| |
| template<typename FunctorType, typename Scalar=double> |
| class LevenbergMarquardt |
| { |
| public: |
| LevenbergMarquardt(FunctorType &_functor) |
| : functor(_functor) { nfev = njev = iter = 0; fnorm=gnorm = 0.; } |
| |
| enum Status { |
| Running = -1, |
| ImproperInputParameters = 0, |
| RelativeReductionTooSmall = 1, |
| RelativeErrorTooSmall = 2, |
| RelativeErrorAndReductionTooSmall = 3, |
| CosinusTooSmall = 4, |
| TooManyFunctionEvaluation = 5, |
| FtolTooSmall = 6, |
| XtolTooSmall = 7, |
| GtolTooSmall = 8, |
| UserAsked = 9 |
| }; |
| |
| struct Parameters { |
| Parameters() |
| : factor(Scalar(100.)) |
| , maxfev(400) |
| , ftol(ei_sqrt(epsilon<Scalar>())) |
| , xtol(ei_sqrt(epsilon<Scalar>())) |
| , gtol(Scalar(0.)) |
| , epsfcn(Scalar(0.)) {} |
| Scalar factor; |
| int maxfev; // maximum number of function evaluation |
| Scalar ftol; |
| Scalar xtol; |
| Scalar gtol; |
| Scalar epsfcn; |
| }; |
| |
| Status lmder1( |
| Matrix< Scalar, Dynamic, 1 > &x, |
| const Scalar tol = ei_sqrt(epsilon<Scalar>()) |
| ); |
| |
| Status minimize( |
| Matrix< Scalar, Dynamic, 1 > &x, |
| const int mode=1 |
| ); |
| Status minimizeInit( |
| Matrix< Scalar, Dynamic, 1 > &x, |
| const int mode=1 |
| ); |
| Status minimizeOneStep( |
| Matrix< Scalar, Dynamic, 1 > &x, |
| const int mode=1 |
| ); |
| |
| static Status lmdif1( |
| FunctorType &functor, |
| Matrix< Scalar, Dynamic, 1 > &x, |
| int *nfev, |
| const Scalar tol = ei_sqrt(epsilon<Scalar>()) |
| ); |
| |
| Status lmstr1( |
| Matrix< Scalar, Dynamic, 1 > &x, |
| const Scalar tol = ei_sqrt(epsilon<Scalar>()) |
| ); |
| |
| Status minimizeOptimumStorage( |
| Matrix< Scalar, Dynamic, 1 > &x, |
| const int mode=1 |
| ); |
| Status minimizeOptimumStorageInit( |
| Matrix< Scalar, Dynamic, 1 > &x, |
| const int mode=1 |
| ); |
| Status minimizeOptimumStorageOneStep( |
| Matrix< Scalar, Dynamic, 1 > &x, |
| const int mode=1 |
| ); |
| |
| void resetParameters(void) { parameters = Parameters(); } |
| Parameters parameters; |
| Matrix< Scalar, Dynamic, 1 > fvec; |
| Matrix< Scalar, Dynamic, Dynamic > fjac; |
| VectorXi ipvt; |
| Matrix< Scalar, Dynamic, 1 > qtf; |
| Matrix< Scalar, Dynamic, 1 > diag; |
| int nfev; |
| int njev; |
| int iter; |
| Scalar fnorm, gnorm; |
| private: |
| FunctorType &functor; |
| int n; |
| int m; |
| Matrix< Scalar, Dynamic, 1 > wa1, wa2, wa3, wa4; |
| |
| Scalar par, sum; |
| Scalar temp, temp1, temp2; |
| Scalar delta; |
| Scalar ratio; |
| Scalar pnorm, xnorm, fnorm1, actred, dirder, prered; |
| }; |
| |
| template<typename FunctorType, typename Scalar> |
| typename LevenbergMarquardt<FunctorType,Scalar>::Status |
| LevenbergMarquardt<FunctorType,Scalar>::lmder1( |
| 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 = 100*(n+1); |
| |
| return minimize(x); |
| } |
| |
| |
| template<typename FunctorType, typename Scalar> |
| typename LevenbergMarquardt<FunctorType,Scalar>::Status |
| LevenbergMarquardt<FunctorType,Scalar>::minimize( |
| Matrix< Scalar, Dynamic, 1 > &x, |
| const int mode |
| ) |
| { |
| Status status = minimizeInit(x, mode); |
| while (status==Running) |
| status = minimizeOneStep(x, mode); |
| return status; |
| } |
| |
| template<typename FunctorType, typename Scalar> |
| typename LevenbergMarquardt<FunctorType,Scalar>::Status |
| LevenbergMarquardt<FunctorType,Scalar>::minimizeInit( |
| 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>::minimizeOneStep( |
| Matrix< Scalar, Dynamic, 1 > &x, |
| const int mode |
| ) |
| { |
| int i, j, l; |
| |
| /* calculate the jacobian matrix. */ |
| |
| int df_ret = functor.df(x, fjac); |
| if (df_ret<0) |
| return UserAsked; |
| if (df_ret>0) |
| // numerical diff, we evaluated the function df_ret times |
| nfev += df_ret; |
| else njev++; |
| |
| /* 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>::lmstr1( |
| Matrix< Scalar, Dynamic, 1 > &x, |
| const Scalar tol |
| ) |
| { |
| n = x.size(); |
| m = functor.values(); |
| Matrix< Scalar, Dynamic, Dynamic > fjac(m, n); |
| VectorXi ipvt; |
| |
| /* check the input parameters for errors. */ |
| if (n <= 0 || m < n || tol < 0.) |
| return ImproperInputParameters; |
| |
| resetParameters(); |
| parameters.ftol = tol; |
| parameters.xtol = tol; |
| parameters.maxfev = 100*(n+1); |
| |
| return minimizeOptimumStorage(x); |
| } |
| |
| template<typename FunctorType, typename Scalar> |
| typename LevenbergMarquardt<FunctorType,Scalar>::Status |
| LevenbergMarquardt<FunctorType,Scalar>::minimizeOptimumStorageInit( |
| 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>::minimizeOptimumStorageOneStep( |
| Matrix< Scalar, Dynamic, 1 > &x, |
| const int mode |
| ) |
| { |
| int i, j, l; |
| bool sing; |
| |
| /* 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.); |
| int rownb = 2; |
| for (i = 0; i < m; ++i) { |
| if (functor.df(x, wa3, rownb) < 0) return UserAsked; |
| temp = fvec[i]; |
| ei_rwupdt<Scalar>(n, fjac.data(), fjac.rows(), wa3.data(), qtf.data(), &temp, wa1.data(), wa2.data()); |
| ++rownb; |
| } |
| ++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(), 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 = parameters.factor * xnorm; |
| if (delta == 0.) |
| delta = parameters.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 <= 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>::minimizeOptimumStorage( |
| Matrix< Scalar, Dynamic, 1 > &x, |
| const int mode |
| ) |
| { |
| Status status = minimizeOptimumStorageInit(x, mode); |
| while (status==Running) |
| status = minimizeOptimumStorageOneStep(x, mode); |
| 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; |
| } |
| |
| |
| |
