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https://gitlab.com/libeigen/eigen.git
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remove some duplicated code LevenbergMarquardt::minimizeNumericalDiff*() by
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
parent
87be19de4a
commit
d3850641a1
@ -26,6 +26,7 @@
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#define EIGEN_NONLINEAR_MODULE_H
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#include <Eigen/Core>
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#include <unsupported/Eigen/NumericalDiff>
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namespace Eigen {
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@ -54,24 +54,13 @@ public:
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const int mode=1
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);
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Status lmdif1(
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static Status lmdif1(
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FunctorType &_functor,
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Matrix< Scalar, Dynamic, 1 > &x,
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int *nfev,
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const Scalar tol = ei_sqrt(epsilon<Scalar>())
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);
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Status minimizeNumericalDiff(
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Matrix< Scalar, Dynamic, 1 > &x,
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const int mode=1
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);
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Status minimizeNumericalDiffInit(
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Matrix< Scalar, Dynamic, 1 > &x,
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const int mode=1
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);
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Status minimizeNumericalDiffOneStep(
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Matrix< Scalar, Dynamic, 1 > &x,
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const int mode=1
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);
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Status lmstr1(
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Matrix< Scalar, Dynamic, 1 > &x,
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const Scalar tol = ei_sqrt(epsilon<Scalar>())
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@ -392,283 +381,6 @@ LevenbergMarquardt<FunctorType,Scalar>::minimizeOneStep(
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return Running;
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}
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template<typename FunctorType, typename Scalar>
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typename LevenbergMarquardt<FunctorType,Scalar>::Status
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LevenbergMarquardt<FunctorType,Scalar>::lmdif1(
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Matrix< Scalar, Dynamic, 1 > &x,
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const Scalar tol
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)
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{
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n = x.size();
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m = functor.values();
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/* check the input parameters for errors. */
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if (n <= 0 || m < n || tol < 0.)
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return ImproperInputParameters;
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resetParameters();
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parameters.ftol = tol;
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parameters.xtol = tol;
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parameters.maxfev = 200*(n+1);
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return minimizeNumericalDiff(x);
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}
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template<typename FunctorType, typename Scalar>
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typename LevenbergMarquardt<FunctorType,Scalar>::Status
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LevenbergMarquardt<FunctorType,Scalar>::minimizeNumericalDiffInit(
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Matrix< Scalar, Dynamic, 1 > &x,
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const int mode
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)
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{
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n = x.size();
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m = functor.values();
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wa1.resize(n); wa2.resize(n); wa3.resize(n);
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wa4.resize(m);
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fvec.resize(m);
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ipvt.resize(n);
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fjac.resize(m, n);
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if (mode != 2 )
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diag.resize(n);
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assert( (mode!=2 || diag.size()==n) || "When using mode==2, the caller must provide a valid 'diag'");
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qtf.resize(n);
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/* Function Body */
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nfev = 0;
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njev = 0;
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/* check the input parameters for errors. */
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if (n <= 0 || m < n || parameters.ftol < 0. || parameters.xtol < 0. || parameters.gtol < 0. || parameters.maxfev <= 0 || parameters.factor <= 0.)
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return ImproperInputParameters;
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if (mode == 2)
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for (int j = 0; j < n; ++j)
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if (diag[j] <= 0.)
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return ImproperInputParameters;
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/* evaluate the function at the starting point */
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/* and calculate its norm. */
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nfev = 1;
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if ( functor(x, fvec) < 0)
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return UserAsked;
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fnorm = fvec.stableNorm();
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/* initialize levenberg-marquardt parameter and iteration counter. */
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par = 0.;
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iter = 1;
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return Running;
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}
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template<typename FunctorType, typename Scalar>
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typename LevenbergMarquardt<FunctorType,Scalar>::Status
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LevenbergMarquardt<FunctorType,Scalar>::minimizeNumericalDiffOneStep(
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Matrix< Scalar, Dynamic, 1 > &x,
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const int mode
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)
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{
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int i, j, l;
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/* calculate the jacobian matrix. */
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if ( ei_fdjac2(functor, x, fvec, fjac, parameters.epsfcn) < 0)
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return UserAsked;
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nfev += n;
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/* compute the qr factorization of the jacobian. */
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ei_qrfac<Scalar>(m, n, fjac.data(), fjac.rows(), true, ipvt.data(), wa1.data(), wa2.data());
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ipvt.cwise()-=1; // qrfac() creates ipvt with fortran convetion (1->n), convert it to c (0->n-1)
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/* on the first iteration and if mode is 1, scale according */
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/* to the norms of the columns of the initial jacobian. */
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if (iter == 1) {
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if (mode != 2)
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for (j = 0; j < n; ++j) {
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diag[j] = wa2[j];
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if (wa2[j] == 0.)
