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288 lines
8.5 KiB
C++
288 lines
8.5 KiB
C++
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template<typename Functor, typename Scalar>
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int ei_lmder(
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Matrix< Scalar, Dynamic, 1 > &x,
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Matrix< Scalar, Dynamic, 1 > &fvec,
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int &nfev,
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int &njev,
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Matrix< Scalar, Dynamic, Dynamic > &fjac,
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VectorXi &ipvt,
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Matrix< Scalar, Dynamic, 1 > &qtf,
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Matrix< Scalar, Dynamic, 1 > &diag,
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int mode=1,
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Scalar factor = 100.,
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int maxfev = 400,
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Scalar ftol = ei_sqrt(epsilon<Scalar>()),
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Scalar xtol = ei_sqrt(epsilon<Scalar>()),
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Scalar gtol = Scalar(0.),
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int nprint=0
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)
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{
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const int m = fvec.size(), n = x.size();
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Matrix< Scalar, Dynamic, 1 > wa1(n), wa2(n), wa3(n), wa4(m);
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ipvt.resize(n);
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fjac.resize(m, n);
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diag.resize(n);
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qtf.resize(n);
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/* Local variables */
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int i, j, l;
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Scalar par, sum;
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int iter;
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Scalar temp, temp1, temp2;
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int iflag;
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Scalar delta;
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Scalar ratio;
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Scalar fnorm, gnorm;
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Scalar pnorm, xnorm, fnorm1, actred, dirder, prered;
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int info;
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/* Function Body */
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info = 0;
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iflag = 0;
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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 || ftol < 0. || xtol < 0. ||
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gtol < 0. || maxfev <= 0 || factor <= 0.)
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goto L300;
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if (mode == 2)
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for (j = 0; j < n; ++j)
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if (diag[j] <= 0.) goto L300;
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/* evaluate the function at the starting point */
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/* and calculate its norm. */
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iflag = Functor::f(x, fvec);
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nfev = 1;
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if (iflag < 0)
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goto L300;
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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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/* beginning of the outer loop. */
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while(true) {
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/* calculate the jacobian matrix. */
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iflag = Functor::df(x, fjac);
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++njev;
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if (iflag < 0)
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break;
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/* if requested, call Functor::f to enable printing of iterates. */
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if (nprint > 0) {
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iflag = 0;
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if ((iter - 1) % nprint == 0)
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iflag = Functor::debug(x, fvec, fjac);
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if (iflag < 0)
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break;
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}
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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(), n, 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 = factor * xnorm;
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if (delta == 0.)
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delta = 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 <= gtol) {
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info = 4;
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}
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if (info != 0)
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break;
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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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}
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/* evaluate the function at x + p and calculate its norm. */
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iflag = Functor::f(wa2, wa4);
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++nfev;
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if (iflag < 0)
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goto L300;
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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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}
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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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}
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else {
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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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}
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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) <= ftol && prered <= ftol && Scalar(.5) * ratio <= 1.)
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info = 1;
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if (delta <= xtol * xnorm)
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info = 2;
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if (ei_abs(actred) <= ftol && prered <= ftol && Scalar(.5) * ratio <= 1. && info == 2)
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info = 3;
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if (info != 0)
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goto L300;
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/* tests for termination and stringent tolerances. */
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if (nfev >= maxfev)
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info = 5;
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if (ei_abs(actred) <= epsilon<Scalar>() && prered <= epsilon<Scalar>() && Scalar(.5) * ratio <= 1.)
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info = 6;
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if (delta <= epsilon<Scalar>() * xnorm)
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info = 7;
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if (gnorm <= epsilon<Scalar>())
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info = 8;
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if (info != 0)
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goto L300;
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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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}
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L300:
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/* termination, either normal or user imposed. */
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if (iflag < 0)
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info = iflag;
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if (nprint > 0)
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iflag = Functor::debug(x, fvec, fjac);
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return info;
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}
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