mirror of
https://gitlab.com/libeigen/eigen.git
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417 lines
9.7 KiB
C++
417 lines
9.7 KiB
C++
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template<typename Functor, typename Scalar>
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int ei_lmstr(
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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 > &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 >
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qtf(n),
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wa1(n), wa2(n), wa3(n),
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wa4(m);
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int ldfjac = m;
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ipvt.resize(n);
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fjac.resize(ldfjac, n);
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diag.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 sing;
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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, 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 || ldfjac < n || ftol < 0. || xtol < 0. ||
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gtol < 0. || maxfev <= 0 || factor <= 0.) {
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goto L340;
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}
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if (mode != 2) {
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goto L20;
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}
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for (j = 0; j < n; ++j) {
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if (diag[j] <= 0.) {
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goto L340;
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}
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/* L10: */
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}
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L20:
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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, wa3, 1);
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nfev = 1;
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if (iflag < 0) {
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goto L340;
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}
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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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L30:
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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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goto L40;
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}
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iflag = 0;
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if ((iter - 1) % nprint == 0) {
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iflag = Functor::f(x, fvec, wa3, 0);
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}
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if (iflag < 0) {
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goto L340;
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}
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L40:
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/* compute the qr factorization of the jacobian matrix */
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/* calculated one row at a time, while simultaneously */
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/* forming (q transpose)*fvec and storing the first */
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/* n components in qtf. */
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for (j = 0; j < n; ++j) {
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qtf[j] = 0.;
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for (i = 0; i < n; ++i) {
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fjac(i,j) = 0.;
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/* L50: */
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}
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/* L60: */
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}
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iflag = 2;
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for (i = 0; i < m; ++i) {
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if (Functor::f(x, fvec, wa3, iflag) < 0) {
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goto L340;
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}
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temp = fvec[i];
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ei_rwupdt<Scalar>(n, fjac.data(), ldfjac, wa3.data(), qtf.data(), &temp, wa1.data(), wa2.data());
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++iflag;
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/* L70: */
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}
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++njev;
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/* if the jacobian is rank deficient, call qrfac to */
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/* reorder its columns and update the components of qtf. */
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sing = false;
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for (j = 0; j < n; ++j) {
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if (fjac(j,j) == 0.) {
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sing = true;
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}
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ipvt[j] = j;
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wa2[j] = fjac.col(j).start(j).stableNorm();
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// wa2[j] = ei_enorm<Scalar>(j, &fjac[j * ldfjac + 1]);
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// sum += fjac[i + j * ldfjac] * (qtf[i] / fnorm);
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/* L80: */
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}
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if (! sing) {
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goto L130;
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}
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ipvt.cwise()+=1;
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ei_qrfac<Scalar>(n, n, fjac.data(), ldfjac, true, ipvt.data(), n, wa1.data(), wa2.data(), wa3.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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for (j = 0; j < n; ++j) {
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if (fjac(j,j) == 0.) {
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goto L110;
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}
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sum = 0.;
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for (i = j; i < n; ++i) {
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sum += fjac(i,j) * qtf[i];
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/* L90: */
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}
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temp = -sum / fjac(j,j);
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for (i = j; i < n; ++i) {
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qtf[i] += fjac(i,j) * temp;
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/* L100: */
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}
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L110:
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fjac(j,j) = wa1[j];
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/* L120: */
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}
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L130:
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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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goto L170;
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}
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if (mode == 2) {
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goto L150;
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}
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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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/* L140: */
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}
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L150:
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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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for (j = 0; j < n; ++j) {
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wa3[j] = diag[j] * x[j];
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/* L160: */
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}
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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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L170:
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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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goto L210;
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}
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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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goto L190;
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}
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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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/* L180: */
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}
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/* Computing MAX */
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gnorm = std::max(gnorm, ei_abs(sum/wa2[l]));
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L190:
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/* L200: */
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;
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}
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L210:
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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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goto L340;
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}
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/* rescale if necessary. */
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if (mode == 2) {
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goto L230;
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}
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for (j = 0; j < n; ++j) /* Computing MAX */
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diag[j] = std::max(diag[j], wa2[j]);
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L230:
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/* beginning of the inner loop. */
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L240:
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/* determine the levenberg-marquardt parameter. */
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ipvt.cwise()+=1; // lmpar() expects the fortran convention (as qrfac provides)
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ei_lmpar<Scalar>(n, fjac.data(), ldfjac, ipvt.data(), diag.data(), qtf.data(), delta, par,
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wa1.data(), wa2.data(), wa3.data(), wa4.data());
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ipvt.cwise()-=1;
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/* store the direction p and x + p. calculate the norm of p. */
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for (j = 0; j < n; ++j) {
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wa1[j] = -wa1[j];
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wa2[j] = x[j] + wa1[j];
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wa3[j] = diag[j] * wa1[j];
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/* L250: */
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}
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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, wa3, 1);
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++nfev;
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if (iflag < 0) {
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goto L340;
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}
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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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for (j = 0; j < n; ++j) {
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wa3[j] = 0.;
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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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/* L260: */
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}
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/* L270: */
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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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}
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/* update the step bound. */
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if (ratio > Scalar(.25)) {
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goto L280;
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}
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if (actred >= 0.) {
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temp = Scalar(.5);
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}
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if (actred < 0.) {
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temp = Scalar(.5) * dirder / (dirder + Scalar(.5) * actred);
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}
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if (Scalar(.1) * fnorm1 >= fnorm || temp < Scalar(.1)) {
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temp = Scalar(.1);
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}
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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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goto L300;
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L280:
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if (par != 0. && ratio < Scalar(.75)) {
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goto L290;
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}
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delta = pnorm / Scalar(.5);
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par = Scalar(.5) * par;
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L290:
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L300:
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/* test for successful iteration. */
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if (ratio < Scalar(1e-4)) {
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goto L330;
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}
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/* successful iteration. update x, fvec, and their norms. */
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for (j = 0; j < n; ++j) {
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x[j] = wa2[j];
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wa2[j] = diag[j] * x[j];
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/* L310: */
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}
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for (i = 0; i < m; ++i) {
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fvec[i] = wa4[i];
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/* L320: */
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}
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xnorm = wa2.stableNorm();
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fnorm = fnorm1;
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++iter;
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L330:
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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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}
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if (delta <= xtol * xnorm) {
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info = 2;
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}
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if (ei_abs(actred) <= ftol && prered <= ftol && Scalar(.5) * ratio <= 1. && info
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== 2) {
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info = 3;
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}
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if (info != 0) {
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goto L340;
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}
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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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}
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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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}
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if (delta <= epsilon<Scalar>() * xnorm) {
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info = 7;
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}
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if (gnorm <= epsilon<Scalar>()) {
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info = 8;
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}
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if (info != 0) {
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goto L340;
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}
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/* end of the inner loop. repeat if iteration unsuccessful. */
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if (ratio < Scalar(1e-4)) {
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goto L240;
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}
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/* end of the outer loop. */
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goto L30;
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L340:
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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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}
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iflag = 0;
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if (nprint > 0) {
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iflag = Functor::f(x, fvec, wa3, 0);
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}
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return info;
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/* last card of subroutine lmstr. */
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} /* lmstr_ */
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