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remove some duplicated code LevenbergMarquardt::minimizeNumericalDiff*() by

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using the generic Eigen NumericalDiff recently introduced.

LevenbergMarquardt::lmdif1(), which is provided as a convenience method for
people porting code from (c)minpack, is now a static function
This commit is contained in:
Thomas Capricelli 2009-09-28 03:26:42 +02:00
parent 87be19de4a
commit d3850641a1
3 changed files with 45 additions and 300 deletions
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1
unsupported/Eigen/NonLinear
View File

@ -26,6 +26,7 @@
#define EIGEN_NONLINEAR_MODULE_H
#include <Eigen/Core>
#include <unsupported/Eigen/NumericalDiff>
namespace Eigen {

326
unsupported/Eigen/src/NonLinear/LevenbergMarquardt.h
View File

@ -54,24 +54,13 @@ public:
const int mode=1
);
Status lmdif1(
static Status lmdif1(
FunctorType &_functor,
Matrix< Scalar, Dynamic, 1 > &x,
int *nfev,
const Scalar tol = ei_sqrt(epsilon<Scalar>())
);
Status minimizeNumericalDiff(
Matrix< Scalar, Dynamic, 1 > &x,
const int mode=1
);
Status minimizeNumericalDiffInit(
Matrix< Scalar, Dynamic, 1 > &x,
const int mode=1
);
Status minimizeNumericalDiffOneStep(
Matrix< Scalar, Dynamic, 1 > &x,
const int mode=1
);
Status lmstr1(
Matrix< Scalar, Dynamic, 1 > &x,
const Scalar tol = ei_sqrt(epsilon<Scalar>())
@ -392,283 +381,6 @@ LevenbergMarquardt<FunctorType,Scalar>::minimizeOneStep(
return Running;
}
template<typename FunctorType, typename Scalar>
typename LevenbergMarquardt<FunctorType,Scalar>::Status
LevenbergMarquardt<FunctorType,Scalar>::lmdif1(
Matrix< Scalar, Dynamic, 1 > &x,
const Scalar tol
)
{
n = x.size();
m = functor.values();
/* check the input parameters for errors. */
if (n <= 0 || m < n || tol < 0.)
return ImproperInputParameters;
resetParameters();
parameters.ftol = tol;
parameters.xtol = tol;
parameters.maxfev = 200*(n+1);
return minimizeNumericalDiff(x);
}
template<typename FunctorType, typename Scalar>
typename LevenbergMarquardt<FunctorType,Scalar>::Status
LevenbergMarquardt<FunctorType,Scalar>::minimizeNumericalDiffInit(
Matrix< Scalar, Dynamic, 1 > &x,
const int mode
)
{
n = x.size();
m = functor.values();
wa1.resize(n); wa2.resize(n); wa3.resize(n);
wa4.resize(m);
fvec.resize(m);
ipvt.resize(n);
fjac.resize(m, n);
if (mode != 2 )
diag.resize(n);
assert( (mode!=2 || diag.size()==n) || "When using mode==2, the caller must provide a valid 'diag'");
qtf.resize(n);
/* Function Body */
nfev = 0;
njev = 0;
/* check the input parameters for errors. */
if (n <= 0 || m < n || parameters.ftol < 0. || parameters.xtol < 0. || parameters.gtol < 0. || parameters.maxfev <= 0 || parameters.factor <= 0.)
return ImproperInputParameters;
if (mode == 2)
for (int j = 0; j < n; ++j)
if (diag[j] <= 0.)
return ImproperInputParameters;
/* evaluate the function at the starting point */
/* and calculate its norm. */
nfev = 1;
if ( functor(x, fvec) < 0)
return UserAsked;
fnorm = fvec.stableNorm();
/* initialize levenberg-marquardt parameter and iteration counter. */
par = 0.;
iter = 1;
return Running;
}
template<typename FunctorType, typename Scalar>
typename LevenbergMarquardt<FunctorType,Scalar>::Status
LevenbergMarquardt<FunctorType,Scalar>::minimizeNumericalDiffOneStep(
Matrix< Scalar, Dynamic, 1 > &x,
const int mode
)
{
int i, j, l;
/* calculate the jacobian matrix. */
if ( ei_fdjac2(functor, x, fvec, fjac, parameters.epsfcn) < 0)
return UserAsked;
nfev += n;
/* compute the qr factorization of the jacobian. */
ei_qrfac<Scalar>(m, n, fjac.data(), fjac.rows(), true, ipvt.data(), 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 = parameters.factor * xnorm;
if (delta == 0.)
delta = parameters.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 <= parameters.gtol)
return CosinusTooSmall;
/* 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. */
if ( functor(wa2, wa4) < 0)
return UserAsked;
++nfev;
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) <= parameters.ftol && prered <= parameters.ftol && Scalar(.5) * ratio <= 1. && delta <= parameters.xtol * xnorm)
return RelativeErrorAndReductionTooSmall;
if (ei_abs(actred) <= parameters.ftol && prered <= parameters.ftol && Scalar(.5) * ratio <= 1.)
return RelativeReductionTooSmall;
if (delta <= parameters.xtol * xnorm)
return RelativeErrorTooSmall;
/* tests for termination and stringent tolerances. */
if (nfev >= parameters.maxfev)
return TooManyFunctionEvaluation;
if (ei_abs(actred) <= epsilon<Scalar>() && prered <= epsilon<Scalar>() && Scalar(.5) * ratio <= 1.)
return FtolTooSmall;
if (delta <= epsilon<Scalar>() * xnorm)
return XtolTooSmall;
if (gnorm <= epsilon<Scalar>())
return GtolTooSmall;
/* end of the inner loop. repeat if iteration unsuccessful. */
} while (ratio < Scalar(1e-4));
/* end of the outer loop. */
return Running;
}
template<typename FunctorType, typename Scalar>
typename LevenbergMarquardt<FunctorType,Scalar>::Status
LevenbergMarquardt<FunctorType,Scalar>::minimizeNumericalDiff(
Matrix< Scalar, Dynamic, 1 > &x,
const int mode
)
{
Status status = minimizeNumericalDiffInit(x, mode);
while (status==Running)
status = minimizeNumericalDiffOneStep(x, mode);
return status;
}
template<typename FunctorType, typename Scalar>
typename LevenbergMarquardt<FunctorType,Scalar>::Status
LevenbergMarquardt<FunctorType,Scalar>::lmstr1(
@ -966,4 +678,36 @@ LevenbergMarquardt<FunctorType,Scalar>::minimizeOptimumStorage(
return status;
}
template<typename FunctorType, typename Scalar>
typename LevenbergMarquardt<FunctorType,Scalar>::Status
LevenbergMarquardt<FunctorType,Scalar>::lmdif1(
FunctorType &functor,
Matrix< Scalar, Dynamic, 1 > &x,
int *nfev,
const Scalar tol
)
{
int n = x.size();
int m = functor.values();
/* check the input parameters for errors. */
if (n <= 0 || m < n || tol < 0.)
return ImproperInputParameters;
NumericalDiff<FunctorType> numDiff(functor);
// embedded LevenbergMarquardt
LevenbergMarquardt<NumericalDiff<FunctorType> > lm(numDiff);
lm.parameters.ftol = tol;
lm.parameters.xtol = tol;
lm.parameters.maxfev = 200*(n+1);
Status info = Status(lm.minimize(x));
if (nfev)
* nfev = lm.nfev;
return info;
}