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diag[j] = 1.;
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}
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/* on the first iteration, calculate the norm of the scaled x */
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/* and initialize the step bound delta. */
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wa3 = diag.cwise() * x;
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xnorm = wa3.stableNorm();
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delta = parameters.factor * xnorm;
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if (delta == 0.)
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delta = parameters.factor;
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}
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/* form (q transpose)*fvec and store the first n components in */
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/* qtf. */
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wa4 = fvec;
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for (j = 0; j < n; ++j) {
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if (fjac(j,j) != 0.) {
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sum = 0.;
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for (i = j; i < m; ++i)
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sum += fjac(i,j) * wa4[i];
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temp = -sum / fjac(j,j);
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for (i = j; i < m; ++i)
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wa4[i] += fjac(i,j) * temp;
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}
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fjac(j,j) = wa1[j];
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qtf[j] = wa4[j];
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}
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/* compute the norm of the scaled gradient. */
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gnorm = 0.;
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if (fnorm != 0.)
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for (j = 0; j < n; ++j) {
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l = ipvt[j];
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if (wa2[l] != 0.) {
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sum = 0.;
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for (i = 0; i <= j; ++i)
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sum += fjac(i,j) * (qtf[i] / fnorm);
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/* Computing MAX */
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gnorm = std::max(gnorm, ei_abs(sum / wa2[l]));
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}
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}
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/* test for convergence of the gradient norm. */
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if (gnorm <= parameters.gtol)
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return CosinusTooSmall;
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/* rescale if necessary. */
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if (mode != 2) /* Computing MAX */
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diag = diag.cwise().max(wa2);
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/* beginning of the inner loop. */
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do {
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/* determine the levenberg-marquardt parameter. */
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ei_lmpar<Scalar>(fjac, ipvt, diag, qtf, delta, par, wa1, wa2);
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/* store the direction p and x + p. calculate the norm of p. */
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wa1 = -wa1;
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wa2 = x + wa1;
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wa3 = diag.cwise() * wa1;
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pnorm = wa3.stableNorm();
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/* on the first iteration, adjust the initial step bound. */
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if (iter == 1)
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delta = std::min(delta,pnorm);
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/* evaluate the function at x + p and calculate its norm. */
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if ( functor(wa2, wa4) < 0)
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return UserAsked;
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++nfev;
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fnorm1 = wa4.stableNorm();
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/* compute the scaled actual reduction. */
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actred = -1.;
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if (Scalar(.1) * fnorm1 < fnorm) /* Computing 2nd power */
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actred = 1. - ei_abs2(fnorm1 / fnorm);
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/* compute the scaled predicted reduction and */
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/* the scaled directional derivative. */
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wa3.fill(0.);
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for (j = 0; j < n; ++j) {
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l = ipvt[j];
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temp = wa1[l];
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for (i = 0; i <= j; ++i)
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wa3[i] += fjac(i,j) * temp;
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}
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temp1 = ei_abs2(wa3.stableNorm() / fnorm);
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temp2 = ei_abs2(ei_sqrt(par) * pnorm / fnorm);
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/* Computing 2nd power */
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prered = temp1 + temp2 / Scalar(.5);
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dirder = -(temp1 + temp2);
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/* compute the ratio of the actual to the predicted */
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/* reduction. */
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ratio = 0.;
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if (prered != 0.)
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ratio = actred / prered;
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/* update the step bound. */
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if (ratio <= Scalar(.25)) {
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if (actred >= 0.)
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temp = Scalar(.5);
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if (actred < 0.)
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temp = Scalar(.5) * dirder / (dirder + Scalar(.5) * actred);
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if (Scalar(.1) * fnorm1 >= fnorm || temp < Scalar(.1))
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temp = Scalar(.1);
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/* Computing MIN */
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delta = temp * std::min(delta, pnorm / Scalar(.1));
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par /= temp;
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} else if (!(par != 0. && ratio < Scalar(.75))) {
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delta = pnorm / Scalar(.5);
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par = Scalar(.5) * par;
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}
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/* test for successful iteration. */
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if (ratio >= Scalar(1e-4)) {
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/* successful iteration. update x, fvec, and their norms. */
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x = wa2;
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wa2 = diag.cwise() * x;
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fvec = wa4;
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xnorm = wa2.stableNorm();
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fnorm = fnorm1;
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++iter;
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}
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/* tests for convergence. */
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if (ei_abs(actred) <= parameters.ftol && prered <= parameters.ftol && Scalar(.5) * ratio <= 1. && delta <= parameters.xtol * xnorm)
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return RelativeErrorAndReductionTooSmall;
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if (ei_abs(actred) <= parameters.ftol && prered <= parameters.ftol && Scalar(.5) * ratio <= 1.)
