev, njev, diag);
// check return values
VERIFY( 1 == info);
@ -541,8 +541,8 @@ void testLmdif1()
// do the computation
lmdif_functor functor;
LevenbergMarquardtNumericalDiff<lmdif_functor> lm(functor);
info = lm.minimize(x);
LevenbergMarquardt<lmdif_functor> lm(functor);
info = lm.minimizeNumericalDiff(x);
// check return value
VERIFY( 1 == info);
@ -569,8 +569,8 @@ void testLmdif()
// do the computation
lmdif_functor functor;
LevenbergMarquardtNumericalDiff<lmdif_functor> lm(functor);
info = lm.minimize(x, nfev, diag);
LevenbergMarquardt<lmdif_functor> lm(functor);
info = lm.minimizeNumericalDiff(x, nfev, diag);
// check return values
VERIFY( 1 == info);