18
unsupported/test/NonLinear.cpp
View File

@ -524,8 +524,6 @@ struct lmdif_functor : Functor<double>
lmdif_functor(void) : Functor<double>(3,15) {}
int operator()(const VectorXd &x, VectorXd &fvec) const
{
/* 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,
@ -551,22 +549,23 @@ void testLmdif1()
const int n=3;
int info;
VectorXd x(n);
VectorXd x(n), fvec(15);
/* the following starting values provide a rough fit. */
x.setConstant(n, 1.);
// do the computation
lmdif_functor functor;
LevenbergMarquardt<lmdif_functor> lm(functor);
info = lm.lmdif1(x);
int nfev;
info = LevenbergMarquardt<lmdif_functor>::lmdif1(functor, x, &nfev);
// check return value
VERIFY( 1 == info);
VERIFY(lm.nfev==21);
VERIFY(nfev==21);
// check norm
VERIFY_IS_APPROX(lm.fvec.blueNorm(), 0.09063596);
functor(x, fvec);
VERIFY_IS_APPROX(fvec.blueNorm(), 0.09063596);
// check x
VectorXd x_ref(n);
@ -587,8 +586,9 @@ void testLmdif()
// do the computation
lmdif_functor functor;
LevenbergMarquardt<lmdif_functor> lm(functor);
info = lm.minimizeNumericalDiff(x);
NumericalDiff<lmdif_functor> numDiff(functor);
LevenbergMarquardt<NumericalDiff<lmdif_functor> > lm(numDiff);
info = lm.minimize(x);
// check return values
VERIFY( 1 == info);