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return RelativeReductionTooSmall;
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if (delta <= parameters.xtol * xnorm)
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return RelativeErrorTooSmall;
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/* tests for termination and stringent tolerances. */
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if (nfev >= parameters.maxfev)
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return TooManyFunctionEvaluation;
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if (ei_abs(actred) <= epsilon<Scalar>() && prered <= epsilon<Scalar>() && Scalar(.5) * ratio <= 1.)
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return FtolTooSmall;
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if (delta <= epsilon<Scalar>() * xnorm)
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return XtolTooSmall;
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if (gnorm <= epsilon<Scalar>())
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return GtolTooSmall;
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/* end of the inner loop. repeat if iteration unsuccessful. */
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} while (ratio < Scalar(1e-4));
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/* end of the outer loop. */
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return Running;
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}
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template<typename FunctorType, typename Scalar>
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typename LevenbergMarquardt<FunctorType,Scalar>::Status
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LevenbergMarquardt<FunctorType,Scalar>::minimizeNumericalDiff(
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Matrix< Scalar, Dynamic, 1 > &x,
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const int mode
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)
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{
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Status status = minimizeNumericalDiffInit(x, mode);
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while (status==Running)
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status = minimizeNumericalDiffOneStep(x, mode);
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return status;
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}
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template<typename FunctorType, typename Scalar>
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typename LevenbergMarquardt<FunctorType,Scalar>::Status
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LevenbergMarquardt<FunctorType,Scalar>::lmstr1(
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@ -966,4 +678,36 @@ LevenbergMarquardt<FunctorType,Scalar>::minimizeOptimumStorage(
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return status;
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}
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template<typename FunctorType, typename Scalar>
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typename LevenbergMarquardt<FunctorType,Scalar>::Status
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LevenbergMarquardt<FunctorType,Scalar>::lmdif1(
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FunctorType &functor,
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Matrix< Scalar, Dynamic, 1 > &x,
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int *nfev,
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const Scalar tol
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)
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{
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int n = x.size();
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int m = functor.values();
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/* check the input parameters for errors. */
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if (n <= 0 || m < n || tol < 0.)
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return ImproperInputParameters;
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NumericalDiff<FunctorType> numDiff(functor);
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// embedded LevenbergMarquardt
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LevenbergMarquardt<NumericalDiff<FunctorType> > lm(numDiff);
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lm.parameters.ftol = tol;
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lm.parameters.xtol = tol;
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lm.parameters.maxfev = 200*(n+1);
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Status info = Status(lm.minimize(x));
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if (nfev)
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* nfev = lm.nfev;
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return info;
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}
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@ -524,8 +524,6 @@ struct lmdif_functor : Functor<double>
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lmdif_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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/* function fcn for lmdif1 example */
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int i;
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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-1,3.9e-1,
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@ -551,22 +549,23 @@ void testLmdif1()
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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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VectorXd x(n), fvec(15);
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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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lmdif_functor functor;
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LevenbergMarquardt<lmdif_functor> lm(functor);
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info = lm.lmdif1(x);
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int nfev;
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info = LevenbergMarquardt<lmdif_functor>::lmdif1(functor, x, &nfev);
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// check return value
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VERIFY( 1 == info);
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VERIFY(lm.nfev==21);
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VERIFY(nfev==21);
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// check norm
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VERIFY_IS_APPROX(lm.fvec.blueNorm(), 0.09063596);
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functor(x, fvec);
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VERIFY_IS_APPROX(fvec.blueNorm(), 0.09063596);
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// check x
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VectorXd x_ref(n);
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@ -587,8 +586,9 @@ void testLmdif()
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// do the computation
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lmdif_functor functor;
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LevenbergMarquardt<lmdif_functor> lm(functor);
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info = lm.minimizeNumericalDiff(x);
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NumericalDiff<lmdif_functor> numDiff(functor);
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LevenbergMarquardt<NumericalDiff<lmdif_functor> > lm(numDiff);
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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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